Simulation of NMR observables of carbohydrates
(FULL VERSION of Recent Advances in Computational Predictions of NMR Parameters for
Structure Elucidation of Carbohydrates: Methods and Limitations, DOI: 10.1039/b000000x)
Filip V. Toukach, Valentine P. Ananikov*
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Zelinsky Institute of Organic Chemistry, Russian Academy of Sciences, Leninsky Prospekt 47, Moscow, 119991, Russia. Fax: +7 499 135 5328;
E-mail: [email protected]
All living systems are comprised of four fundamental classes of macromolecules - nucleaic acids, proteins, lipids,
and carbohydrates (glycans). Glycans play a unique role of joining three principal hierarchical levels of the living
world: 1) molecular level (pathogenic agent and vaccine recognition by the immune system; metabolic pathways
involving saccharides that provide cells with energy; and energy accumulation via photosynthesis); 2) nanoscale
level (cell membrane mechanics; structural support of biomolecules; and glycosylation of macromolecules); 3)
microscale and macroscale levels (polymeric materials, such as cellulose, starch, glycogen, and biomass). NMR
spectroscopy is the most powerful research approach for getting insight into solution structure and function of
carbohydrates at all hierarchical levels, from monosaccharides to oligo- and polysaccharides. Recent progress in
computational procedures opened a novel opportunity to reveal structural information available in the NMR
spectra of saccharides and to advance our understanding of corresponding biochemical processes. The ability to
predict the molecular geometry and NMR parameters is crucial for elucidation of carbohydrate structures. In the
present paper, we review the major NMR spectrum simulation techniques in regard to chemical shift, coupling
constant, relaxation rate and nuclear Overhauser effect prediction applied to the three levels of glycomics.
Outstanding development in the related fields of genomics and proteomics has clearly shown that it is the
advancement of research tools (automated spectrum analysis, structure elucidation, synthesis, sequencing and
amplification) that drives grand challenges in modern science. Combination of NMR spectroscopy and
computational analysis of structural information encoded in the NMR spectra reveals the way to automated
elucidation of the structure of carbohydrates.
1. Introduction
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Contents
1. Introduction
2. Computation of the NMR parameters of carbohydrates
3. Empirical methods of NMR parameter prediction
3.1. Database approach
3.2. Usage of neural networks
3.3. Regression-based methods
3.4. CHARGE approach
3.5. Incremental approach at the residual level
4. Models and methods for carbohydrate 3D structural studies
4.1. Molecular mechanics and molecular dynamics
4.2. Semi-empirical methods
4.3. Ab initio and density functional modeling
4.4. Hybrid QM/MM, QM/QM and ONIOM approaches
4.5. Interaction with solvent
5. Computation of NMR chemical shifts
5.1. Monosaccharides and derivatives
5.2. Oligosaccharides and polysaccharides
6. Computation of NMR coupling constants
6.1. Intra-residue coupling constants
6.2. Inter-residue coupling constants
7. Computation of NMR relaxation rates
8. Computation of other NMR parameters
9. Conclusions
10. Abbreviations
11. Acknowledgements
12. References
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This journal is © The Royal Society of Chemistry 2013
Glycochemical and glycobiological research has recently shown a
tremendous growth and rapidly developed into one of the leading
forces in modern science. Novel synthetic approaches and
rational design of carbohydrates and glycoconjugates revealed
new opportunities in drug and vaccine discovery.1-5 Detailed
insight was gained into the key role of carbohydrates in biological
recognition, development of diseases and control of the immune
response.6-11 Nowadays a lot of new carbohydrate drugs are
licensed or are in clinical testing.2-4, 6-13 Glyco-nanomaterials are
perspective building blocks for such applications as biosensors or
multivalent scaffolds for drug delivery.14 With such an
outstanding progress demonstrated in recent decades a new era
has emerged in medicinal and pharmaceutical applications of
carbohydrates.
The role of oligo- and polysaccharides and their conjugates in
cellular biology can hardly be overestimated.15-19 Carbohydrate
functions in living organisms vary from the energy storage and
the maintenance of the cellular shape to provision of the
immunological uniqueness of microorganisms. The high
structural diversity of saccharide residues and their linkages
allows carbohydrate-containing molecules to present a huge
number of signals to their surroundings, making them well suited
for the control of molecular recognition in living cells,20 highly
involved in signal transduction,21 and in multiple biosynthetic
pathways.22 Carbohydrate microarrays and other analytical
techniques dedicated to probing of glycan-related processes in
cells have been developed.23-25
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Fig. 1. Representative 1H NMR spectra in D2O: (A) cyclic pentapeptide
showing individual signals in a wide range of chemical shifts from
0 to 11 ppm 26; (B) regular polymer with pentasaccharide repeating unit
showing signals in two narrow regions 1.0–2.5 ppm and 3.0–6.0 ppm,
including a strong overlap in a range 3.5-4.5 ppm.27 (reproduced with
permission, © Elsevier Ltd., 2005)
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Cellulose and chitin are two most abundant natural polymers
on Earth and their industrial utilization is the question of primary
importance within a widely accepted sustainable concept.
Diversity of industrial applications benefits from employing
procedures developed in carbohydrate chemistry towards biomass
processing. Carbohydrates contribute up to 75% to world
renewable biomass.28-30 Development of practically useful and
efficient procedures for conversion of cellulose into platform
chemicals and biofuels was identified as one of the central
research challenges in the coming century.31-34 The estimations
have shown that up to 30% of the transportation fuel demands
could be fulfilled by cellulose biomass.31-35
However, in spite of massive development of fascinating
applications, carbohydrates remain the least structurally
characterized among the major classes of biological molecules.
Carbohydrates are very difficult to crystallize and in most cases
single crystals of sufficient quality for X-ray analysis cannot be
obtained36, 37. Moreover, even for such minority of successful
crystallizations, X-ray crystallography was reported to give
poorly resolved structures of glycan moieties36-39. Limited
application of X-ray structure determination for carbohydrates is
in sharp contrast to proteins, where crystallization and X-ray
structure elucidation have become a standard research tool40-42.
Mass-spectrometry of carbohydrates is a useful technique,
however it is not sufficient as a structural tool alone since the
crucial issue of stereochemistry of carbohydrates cannot be
solved by routinely available methods43.
Unlike many high-throughput analytical methods, NMR
spectroscopy is tolerant to the incompleteness of reference data
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and thus plays a key role in primary structural elucidation of new
natural glycans44. Besides its ubiquitous use in structural studies
of carbohydrates it makes a significant insight into the
mechanisms of their biological action38, 43, 45, 46. In fact, NMR
spectroscopy provided most of the experimental data on solution
structure of carbohydrates, complex equilibriums and
interconversions of sugar units, monitoring of chemical reactions
involving carbohydrates, characterization of carbohydrate binding
to other bioactive molecules and other processes of biological
relevance38, 43, 45-48. It has been recognized as a valuable tool for
quality control and characterization of carbohydrates-containing
drugs49. NMR-based approaches were incorporated into the
World Health Organization recommendations on the production
and quality control of glycoconjugate vaccines50.
Important advantage of the NMR spectroscopy concerns
determination of three-dimensional structure directly in water
solution (in water and organic solvents), where the processes of
biological and chemical relevance occur. To achieve this goal
several experimental methods were developed for measurement
of the key NMR parameters: chemical shifts, coupling constants,
NOE data and relaxation rates. Highly sensitive and powerful 1D
and 2D NMR experiments were developed and optimized to carry
out the measurements of carbohydrates15, 36, 43, 51. Rapid progress
in the NMR hardware and development of new NMR
experiments made structural elucidations routinely available in
everyday practice in chemical and biological research
laboratories.
Such an impressive development has clearly identified stateof-the-art challenge in the field of structural studies of
carbohydrates. However, further insight in this fascinating area of
research is limited by difficulties in interpretation of the NMR
parameters, rather than by recording of the NMR spectra. Indeed,
proving correct signal assignment and understanding the
relationship between measured NMR parameters and molecular
structure is still a tedious task, especially for such chemically
diverse class of compounds as carbohydrates.
In spite of wide structural diversity of carbohydrates, the
majority of their NMR studies is limited to 1H and 13C nuclei in
contrast to proteins (1H, 13C and 15N) and nucleic acids (1H, 13C,
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N and 31P). Isotope labeling, routinely used in protein NMR
spectroscopy to enhance automated structure analysis, is only
limitedly applicable to carbohydrates52-56. Although the building
blocks of carbohydrates are more diverse in nature compared to
structural units of nucleic acids and proteins, their NMR chemical
shifts are located in much narrower region (Fig. 1). Thus,
assignment and interpretation of the NMR spectra remain a
challenge in modern structural glycoscience. Proper interpretation
of the NMR parameters requires a theoretical analysis.
Particularly, to correlate the time-averaged experimental NMR
data with the primary and secondary chemical structure, the
former can be computed by molecular modeling48. Modelling of
the carbohydrate structure and molecular properties has benefit
from a variety of computational methods57.
In the present review we discuss recent progress in
development of computational approaches for modeling of the
NMR parameters of carbohydrates. The review covers a set of
topics important for structure elucidation: i) theoretical
calculations and analysis of 1H, 13C, 15N, 17O, 31P chemical shifts;
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Fig. 2. Selected monosaccharides used in this review, shown in pyranose form, and their IUPAC abbreviations. The monosaccharides that typically exhibit
an equlibrium are shown in both forms (A). Various forms of monosaccharides exemplified by D-glucose (IUPAC abbreviations in red). Numbers stand
for carbon atom enumeration (B). Schematic representation of some 4C1 and 1C4 chair hydroxyl and hydroxymethyl rotamers of β-D-glucose. The
idealized torsions are denoted by g+, t and g- for gauche clockwise (60°), anti (180°), and gauche counterclockwise (-60°) respectively. The idealized O5C5-C6-O6 dihedral angles for the hydroxymethyl group are denoted by capital letters: G+, T, and G-. g++ or g-- notate torsions far from the idealized
values for 1C4 chair conformer58 (C, reproduced with permission, © Elsevier Science B.V., 1996).
This journal is © The Royal Society of Chemistry 2013
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Fig. 3. Representative parts of 2D 1H,13C HSQC (A) and homonuclear NOESY (B) spectra of a sulfated trisaccharide recorded in D2O at 500 MHz59. In
spite of strong signal overlap in 1D spectra, the cross-peaks are clearly resolved in 2D spectra. Reproduced with permission, © Elsevier Ltd., 2005.
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ii) computations of chemical shielding tensors and chemical shift
surfaces; iii) prediction of H-H, P-H, C-H and C-C coupling
constants essential for structural studies; iv) modeling of
relaxation parameters; v) prediction of nuclear Overhauser effects
and other NMR parameters.
A discussion is provided on the scope and limitations of
available theoretical approaches including ab initio, density
functional, semiempirical, molecular mechanics, molecular
dynamics, empirical and hybrid calculations in relation to the
NMR structural analysis. Application of modern approaches for
theoretical prediction of the NMR properties, together with
experimental data, results in revealing the key information
concerning the molecular structure. One of the major goals of the
theoretical NMR calculations is a faithful reproduction, and, later,
prediction of the experimental data.
The present reviews focuses on the prediction and analysis of
NMR parameters of carbohydrates and their derivatives using
empirical methods and expert systems60, 61, as well as calculations
at quantum-chemical level61-65.
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2. Computation of the NMR parameters of
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Increasing demand in the NMR structure analysis of
carbohydrates emerged development of wide variety of
computational approaches to predict and analyze chemical shifts,
spin-spin coupling constants, relaxation rates and other
parameters.
The first class of approaches includes empirical methods,
which operate with molecules basing on the connectivity of
atoms or residues. These methods do not require thorough
evaluation of atomic coordinates, except for rough
stereochemistry. A series of easy to use and computationally
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efficient tools were developed based on empirical methods, and
these tools are now routinely used in everyday research practice.
The concise overview of the empirical methods is given in
section 3.
Straightforward “first principles” modeling of the NMR
parameters with ab initio and density functional methods requires
calculation of a molecular structure followed by derivation of the
NMR data. The necessary description of models and methods
important for NMR structural studies of carbohydrates is
summarized in section 4. Detailed discussion of application of the
computational methods for structure elucidation of carbohydrates
is divided to: a) calculation of NMR chemical shifts (section 5);
b) calculation of spin-spin coupling constants (section 6); c)
prediction of other NMR parameters (sections 7 and 8).
In spite of rapid development of ab initio and density
functional methods facilitated by the increasing performance of
computational hardware, it should be pointed out that empirical
predictions are still widely used. A rough estimation of NMR
prediction quality using standard “out-of-box” protocols shows
that empirical methods produce good accuracy and are very fast.
As is discussed below, there are several options available to
improve the performance of ab initio and density functional
predictions of the NMR parameters of carbohydrates. However,
these options are mostly described in the specialized theoretical
articles without being widely known to researchers working on
the the experimental data analysis and structure elucidation.
Exchange of knowledge between these fields is an important goal
of the present review.
Typical carbohydrate building blocks and characteristic
geometrical features are shown in Fig. 2 (for the list of
abbreviations see section 10). On the one hand, a diversity of
building blocks and a variety of available inter-residue
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connections generate a huge number of possible carbohydrate
structures. On the other hand, this abundant structural information
usually cannot be deduced from 1D 1H and 13C NMR spectra due
to ambiguous assignment pathways and strong signal overlap.
Nowadays, multidimensional spectroscopy allows determination
of the NMR parameters and reliable structure elucidation of
carbohydrates43, 49, 51, 66. Indeed, even addition of ony one spectral
dimension (2D NMR spectroscopy) results in clearly resolved
signals (Fig. 3) as compared to 1D spectra (Fig. 1B). The aim of
computational prediction and analysis of 2D NMR spectra
highlights the most important challenge in the field since accurate
calculation of 1H and 13C NMR chemical shifts and coupling
constants is required.
3. Empirical methods of NMR parameter
prediction
Since 1975, a number of chemical shift collections dedicated
solely to carbohydrates have evolved43, encouraging many groups
to develop algorithms that can utilize this information in
computational prediction of the NMR spectra of carbohydrates.
Most of the chemical shift databases provided a signal search
tool, making NMR data easily interpretable in terms of structure.
The simplest class of empirical methods implies only a small
reference database (so called base values) and a multitude of
additive rules and increments parameterized for every class of
compounds. This approach has developed to a number of
initiatives discussed in the present section of the review. As a
representative example, in case of 1H NMR a mean deviation of
0.2-0.3 ppm was observed for prediction of 90% of all CHxgroups chemical shifts in unpolar solvents and in case of 13C
NMR >95% of the chemical shifts were predicted by CHARGE
with a mean deviation of 3.8 ppm67.
Empirical methods, as well as usage of neural networks, enable
the fastest and fully automatized calculation that can generate up
to 10,000 chemical shifts per second on a desktop computer with
an accuracy of 1.6-1.8 ppm68. Programs utilizing statistical
processing of reference chemical shifts databases provide similar
or better accuracy at slower but still acceptable performance69.
Every structural fragment is assigned a descriptor that correlates
with its major structural peculiarities. When the database is
queried with the descriptor, similar structures are identified, and
the resulting values are weighted averages of the experimental
NMR data corresponding to these structures.
However, the predictions are solely limited to the structural
information deposited in a database. As a result, empirical
methods have only a limited application in the elucidation of
secondary structure, as they are unable to predict non-averaged
properties of molecules in a certain conformation or under
conditions different from those utilized in the database. Another
known drawback concerns inability to account varying conditions
of spectra recording. It was reported that the use of different
solvents may strongly increase the deviations and deteriorate the
accuracy of prediction67.
In spite of these limitations, simple algorithms and very fast
calculations with reasonable accuracy in basic cases govern
ubiquitous application of empirical methods in modern NMR
structural analysis of carbohydrates. Incremental empirical or
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neural network methods of chemical shift prediction can be
successfully used at the selection stage of structural hypotheses
which are later verified by time-consuming molecular geometry
optimization and ab initio calculations of chemical shifts70.
Below we provide a brief review of empirical techniques useful
for research and educational purpose in the field.
3.1. Database approach
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Historically the first database approach to chemical shift
prediction was described by Bremser71 and was called a
hierarchical organization of spherical environments (HOSE).
Since then it has been improved and remains the most popular
structure description algorithm in database-oriented NMR
predictors. Particularly this algorithm was used as one of the
approaches in ACDLabs ACD/NMR and Modgraph
Consultants Ltd. NMR prediction software72, 73. The HOSE starts
at the atom whose chemical shift has to be predicted, expands one
bond away from the atom (“1st sphere”) and tries to find this
environment in the reference database. If the search is successful
it moves two bonds away (“2nd sphere”) and tries again and so
until either the fragment is not deposited in the database or the
molecule boundary is reached. The HOSE approach exhibits
good results for the structures where the fragments are well
represented in the reference collection. As a rule of thumb, if the
analyzed atoms can be predicted using three or more spheres the
prediction is considered reliable. In modern implementations,
HOSE is extended to treat stereochemistry (3D HOSE), by
assigning higher weight to the structural database entries that
describe the same stereochemistry as the fragments under
analysis72.
As realized in ACDLabs 8.0 NMR predictor this approach
provided a standard error of 0.22 ppm per 1H resonance (tested on
54,608 organic molecules), and 2.33 ppm per 13C resonance
(tested on 68,129 organic molecules). 62% of predicted 1H NMR
chemical shifts were less than 0.1 ppm from the experimental
values, and 64% of 13C NMR chemical shifts were less than
1 ppm from the experimental values74. Novel versions of
ACD/NMR predictors utilize the combined approach, where the
results from HOSE and neural network algorithm (discussed in
the next section) are compared to retrieve the best-fitting value.
The Table 1 illustrates the statistics on the reference databases for
several nuclei valuable in carbohydrate chemistry75. More details
about ACD/NMR predictor are available in a review of
Elyashberg and coworkers60.
Table 1. ACD/NMR reference databases available for NMR spectra
prediction (data for version 11 75).
Nuclei
1
H
210 000
1.7 million
191 900
2.5 million
N
9 287
21 782
27 578
34 020
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105
Number of chemical shifts
C
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15
Number of structures
P
Another family of computational products utilizing HOSE
approach includes Modgraph-based general-purpose 13C and
heteronuclei NMR predictors73 (implemented and tested in a
number of software packages, such as MestreLabs NMRPredict76
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and PerkinElmer ChemBioOffice77). Currently Modgraph uses a
HOSE code algorithm capable to analyze up to five spheres and a
database of 193,352 most highly verified 13C records abstracted
from the literature by Robien and coworkers78. This database is a
further development of a product reported earlier79. Additionally,
185,517 13C and 86,480 heteronuclei records from Chemical
Concepts are available as an option.
Modgraph automatically selects a better 13C NMR prediction
for each atom from HOSE and neural network prediction
methods (see section 3.2 for the latter). The higher the number of
HOSE spheres was reached for each atom, the more emphasis is
given to the HOSE code prediction. The target mean error of 0.18
ppm per resonance was reported after evaluation of ca. 90,000
structures and stereochemistry of the molecule was considered.
Several other 13C and heteronuclei chemical shift databases
were reported: CSEARCH80, Chemical Concepts SpecSurf /
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SpecInfo81, WINDAT , freely-accessible NMRshiftDB83.
Some of these projects were continuously developed and
transformed into a dedicated computational tools for empirical
spectra predictions.
An alternative approach to encode stereochemical information
in HOSE-based predictors was developed by Satoh and
coworkers84. This encoding scheme, called CAST (Canonical
representation of stereochemistry), includes different descriptors
at the planar, conformational and configurational levels for each
atom. Although no usage of CAST for carbohydrates has been
reported, predictions of chemical shifts in a linear triol part of 20hydroxyecdysone exhibited an average deviation from the
experimental spectrum within 0.5 ppm per resonance85.
Kelleher and Simpson carried out 1H and 13C NMR predictions
in the form of HSQC spectrum for the 2D model of humic acid
and compared it with HSQC spectra of the soil samples,
including the amylopectin carbohydrate moiety86. The predictions
were based on HOSE code matches and incremental algorithms
implemented in ACDLabs Spec Manager 9.06. Although this
approach has been used to produce accurate predictions for noncarbohydrate soil components87, there was generally poor
correlation between experimental signals and those simulated for
the proposed structural model.
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3.2. Usage of neural networks
Neural network is a mathematical construction allowing
optimization of non-linear dependencies between input
descriptors and output values88-90. It consists of artificial neurons
organized in a number of layers, where each neuron is a function
that transforms its input value to the output value. The first layer
(“input layer”) gathers numerical atomic descriptors and no
calculations are performed on it. Input layer is fed with structural
parameters that are converted to numbers using HOSE,
increments or other structure description schema. In chemical
shift prediction, the last layer (“output layer”) contains a single
neuron that produces the predicted chemical shift. The output
value of each neuron in hidden layers in between is an input to
the neuron in the next layer. Different connections between
neurons have different weight parameter, and the total output
depends on the input non-linearly.
Prediction approaches based on neural networks benefit from
self-learning and ability to model properties of compounds
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without understanding of the underlying phenomena, which is
especially demanded for non-linear relationships typical for
instrumental analytical chemistry91. To make use of a neural
network in NMR data prediction, it should be trained against a
database of known chemical shifts in order to optimize the
weights of neuron connections88, 90, 91.
Radomski and coworkers showed the ability of neural
networks to recognize and process spectra with low signal-tonoise ratio, which could hardly be analyzed by regular visual
inspection92. Since then a number of applications of neural
networks to prediction of the NMR chemical shifts, especially
13
C, have been reported for general organic compounds91, 93 and
certain biomolecular classes, including proteins94.
Gerbst and coworkers demonstrated that ART1-type neural
network is capable to identify the class of fucoidan
polysaccharides from the characteristic 13C NMR signals.
However, the structure abalysis quality was satisfactory only if
the neural network training set contained exactly the residues
present in a molecule to identify95.
A combination of fragmental approach and usage of a neural
network is implemented in various computational tools.
Particularly, ModGraph 13C NMR predictor includes a neural
network algorithm to help the prediction of molecules, which are
not well represented in the HOSE reference database. Testing of
this neural network on 345,000 reference spectra exhibited an
average deviation between experimental and calculated chemical
shifts of below 2 ppm96.
Purtuc and coworkers designed a neural network with
extensive utilization of stereochemical information in 13C NMR
chemical shift prediction with no need in 3D atomic
coordinates97. The data used during training and evaluation of the
network were selected from the CSEARCH database of ca.
230,000 13C NMR spectra (ca. 2,700,000 chemical shifts). A
typical training set consisted of 400,000 examples selected on a
random basis to reduce the resource consumption during network
optimization79.
Le Bret reported a neural network trained on 8,342 13C NMR
chemical shifts described by 314 topological and chemical
descriptors related to the atom itself and its nearest neighborhood.
The average deviation of 4.5 ppm was claimed to be independent
on the size and complexity of the molecule. However only
routine molecular types and molecules smaller than 64 carbons
were considered98.
Meiler and coworkers constructed a three-layer neural network
that considered 28 atom types and two summarizing parameters
in every of six spheres. The best results (standard deviation
2.1 ppm for ca. 15,000 test atoms) were achieved with a number
of hidden neurons from 5 to 2099. Later this network was used to
elucidate structures of up to 20 carbons by a genetic algorithm100
and improved by the introduction of an extended hybrid
numerical description of the carbon atom environment. Genetic
algorithm is an iterative search heuristic utilizing benefits of
evolutional algorithms, in which solution generations undergo
inheritance, mutation, selection and crossover101. Standard
deviation for an independent test data set of ca. 42,500 carbons
was reported as 2.4 ppm102.
The neural network designed by Smurnyy and coworkers
recognized 32 atom types and double bond stereochemistry (as a
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separate sphere), and its output was additionally corrected with
rule-based algorithm that used increments shared by two or more
substituents (“cross-increments”). The network was trained on a
database of 190,000 structures and about two million chemical
shifts, and validated on a database of 8,500 structures and
~118,000 chemical shifts. It is difficult to design a single network
that covers all the range of 13C NMR chemical shifts, thus
reference database was split into subdatabases accordingly to the
nature of the central atom103. This neural network was used as
one of the algorithms implemented in ACD Labs/NMR68.
Smurnyy and coworkers compared neural network and leastsquare linear regression approaches in prediction quality and
performance, and optimized several parameters (number of
subdatabases, number of structural descriptors, network
parameters etc.). As a result, they obtained an average error of
1.5 ppm for 13C and 0.2 ppm for 1H NMR chemical shifts, and
supposed that further improvement is much more dependent on
the choice of structural, and especially stereochemical,
descriptors and quality of the training databases rather than on the
regression method. Linear regression and neural network
produced results of similar accuracy, however linear regression
was 2-3 times faster68.
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3.3. Regression-based methods
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Linking of structural descriptors and chemical shifts (especially
for carbons) by a mathematical relationship and obtaining weight
factors has been a challenging task for several decades. In 1987
McIntyre and Small developed a methodology for simulation of
the 13C NMR spectra of monosaccharides. Using experimental
data from literature and own recorded spectra of 35 pyranoses
and methyl pyranosides, the authors constructed models that
related observed chemical shifts to 2-6 numerical parameters
encoding aspects of carbon atom chemical environment
(functions of distances, van der Waals’ energies, etc.). These
parameters encoded the effects of multiple oxygen atoms in the
carbon atom surrounding. They were derived from the atomic
coordinates optimized by MM2 calculations of both chair
conformations of every monosaccharide. The authors applied a
multiple linear regression analysis to construct chemical shift
models independently for five carbon types in pyranose residues.
The models were tested on 15 pyranoses and methyl pyranosides
not included in the reference set. The standard prediction error
appeared to be from 0.43 to 0.85, depending on the atom type.
This pioneering study104 encouraged further development of
regression-based methods in computational analysis on NMR
structural data of carbohydrates.
It was shown that a chemical shift can be represented as a
function of variables describing characteristic molecular features.
Within every proposed mathematical model, an experimental
database can be used to calculate the regression parameters and to
check the prediction. Least-square regression techniques, neural
network or HOSE approach were used to formulate the additivity
rules within the NMR parameter prediction by incremental
method on the atomic level68. In contrast to other incremental
schemes, such combination requires a potentially smaller number
of examples from which the necessary rules can be established,
followed by application to a broader range of chemical structures.
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The general-purpose atom-based regression scheme, derived
using least-square method, has been recently designed by Blinov
and coworkers. As compared to neural network approach, usage
of linear regression provided ultra-fast calculation (ca. 10,000 13C
NMR chemical shifts per second on a desktop computer) with an
average deviation of 1.85 ppm 105. Within this scheme every atom
surrounding an atom under consideration is characterized with 9
parameters (element, hybridization state, valence, etc.). The
concept of “atom pairs” was introduced to the single-atom
increments and to add more descriptors to the structure
encoding105.
Mitchell and Jurs developed linear-regression mathematical
models to obtain 13C NMR chemical shifts from a number of
atom-based structural descriptors of monosaccharides106. These
descriptors included topological, geometric, and electronic
information about carbon atoms in a conformation obtained by
energy minimization using MM2 force field. The training data set
included 55 pyranoses and 56 furanoses. As a result of multiple
linear regression analysis, an eleven-descriptor model was
designed for pyranoses and an eight-descriptor model was
designed for furanoses. The models were submitted to neural
networks, giving improved results with final RMS deviation of
1.03 ppm for pyranoses and pyranosides and 1.58 ppm for
furanoses and furanosides106.
A similar approach has been used by Clouser and Jurs for
prediction of 13C NMR chemical shifts of 17 ribonucleosides107.
The atoms to predict were divided into two subsets, one for those
inside the ribofuranose ring, and the other for those contained in
nucleosides. Multiple linear regression allowed building of a
four-descriptor model (three topological descriptors and one
geometrical) for the former subset and an eleven-desciptor model
(four electronic, three topological and two geometrical
descriptors) for the latter one. Submission of the derived models
to a three-layer fully-connected neural network made it possible
to reach the accuracy of 0.39 ppm for the first subset and 0.98 for
the second one. The former value does not differ much from a
regression model output as there are not enough input descriptors
to make use of non-linearity of a neural network. In the case of
the second subset usage of neural networks significantly
improved the prediction accuracy as compared to a regression
model output107.
3.4. CHARGE approach
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CHARGE is a semi-empirical incremental scheme based on
electronic, steric and other effects parameterized for a variety of
functional groups108, 109. CHARGE algorithms do not include
geometry optimization but should be given a determined
geometry of a molecule to process. CHARGE is implemented as
a part of ModGraph 1H NMR chemical shift predictor73
(implemented in MestreLabs MestreNova and Cambridge
ChemBioOffice). This predictor starts with generation of all 3D
conformers from a primary structure, followed by CHARGE
prediction for each conformer and resulting in a weighted average
spectrum. The prediction includes the substituent chemical shifts
approach, which is a general-purpose additive incremental
scheme utilizing 3D structures. This approach is the extension of
the Proton Shift program developed earlier110.
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The CHARGE approach combines short-range and long-range
substituent effects. The short range effects are reflected in the
calculation of the partial atomic charge of the atom under
consideration, based upon electronegativity and polarizability of
atoms in close proximity and the dihedral angles. The calculated
α-, β- and γ-effects produce a partial charge on the given atom,
which is converted to the charge-derived chemical shift using the
equation δcharge = 160.84×q-6.68. The effects of more distant
atoms on the 1H NMR chemical shifts are represented as a sum of
steric, electric field, anisotropic, π-electron and ring current
contributions.
CHARGE is considered less fundamental but faster and more
convenient in routine usage than ab initio calculations. No
dedicated parameterization for carbohydrates has been reported,
however parameterization of CHARGE for polyatomic alcohols,
including inositol, provided acceptable agreement with the
experimental data109. Escalante-Sanchez and Pereda-Miranda
used this approach to simulate oligosaccharide 1H NMR spectra
and to find proper parameters for the 1st and 2nd-order analysis of
the experimental 1D NMR data111. The scope of the study
included batatin I, batatin II and two ester-type dimers of acylated
plant pentasaccharides. The experimental NMR spectroscopic
values registered for batatinoside I were used as a starting point
for the NMR simulation of batatins I and II. Spectroscopic
simulation carried out in Mestre-C was used to reproduce the
registered 1H NMR data and thus permitted a correct assignment
for the chemical shifts and coupling constants of all
superimposed protons in batatins I and II111.
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Rigorous verification of BIOPSEL predictions was carried out
on repeating units of Proteus bacterial polysaccharides113. The
published experimental structures were found among the five
highest ranked predicted structures in 80% cases, of which in
60% cases the correct structure was ranked the highest. The
simulated spectra showed average deviation from the
experimental data in the range from 0.13 to 0.45 ppm. Recently
chemical shift prediction module of this software became a part
of Bacterial Carbohydrate Structure Database114, got webinterface115, and was extended to predict 13C NMR chemical
shifts and glycosylation effects for oligomeric or polymeric
glycans, including those containing rare monosaccharides.
Widmalm and coworkers designed a web-interface116 to the
CASPER program for structure elucidation of oligo- and
polysaccharides using 13C and 1H NMR data, including chemical
shift correlation experiments117. They provided a schema for
structural elucidation of polysaccharides based solely on the
NMR data118. The algorithm of CASPER, which uses an
incremental approach to the calculation of 13C and 1H NMR
chemical shifts, was developed earlier119. There are three data
3.5. Incremental approach at the residual level
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General-purpose computational tools discussed above, based on
incremental and neural network approaches, do not provide the
accuracy sufficient for 13C NMR “fingerprint” of natural glycans.
In contrast to the fragmental approach on the atomic level,
algorithms that partition structures on the level of residues were
much better parameterized for carbohydrates. The latter approach
implies application of the substitution effects to the spectra of
monosaccharides or other small structural fragments. The
substitution effects reflect chemical shift changes caused by
addition of certain structural units to a known position in a
monosaccharide. The more structural features of substituents are
taken into consideration, the better the spectrum simulation
accuracy of is. Thus, the accuracy of chemical shift
computational prediction significantly depends on completeness
of the spectroscopic databases for a given class of
monosaccharides.
Toukach and Shashkov implemented incremental 13C NMR
prediction scheme developed earlier112 in the computational tool
BIOPSEL, capable to predict 13C NMR chemical shifts of regular
glycopolymers in water solutions113. Incremental approach was
used in calculations to elucidate polymeric glycan structures
based on 13C NMR data only. An empirical database of chemical
shifts of mono-, di- and trisaccharide fragments was obtained
from retrospective literature analysis and applied in calculations.
A substitution effect database derived from published spectra of
di- and trisaccharides was used to calculate chemical shifts of the
unknown structural entities.
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Fig. 4. Conformation of a tetrasaccharide repeating unit of Shigella
dysenteriae type 2 O-antigen predicted by MM3(1996) with the use of
genetic algorithms120. Reproduced with permission, © Elsevier Ltd.,
2005.
categories utilized in the simulation of NMR spectra: chemical
shifts in monosaccharides, glycosylation shifts in disaccharides,
and correction sets being the differences between the observed
chemical shifts for spatially strained trisaccharide models and
those calculated by the additive approach119.
The interface and the underlying program have been
extensively tested using published data and proved to be able to
simulate 13C NMR spectra for >200 structures with an average
error of about 0.3 ppm/resonance. When applied to the repeating
units of Escherichia coli bacterial polysaccharides, the published
structures were found among the five highest ranked predicted
structures in 75% cases. The average deviation between
calculated and experimental chemical shifts was 0.54 ppm and
0.06 ppm for 13C and 1H nuclei, respectively. Oligosaccharide 13C
spectra were calculated with the average error of 0.23
ppm/resonance and the correct structure was ranked first or
second in all the cases examined121.
This journal is © The Royal Society of Chemistry 2013
4. Models and methods for carbohydrate 3D
structural studies
5
In the present section we discuss only those theoretical models
and methods that were coupled with the NMR structure analysis.
Other computational approaches used in the studies of
carbohydrates has been reviewed elsewhere122-125.
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4.1. Molecular mechanics and molecular dynamics
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Molecular mechanics (MM) uses Newtonian mechanics to model
molecular systems and calculates the potential energy using the
sets of atomistic parameters derived from small model
compounds (force fields). The basics of this method are described
in a monograph by Burkert and Allinger126.
Several MM force fields, such as CHARMM and GLYCAM,
have been specially optimized for carbohydrates44. A multitude of
force field parameterizations have been studied in order to
account a flexible nature of carbohydrates. Of general-purpose
force fields, MM3 has been one of the most popular ones for the
optimization of the oligosaccharide structure. An example of
atomic coordinates produced by MM3 energy calculations and
genetic algorithms is depicted on Fig. 4. The search using
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geometrical optimization of carbohydrates were reviewed by
Imberty and Perez36.
Energy minimization procedures based on molecular
mechanics and molecular dynamics are widely implemented in
dedicated (Wavefunction Inc. Spartan127, Schrödinger
MacroModel128, 129, MOSCITO130, 131, COSMOS132, 133 and other)
or general-purpose (Gaussian Inc. Gaussian134, 135, GAMESS136138
, Hypercube Inc. HyperChem139, 140 and other) software.
Molecular dynamics (MD) is a form of computer simulation in
which particles are allowed to interact for a period of time by
approximations of known physics, giving a view of their motion.
MM and MD usually share the same classical force fields, but
unlike MM, MD may be based on quantum chemical levels of
theory. However, MD simulation capable to achieve convergence
of rotamer population of the exocyclic C-C torsions with
consideration of solvent requires longer timescale than assumed
by a reasonable computational cost44. More detailed view on MD
methods is presented in a review by Adcock and McCammon141.
The MD simulation technique is a good way to study inherent
flexibility of a molecule since all degrees of freedom are explored
simultaneously, although barrier crossing may still require very
long simulations. The ensemble of MD-generated conformations
may be subsequently used for the prediction of parameters for
which only a poor quantum mechanical experience exists. MD is
of particular importance to analyze and predict NOEs in the NMR
spectra of carbohydrates142-144.
Replica-exchange molecular dynamics (REMD)145 employs a
set of frequently exchanged simulations with different
temperatures, allowing a one-dimensional random walk in
temperature and potential energy space. Usage of REMD for
conformational studies of carbohydrates has been recently
reviewed146.
4.2. Semi-empirical methods
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Fig. 5. Relative usage of modern carbohydrate force fields (based on
citation index during 2005-2010)123. Reproduced with permission, ©
Elsevier Ltd., 2010.
GLYCAL software was performed in the conformational space of
torsion angles of glycosidic bonds and exocyclic groups. Genetic
algorithms use operators like mutation and crossover to generate
offsprings over a random population of conformations evaluated
by MM3 energy, and terminate after a fixed number of
generations or at no further improvement. This approach allows
significant expansion of conformational space that can be
explored at reasonable computational costs120.
A brief guide to the MM force fields used for carbohydrate
calculations is given in Table 2, and the usage statistics is
depicted in Fig. 5. A more complete list of force fields ever used
for carbohydrates is provided in a review by Gerbst and
coworkers124. Useful classical force fields applicable to
This journal is © The Royal Society of Chemistry 2013
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Semi-empirical methods use sets of parameters derived from the
experimental data in order to simplify the approximation of the
Schrödinger equation. Therefore, relatively low computational
resources are required and the calculations can be practically
applied to large molecules147, or used to obtain a starting point for
subsequent ab initio calculations. Most of semi-empirical
methods are known to operate poor on molecules with hydrogen
bonding, transition structures, and molecules containing atoms
for which they are poorly parameterized147. Among the semiempirical methods employed in 3D structure elucidations of
carbohydrates were AM1, PM3, and MNDO148, 149. Some of the
studies used AM1 for the geometry optimization with subsequent
DFT calculations of shielding in oligosaccharides150-152. Later
publications often involved PM5 and PM6 methods153 applied to
carbohydrates and glycoconjugates154.
Bond polarization theory (BPT) is a semi-empirical approach,
designed by Sternberg and coworkers in 1988155, which linearly
correlates atomic charges and chemical shifts to bond polarization
energies. It was applied to the calculation of 13C NMR chemical
shift tensors with accuracy comparable to ab initio methods as
they were in 1997156 and gave rise to a number of improvements
such as COSMOS force field132. This force field allowed
calculation of solid state chemical shifts at reasonable
Chemical Society Reviews, 2013, 0, 00–00 | 9
Table 2. MM force fields reported for calculations of carbohydrates. a
Name
2nd generation molecular mechanics force field for C, H, O and N atoms. It has been
extensively used for carbohydrates. The MM3 force field takes into account the stretching,
bending, stretch-bending, torsional and dipolar contributions and van der Waals interactions.
It accounts for the anomeric and the exo-anomeric effects and has some provisions for
estimation of hydrogen bonding159.
GAUSSIAN 134, 135,
PCModel 160,
Tinker 161
162
MM+(91)
MM+
A variant of MM2 combining a functional from MM2(77) and parameterization from
MM2(91) with a number of extensions.
HyperChem 139, 140
163
CHARMM
CHARM22
CHARM27
Chemistry at Harvard macromolecular mechanics, a family of classical force fields for the
calculation of macromolecules using molecular dynamics, and an associated software
package. CHARM22, originally designed for proteins, was parameterized for explicit water
model. CHARMM27 was reported to be suitable for sugars within nucleic acids.
CHARMM 164,
GROMACS 165, 166,
Tinker161
167, 168
164, 165,
;
169
(review)
-
All-atom additive empirical force field consistent with CHARMM and parameterized for the
hexopyranose monosaccharides and linkages between them.
CHARMM
170, 171
-
Parameterization of the additive all-atom CHARMM force field for acyclic polyalcohols,
acyclic carbohydrates, and inositol.
CHARMM
172
PARM22/SU01
CHARMM22 modified for pyranosidic carbohydrates.
CHARMM
173
HSEA
Hard sphere approach with consideration of the exo-anomeric effect. It was shown to be able
to predict the 3D structure and conformation of large oligosaccharides.
GESA, GEGOP
174
CHEAT95
Extended atom force field for hydrated oligosaccharides, a modification of CHARM22 with
special atom type to account hydrogen bonding.
CHARMM
175
HGFB
A revised CHARMM-type molecular mechanics potential energy function specially
developed for use in the dynamical simulation of simple carbohydrates in aqueous solution.
The force field was shown to represent the vibrational spectrum and ring pucker of pyranoses.
CHARMM (?)
176
PHLB
Molecular dynamics force field aimed to correct the unrealistic flexibility of the HGFB
carbohydrate model. Specific dihedral angle terms are parameterized to reproduce
experimental vibrational frequency data and small molecule ab initio dihedral angle rotational
energy profiles.
CHARMM
177
GLYCAM_93
GLYCAM2000
GLYCAM06
This generalizable biomolecular force field was initially designed to add carbohydrate
functionality to AMBER. Later this dependence was removed, as well as all general or
default parameters, and explicit water was accounted for.
AMBER 178, 179
180, 181
GROMOS
This classical general-purpose force field associated with MD simulation software package
for the study of biomolecules (A-version) has been developed for application to aqueous or
unpolar solutions of proteins, nucleotides and sugars. A gas phase version (B-version) for
simulation of isolated molecules is also available.
GROMOS 182-184,
GROMACS
185, 186
45A4
This parameter set based on GROMOS, was developed for the explicit solvent simulation of
hexopyranose based carbohydrates.
GROMOS (?)
187
OPLS-AA
Originally designed as optimized potentials for liquid simulations (all-atom) it was later
extended for carbohydrates and parameterized to reproduce the ab initio calculation of
energies of 4C1 pyranoses with explicit water.
MOE, Tinker,
Towhee
188
COSMOS-NMR
Hybrid QM/MM force field that uses localized bond orbitals with fast BPT formalism for
semi-empirical calculation of atomic charges and NMR parameters. It was adapted to a
variety of compounds including macromolecules and optimized for the NMR-based structure
elucidation. Explicit quantum-mechanical calculation of electrostatic properties is utilized.
COSMOS 132, 133
132
CSFF
A development of the PHLB and HGFB carbohydrate force fields optimized for carbohydrate
solutions and having improved hydroxymethyl rotations.
CHARMM
189
AMBER
A functional form from which a family of classical explicit-solvent force fields are derived
for molecular dynamics of biomolecules (GAFF, GLYCAM).
MacroModel 128, 129,
AMBER 178, 179,
other
190
BIO+
5
ref.
MM3
MM3(1992)
MM3(1996)
MM3(2000)
Amber-H
a
Implementation a
Description
Derived from AMBER for conformational analysis of oligosaccharides.
A force field based on CHARM22 and CHARM27.
Insight II
192
HyperChem
;
191
(review)
193
139, 140
Only implementations cited in carbohydrate studies are listed; other implementations used for carbohydrates implicitly are not covered here.
computational cost, as DFT methods under periodic boundary
conditions demanded much higher computational power157.
Later Sternberg and coworkers used COSMOS force field in
combination with 13C solid state chemical shift target functions to
investigate the structure of cellulose I and II158. The parameters of
linear polarization model for BPT were determined from a least
This journal is © The Royal Society of Chemistry 2013
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square fit to atomic charges in small molecules obtained by ab
initio calculations using the 6-31G(d,p) basis set. The average
deviation between calculated and experimental data, derived from
reported chemical shifts was 0.47 ppm, 0.89 ppm and 0.67 ppm
for cellulose-II, cellulose-Iα and cellulose-Iβ, respectively.
Chemical Society Reviews, 2013, 0, 00–00 | 10
Witter and coworkers investigated the spectrum assignment for
C-enriched bacterial cellulose Iα 194. The crystal structure was
refined using the 13C NMR chemical shifts as target functions,
giving 0.37 Å RMS difference with the structure determined by
neutron diffraction (for heavy atoms only). Starting with
coordinates derived from neutron scattering, the MD simulations
yielded four ensembles containing 800 structures. These four
models were geometrically optimized with the given isotropic
NMR chemical shift constraints and application of the
crystallographic boundary conditions. 13C NMR chemical shift
tensors were simulated for each model (using BPT with
coordinate-dependent charges) and compared with the
experimental chemical shift anisotropy information obtained by
2D iso-aniso RAI acquired at magic angle spinning speed of 10
kHz. The calculations based on the COSMOS force field allowed
obtaining isotropic chemical shifts with average deviation of 0.59
ppm per resonance.
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4.3. Ab initio and density functional modeling
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A quantum chemistry modeling approach implies a combination
of a theoretical method (level of theory) with a basis set. Each
unique pairing of method with basis set represents a certain
approximation of the Schrödinger equation. Results for different
systems may only be compared when they have been predicted
via the same model147. The more electron correlations are
considered in a theory level and the bigger a basis set is, the more
accurate but more computationally-expensive the calculation is.
Hybrid functionals define the exchange functional as a linear
combination of Hartree-Fock, local, and gradient-corrected
exchange terms. The hybrid functionals most widely reported in
structural studies of carbohydrates are Becke's three-parameter
formulations (B3LYP195, 196 and B3PW91195, 197) and their
modifications. Detailed description of functionals and basis sets
is beyond the scope of this review, and is reviewed elsewhere147.
During recent decades density functional theory (DFT) gained
increasing popularity in computations of various biomolecular
systems. Good accuracy at reasonable demand in computational
resources is the important advantage of DFT calculations.
Detailed descriptions of various functionals as well as of the
scope and applications of DFT calculations were published198-204.
Time-dependent DFT was reported in context of description of
electromagnetic field to substance interaction205, 206.
QM calculations are carried out in two stages to predict the
NMR properties of molecules: 1) geometry optimization to obtain
three-dimensional structure; and 2) calculation of NMR
parameters for a certain geometry. Very often different levels of
theory are applied at these stages and in most cases calculation of
the NMR parameters (stage 2) requires more sophisticated level
as compared to geometry optimization (stage 1). Choozing a
proper combination of theory levels is an important question
discussed in more details below (sections 4.3 and 4.4).
Several computational approaches were developed for
prediction of the magnetic properties and NMR parameters.
Gauge-independent atomic orbitals (GIAO) method for NMR
shieldings proposed by Ditchfield in 1974207 implies that atomic
orbitals have their own local gauge origins placed on the orbital
center and defining the vector potential of the external magnetic
field. Incorporation of such features of DFT as accurate non-local
This journal is © The Royal Society of Chemistry 2013
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exchange-correlation functional and bigger basis sets in GIAO
calculations led to significant improvement of the shielding
tensor calculation quality208.
Attempts to improve the efficiency of the magnetic property
calculations have been undertaken by applying the gauge factors
to localized molecular orbitals instead of every atomic orbital.
These attempts were formalized in the individual gauge localized
orbital (IGLO) method209 and the localized orbital/local origin
(LORG) method210. The performance of IGLO was studied on
small organic molecules at first,211 and later the method was
combined with DFT calculations212. A few studies reported usage
of GIPAW for solid state chemical shift prediction in
carbohydrates213. GIPAW is a theory for all-electron magnetic
response within the pseudopotential approximation, based on
extension of Blöchl’s PAW approach. As a valuable feature,
GIPAW is valid for both finite and periodic-boundary
conditions214. Density functionals commonly used in GIPAW
studies have been PBE215 and KT3216. The latter is a
semiempirical exchange-correlation functional specially designed
for the calculation of organic nuclei shielding tensors and
reported to outperform hybrid functionals for molecules forming
hydrogen bonds217.
Comparison of GIAO, IGLO and LORG calculations showed
better efficiency of GIAO in terms of the required basis set and
provided more accurate results218. GIAO internally extends the
basis set with higher angular momentum orbitals, which are
necessary for the correct description of the perturbed systems. In
contrast, all atomic orbitals participating in a localized molecular
orbital share the same gauge factor. As compared to localized
methods, GIAO is less sensitive to the quality of the employed
basis set, and thus provides faster convergence of the calculated
chemical shielding and does not require polarization functions to
achieve the same level of accuracy218.
Nowadays, the main drawback of GIAO as compared to the
localized methods, i.e. lower calculation performance, has been
significantly compensated by development of computer
hardware. The performance of modern desktop computers is now
sufficient to predict NMR properties of small and medium sized
molecular systems with reasonable accuracy. As a result, GIAO
calculations combined with density functional theory level from
early 90s 219 are often used to predict NMR properties of organic
and biomolecular systems.
An important issue for reliable computational prediction of the
NMR parameters is a selection of a proper theory level for
geometry optimization. NMR shielding tensor is a property that
can be computed in the context of a single point energy
calculation. HF/6-31G(d) on geometry optimized with B3LYP/
6-31G(d) was cited as minimal model for predicting the NMR
parameters220. Due to hydrogen bonding, the basis set properly
describing energies of carbohydrates should include diffuse
functions; B3LYP/6-311++G(2d,2p) was reported as minimal for
accurate description of aldo- and keto-hexoses in both furanose
and pyranose forms221.
Reduction of scaling of QM calculations to the lower powers
of molecular size has been a challenge. It became possible to
linearize the scaling for the geometrical222 and energetic (DFT)
calculations223. Within a method for the calculation of NMR
chemical shielding introduced by Ochsenfeld and coworkers224,
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the cubic increase of the computational effort with molecular size
is reduced to linear. This allowed treatment of large molecules
(>1000 atoms with no need for molecular symmetry) at the HF
and DFT levels.
According to a survey of approaches to CST calculation done
by Sefzik and coworkers225, in most cases none of DFT
functionals could perform better than HF in calculation of
chemical shielding tensor components in eight solid state
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Fig. 6. The structure (A) and C NMR chemical shift surface for the
anomeric carbon at the glycosidic bond (B) of α-D-Glcp-(1-4)-α-D-Glcp
disaccharide in water obtained using ONIOM(DFT:HF) method226.
Reproduced with permission, © Elsevier Ltd., 2009.
1-methylpyranosides, erythritol and sucrose, however absolute
values were close to the experiment. cc-pVDZ and cc-PVTZ
basis sets were used.
A number of other methods to predict chemical shifts using
quantum-mechanics calculations, were summarized by Gregor
and Mauri227. General topics related to calculation of magnetic
properties and the NMR parameters are well-reviewed in the
scientific literature61, 64, 228, 229. The main scope of the present
review are the NMR computational studies of carbohydrates and
their limitations.
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4.4. Hybrid QM/MM, QM/QM and ONIOM approaches
25
Recent development of hybrid theoretical approaches made it
possible to divide large molecular systems into several
subsystems (layers) and to treat them at different levels230-233. In
these hybrid calculations the most important and relatively small
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part of the molecule (higher layer) is treated at more accurate
quantum mechanical theory levels, whereas other parts of the
molecule are treated at the less computationally-demanding
levels, such as MM or low level QM. The molecules or molecular
systems are usually partitioned into two (high and low) or three
(high, medium and low) subsystems. In the two-layer approach
the resulted hybrid methods are noted as QM/MM, QM/QM,
ONIOM(QM:MM) or ONIOM(QM:QM)234. In the three-layer
approach the system of interest can be described as ONIOM
(QM:QM:MM) with several combinations of theory levels for
different layers.
Utilization of hybrid approaches significantly speeds up the
calculation and overcomes the size limitation in computational
studies. In the best case hybrid approach combines the accuracy
of high level QM calculations at the speed of relatively fast low
level methods (MM, etc.). The scope and limitations of hybrid
approaches for studying organic and biomolecular systems were
reviewed in the literature230-233 including the description of
developed computational tools235. ONIOM(DFT:MM) and
ONIOM(DFT:HF)
calculations
have
shown
excellent
performance in structure optimization and energy calculations,
particularly for derivation of chemical shift surfaces of glycosidic
bond carbons (example in Fig. 6, discussed below)226.
Two general strategies are explored in modern carbohydrate
studies involving hybrid calculations. The first strategy is based
on hybrid calculations only at the geometry optimization step,
followed by derivation of the NMR properties with regular
methods and treatment of the whole molecule at the same level
(usually it is the highest QM level achievable with existing
computational resources). This approach benefits mainly from
performance increase on the stage of molecular structure
optimization. It is a reasonable and very useful combination since
geometry optimization is often much more time-consuming
compared to GIAO calculations of chemical shifts236.
The second strategy allows utilization of the hybrid approach
features both in geometry optimization and in magnetic properties
calculation. Morokuma and coworkers have demonstrated the
efficiency of the hybrid approach to calculate the NMR chemical
shifts using the two-layer ONIOM scheme237. In this calculations
the small (model) system containing the atoms of interest was
described at a higher level of theory, and the rest of the molecule
was described at a lower level. The resulting shieldings were
expressed as: σiso [ONIOM] = σiso (high level, model) + σiso (low
level, whole molecule) - σiso (low level, model). A general
recommendation for molecule partitioning says that a minimal
model system for the NMR property calculation should include a
nucleus for which the high accuracy is needed and its closest
heavy neighbors237.
The usage of combined QM/MM method for the validation of
the geometrical modeling of the complex of E-selectin with sialyl
Lewis X was reported by Ishida238. A combined modeling was
proposed to identify complex sugar-chain conformations on the
reduced free energy surface. The free energy profile was
evaluated by classical MD simulation followed by ab initio
QM/MM energy corrections. Flexible carbohydrate structures
were mapped onto the reduced QM/MM 2D free energy surface,
and the details of molecular interactions between each
monosaccharide component and the amino acid residues at the
This journal is © The Royal Society of Chemistry 2013
carbohydrate-recognition domain were identified. Using the
computational procedure of the chemical shielding tensor
evaluation239 the calculations for large molecules including a
carbohydrate ligand were performed. This study confirmed the
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modeling validity by evaluation of the 1H NMR chemical shifts
by ab initio QM/MM-GIAO computations at HF/6-31G*. 20
QM/MM-refined geometries sampled from the minimum free
Fig. 7. Two conformations of the IdoA2S residue of a heparin disaccharide in water: 1C4 (A) and 2S0 (B). The GlcN6S residue is in the 4C1 form. Violet
dots represent sodium ions. Only a part of water molecules is shown for clarity240. Reproduced with permission, © American Chemical Society, 2011.
energy region in the free energy surface were used, and the
averaged theoretical data were compared to the experimental
NMR spectrum238. Although most proton chemical shifts were
reasonably assigned by QM/MM-GIAO averaging, some
resonances showed an upfield shift by 0.2-0.3 ppm, as compared
to the experiment. Most of these deviations were observed when
monosaccharide units were exposed to a solvent-accessible
region and had a relatively high flexibility. The study confirmed
excellent potential of hybrid approach to study carbohydrates, as
well as it pointed out the necessity of more accurate consideration
of solvent effects.
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predominate in MD studies due to faster calculation and better
correspondence with existing force fields242.
In contrast to rigid and non-polar molecules, carbohydrates
possess strong and specific solute–solvent interactions due to
hydrogen bonding and have conformational degrees of freedom,
possibly with solvent-dependent distribution. Due to these factors
the full dynamics of carbohydrate molecules in solution is a
4.5. Interaction with solvent
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35
The ability of carbohydrates, especially polysaccharides, to adopt
a wide range of dynamic conformations in solution was
recognized as the central factor for many of their biological
functions, and thus interaction with solvent cannot be neglected.
Not only NMR properties, but also the geometry should be
simulated with consideration of the solvent effects. A multitude
of hydroxyl groups present in carbohydrates lead to noticeable
contribution of the solvent-solute interaction and introduce
visible differences between solution and X-ray structures36.
Structure of carbohydrates in solution is strongly influenced by
solvent, which is in most cases water. In classical simulations
water is often represented using a three-site (TIP3P), a four-site
or a five-site water model241. As implemented in CHARMM, this
model implies that each atom in a water molecule is represented
by a point charge and a Lennard-Jones potential energy term, and
the algorithm used does not allow the water molecule geometry to
change throughout the simulation. Simple water models
This journal is © The Royal Society of Chemistry 2013
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Fig. 8. 13C NMR chemical shift surfaces for two transglycosidic carbons
of α-(1-4)-linked D-Glcp disaccharides, as a function of the glycosidic
bond dihedrals151. Reproduced with permission, © Elsevier Ltd., 2005.
challenging topic243. A common approach to the description of
the dynamics is running an MD simulation for solute surrounded
by solvent molecules with subsequent extraction of snapshots
from the trajectory file. Calculation of the NMR properties
implies averaging over these molecular clusters as well244.
However, MD simulation capable to achieve convergence of
rotamer population of the exocyclic C-C torsions with
consideration of solvent requires a timescale of more than
100 ns 245. This timescale is longer than assumed by reasonable
computational cost44.
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In quantum chemical calculation using HF and DFT levels, a
number of solvation models have emerged. To improve the
calculation performance polarizable continuum model (PCM)
represents solvent as a continuum rather than individual
molecules246. Several modifications of the continuum model
differing in interpretation of the solvent electric conductivity led
to development of DPCM (solvent is treated as a dielectric) and
CPCM (solvent is treated as a conductor) models247. The
performance of continuum models in various solvents and their
influence on geometry optimization of solute molecules were
addressed248, 249. Marenich and coworkers presented several
solvent-independent continuum solvation models, including those
based on the quantum mechanical charge density of a solute and
parameterized for various organic compounds250, 251. Among
them, SM8 claimed to be the most accurate continuum solvation
model for prediction of the free energies of solvation of
molecular solutes252.
Conductor-like screening model (COSMO) of solvation treats
solvent as a conducting continuum located outside the molecular
cavity. The shape of the cavity depends on a certain
representation of method and is usually constructed from Wan
der Vaals radii of the atoms of the modeled compound. In
contrast to PCM, COSMO derives the solvent polarization from
the distribution of the electric charge of the solute. It is more
accurate for solvents with higher permittivity, such as water,
which can be more likely modeled as a conductor253.
Bagno and coworkers tested the QM prediction of the NMR
parameters of glucose in water for the snapshots taken from the
MD simulation of a target molecule with up to 5.5Å water sphere.
Application of COSMO at the last step of DFT processing did not
have a valuable effect on the accuracy of chemical shift
calculations254.
An explicit solvent model is physically appropriate for charged
molecules with strong solute-solvent interactions255. As an
example, explicit inclusion of water molecules and counterions
allowed a comparative study of conformational, solvent, and
counterion effects on coupling constants in a heparin unit (Fig.
7)240. An example of explicit inclusion of water in HF GIAO
calculations of a large molecular system within a linear-scaling
method has been described224. The hybrid implicit/explicit
solvation was investigated by Lee and coworkers, implying
explicit hydration of a solute by a layer or a sphere of water
45
molecules, while the bulk solvent is modeled as a continuum256.
ONIOM-PCM approach provides a good opportunity for
investigation of hybrid solvation models257.
For further details of particular solvation methods and their
scope and limitations please refer to the dedicated publications242,
258
.
5. Computation of NMR chemical shifts
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Chemical shifts have been recognized as characteristic indicators
of primary and regular secondary structure of carbohydrates. This
section summarizes recent applications of semi-empirical and
quantum chemical computations to the prediction of the NMR
shielding parameters in glycans and their derivatives. Techniques
used to calculate chemical shift tensors in general organic
chemistry were reviewed elsewhere259.
It should be noted that a direct output of chemical shift
calculations (e.g. GIAO) is an anisotropic chemical shielding
tensor, which can be later converted to the isotropic chemical
shielding observed in liquids: σiso=(σ11+ σ22+ σ33)/3, where σii are
the principal components of a magnetic shielding tensor
expressed along three orthogonal axes in a molecule. The
chemical shift is expressed as the difference between shielding of
a reference compound (normally TMS, processed at the same
level of theory as a target molecule) and the calculated shielding.
The operation of conversion of the shielding tensor to the
isotropic chemical shift is often implemented in programs
providing the interface to quantum chemical software packages.
A chemical shift surface (CSS, example in Fig. 8, discussed
below) term is used to reflect the dependence of the chemical
shift of the atoms in close proximity to the glycosidic bond on its
φ and ψ torsion angles.
5.1. Monosaccharides and derivatives
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The following analysis of available literature data and
corresponding discussion are sorted by the increasing complexity
of the studied system. The current section covers the results
obtained for monosaccharides and their derivatives containing a
single sugar ring, where the basic fundamental properties and
relationship between the NMR data and molecular structure can
be revealed (Table 3).
Table 3. GIAO prediction of chemical shifts in monosaccharides, their derivatives and conjugates
Object (molecule)
α-D-Glcp,
β-D-Glcp
(population-weighted
conformers in aqueous
solution)
β-D-Glcp
(five conformers)
α-D-Glcp,
β-D-Glcp
Parameter a
: nuclei
CS: 1H, 13C
CS:
H, 13C, 17O
Calculation method
Geometry
B3LYP/
6-31G(d,p),
Solvation
energies:
B3LYP/6-311++
G(2d,2p)
Shielding
B3LYP/pcJ
MP2/cc-pVDZ
ONIOM [MP2 : HF/
6-311++G(2d,2p)]
1
Application
Software
Gaussian 03 134,
135
Gaussian 98,
TURBOMOLE
261, 262
CS:
1
H, 13C, 17O
MM+
14 | Chemical Society Reviews, 2013, 0, 00–00
B3PW91/6-31+G(d)
RHF
Gaussian 94,
HyperChem 4.5
139, 140
ref.
analysis of the experimental
data
260
validation of ONIOM and
providing guidelines for the
selection of ONIOM model
systems
validation of a DFT GIAO
calculation on an MM+
geometry
263
264
This journal is © The Royal Society of Chemistry 2013
Table 3, continued
β-D-Glcp
CS: 13C
(solid state)
X-ray
B3LYP/
6-311+G(2d,p)
(GAIOCHF
procedure)
Gaussian 03
theoretical investigation of
effects of the conformation
and hydrogen bonding on 13C
isotropic chemical shifts
265
α-D-GlcpNH3+-1,4Me2
(chitosan monomer model)
CST: 1H,
15
N, 17O
(solid state)
CST:
1
H, 15N, 17O
(solid state)
X-ray; B3LYP/
6-31++G(d,p) for
protons only
X-ray; B3LYP/
6-31++G(d,p) for
hydrogens only
B3LYP/
6-311++G(d,p),
B3LYP/6-31++G(d,p)
B3LYP/
6-311++G(d,p)
B3LYP/6-31++G(d,p)
Gaussian 98
266
α-D-Glcp
(gas phase)
CS: 1H, 13C
B3LYP/
6-31G(d,p),
B3LYP/
6-31+G(d,p)
B3LYP/cc-pVTZ;
B3LYP/aug-cc-pVTZ
α-D-Glcp
(in aqueous solution)
CS: 1H, 13C
B3LYP/
6-31G(d,p),
MD (OPLS-AAtype)
(PhO)2-P-6)-α-D-Glcp1OMe,
PhO-P-6)-α-D-Glcp1OMe,
PhO-P-6)[L-Gly(1-3)]-αD-Glcp-1OMe,
β-D-Fucp × Toluene,
β-D-Glcp ×
3-methylindole,
β-D-Glcp ×
p-hydroxytoluene
CS:
13
C, 1H, 31P
B3LYP/6-31G(d)
glucose:
B3LYP/cc-pVTZ;
BP86/TZ2P;
water:
TZP.1s;
B3LYP/6-31G**
B3LYP/6-31G(d)
Gaussian 03
(QM
calculations);
MOSCITO130,
131
(MD
simulations)
investigation of the
hydrogen-bonding effects on
the CS tensors
investigation of the
hydrogen-bonding effects on
the CS tensors of an
anhydrous crystalline
structure
investigation of the solvent
effects and comparison of
calculation methods
Gaussian 03
clarifying the structural
details of the synthesized
esterified methyl α-Dglucopyranoside derivatives
268
CS: 1H
DFT-D
BLYP/TZV2D
BLYP/TZV2D
Gaussian 03
(modified)
investigation of the
carbohydrate–protein
recognition on models
269
α-D-Lyxp-OMe,
α-D-Lyxp-OMe × (H2O)1-3
13
C
(solid state,
shielding
constants)
X-ray data + PM3
B3LYP/6-31G(d)
CS: 1H, 13C,
17
O
(solid state)
GIPAW
PBE/planewave,,
KT3/planewave
(PhB) β-D-Ribp2,4H-2,
(PhB)2 β-D-ArapH-4,
(PhB)2 α-D-XylfH-4,
(PhB) α-D-Lyxf2,3H-2
(phenylboronic esters)
α-D-Lyxf,
α-D-Lyxp 1C4,
α-D-Lyxp 4C1,
α-D-Glcp 4C1,
α-D-Glcf
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PBE/planewave,
KT3/planewave,
Vanderbilt's
“Ultrasoft”
pseudopotentials
B3LYP/
6-31+G(2d,p),
PCM
confirmation of the 13C
CP/MAS NMR and crystal
structure analysis data and
studies of the hydrogen
bonding effects
distinguishing hydrogen
bonding network patterns by
1
H chemical shift analysis;
comparison of PBE and KT3
270
α-D-Galp
Gaussian 98
(QM
calculations)
HyperChem
5.02 (geometry)
CASTEP271-273
PBE1PBE/
6-311++G(2d,p), PCM
Gaussian 03
approval of a QM method as
a tool for 13C NMR chemical
shifts prediction
275
CS: 13C,
1
H (α-DGlcp)
BP86/TZVP,
B3LYP/TZVP,
MP2/TZVP,
AM1
BP86/TZVP,
B3LYP/TZVP,
MP2/TZVP,
HF SCF/TZVP
comparison and validation of
theory levels and solvent
models; the study of C6-O6
torsion effect on 13C NMR
chemical shifts
276
CST: 13C
(solid state)
Neutron
diffraction data
RHF, HFB, HFS,
BLYP, B3LYP,
B3P86, BVWN,
SVWN, MPW1PW91
TURBOMOLE
(QM
calculations),
HyperChem
(semi-empirical
calculations)
Gaussian 03
comparison of DFT and HF
functionals
225
α-D-GlcpN
(chitosan monomer)
D-Manp-1OMe,
D-Galp-1OMe,
D-Glcp-1OMe,
D-Xylp-1OMe,
D-Frup-1OMe,
L-Sorp-1OMe,
L-Rhap-1OMe,
Erythritol
(statistical study)
C
(shielding
constants)
This journal is © The Royal Society of Chemistry 2013
Gaussian 98
267
254
274
/cc-pVDZ, /cc-pVTZ
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Table 3, continued
P-3:5)β-D-Ribf-1U
(cUMP in aqueous
solution)
CS: 1H, 13C
B3LYP/
6-31G(d,p)
B3LYP/cc-pVTZ
Gaussian 03
testing the prediction method
and selection of the
appropriate solvent model
277
β-D-2-deoxy-Ribf-A,
β-D-2-deoxy-Ribf-G,
β-D-2-deoxy-Ribf-C,
β-D-2-deoxy-Ribf-T
CST: 13C
(C1’),
15
N (sugarlinked
nitrogen)
B3LYP/
6-31G(d,p)
B3LYP/
(9s,5p,1d/5s,1p)
[6s,4p,1d/3s,1p] for C,
N and O; B3LYP/
(5s,1p) [3s,1p] for H
(IGLO II)
Gaussian 03
studying the dependence of
N1/9 and C1’ chemical
shielding tensors on the C1’N torsion angle and sugar
pucker
278
β-D-Glcp
α-D-Glcp
β-D-Glcp-2,3,6Ac
α-D-Glcp-2,3,6Ac
CS: 13C
(C1)
(solid state)
B3LYP/
6-311+g(d,p)
B3LYP/6-311+g(d,p)
Gaussian 03
279
β-D-Xylp-OMe
CS: 13C
(all)
CST: 13C
(all),
O1, O5, H1
CS: 13C
(all)
CST: 13C
(all),
BP86/TZVP
MM2
PW91/IGLO-III
PW91/TZVP
MM
PW91/B-III
deMon-KS,
demon-NMR280282
,
MacroModel 128,
129
V5.0 (MM
calculations)
studying molecular
environment in the chiral
cavities of commercial
polysaccharide-based
sorbents (CDMPC, ADMPC,
ASMBC)
calculation of chemical
shielding dependence on the
dihedral angle between C1
and methyl group
MM3,
B3LYP/
6-31+G**
(selected
conformers)
GIAO
α-D-Xylp-OMe
R-(1-4)-3,6-anhydro-α-DGalp-OMe,
R-(1-4)-3,6-anhydro-DGal-ol,
CS: 1H, 13C
modified MM3
(1992-2000) 162,
285
(MM
calculations),
Gaussian 98W
(QM
calculations)
(R = 3,4-dideoxy-β-Derythro-hexopyranose)
a
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284
study of signal displacement
upon transition from a
pyranose to the open form of
anhGal
286
Notations: CS – chemical shift; CST – chemical shift tensor.
Roslund and coworkers performed a complete assignment of
the NMR spectra of α- and β-D-glucopyranose by iterative fit
using PERCHit software. To support the experimental data they
calculated the 1H and 13C NMR chemical shifts of the glucose
non-hydroxyl protons at the B3LYP/pcJ-2 (NMR data) and
B3LYP/6-31G(d,p) (geometry) levels of theory. The authors
chose a set of three conformers for α-D-glucose and five for β-Dglucose, as most stable in aqueous solution. They obtained
relative stability of the conformers (∆G°+solvation energies) and
estimated their population assuming Boltzmann conformer
distribution. The correlation between the population weighted
averages of the calculated 1H NMR chemical shifts and the
corresponding experimental values were surprisingly good (linear
correlation 0.976-0.977; MAD 0.11 ppm for α-D-Glcp and 0.07
ppm for β-D-Glcp). The correlation factor of calculated vs.
experimental 13C NMR chemical shifts was also good (0.9940.995), however the calculated spectrum was systematically ~10
ppm downfield260. The coupling constants in glucose were also
predicted (see details in section 6.1).
Rickard and coworkers263 compared 13C, 1H, and 17O NMR
chemical shifts obtained by HF-GIAO, MP2-GIAO, and
ONIOM(MP2-GIAO:HF-GIAO) for five most stable conformers
of β-D-Glcp and provided sample model systems for usage in
post-HF chemical shift predictions of larger carbohydrates. Six
small model systems including 6 or 7 heavy atoms were taken out
of the whole molecule of each conformer without changing its
geometry. Severed bonds were saturated with hydrogens.
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The results from HF-GIAO and MP2-GIAO differed
dramatically, especially for the anomeric carbon and the ring
oxygen. ONIOM(MP2-GIAO:HF-GIAO) with three-carbon
model system was capable to yield chemical shieldings in good
agreement with the results from the whole-molecule MP2-GIAO
calculations, except for the ring oxygen. Maximal discrepancies
for 4C1 conformers were: 2 ppm for 13C (C5), 0.09 ppm for 1H
(hydroxyl group at C4) and 2.21 ppm for hydroxyl 17O
(hydroxymethyl group). Maximal discrepancies for 1C4
conformers were: 1.15 ppm for 13C, 0.29 ppm for 1H (anomeric
hydroxyl group).
The results for the ring oxygen in the 4C1 conformer indicated
that a small model system, in which the severed bonds are only
one bond away from the atom under calculation, was not enough
to model the shielding of this atom. In contrast, 1C4 conformer
exhibited good agreement for the ring oxygen chemical shift and
poor agreement for hydroxyl oxygens that formed hydrogen
bonds to non-neighboring centers. To resolve these issues authors
used 9-atom model system and decreased the discrepancy to 1.40
ppm (4C1 ring oxygen) and to less than 0.5 (1C4 hydroxyl
oxygens). Authors conclude that a model system should preserve
outcoming hydrogen bonds for the accurate prediction of the
oxygen chemical shifts.
The best correlation between experimental and calculated 13C
NMR chemical shifts was achieved on the 4C1G+ and 4C1Gconformers (see Fig. 2), as expected from the predominance of
these two forms in aqueous solution287. Both MP2 and
ONIOM(MP2-GIAO:HF-GIAO) levels were found to represent
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proton and carbon chemical shifts well, whereas gas-phase
prediction of the oxygen chemical shifts much poorer correlated
with the solution experimental data263. These calculations
confirmed the earlier work by Kupka et al., in which DFT GIAO
demonstrated better convergence than RHF method in application
to 1H, 13C and 17O chemical shifts of glucopyranose and its
1-C-methyl and 1-O-methyl derivatives264.
Hydrogen bonds play an important role in shaping of
polysaccharide molecules, and their characterization can reveal
biological properties of polysaccharides266, such as recognition of
carbohydrate antigens by host antibodies. The nature of hydrogen
bonds is strongly dependent on the electrostatic interaction, and
the chemical shielding tensors at the magnetic nuclei were shown
to be highly sensitive to hydrogen bond effects. High-level QM
calculations were essential for the interpretation of the
experimentally observed isotropic chemical shifts. It was
suggested that analysis of hydrogen bonding network with
optimized proton positions and subsequent 1H chemical shift
prediction can not only confirm, but also reveal a carbohydrate
structure274.
Suzuki and coworkers have conducted a theoretical
investigation of effects of conformation and hydrogen bonding on
solid state isotropic 13C NMR chemical shifts for β-D-glucose
and its oligomers. The absolute values of the predicted chemical
shifts of a β-D-Glcp molecule extracted from the X-ray structure
without further optimization exposed a bias against the
experimental CP/MAS 13C NMR, but the relative resonance
positions were in reasonable agreement. The experimental linear
relationship288 between the C6 chemical shift and the C6-O6
torsion angle in three predominant conformations of the
hydroxymethyl group was reproduced computationally, as well as
dependencies for C4 and C5. In order to examine the effect of the
intramolecular hydrogen bonding on 13C NMR chemical shifts in
D-glucose (in gt conformation, see Fig. 2), authors calculated
chemical shifts of the ring carbons as a function of the torsion
angle around the C3-O3 bond. C2 and C4 showed a strong
dependency, which was explained by γ-gauche effect produced
by the hydrogen atom. In contrast to the well-known γC-gauche
effect of approx. -5 ppm289, γH-gauche effect induced an increase
of the 13C NMR chemical shift by +3..+5 ppm if not reduced by
the formation of intramolecular hydrogen bonds265. Effects of
various possible hydrogen bonds (including those with
hydroxymethyl group) on the chemical shifts of all carbons in βD-Glcp were analyzed.
Khodaei and coworkers conducted a DFT study to calculate
the solid-state NMR parameters in crystalline chitosan/HI type I
salt and showed the hydrogen bonding effects on the CS
tensors266. They calculated the CS tensors of 17O, 15N, 13C, and 1H
nuclei for two model systems: the monomer (non-hydrogenbonded α-D-GlcpNH3+-1,4Me2) and the target molecule in a
cluster. Both models were created from the X-ray coordinates,
with subsequent optimization of protons at B3LYP/631++G(d,p). Esrafili et al. studied hydrogen bonding effects on
the 17O, 15N, 13C and 1H CS tensors of crystalline anhydrous
chitosan by comparison of the chitosan hexameric cluster to a
corresponding gas-phase monomer (α-D-GlcpN) 267. Both studies
were dedicated mainly to a cluster model and corresponding
details are given in the next section.
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Bagno and coworkers applied several computational protocols
combined from DFT and MD simulations to the prediction of the
alkyl 1H and 13C NMR chemical shifts of α-D-glucose in
water254. For gas-phase calculations, geometry optimizations
were carried out at B3LYP/6-31G** level. B3LYP/6-31+G**
level of theory was also used to test the effect of adding diffuse
functions, which were reported to be very important for
carbohydrates290. The NMR parameters were calculated using the
adopted cc-pVTZ or aug-cc-pVTZ basis sets. MAD averaged
from data for the three conformers concerning population
distribution amounted to 7.1 ppm (13C) and 0.14 ppm (1H). In
spite of satisfactory MAD on the absolute scale, the accuracy was
insufficient to assign all signals. Although a good correlation was
observed (R2=0.994), 13C NMR chemical shifts were
systematically overestimated. Having compared the calculated
spectrum to the experimental one, the study showed that both the
flexibility of the glucose molecule and the strong effect exerted
by water should be taken into account.
In case of solution phase calculations, a structure can hardly be
simulated by DFT calculations on the solute embedded in a small
cluster of solvent molecules. The bias introduced by size effects
and the flat potential energy surface is additionally complicated
by a flexible solute, such as glucose. To separate structural and
solvent effects, glucose shieldings have been calculated at the
B3LYP/cc-pVTZ as averages over 50-100 MD snapshots (until
the convergence was reached) using a series of protocols, each of
them emphasizing either a solute or a solvent.
In protocol a, authors used the glucose molecule geometry
from the modified OPLS-AA force field calculation without
explicit water molecules, but included the solvent effects using a
PCM. Protocol b differed from protocol a by reoptimization of
Glc at B3LYP/6-31G** prior to the NMR calculation. These two
protocols allowed sampling of the conformations of glucose
hydroxyl groups and their rotameric distribution, included the
solvent reaction field but did not include specific solvent effects.
The protocols c-f employed the geometry of glucose obtained
from MD simulations. In protocol c the authors included water
molecules surrounding glucose up to 5.5 Å from the glucose
center of mass. Water molecules were modeled by TIP3P point
charges and combined with glucose using ONIOM. In protocol d,
glucose was simulated at BP86/TZ2P and water was at
BP86/TZP.1s. Protocol e utilized B3LYP/6-31G** for water and
PCM solvent; f was the same as d plus COSMO solvent.
The only protocol with DFT optimization of the glucose,
namely protocol b, demonstrated the best correlation for both 1H
(R2=0.987) and 13C (R2=0.997) NMR chemical shift simulations,
and also produced the lowest MAD for 13C (1.12 ppm). From this
data the authors concluded that the most important factor that
affected the accuracy of computed 1H NMR chemical shifts was
the solute geometry, while the solvent effect could be reasonably
described by self-consistent reaction field models. As judged by
protocol performance comparison, glucose geometry could not be
accurately modeled by MD simulations alone. Surprisingly, there
was no need of explicit water inclusion for the shielding constant
calculation254. 13C NMR chemical shifts exhibited only a minor
dependence on the solvent.
Chelmeka and coworkers carried out DFT GIAO calculations
of 1H, 13C and 31P NMR chemical shifts at B3LYP/6-31G* level
Chemical Society Reviews, 2013, 0, 00–00 | 17
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for three synthesized methyl α-D-glucopyranoside 6-phosphate
derivatives esterified by phenyloxy groups and glycine. Based on
the comparison of the calculated and the experimental data
authors concluded that the target compound having an amino
group and a phosphate occurs in the neutral form, rather than as a
zwitterion, and selected one of two stereoisomers differing in the
absolute configuration of a phosphorus atom. The details of
comparison, deviation values and correlation factors were not
reported268.
Electronic structure calculations were performed on complexes
of β-D-fucose and β-D-glucose with toluene, p-hydroxytoluene
and 3-methylindole in order to model the carbohydrate–protein
recognition269. The three aromatic molecules were used as
analogues of phenylalanine, tyrosine and tryptophan,
respectively. The work focused mainly on vibrational frequencies
and energy predictions using a DFT model with added empirical
atom-atom dispersive term with r-6 distance dependence. The
authors validated this combined model known as DFT-D291
against PM2/aug-cc-pVTZ calculations and showed that
difference between DFT-D and high-level ab initio results was
less than 1 kcal/mol for galactose-benzene and fucose-toluene
complexes.
Proton chemical shifts for the geometries from DFT-D were
calculated using DFT GIAO at BLYP/TZV2D level and
confirmed the observation that they are strongly perturbed by
complexation with aromatic groups292. The reproduction of the
experimental chemical shifts was poor, however their values,
relative to those in free sugars, corresponded to the vibrational
frequencies of CH protons269.
Paradowska et al. utilized GIAO DFT calculations to confirm
the results of 13C CP/MAS NMR and crystal structure analysis of
a series of methyl pentopyranosides. The authors used the GIAO
CPHF approach at B3LYP/6-31G* level to study a hydrogen
bonding effect on α-D-Lyxp-OMe surrounded by water
molecules forming mono- to tri-hydrates at C2, C3 and C4. The
starting geometry of D-Lyxp-OMe was taken from the X-ray data
and optimized in PM3 empirical force field. The calculations
yielded 13C shielding constants correlated with experimental
chemical shifts with R2 = 0.993 (isolated molecule) and R2 =
0.992..0.997 (hydrates) 270. The authors could not separate effects
produced by different hydrogen bonds but confirmed an increase
of stability with every next hydrogen bond observed for
α-D-lyxofuranoside earlier293.
NMR observables of methyl D-xylopyranosides were
predicted with the use of DFT for geometries optimized with the
fixed dihedral angle φ of the C1-OMe bond283, 284. Comparison of
the calculated chemical shifts with the experimental data from αand β-anomers both in solid state and in solution allowed authors
to point out the basic dependencies of the chemical shifts on this
dihedral angle. The derived dependence of 1J and 3J on the C1O1 torsion angle was proposed as a conformational probe.
Reichvilser and coworkers studied four aldo-pentoses to test
their suitability as linear linkers for the formation of covalent
organic boronic ester networks. As judged by the X-ray structures
of the reaction products with phenylboronic acid, arabinose and
xylose formed diesters, while lyxose and ribose formed 2,3- and
2,4-monoesters, respectively. 13C NMR shielding constants were
calculated by DFT GIAO at PBE1PBE/6-311++G(2d,p) level of
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theory in order to prove the applicability of QM methods to the
prediction of 13C NMR chemical shifts of these and similar
compounds.
The structures were optimized at B3LYP/6-31+G(2d,p) with
tight convergence criteria and an ultra-fine integration grid, and
proved by frequency analyses. PCM was used to model solvation
in DMSO during both geometry and NMR calculations. The
authors achieved a linear correlation between experimental
chemical shifts and predicted shielding constants (correlation
factor and numerical values of shielding constants were not
provided) 275.
Taubert and coworkers studied the 13C NMR chemical shifts
for α-D-lyxofuranose, α-D-lyxopyranose 1C4, α-D-lyxopyranose
4
C1, α-D-glucopyranose 4C1, and α-D-glucofuranose at ab initio
and DFT theory levels using TZVP basis set276. Test calculations
showed B3LYP/TZVP and BP86/TZVP to be cost-efficient levels
of theory for calculation of the NMR chemical shifts in
monosaccharides. Geometry and NMR parameter calculation
were checked against ab initio HF SCF and MP2 predictions and
X-ray data. The basis set convergence was checked on
tetramethylsilane by employing a variety of basis sets, including
large ones. Molecular structures and chemical shifts calculated at
B3LYP/TZVP level was similar to those obtained at the MP2
level (-0.6..+0.6 ppm for pyranoses and +0.4..+4.0 ppm for
furanoses).
MAD of the calculated (both at B3LYP and MP2; without
solvent effects) 13C NMR chemical shifts from the measured
values was 5.0-5.7 ppm, and is 7.2 ppm at BP86. Authors pointed
out that a better shielding reference, such as methanol, decreased
the largest deviation to 4 ppm and subsequent adding empirical
constant shift (-1..-2 ppm) to the calculated values improved the
agreement further. As judged by the dedicated investigation of
α-D-Glcf at fixed values of the C5–C6–O6–H dihedral, torsional
movement of C6 introduced up to ±2 ppm chemical shift
correction (to all carbon atoms) at those angles that existed in the
equilibrium.
The authors also tested four explicit solvent models for
α-D-Glcf: either a shell of 116 water molecules or a shell of those
11 water molecules forming hydrogen bonds with a solute; either
allowing or forbidding the whole system to relax after water
addition. None of the models was good enough to reproduce
experimental 13C NMR chemical shifts with acceptable accuracy.
COSMO solvent model253 provided better results but still -9 ppm
deviation for C6, which made the model inappropriate.
As for 1H NMR chemical shifts, they were predicted for
α-D-Glcp 4C1. The systematic deviation of ca. 3 ppm for
hydroxyl protons was accounted for hydrogen bonding, whereas
solvent effects on the 1H NMR chemical shifts of the aliphatic
protons were small (less than 0.4 ppm, except 1.3 ppm for the
anomeric proton) 276.
Bagno and coworkers presented an experimental and quantum
chemical NMR study of the mononucleotide cyclic
uridinemonophosphate in water277. They calculated 1H and 13C
NMR chemical shifts and 1H–1H, 13C–1H, 31P–13C and 31P–1H
coupling constants using DFT. The NMR parameters and the
conformer distribution were calculated at B3LYP/cc-pVTZ level.
Solvent reaction field has been included using the PCM model for
NMR only (protocol b), for both geometry and NMR (protocol c),
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or for none of (protocol a). cUMP has only two conformational
degrees of freedom: the hydroxyl group on C2’ and the dihedral
angle C6–N1–C1’–C2’ between the ribose residue and the
nucleobase. Due to this, a search for the conformers was done by
scanning the potential energy surface, rather than by full MD
simulation. After optimization at B3LYP/6-31G(d,p), 24 obtained
structures converged to three minima almost isoenergetic in
aqueous solution.
Protocol c allowed obtaining a good correlation with the
experimental chemical shifts (R2=0.986 for 1H; R2=0.996 for 13C)
and placement of signals in the correct order. Comparison of data
from different protocols showed that the solvent effects were
essential for the calculation of the NMR properties but not
important for the geometry optimization, as observed earlier for
D-glucose in water254.
This study confirmed that the 1H and 13C spectra of polar,
flexible molecules in aqueous solution can be predicted with the
same accuracy as less complex systems. No explicit inclusion of
water molecules was needed to achieve this accuracy, but the
usage of PCM was necessary277.
Sychrovsky and coworkers applied QM methods to investigate
the dependence of N1/N9 and C1′ CS tensors on the glycosidic
torsion angle and sugar pucker in four standard
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2′-deoxynucleosides (dAde, dGua, dCyt, dThy). The study aimed
at prediction of the cross-correlated relaxation rates between the
shielding tensor of the sugar-linked nitrogen of a nucleobase and
the C1′-H1′ dipole-dipole278 (see section 7).
All geometrical parameters were gradient optimized at the
B3LYP/6-31G(d,p) level, except the C1’-N torsion angle fixed at
different values. The shielding tensors were calculated using
IGLO II basis sets specific for each nuclei and exhibited a
significant degree of conformational dependence on C1’-N
dihedral angle and sugar pucker. No numerical values for CST
components and chemical shifts were provided except
dependence of the isotropic 15N chemical shift on the glycosidic
torsion angle for C2’-endo and C3’-endo sugar puckers of every
deoxynucleoside.
5.2. Oligosaccharides and polysaccharides
40
Combining monosaccharides into the more complex and diverse
structures of oligo- and polysaccharides leads to various
structural changes reflected by the NMR observables. Therefore,
discussion of computational modeling and NMR structural
studies of complex glycans and their derivatives (Table 4) is
essential.
45
Table 4. Prediction of chemical shifts in oligo- and polysaccharides.
Object (molecule)
Parameter a
: nuclei
Calculation method
Geometry
Shielding
Application
ref.
Software
β-D-Glcp-(1-4)-β-D-Glcp
(from 4-fold helical
ASMBC)
α-D-Glcp-(1-4)-α-D-Glcp
(from 3-fold helical
CDMPC)
CS: 13C
(C1)
(solid state)
B3LYP/
6-311+g(d,p)
B3LYP/
6-311+g(d,p)
Gaussian 03134, 135
studying molecular
environment in the chiral
cavities of commercial
polysaccharide-based
sorbents (CDMPC,
ADMPC, ASMBC)
279
β-D-Glcp-(1-1)-β-D-Glcp
α-D-Glcp-(1-1)-α-D-Glcp
α/β-D-Glcp-(1-2)-D-Glcp
α/β-D-Glcp-(1-3)-D-Glcp
α/β-D-Glcp-(1-4)-D-Glcp
α/β-D-GlcpNAc-(1-3)-LThr,1-NHMe,2Ac
α/β-D-GlcpNAc-(1-3)-LSer,1-NHMe,2Ac
α-D-Glcp-(1-1)-α-D-Glcp,
β-D-Glcp-(1-4)-β-D-Glcp,
[-4)-β-D-Glcp-(1-]4,
[-4)-β-D-Glcp-(1-]6,
-4)-β-D-Glcp-(1-,
-4)-α-D-Glcp-(1-
CSS(φ,ψ):
13
C (C1)
AM1
HF/3-21G,
HF/6-311G**
Tripos Sybyl294 6.5
(model build),
Spartan127 5.0.1 (semiempirical calculations),
Gaussian 98 (QM
calculations),
Wolfram Mathematica295
3.0 (trigonometric fit)
studying the dependence
of the anomeric carbon
chemical shift on the
glycosidic bond dihedral
angles in oligosaccharide
and glycopeptide model
compounds
152
CSS(φ,ψ):
13
C
(glycosidic
bond
carbons)
AM1
(monosaccharides
constrained in 4C1)
HF/3-21G,
HF/6-311G**
Sybyl 6.5 (model build)
Spartan 5.0.1 (semiempirical calculations)
Gaussian 98
(QM calculations)
Mathematica 3.0
(trigonometric fit)
determination of a 3D
structure
151
D-Glcp-α-(1→4)-D-Glcp
(α-, β-, γ-, ε-, and ιcyclodextrins)
CSS(φ,ψ):
13
C (C1)
X-ray,
AM1
HF/3-21G,
6-311G**
testing the prediction
methodology and
computation of the
anomeric carbon
chemical shifts in
cyclodextrins
150
D-Glcp-α-(1→4)-D-Glcp
(α-, β-, γ-, ε-, and ιcyclodextrins)
CSS(φ,ψ):
13
C (C1)
HF/6-31G*
ONIOM (B3LYP/
6-31G*:
HF/6-31G*)
B3LYP/6-31G*
ONIOM (B3LYP/
6-31G* :
HF/6-31G*)
Sybyl 6.8 (model build),
Spartan 5.0.1 (semiempirical calculations),
Gaussian 98 (QM
calculations),
AMBER 6.0 178, 179 (MD
simulations),
Mathematica 3.0
(trigonometric fit)
Gaussian 03,
Mathematica 3.0
(trigonometric fit)
computation of the
anomeric carbon
chemical shifts in
cyclodextrins
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Table 4, continued
β-D-Glcp-(1-4)-β-D-Glcp
(cellobiose)
CS:13C
X-ray
B3LYP/6311+G(2d,p)
(GAIOCHF
procedure)
Gaussian 03
β-D-Glcp-(1-4)-β-D-Glcp
(cellobiose)
CS: 13C
(C1-C4)
MD (GROMOS)
HF/6-31G(d)
Gaussian 09 (QM
calculations),
GROMACS166 3.3 (MD
simulations)
-4)-β-D-Glcp(1(Iα and Iβ cellulose)
-4)-β-D-Glcp(1(Iα and Iβ cellulose)
CS: 13C
(solid state)
CS:
1
H, 13C, 17O
(solid state)
GIPAW
PBE/planewave
B3LYP/6–31+G*
(hydrogens only)
mPW1PW91/
6-31G(d)
B3LYP/6-31+G*,
B3LYP/
6-31++G**
VASP297 5.4 (geometry),
Gaussian 09 (NMR)
Gaussian 03
α-D-Glcp-(1-4)-α-D-Glcp,
α-D-Glcp-(1-4)-β-D-Glcp
CS: 1H, 13C
(solid state)
PBE/planewave
GIPAW
PBE/planewave
CASTEP271-273 (geometry
optimization),
PARATEC code300, 301
(QM calculations)
α-D-Glcp-(1-2)-β-D-Fruf
(sucrose)
CST: 13C
(solid state)
Neutron
diffraction data
RHF, HFB, HFS,
BLYP, B3LYP,
B3P86, BVWN,
SVWN,
MPW1PW91
/cc-pVDZ,
/cc-pVTZ
α-D-Glcp-(1-1)-α-D-Glcp
(α,α-D-trehalose),
β-D-Galp-(1-4)-β-D-Glcp,
α-D-Glcp-(1-2)-β-D-Fruf
(sucrose)
CSS(φ,ψ):
13
C (C1)
(amorphous
state)
MM (BIO85,
CHARM27,
AMBER) on fixed
φ and ψ
complex of E-selectin with
sialyl Lewis X b
CS: 1H
QM/MM
(see section 4.4)
TNDO,
B3LYP/
6-31+G(d,2p),
B3LYP/
3-21+G**,
B3PW91/
3-21+G**
QM/MM-GIAO
(HF/6-31G*)
α-D-Glcp-(1-2)-β-D-Fruf
(sucrose),
α-D-Glcp-(1-1)-α-D-Glcp
(α,α-D-trehalose),
α-D-Glcp-(1-4)-α-D-Glcp
(D-maltose)
CS, CST:
13
C
(solid state)
X-ray and neutron
diffraction data,
PBE/planewave,
Vanderbilt's
“Ultrasoft”
pseudopotentials
GIPAW
PBE/planewave,
Troullier-Martins
norm-conserving
pseudopotentials
α-D-GlcpNH3+ / I(chitosan salt cluster)
CST:
1
H, 13C,
15
N, 17O
(solid state)
X-ray;
B3LYP/
6-31++G(d,p) for
hydrogens only
α-D-GlcpN
(chitosan cluster)
CST:
1
H, 13C,
15
N, 17O
(solid state)
X-ray; B3LYP/
6-31++G(d,p) for
hydrogens only
LD: B3LYP/
6-311++G(d,p),
B3LYP/
6-31++G(d,p),
6-31G (other),
LANL2DZ
(iodine ions)
B3LYP/
6-311++G(d,p),
B3LYP/
6-31++G(d,p)
β-L-Fucp(1-4)α-D-GalpOMe,
β-L-Fucp (1-4)α-D-GlcpOMe,
β-L-Fucp (1-3)α-D-GlcpOMe
CS: 1H
(hydroxyl
protons)
B3LYP/ 6-31G(d)
HF/
6-311++G(2d,2p),
B3LYP/
6-311++G(2d,2p)
MM3 (geometry),
Gaussian 98 (QM
calculations)
a
Notations: CS – chemical shift; CST – chemical shift tensor; CSS – chemical shift surface.
b
Sialyl Lewis X is α-Neup5Ac-(2-3)-β-D-Galp-(1-4)-β-D-GlcpNAc-(3-1)-α-D-Fucp
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theoretical investigation
of effects of the
conformation and
hydrogen bonding on 13C
isotropic chemical shifts
modelling of the
conformational space of
amorphous cellulose
265
conformational studies
of cellulose
investigation differences
in crystalline structure
and hydrogen bond
pattern in Iα and Iβ
cellulose
investigation of weak
hydrogen bonding
298
Gaussian 03
comparison of DFT and
HF functionals
225
HyperChem 139, 140
(geometry),
Gaussian 03 (chemical
shifts)
exploration of the local
structure of sugars in
glassy state
303
Own QM/MM program
based on HONDO
package304
CASTEP271-273
validation of the
geometrical modeling
238
comparison of
calculations to the
chemical shift anisotropy
amplification data
305
Gaussian 98
investigation of the
hydrogen bonding
effects on the CS tensors
266
Gaussian 98
investigation of the
hydrogen bonding
effects on the CS tensors
of anhydrous crystalline
structure
studying the effect of
hydration on the
chemical shift of
hydroxyl protons
267
296
299
302
306
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13
C NMR chemical shifts of the anomeric carbons in oligoand polysaccharides can be used as conformational probes due to
their periodic dependence on the glycosidic bond dihedral
angles307.
Kasat and coworkers used GIAO calculations at DFT level to
predict the 13C NMR chemical shifts of the anomeric carbons in a
carbohydrate backbone, as well as of carbons in noncarbohydrate side chains while studying molecular environment
in the chiral cavities of polysaccharide-based sorbents, cellulose
tris(3,5-dimethylphenylcarbamate) (CDMPC), amylase tris(3,5dimethylphenylcarbamate) (ADMPC), and amylase tris[(S)-αmethylbenzylcarbamate] (ASMBC)279. The authors computed the
anomeric carbon 13C NMR chemical shielding in the monomers
of cellulose, amylase, amylase acetate and cellulose acetate
(summarized in Table 3) and in dimers extracted from ASMBC
octamer with 4-fold helix and CDMPC nonamer with 3-fold helix
optimized by DFT methods. The geometry of the octa- and
nonamers was constructed from the X-ray data using linked-atom
least-squares method308.
The simulations showed that helicity strongly affects the C1
chemical shift, clarified effects of the side chains on polymer
conformations and supported the hypothesis of a 3-fold helical
conformation of CDMPC and of a 4-fold one of ADMPC, which
is important for the explanation of enanthioseparation of
racemates on these sorbents due to differences in their high-order
structure309. The authors conclude that the strength of H-bonds of
the C=O and NH groups in the chiral cavities of these
polysaccharide-based polymers are significantly different, which
may be a major factor affecting the selectivity of chiral solutes279.
Swalina and coworkers used GIAO calculation to study the
dependence between the anomeric carbon chemical shift and the
glycosidic bond 〈φ,ψ〉 dihedral angles in oligosaccharide and
glycopeptide model compounds152. They computed full chemical
shift surfaces (CSSs) versus φ and ψ for D-Glcp-D-Glcp
disaccharides with (1→1), (1→2), (1→3), and (1→4) linkages in
both α- and β-configurations. φ and ψ were fixed in 20° steps and
the geometries were optimized using the AM1 semi-empirical
Hamiltonian. To simulate an observed chemical shift CSSs were
corrected by adding a correction factor of +7.1 ppm calculated
from comparison of TMS and dioxane as references. After
Bolzmann averaging of CSS, accounting for the distribution of
conformers, predicted chemical shift values exhibited an RMS
deviation of 1.4 ppm from the experimental data. The authors
derived empirical equation of the form 13C δC1=f(φ,ψ) obtained by
fitting the raw ab initio data to the trigonometric series
expansions, following Le and coworkers310, and realized it as a
Perl script. For a series of 91 and 325 terms, RMS between the
raw and derived chemical shift values was 0.56 ppm and
0.31 ppm, respectively.
To reduce the computational cost CSSs were calculated using
the 3-21G basis set and scaled using the reference 6-311** level
calculations. To obtain the scaling factor, duplicate GIAO 13C
calculations using the 3-21G and 6-311G** basis sets were
performed on AM1-optimized models of eight disaccharides (96
carbons). The 13C NMR chemical shifts predicted using both
basis sets were then correlated (R2=0.992), and the resulting
linear relationship was employed to scale 3-21G results. To test
the approach, 13C CSSs were calculated using a locally-dense
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basis set (6-311** for the anomeric carbons and nearest
neighbors; 3-21G for the remaining atoms311) or 6-311G** basis
set in particular cases. The RMS deviation between the scaled
CSS and the test CSS obtained with locally-dense or large basis
set was less than 1 ppm for disaccharides.
Similar surfaces were also obtained for GlcNAc-Thr and
GlcNAc-Ser model glycopeptides in α- and β-configurations.
Selection of any of three different conformations of the peptide
moiety (freely relaxed, extended and α-helical) virtually did not
affect the CSSs. In contrast to the threonine derivative, the serine
derivative possessed two CS maxima on the CSS. Authors
explained it by the sterically induced polarization of the electron
density around the anomeric carbon caused by the methyl group
of threonine152.
The above methodology was used later in a number of studies.
Particularly, Sergeev and Moyna utilized derivation of 13C CSSs
for the determination of the spatial structure of glucose
oligosaccharides in solid state from the experimental 13C NMR
data of glycoside bond carbons (Fig. 8)151. During the CSS
derivation the level of theory, basis set and scaling procedure
were the same as reported for model glycopeptides152. In order to
take into account the experimental chemical shifts of the
glycosidic bond carbons during molecular modeling, the potential
energy function of the MMFF94 force field was augmented with
an NMR pseudopotential energy term. This term included a
function derived from CSS using a 91-term trigonometric fit, and
a constant chosen so as to give the force field energy term
compatible weight.
The authors approved the method on α-(1→1) and β-(1→4)linked oligosaccharides by reproducing the three-dimensional
structure obtained from the X-ray studies with an RMS deviation
of heavy atom positions equal to 0.14Å, 0.12Å and 0.25Å
(trehalose, cellobiose and cellotetraose, respectively)151. In
contrast, lowest energy conformer of cellotetraose predicted in
vacuo by MMFF94 without NMR constraints was significantly
different. Further, the authors determined the spatial structure of
cellohexaose and generated structural models for cellulose II and
amylose V6, using hexasaccharides as models and CSSs obtained
from disaccharides. These studies supported φ and ψ estimates
reported earlier312, 313.
O’Brien and Moyna tested the same method on cyclooligomaltoses (α-, β-, γ-, ε-, and ι-cyclodextrin) and
α-cyclodextrin inclusion complexes with 1,4-disubstituted
benzenes in solid state and in solution. They used the same
approach as Swalina and coworkers, and the same basis sets for
generation of the anomeric carbon CSSs and derivation of the
empirical formula for the chemical shift. For the solid-state
structures, D-Glcp-α-(1→4)-D-Glcp glycosidic bond dihedral
angles were taken directly from the X-ray data.
The calculated solid-state 13C NMR chemical shifts of
anomeric carbons of all residues in α-, β- and γ-cyclodextrin
overestimated the observed CP/MAS data by ca. 0.8 ppm
(cyclodextrins) and 0.4-0.6 ppm (inclusion complexes).
Calculations on ε-, and ι-cyclodextrins also predicted an average
chemical shift within +0.8 ppm from the solution data and
allowed characterization the band-flipped residues by the
abnormal upfield shift of the anomeric carbon signal.
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O’Brien and Moyna also employed derivation of 13C NMR
chemical shifts from averaging back-calculated 13C shift
trajectories from a series of 5 ns MD simulations of α-, β- and γcyclodextrin with explicit TIP3P water molecules filling an
octahedral buffer of 10 Å. Application of the empirical formula
obtained from solid-state CSSs calculation gave an excellent
agreement with the solution 13C NMR data (MAD 0.36 ppm)150.
Lefort and coworkers studied the local structure and
conformational disorders of selected disaccharides in amorphous
state by comparison of CPMAS data to 13C NMR chemical shift
surfaces of C1 calculated by GIAO for MM-optimized
geometries. They provided a numerical procedure to treat
discontinuities in the CPMAS spectrum, and demonstrated that
force field geometry optimization did not critically hamper the
accuracy of the results303.
Tafazzoli and Ghiasi studied the anomeric carbon chemical
shifts of α-, β- and γ-cyclodextrins in solution using two-layer
ONIOM method237. The higher level of theory (B3LYP/6-31G*)
included all atoms in the pyranose rings, and the lower one
(HF/6-31G*) included all other atoms. The PCM model was
employed to model the solvent effects.
The 13C NMR chemical shift surfaces for C1 in D-Glcp-α(1→4)-D-Glcp fragment in gas phase and in solution were
calculated employing the GIAO B3LYP/6-31G* method and
compared to the ONIOM (B3LYP/6-31G*: HF/6-31G*) results
obtained for a disaccharide model. The empirical equation
relating isotropic 13C shifts with the glycosidic bond ϕ and ψ
dihedral angles was derived using a trigonometric expansion. The
calculated average chemical shift in solution deviated from the
experimental data by -0.4..+0.8 ppm, and deviations of C1
chemical shifts for residues 1 and 2 in α-cyclodextrin were
predicted with an accuracy of 0.6 ppm and 0.5 ppm,
respectively226.
Conformation of the cellulose fragments have been explored
and probed against experimental NMR observables in a number
of publications151, 265, 296, 303. Kubicki and collegues achieved an
RMS error less than 3 ppm for 13C chemical shift simulation with
GIPAW in periodic boundary condition for tg/NetA
conformations of cellulose Iα and Iβ298. Esrafili and coworkers
obtained MAD of less than 7% in DFT 13C calculations of
cellulose spectra, and showed that 13C chemical shifts could serve
a probe for differentiation between Iα and Iβ structures299.
Suzuki and coworkers applied DFT calculations to reproduce
experimental dependences of 13C NMR chemical shifts on the
conformation of β-D-Glcp (see details in the previous section),
cellobiose and cellobiose units of native cellulose capped with
hydrogen atoms. The geometry was extracted from the X-ray
structure without further optimization. D-Cellobiose and the
cellobiose units revealed appreciable dependences of the
predicted C1’ and C4 chemical shifts on the torsion angles in the
(1→4)-β-glycosidic linkage. In a region of the crystalline
conformational minimum C1’ chemical shift was found to depend
mainly on φ, whereas C4 on both φ and ψ265. The authors
explained calculated chemical shifts in disaccharide units basing
on γH-gauche effects and their reduction by intra-residue
hydrogen bonding. On the contrary, inter-residue hydrogen
bonding had almost no effect on 13C NMR chemical shifts.
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Khodaei and coworkers used a molecule in a cluster as a model
system for the chitosan/HI salt and calculated hydrogen bonding
effects on the CST of 17O, 15N, 13C, and 1H nuclei (see details in
the previous section). According to the locally dense basis set
method314 used to speed up the calculation, the target molecule
and the neighboring nuclei directly involved in its hydrogen
bonding were calculated at 6-311++G(d,p) and 6-31++G(d,p)
basis sets, whereas the other nuclei were calculated at 6-31G and
LANL2DZ (iodine ions) basis sets. The authors observed that the
theoretical B3LYP/6-311++G(d,p) isotropic 13C NMR chemical
shifts overestimated the experimental values (MAD 5.8, least
square linear fit with R2=0.97), while chemical shifts obtained
from B3LYP/6-31++G(d,p) underestimated them (MAD 5.0,
least square linear fit with R2=0.96). They report the results from
the 6-311++G(d,p) basis set as more reliable than those from the
6-31++G(d,p) one.
The difference in the isotropic shielding between monomer
and target molecule in a cluster was analyzed in respect with
O6H…O, O6H…I, NH..O and NH..I hydrogen bonding. The
authors revealed a 40 ppm increase of predicted O6 chemical
shift due to the intermolecular hydrogen bonding in a cluster, as
compared to the monomer, while the difference at other oxygen
sites was not so dramatic. NH hydrogen bonds reduced the
predicted isotropic 15N chemical shift by 18.39 ppm266.
Esrafili and coworkers investigated hydrogen-bonding effects
on the 17O, 15N, 13C and 1H CS tensors of anhydrous chitosan as
compared to its monomeric unit (α-D-GlcpN) in gas phase. The
DFT calculations were performed at B3LYP/6-311++G(d,p) and
6-31++G(d,p) for the X-ray geometry with protons reoptimized at
B3LYP/6-31++G(d,p). Authors explained deviations in 17O, 15N,
and 1H CST components and anisotropy by the formation of the
hydrogen bonds, primarily O3H…O and NH…O. Good
correlation between the predicted and experimental isotropic 13C
NMR chemical shifts (R2=0.985) indicated that hydrogen
bonding effects in chitosan are sufficiently described when the
neighboring chains are represented by monomeric units only. As
followed from the QM calculations, the intra- and intermolecular
hydrogen bonding played an essential role in determination of the
relative orientation of oxygen and nitrogen CST principal
components in the molecular frame axes267.
Bekiroglu and coworkers performed the comparative QM
calculations on the disaccharides (β-L-Fucp-(1→4)-α-D-GalpOMe, β-L-Fucp-(1→4)-α-D-Glcp-OMe, and β-L-Fucp-(1→3)-αD-Glcp-OMe) using HF and DFT methods. They calculated the
chemical shift difference (∆δ) between the hydroxyl protons in
the disaccharide and the corresponding monosaccharide methyl
glycoside.
The lowest energy geometries of MM3 calculations were taken
as starting conformers for a full DFT optimization. The ∆δ values
obtained from HF and DFT calculations were similar, although
the HF calculations gave systematically more upfield values than
DFT calculations.
The calculations in vacuo showed that one or two OH protons
in each disaccharide, which exhibit hydrogen bonding to the
neighboring ring oxygens, are strongly deshielded (∆δ>0). In
contrast, the experimental NMR data indicated shielding of these
protons (∆δ<0)315. This discrepancy was accounted for the
solvent effects, which were confirmed by monitoring the
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Fig. 9. Dependence of 3JC1-2OH on the glycosidic torsion angle ω and the
C1/HO2 dihedral angle θ calculated by DFT for methyl α- and β-Dglucopyranoside mimics (A, B), respectively) and methyl α- and β-Dmannopyranoside mimics (C, D, respectively), all having deoxy functions
at C3, C4, and C6316. Reproduced with permission, © Elsevier Ltd., 2009.
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chemical shift of the hydroxyl proton of methanol in water and
other solvents, modeling the acetal groups of disaccharides.
Intramolecular hydrogen bonding leads to the reduced hydration
of a particular hydroxyl proton, and to a consequent upfield
shift306.
Yates and coworkers studied the anomeric forms of maltose by
1
H-13C MAS-J-HMQC solid-state NMR spectroscopy. They used
chemical shift calculations for the assignment of 1H NMR
spectrum. Further calculations showed that the difference in the
calculated 1H NMR chemical shift between the crystal and an
isolated molecule with the same geometry was a quantitative
measure of weak intermolecular C-H⋅⋅⋅O hydrogen bonding302.
Geometry optimizations were performed using the DFT code
CASTEP271-273, which utilized a planewave basis set to expand
the charge density and electronic wave functions, and
pseudopotentials to represent the core electrons. The PBE
exchange-correlation function215 and “ultrasoft” pseudopotentials
with a maximum planewave cutoff of 30Ryd were used. The
NMR chemical shifts were computed using the PARATEC300, 301
code that employs the GIPAW method214, which is based on DFT
and the plane-wave pseudopotential approach301. The calculations
used a PBE exchange-correlation functional, a plane-wave basis
set with a maximum energy of 80Ryd and Trouiller-Martins317
norm-conserving pseudopotentials. MAD of the calculated
isotropic 13C NMR chemical shift from the experimental values
was 1.0 ppm for the α-anomer and 0.9 ppm for the β-anomer, the
highest deviations being observed for the anomeric (up to
+3.0 ppm) and C6 (up to -1.4 ppm) carbons.
6. Computation of NMR coupling constants
40
Empirical relationships between molecular geometry of
saccharides, such as torsion angles, and the spin-spin coupling
were historically widely and successfully applied for NMR
structure elucidation, especially for the identification of
monomeric composition of oligo- and polysaccharides43, 318, 319.
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However, in spite of important scope and several useful
applications, such approach is subject to fail for compounds
different from those used for the calibration of the empirical
equations. Especially difficult are the cases of intermolecular
aggregation and intercation with polar solvents and atypical
functional groups. Undoubtedly, computational modeling of spinspin coupling and its interdependencies with distinct structural
parameters (like bond angles and dihedral angles) is one of the
most demanding areas of research. Scalar couplings are averaged
linearly among conformers in solution, and thus their
interpretation in terms of conformationally flexible molecular
structure more straightforward320. The averaging allows easy
connection with MD simulations and provides the NMR
description of structural flexibility in carbohydrates.
A widely used non-relativistic approach to the simulation of
nuclear coupling originates from well-known Ramsey
equations321. Indirect scalar nuclear spin–spin coupling constant
is associated with four terms: Fermi contact (dominant term, FC),
orbital diamagnetic (DSO), orbital paramagnetic (PSO), spindipole (SD). The Fermi term contribution is often dominating322,
especially in carbon-hydrogen saturated systems. The
computational cost can be significantly reduced by calculation of
the dominating FC term in a larger basis set and the
computationally expensive but smaller remaining contributions
from the other terms in a smaller basis set323.
Quantum-chemical approaches to the calculation of indirect
spin-spin coupling constants have been reviewed in details
recently63. As follows from the comparison of computational cost
of electronic wave function and electronic density approaches in
calculation of spin couplings, the latter performs faster. DFT was
recognized as a good tool for accurate prediction of coupling
constants in medium and large molecules. In calculation of the
coupling constants, DFT has been shown to give reasonable
potential energy surfaces for aldo- and ketohexoses and to reduce
the basis superposition error in hydrogen-bonded systems, such
as monosaccharides324. It was found that improved accuracy in
spin–spin couplings could be obtained from the DFT calculations
at DFT-optimized geometries instead of experimental or higherlevel geometries325. The choice of geometry calculation theory
affects the accuracy of coupling calculations. As tested on methyl
α-xylopyranoside, MM3 geometry gave better results for the
calculation of 1JCH and 2JHH couplings, while DFT geometry
produced slightly better results for 3JHH couplings284.
In contrast to chemical shifts, the quantitative prediction of the
coupling constants is known to have a problem of linear
correlation being far from ideal values (intercept = 0 and slope =
1). This is usually associated with a lack of accuracy in
calculation of the Fermi contact term326. Accurate description of
the electron density at the nuclei, which is needed to calculate this
term, often requires a specially designed basis set327.
The result of coupling constant simulation versus geometrical
parameters of molecules is often expressed in the form of
derivation of the Karplus equation (3J = C0 + C1cosφ + C2cos2φ
or 3J = C3 + C4cosφ + C5cosφ2) 328, which relates a vicinal
coupling constant to the torsional angle around the central bond
of the fragment. Typical values for C3, C4 and C5, obtained by
averaging over different H-C-C-H fragments in heparin
fragments, are 0.2, -0.6. and 9.6 respectively329. Nowadays,
Karplus equations have been derived virtually for every
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combination of nuclei and coupling pathways that occur in
carbohydrates. Except vicinal couplings, these combinations
include atoms not connected by three bonds forming a dihedral
angle, but have coupling dependent on the torsion angles of
substituents either inside or outside the coupling pathway. As an
example, 3JC1-2OH coupling constants surfaces were obtained for
methyl α- and β-D-glucopyranoside mimics with deoxy functions
at C3, C4 and C6 (Fig. 9). These curves indicate a minimal
dependence on the glycosidic torsion angle and strong
dependence on C1/HO2 dihedral angle316.
6.1. Intra-residue coupling constants
15
Analysis of NMR coupling constants is a canonical structural tool
to characterize carbohydrates. A brief review provided in the
present section shows an outstanding potential of computational
studies to make a valuable insight into the structural and
electronic origins of values measured experimentally.
Computations of intra-residue coupling constants (within a single
monosaccharide) are discussed in the present section and
summarized in Table 5.
20
Table 5. Prediction of coupling constants in monosaccharides.
Object (molecule)
Coupling
constant a
(e.g. 3JH-N-C-H)
Calculation method
Geometry
Coupling
β-D-Xylp-OMe
1,2,3
JCH, 3JHH
BP86/TZVP,
MM2
PW91/IGLO-III
α-D-Xylp-OMe
1,2,3
JCH, 3JHH
PW91/TZVP
MM
PW91/B-III
1
C4, 2S0, 4C1
α-L-IdopA2S-OMe, Na+,
(4C1, 2S0), (4C1, 1C4)
α-D-GlcpNS6S-(1→4)α-L-IdopA2S-OMe,
(heparin disaccharide),
3
JH,H
B3LYP/6-31++G**
B3LYP/6-31++G**
2
3
JH,H
S0 α-L-IdopA2S
Application
ref.
Software
deMon-KS, demonNMR280-282,
MacroModel128, 129
5.0 (MM
calculations)
calculation of coupling
constant dependence on
the dihedral angle
between C1 and methyl
group
283
JAGUAR 3.5
(geometry),
Gaussian 03
(couplings)
derivation of a Karplus
equation
329
284
B3LYP/6-31+G*
B3LYP/6-31+G*
[-4)-β-D-GlcpNS6S-(1-4)α-L-IdopA2S-(1-]3
(heparin hexasaccharide)
1
C4 α-L-IdopA2S(1→4)-αD-GlcpN6S-1OMe,
2
S0 α-L-IdopA2S(1→4)-αD-GlcpN6S-1OMe,
(heparin disaccharide)
3
JH,H (in all
IdopA
rings)
MD (GLYCAM03)
Altona and
Haasnoot formalism
AMBER 5.1,
AMBER 6.0 178, 179
investigation of the
conformational
flexibility of IdopA rings
330
3
B3LYP
Gaussian 03,
Gaussian 09134, 135
studying coupling
constants variations upon
counterion and solvent
effects
240
α-L-IdopA2S
3
B3LYP/
6-311++G**,
M05-2X/
6-311++G**
(with explicit
solvent, ONIOM)
MD (GROMOS96,
GLYCAM06),
then HF/6-31G(d)
Altona and
Haasnoot formalism
comparison of the
prediction force of two
force fields
331
α-D-Glcp-(1→1)-α-D-Glcp
3
JH5,C1,
JHH (all
vicinal)
MD, (CHARMM
carbohydrate force
field)
Karplus type
equation with the
Haasnoot-Altona
parameterization
Gaussian 03 (QM
calculations),
GROMACS166 3.3,
AMBER 9.0
(MD simulations)
CHARMM164
332
α-D-Glcp,
β-D-Glcp
3
JH,H
(except
with OH)
B3LYP/6-31G(d,p)
B3LYP/pcJ-2
Gaussian 03
establishing a
comprehensive
understanding of the
hydration pattern of
trehalose
support of the
experimental data
2HOMe-THP (model)
2
HF, B3LYP/
6-311++G (d,p)
FF-DPT (Fermicontact),
B3LYP/
[5s2p1d/3s1d]
Gaussian 03
derivation of the Karplus
equations
333
HF, B3LYP/
6-311++G (d,p)
FF-DPT (Fermicontact),
B3LYP/
6-311++G (d,p)
Gaussian 03
derivation of the Karplus
equations
334
JHH, 1JCH,
JCH (in
rings)
3
JH,H (all in
ring)
3
JH5H6,
JC5,H6,
2
JC6,H5,
3
JC4,H6
3
JH1C1OC,
3
JH1C1SC,
3
JH1C1CC,
3
JH1C1OC,
3
JH1C1SC,
3
JH1C1CC,
in aqueous
and
methanol
solutions
2
β-D-Glcp-1OMe,
β-D-Glcp-1SMe,
β-D-Glcp-1Ethyl,
β-D-Glcp-1OMe,
β-D-Glcp-1SMe,
β-D-Glcp-1Ethyl,
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Table 5, continued
2-hydroxymethyl-THP and
other models
2JH6H6’,
B3LYP/6-31G(d)
B3LYP/
[5s2p1d/3s1d]
Gaussian 94
derivation of the Karplus
equations
335
JC5H6,
JC6H5,
3
JC4H6,
2
JH6R–H6S,
3
JH5H6
1
JC1H1
HF, B3LYP/
6-311++G (d,p)
FF-DPT (Fermicontact),
B3LYP/
6-311++G (d,p)
Gaussian 03
derivation of the Karplus
equations and validation
of the DFT methodology
336
1
B3LYP/6-31G(d)
FF-DPT (Fermicontact),
B3LYP/[5s2p1d/2s]
Gaussian 94
validation of DFT
methodology
320
HF/6-31G(d)
B3LYP/6-31G(d)
FF-DPT (Fermicontact),
B3LYP/[5s2p1d/2s]
Gaussian 94
337
HF/6-31G(d)
B3LYP/6-31G(d)
FF-DPT (Fermicontact),
B3LYP/[5s2p1d/2s]
Gaussian 94
investigation of the
effect of hydroxymethyl
conformation on the
conformational energies
and structure
investigation of the
effect of the amino group
on molecular properties
3JH5,H6,
1JC5,H5, 1JC6,H6
β-D-Glcp-(1-3)-4H-pyran4-one, β-D-4-deoxyXylHexp-(1-3)-4H-pyran4-one, (erigeroside and its
model)
β-D-Glcp-(1-3)-4H-pyran4-one (erigeroside)
2-deoxy-β-D-eryPenf
2
2
JCH, 2JCH,
JCH, 1JCC,
2
JC3C5,
3
JC1C5,
3
JC2C5
1-3
JCH, 1-3JCC
3
2-deoxy-β-D-eryPenf
2-deoxy-β-D-eryPenf1NH2,
2-deoxy-β-D-eryPenf1NH3+
1-3
P-3:5)β-D-Ribf-1U
(cUMP in aqueous
solution)
JHH, JCH,
JPH, JPC
B3LYP/6-31G(d,p)
B3LYP/cc-pVTZ
Gaussian 03
testing the prediction
method and selection of
the appropriate solvent
model
277
α- and β-L-Eryf-1OMe2,3-epoxy
JH,H (all in
ring)
MP2, DFT B3LYP/
6-311++G(d,p)
coupled perturbed
DFT; B3LYP/
4-31G, 6-31G(d,p),
6-311G(d,p),
6-311++G(d,p), augcc-pVDZ, IGLO II,
IGLO III
coupled perturbed
DFT;
B3LYP/IGLO II
Gaussian (geometry
optimization),
Cologne 99 339
(coupling
calculation)
interpretation of the 1HH coupling constants of
synthesized compounds
and comparison of
prediction methods
340
SD, PSO, DSO
terms:
B3LYP/IGLOO-III;
FC term:
B3LYP/HIIIsu3
B3LYP/HIIIsu3 (FC
term only)
Gaussian 03D (QM
calculations),
CHARM (MD
calculations)
studying the dependence
of 3JH-N-C-H coupling on
conformation, dynamics
and solvent;
derivation of the Karplus
curve
341
3
JCH, 1JCC
JCC
α- and β-L-Eryf-1OMe
2,3-epicyclic derivatives
with S, NH, NR
α-D-GlcpNAc
B3LYP/
6-311++G(d,p)
3
β-D-GlcpNAc,
α-GalpNAc
a
5
10
15
JH-N-C-H
B3LYP/6-31G(d,p)
with explicit
solvent: MD
snapshot optimized
in MMX force field
338
1
See Fig. 2 for atom numbering.
Gandhi and Mancera probed two MD force fields in
unconstrained molecular dynamics simulations of 2-O-sulfoα-L-iduronic acid ring conformational flexibility in aqueous
solution331. The authors reported that the GROMOS96186 force
field with the SPC/E water potential could successfully predict
the dominant skew-boat to chair conformational transition of the
IdoA2S in water, whereas the GLYCAM06180 (augmented with
non-bonded parameters for sulfates and sulfamates) and the
TIP3P water potential sampled transitional conformations
between the boat and chair forms. Simulations using
GROMOS96 exhibited no pseudorotational equilibrium
fluctuations and hence no inter-conversion between the boat and
twist boat ring conformers. Simulation of proton NMR coupling
constants showed that in contrast to GLYCAM06 the
GROMOS96 force field could predict the 2S0 (skew-boat) to 1C4
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(chair) conformational ratio (17:83) in better agreement with the
experiment.
Unlike
GLYCAM93,
which
reproduced
experimental couplings well330, GLYCAM06 does not have an
explicit definition of the anomeric carbon, which was considered
a reason of its poorer predictive force. Since a 2S0–1C4 transition
was observed after 81 ps, the 2S0 coupling constants were
averaged over the initial 81 snapshots within GROMOS
simulations, while the 1C4 coupling constants were averaged over
419 random snapshots from the remaining 419 ps. In both
works330, 331 the averaged 3JH,H coupling constants were calculated
using the Altona and Haasnoot formalism319 from the MD data
with respect to conformer ratio, and compared to the reported
experimental values.
A detailed look into influence of counterion and solvent on
conformation and coupling constants in heparin disaccharide was
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reported by Hricovini240. He utilized B3LYP calculations on the
geometries obtained at B3LYP and M05-2X342 theory levels to
compare coupling constants of both conformers (2S0 IdoA2S +
4
C1 GlcN6S and 1C4 IdoA2S + 4C1 GlcN6S) in explicit water
solution and with Na+ and Ca2+ counterions. Better geometry
predictive strength of B3LYP, as compared to M05-2X, was
shown for a disaccharide with Na+ counterions. Comparison of
the calculated averaged vicinal couplings with the experimental
data indicated that the 1C4 conformation of IdoA2S (Ca2+) was
nearly exclusively populated. In contract to direct and
transglycosidic H-C couplings, averaged proton couplings were
hardly affected by solvent effects.
Engels and Perez calculated 3JH,H couplings for vicinal
hydrogens in α,α-trehalose to study the disaccharide dynamics in
water solution332. The authors calculated interglycosidic coupling
as well, and more details on geometry optimization are given in
section 6.2. Intra-residue homonuclear couplings were calculated
using a Karplus type equation with the Haasnoot-Altona
parameterization319 accounting for the coupling dependence not
only on the dihedral angle, but also on the electronegativity of the
participating atoms, and on the orientation of α- and
β-substituents.
Roslund and coworkers calculated coupling constants for αand β-D-glucopyranose, as well as chemical shifts (see section
5.1). All the terms contributing to the J-couplings were predicted
at B3LYP/pcJ-2 on geometry optimized at B3LYP/6-31G(d,p).
The authors estimated conformer populations by applying
Boltzmann distribution to the relative stability of the conformers
(more details are discussed in chemical shift prediction section
above). The correlation factor between the population-weighted
averages of the calculated couplings and the experimental results
was 0.994-0.995 (MAD 0.49 Hz for α-D-Glcp, 0.62 Hz for
β-D-Glcp), but certain deviations were quite significant. Among
vicinal couplings, the most significant differences were observed
for 3JH5,H6 values (73%), indicating that the selected subsets of
hydroxymethyl rotamers and their relative stabilities did not
thoroughly reflect the equilibrium of D-glucose in aqueous
solution. For vicinal coupling within a pyranose ring, deviation
values confirmed a good applicability of the selected method to
reproduce the experimental data260.
There are more J-couplings observed in oligosaccharides, as
compared to the number of NOEs sensitive to the conformational
parameters. Thus, ability to predict coupling constants versus
conformation of a glycosidic bond and an exocyclic group of
sugar residues may become a useful tool in conformational
studies.
Tafazzoli and Giashi derived Karplus equations by least-square
parameterization from non-linear regression analysis of the
simulated vicinal coupling constants related to dihedral angles ω
(C5-C6), θ (C6-O6) andϕ (C1-X) in various glycosides of
glucose and galactose333. These studies demonstrated the ability
of the DFT to predict J-couplings in aqueous solution.
2-hydroxymethyltetrahydropyran was used as a carbohydrate
model. The authors optimized the geometry using a hybrid HFDFT scheme, the adiabatic connection method B3LYP/
6-311++G(d,p) with no initial symmetry restrictions, and the
PCM method for the solvent effects on the conformational
equilibrium. Heteronuclear coupling constants involving a
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hydroxymethyl group were obtained by Fermi-contact FF-DPT
calculations at B3LYP level using a basis set [5s2p1d/3s1d]
designed for calculation of J-couplings in the exocyclic group of
a
carbohydrate
model
compound
(2-hydroxymethyltetrahydropyran)335. Tafazzoli and Giashi used the same model to
simulate 2JH5H6, 2JCH and 1JCH coupling constants.
A multitude of factors affect the CH bond length in the
hydroxymethyl group and direct 13C-1H coupling constants that
are almost reverse-proportional to the bond length343, thus
Karplus equations for these couplings possess large RMS errors.
For each of three stable C5-C6 rotamers, a dependence of 2JC5,H6
on the θ angle was derived. In contrast to 2JC5,H6, 2JC6,H5 values
were almost insensitive to the θ angle because C5-O5 torsion is
fixed by the ring conformation.
Comparison of 3JC4,H6 values calculated for the model
compound with those calculated for the 4-hydroxy-substituted
model, did not reveal any correlation between substitution at
position 4 and ω / θ angular dependence of 3JC4,H6. The Karplus
equations for the couplings above are given in eq. 3-8 of the
original publication333.
These authors studied 3JCXC1H1 dependence on the ϕ angle in
1-substituted glycosides. They used [5s2p1d/3s1d] basis set for
the calculation on β-D-Glcp derivatives (X = O, S, C)333 and
obtained theoretical Karplus equations (e.g., for O-glycosides:
3
JCOC1H1
=
6.68cos2ϕ+0.89cosϕ+0.11;
RMS=0.65 Hz)
resembling an empirical equation proposed previously by
Tvaroska and coworkers for 1-thioglycosides344.
They also applied B3LYP/6-311++G (d,p) calculations to
anomeric vicinal coupling constants of these compounds in order
to model couplings in various derivatives of glucose and
galactose (OMe-, SMe-, Et-, NHMe-, Cl- and F-glycosides ) in
PCM-modeled
water
and
methanol334.
Least-squares
parameterization of the calculated series of coupling constants
gave Karplus equations slightly differing in the last constant term
only, which were close to the Karplus equations derived from the
experiment315.
Stenutz and coworkers studied homo- and heteronuclear
coupling constants involving a hydroxymethyl group of a
carbohydrate
model
(2-hydroxymethyltetrahydropyran)335.
Working on the DFT-optimized geometries of each of three
C5-C6 rotamers, authors designed an extended basis set
[5s2p1d/3s1d] as an improvement of the previously reported set
[5s2p1d/2s]. The new basis set aimed at more accurate simulation
of interproton spin couplings. Three Karplus equations were
derived (2JH6S,H6R, 3JH5,H6R, 3JH5,H6S) and compared to those
obtained from the experimental JHH values in 4,6-pyruvate
derivatives of methyl glucosides and methyl galactosides. The
largest deviation (0.5 Hz) was within an RMS error (0.3-0.9). The
authors showed that θ angle (C6-O6 torsion) affects 2JH6,H6 more
significantly than the H-C-H bond angle.
As for 1JCH, the authors found that fitting the calculated
coupling constants to only two torsion angles ω / θ yields
relatively large RMS errors, presumably due to a solvent effect
on C-O torsional behavior, which agrees with the known solvent
dependence of 1JCH in saccharides345.
Tafazzoli and co-authors performed DFT simulations of the
anomeric center and exocyclic group (in three staggered
orientations) of the β-D-Glcp in erigeroside and
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4-deoxy-β-D-xylo-hexopyranose residues in a model compound
to support data of a detailed NMR investigation of erigeroside
from Satureja khuzistanica. The model differed from erigeroside
by the absence of a hydroxyl group at position 4 and allowed
avoidance of intramolecular hydrogen bonding and study of the
effect of a hydroxyl group on couplings involving C4. The
authors calculated complete hyper surfaces for 1JC1H1, 2JC5H6,
2
JC5H6, 3JC4H6, 2JH6R–H6S and 3JH5H6 and derived Karplus equations
to correlate all these couplings to C5–C6 (ω), C6–O6 (θ) and
C1-O1 (ϕ) torsion angles with RMS deviation from 0.3 to 1.3 Hz.
These calculated J-couplings were in agreement with
experimental values, confirming nearly quantitative prediction of
DFT-calculated heteronuclear coupling constants in aqueous
solution modeled by PCM336.
The performance of DFT and a specially designed basis set
was demonstrated by Cloran and coworkers320 on the example of
2-deoxy-β-D-erythro-pentofuranose, the major component of
DNA. These studies have shown that DFT can be used to
calculate reliable JCH and JCC values in carbohydrates without
scaling, within -6% and +10% of experimental values,
respectively.
Computed molecular parameters and 1JCH spin-spin coupling
constants in ten geometrically optimized envelope shapes were
compared to the scaled values reported from HF and MP2
methods346. As a result, the authors concluded that DFT geometry
optimization substantially contributed to the difference between
the scaled couplings and the DFT-derived 1JCH values. Indirect
JCH exhibited weaker (2JCH) or no (3JCH) dependence on the
geometry optimization method. Computed JCH values were up to
10% larger in DFT calculations than the corresponding scaled
HF/MP2 values, but the coupling trends predicted by both
methods were almost identical.
1
JCC, 2JCC and 3JCC were computed as a function of ring
conformation, and theory level-dependent corrections were
evaluated by comparison with HF calculations. With the accuracy
achieved these coupling constants can be used as monosaccharide
conformational probes. All indirect couplings in the optimized
structures were determined by finite (Fermi-contact) field double
perturbation theory with a basis set [5s2p1d/2s] previously
constructed to recover Fermi contact contribution to 13C-13C
coupling constants347.
Later these authors investigated the effect of a hydroxymethyl
group conformation on the molecular properties of the same ten
geometries of 2-deoxy-β-D-erythro-pentofuranose337. Carboninvolving spin-spin coupling constants were computed using the
same methodology on DFT-reoptimized geometries of a gg
rotamer typical for nucleic acids. The authors presented a detailed
comparison of coupling magnitudes with those observed earlier320
for a gt rotamer in solution. 1JCH appeared to be most affected by
C4-C5 bond rotation, presumably due to substantial changes in
C-H bond length accompanying the rotation. The results for 2JCH,
3
JCH, 2JCC and 3JCC confirmed prior predictions of coupling
dependence on the ring conformation.
Cloran and coworkers investigated the effect of the aminosubstitution at C1 on the molecular properties of the same
compound, including coupling constants338. They compared DFT
predictions at B3LYP/[5s2p1d/2s] for both protonated and
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pentofuranose without an amino group320. These studies proved a
suggestion that a different projection rule is required to predict
2
JC2,H1 in nucleosides348. Accordingly to the reported findings,
N-substitution of O1 exerts only a minor effect on the magnitudes
of 2JC1,H2 and 3JC1,H3, as well as on magnitudes of 3JCCCH, 3JCOCH
and 3JCOCC, regardless of the state of N-protonation. In contrast,
2
JCCH couplings are strongly modulated by substitution at the
carbon bearing a coupled proton; a much smaller effect is
observed when the substitution occurs at the coupled carbon. The
direct couplings were predicted to increase by ca. 10 Hz (1JC1,H1)
and to decrease by ca. 2-4 Hz (1JC1,C2) upon N-protonation, which
makes them a probe of a protonation state of aminosugars in
solution338.
Calculation of homo- and heteronuclear coupling constants, as
well as chemical shifts, of mononucleotide cyclic
uridinemonophosphate was performed by Bagno and
coworkers277. The overview of computational method used,
including conformational search is given above in section 5.1.
The solvent was modeled using PCM both in geometry and
coupling constants calculations.
The calculation of coupling constants included all four Ramsay
terms. In spite of a good correlation between calculated and
experimental values (JHH: R2 = 0.998, MAD = 0.90 Hz; JCH: R2 =
0.974, MAD = 13.4 Hz), slope and intercept of the best fit line
were not ideal, especially for JHH couplings. Nevertheless, this
common problem in coupling constant calculation (see
introduction to this section) did not prevent a qualitative
agreement.
Bour and coworkers interpreted indirect spin-spin NMR 1H-1H
coupling constants of the synthetic erythrofuranose derivatives on
the basis of ab initio modeling340. Epoxy, epithio, and epimino
groups were attached to the sugars to limit their conformational
flexibility. These restrictions improved the calculation
performance and simplified the estimation of the dependence of
the spin coupling on the molecular geometry.
Fully relaxed geometries were optimized with the HF, MP2,
and DFT (B3LYP and BPW91) methods using the 4-31G,
6-31G(d,p), and 6-311++G(d,p) basis sets. The authors modeled
benzene solution using COSMO248. To calculate spin-spin
couplings they used the coupled perturbed approach of the DFT
method349 in vacuum and various basis sets, including NMRoptimized IGLO II and IGLO III 209. B3LYP/IGLO II
computations included all four important magnetic terms in the
Hamiltonian. Typically all coupling constants within methyl
2,3-epoxy-L-erythrofuranoside exhibited only a minor (<15%)
dependence on the selected conformer and a basis set (IGLO II
vs. IGLO III) and fitted the experimental data within 1 Hz.
However, the only short-range coupling constant 2J4R,4S decreased
by 2.1 Hz upon a bigger basis set. The authors used a series of
conformers optimized at MP2/6-311++G(d,p) to test the heminal
and vicinal coupling prediction against different basis sets
containing from 88 to 376 basis functions. Except for 4-31G, the
calculation accuracy was similar but the agreement with the
experiment did not improve with the basis set size increase. This
confirmed the complexity of the spin-spin coupling modeling
regarding all four Hamiltonian terms and confirmed the earlier
findings of Helgaker and coworkers350.
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Mobli and Almond used DFT methods to calculate coupling
constants between HN and H2 in the N-acetylated amino sugars
and to derive Karplus equations for 3JH-N-C-H 341. Ab initio
calculation slightly overestimated the coupling constants. In
contrast to an explicit solvent model explored by MD
simulations, an implicit-solvent PCM method lowered the
magnitude of the calculated values, bringing them closer to the
experiment. The authors explained worse results of explicit
solvent inclusion by highly dynamic interactions with water,
which were difficult to simulate by static DFT equations.
However, models predicted with explicit solvent were more
conformationally realistic.
The D-pyranose rings of the N-acetylated amino sugars were
fixed in the 4C1-chair conformation and optimized at
B3LYP/6-31G(d,p). For every amide group rotamer of
α-D-GlcpNAc, SD, PSO and DSO spin–spin coupling terms were
calculated
at
B3LYP/IGLOO-III
(11s,7p,2d/6s,2p)
[7s,6p,2d/4s,2p]209 while the FC term was calculated using a
bigger HIIIsu3 basis-set351, (14s,7p,2d/9s,2p) [14s,6p,2d/9s,2p].
Due to the observed FC term dominance β-D-GlcpNAc and
α-GalpNAc were processed with FC term only.
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The Karplus equations derived by non-linear least-square
fitting (e.g. for full calculation of α-D-GlcpNAc: 3JH-N-C-H =
9.81cos2(θ+φ)-1.51cos(θ+φ)+0.62) exhibited similar trends to
those previously reported for peptide amide groups, although the
coupling constants were greater in magnitude. The authors
showed that the analysis of molecular dynamics should not be
neglected in order to reproduce experimental values of 3JH-N-C-H.
Dynamical spreads at the acetamido groups were obtained by
integration of a Karplus curve and subsequent analysis of the
group libration range.
6.2. Inter-residue coupling constants
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Detailization of various effects on intra-residue coupling
constants provided in the previous section makes it possible to
reveal the intriguing questions related to structure and bonding of
more complex carbohydrates. Indeed, long-range coupling
constants across glycosidic bonds serve a probe for oligo- and
polysaccharide conformation. Karplus-type interpretation of these
coupling constants (in addition to NOEs) provides spatial
constraints for the glycosidic bond torsion angles352.
Representative examples of predictions of inter-residue coupling
constants in carbohydrates are summarized in Table 6.
Table 6. Prediction of coupling constants in oligo- and polysaccharides
Object (molecule)
Coupling
constant
(e.g. 3JH-N-C-H)
Calculation method
Geometry
Application
Coupling
Software
ref.
α-D-Glcp-(1→1)-α-D-Glcp,
α-D-Glcp-(1→4)-D-Glcp,
β-D-Galp-(1→4)-D-Glcp,
β-D-Glcp-(1→4)-D-Glcp,
β-D-Glcp-(1→6)-D-Glcp,
α-D-Galp-(1→6)-D-Glcp,
α-D-Glcp-(1→3)-D-Glcp,
β-D-Glcp-(1→3)-D-Glcp
3
JCH (interglycosidic)
s-MD
(Amber-H force
field)
Karplus-type
correlation curve
derived by Tvaroska
and coworkers353
Insight II
Molecular
modeling program
192
(v. 4.0.0),
molecular
mechanics /
dynamics package
(v. 2.9)
testing the suitability of the
molecular modeling
approach
354
1
C4 α-L-IdopA2S(1→4)-αD-GlcpN6S-1OMe,
2
S0 α-L-IdopA2S(1→4)-αD-GlcpN6S-1OMe,
(heparin disaccharide)
3
JCH (interglycosidic)
B3LYP/
6-311++G**,
M05-2X/
6-311++G**
(with explicit
solvent, ONIOM)
B3LYP
Gaussian 03,
Gaussian 09 134, 135
studying coupling constant
variations upon counterion
and solvent effects
240
α-D-Glcp-(1→1)-α-D-Glcp
3
JCH (interglycosidic)
MD, (CHARMM
carbohydrate force
field)
Karplus-type
correlation curve
derived by Tvaroska
and coworkers353
CHARMM 164
establishing a
comprehensive
understanding of the
hydration pattern of
trehalose
332
β(1-4)-linked disaccharide
models
2
JCOC (interglycosidic)
B3LYP/6-31G(d)
FF-DPT (Fermicontact),
B3LYP/[5s2p1d,2s]
Gaussian 94
studying the influence of
structural factors on
transglycosidic 2JCOC
355
β-D-Ribf-1OMe-(3-P-5)-β-D-Ribf-1OMe
(RNA backbone) in 16
“experimental”
conformations
2
J, 3J, 4J
between all
1
H, 13C and
31
P
MM/Amber
coupled perturbed
DFT,
B3LYP/IGLO II and
IGLO III
Amber 178, 179
(geometry
optimization),
Gaussian 03
(NMR
calculation)
interpretation of nucleic
acid backbone
conformation using
coupling constants
356
β-D-2-deoxy-Ribf1(N-base),
N-base=A,C,G,U,T
3
B3LYP/6-31G(d)
DFT/FPT
PW86/IGLO-III (FC
term);
SOS-DFPT (PSO
and DSO terms);
Gaussian 98
deMon-NMR 280-
study of relationship
between spin coupling and
the glycosidic torsion angle
357
JC-H1’,
JC-H1’,
1
JC1’-H1’
B3LYP/6-31G(d,p)
(with explicit
solvent)
3
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Cheetham and coworkers calculated the interglycosidic
heteronuclear coupling constants (3JH1Cx and 3JC1Hx) for a series
of eight α- or β-linked glucosyl- and galactosyl-glucopyranoses.
The authors utilized a Karplus relationship of Tvaroska and
coworkers353: J = 5.7cos2φ−0.6cos φ+0.5 with cos2φ and cosφ
conformationally averaged from the s-MD trajectories. The aim
of this calculation was to determine if a molecular modeling
approach would be adequate to provide results similar to those
obtained experimentally. The crystal conformation of each
disaccharide was used as a starting geometry for the MD
simulations in Amber-Homans force field193, with the explicit
inclusion of water. The authors showed that, except for C1-O1Cx-Hx dihedral angle in β(1-4)-linked disaccharides, their
relatively simple modeling could reproduce results close to the
experimental and other modeling studies354.
Engelsen and Perez calculated interglycosidic heteronuclear
coupling constants in α,α-trehalose within a study aimed at
establishing a comprehensive understanding of the hydration
pattern of this disaccharide and its comparison to sucrose332.
Starting from X-ray geometry, the authors ran a 2.5 ns MD
simulation in CHARMM carbohydrate force field with the
explicit inclusion of 485 TIP3P water molecules.
The heteronuclear coupling constant 3JH,C across the glycosidic
linkage was calculated accounting to the obtained adiabatic map
and the equation for the C-O-C-H fragment parameterized by
Tvaroska and coworkers353. The derived value 2.3 Hz was much
closer to the experiment (2.5 or 3.3 H) than 1.5 Hz obtained by
the MD simulation in vacuum. In contrast, precision of intraresidue 3JH5,C1 calculation was not affected by the solvent
inclusion.
Since DFT calculations were shown to yield computed JCC
within ∼10% of experiment without scaling320, 2JCOC values could
be computed to within 0.2-0.3 Hz of the experimental couplings.
This accuracy allowed Cloran and coworkers to study influence
of structural factors on trans-O-glycosidic 2JCOC using DFT
calculations. Geometric optimizations were conducted at
B3LYP/6-31G*. 13C-13C spin coupling constants were obtained
by finite-field double perturbation theory calculations using a
basis set previously constructed for similar systems347. Only the
FC component was recovered, as main component of JCC in
saturated systems. The calculation supported the observation that
JCOC depended mainly on the φ angle of a glycosidic bond. The
increase of a valent angle at oxygen produced more negative JCOC
coupling.
Sychrovsky and coworkers calculated indirect heteronuclear
coupling constants and related them to the backbone torsion
angles and sugar pucker of nucleic acids. The authors used 16
known conformations of the nucleic acid backbone, including
well-characterized double-helical forms (B-DNA, A-DNA, ARNA), and applied them to baseless dinucleoside phosphate as to
a molecular model.
The initial models of the dinucleoside phosphates were
constructed as reported for RNA fragments358 and for the most
prevalent DNA conformations, BI and A359. These
“experimental” geometries were relaxed by molecular mechanics
with torsion angles of the backbone restrained to keep the
conformation close to a class-identifying state. After geometry
relaxation, the nitrogenous bases were substituted by methyl
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groups and both the 5’ and 3’ ends were terminated by hydroxyl
groups.
The coupled perturbed DFT method349 at B3LYP /IGLO II and
IGLO III levels of theory209 was used for the calculation of 1H,
13
C, and 31P coupling constants by including all four coupling
terms. Explicit hydration, the PCM solvent model and their
combination were compared. The PCM hydration accounted for
the dominant part of calculated coupling difference between in
vacuo and the hydrated models. The authors calculated all
possible coupling constants across two, three of four bonds and
correlated them to each of seven torsion angles characterizing a
βDRibf-1OMe(3-P-5)βDRibf-1OMe
fragment,
so
that
experimentally observed conformations of the nucleic acid
backbone could be characterized with a specific set of
J-couplings356.
Three of torsion angles in nucleic acid backbone have sharp
population distribution. Accordingly to the authors, 3J couplings
correlated with “sharp” torsions are not properly described by
classical Karplus equation and should be parameterized with
explicit consideration of other torsions, either as a
multidimensional Karplus curve or a curve parameterized with
neighboring torsions fixed.
Munzarova and Sleknar357 studied correlation of a nonbackbone glycosidic torsion angle in deoxynucleosides with the
heteronuclear coupling constants of the anomeric protons. The
backbone torsion angles were frozen to their values in B-DNA.
The authors derived phase-shifted Karplus equation and
parameterized it separately for every nucleoside, as purine and
pyrimidine nucleosides exhibited different torsional dependence
of couplings.
7. Computation of NMR relaxation rates
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Best and coworkers reported the results of molecular dynamics
simulations compared to the data of the NMR relaxation
experiments for maltose and isomaltose. The 13C longitudinal
relaxation time (T1) is dependent on the dipolar relaxation
between a carbon and its directly attached proton. The relaxation
parameters are a function of a spectral density. The most
frequently used method of experimental characterization of the
spectral density is a model-free formalism. Generalized order
parameters may be directly calculated from simulation. The
equations linking these parameters together were published
elsewhere360. Both maltose vacuum and solution simulations were
started from the saddle point (0,0) between the two major energy
wells on the adiabatic map. On the basis of the adiabatic map, the
lowest minima were chosen as starting points for the simulations
of isomaltose. As a result longitudinal relaxation times were
obtained for each carbon in the maltose and isomaltose (see Table
2 in the original publication).
Later this group ran MD simulations with explicit water on the
minimal model compounds for the α(1-6) branch point of
amylopectin: trisaccharide panose and the tetrasaccharide 62 α-Dglucosylmaltotriose (maltotriose (1-6)-glucosylated at its middle
glucose residue)361. Calculation of the NMR longitudinal
relaxation times for panose showed good agreement with the
experimental values, and validated the simulation dynamics used.
As a check of the validity of the simulation dynamics,
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longitudinal T1 relaxation times sensitive to both the extent and
time scale of molecular motion, were directly calculated from the
trajectories. Model-free formalism is most suitable for molecules
with intramolecular motion much more rapid than molecular
tumbling, which may be wrong for small oligosaccharides.
Besides this, the comparison between the experiment and the
simulation is done through indirectly fitted parameters. To
resolve these issues authors adopted the approach they used
previously to calculate T1 relaxation times directly from MD
simulation360. Relaxation times were simulated separately for CH
and CH2 carbon atoms in each panose ring (see Table 3 in the
original publication).
In both publications by Best and coworkers360, 361, all
calculations were done using the PHLB carbohydrate force field
specifically parameterized for carbohydrates177 and implemented
in CHARMM. This parameter set addressed the excessive
flexibility in the earlier force field (HGFB), and the incorrect
preference of the primary alcohols in that force field for adopting
the tg rotamer. The TIP3P model was used for explicit
representation of water.
The cross-correlated relaxation rates of double- and zeroquantum coherences have widespread applications in structural
and conformational studies of biomolecules, including probing of
the O-glycosidic linkage conformation in carbohydrates362.
Sychrovsky and coworkers applied quantum chemical
calculation methods to investigate the dependence of N1/N9 and
C1′ CS tensors on the glycosidic torsion angle and sugar pucker
in 2′-deoxynucleosides (dAde, dGua, dCyt, dThy). They
calculated cross-correlated relaxation rates using reduced
equations published elsewhere363 and tested applicability of
Ravindranathan’s363
and
Duchardt’s364
methods
to
deoxyribonucleic acids (DNAs). According to their results, these
CS tensors exhibited a significant degree of conformational
dependence on C1’-N torsion angle and sugar pucker, which
should be taken into consideration while interpreting crosscorrelated relaxation rates between the N1/N9 CS tensor and C1′H1′ dipole-dipole in DNAs278.
The geometry of all nucleosides was gradient optimized at
B3LYP/6-31G(d,p) level. All geometrical parameters, except the
C1’-N torsion angle, were freely optimized. The NMR shielding
tensors were calculated using the GIAO B3LYP/(9s,5p,1d/5s,1p)
[6s,4p,1d/3s,1p] for carbon, nitrogen and oxygen and B3LYP/
(5s,1p) [3s,1p] for hydrogen (basis set IGLO II209). A summary of
the CS tensor calculation is included in Table 3 (see above).
Longitudinal and transversal relaxivities are the inverse of the
spin-lattice T1 and spin-spin T2 relaxation times, respectively.
They contain information both on structure and molecular
dynamics. Several attempts have been undertaken to predict
relaxivities of hyaluronan oligomers. Calculations of 13C
relaxivities based on the combination of MD simulation
algorithms with diffusion theory and mode-coupling approach
(MCD) were performed on hyaluronan (HA)2 and (HA)4
oligomers in water solutions365. CHARMM168 was used to
generate a hyaluronan structure and to merge it in a water box.
Authors achieved an agreement between the calculations for the
two oligomers with the experimental data obtained by the
“inversion-recovery” technique. For details about mode-coupling
diffusion please refer to the original publication365.
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Furlan and coworkers presented the calculation of dynamic
properties of the hyaluronan (HA)4 with consideration of the
hydrophobic effect in water solution and local hydrophilic effects
due to hydrogen bonding with the solvent. Several
configurational distributions and dynamical parameters related to
nuclear magnetic relaxation, sensitive both to the molecular
structure and the mobility, were calculated from the replicaexchange Monte Carlo statistics at different temperatures. The
diffusion theory was applied to the calculation of the longitudinal
13
C relaxivities366. With the MD calculation method proved,
authors reported an investigation of molecular structure and
detection of the critical length of a hyaluronan polymer. They
followed the protocol established for the quantitative description
of the size and shape of biopolymer chains including the
construction of chain models by Monte Carlo simulation on the
basis of conformational statistical weights of representative
dimeric units. The OPLS-AA force field was used for the
generation of the conformational energy landscape. The modecoupling diffusion (MCD) theory with the RM2-II basis set was
applied to the calculation of the NMR relaxivities. The computed
relaxivities are within 25% of the experimental data, and in all
cases they are larger than in the experiments367. Parameterization
of the OPLS-AA force field for carbohydrates has been reported
earlier188.
8. Computation of other NMR parameters
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Averaged characteristics of molecular systems, including NOEs,
can be calculated within the studies of the conformational
equilibrium. As soon as a conformational map is calculated, the
averaging is usually performed over energies with an assumption
that population of conformaers fits the Boltzmann distribution124.
Comparison of the resulting predicted NOEs with the
experimental data is a widely used approach to the validation of
MD experiments.
Trajectories obtained from MD simulations in CSFF force
field in TIP3P water model allowed analytical derivation of T1
and T2 relaxation time, cross-correlated relaxation rates and
NOEs. The stochastic approach to processing MD simulation data
was shown suitable for description of diffusion dynamics of
molecules with mainly torsional internal mobility, as
demonstrated for γ-cyclodextrin368 and model tri- and
pentasaccharides369.
MM3 was reported as a good force field to produce
confomation maps for NOE calculations370. Gerbst and coworkers
confirmed the adequacy of molecular modeling of fucoidans by
comparison of the calculated NOEs of protons at a glycosidic
bond to the experimental values. In case of fucobiose, the absence
of signal overlap allowed to utilize steady-state NOE370. Starting
from MM3 conformation maps, the authors calculated NOEs
using the iterative Noggle and Shirmer equation371, and averaged
the results according to Boltzmann distribution. Selection of
conformational minima with energies within 10% of the global
energy minimum gave satisfactory results, particularly average
difference between experimenmtal and calculated relative NOEs
was from 1.3% to 2.5% depending on the disaccharide sufation.
In case of linear sulfated fucotriosides, anomeric proton signal
overlap prohibited a utilization of a steady-state NOE. Transient
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NOEs were calculated as 1/r6, r being an interatomic distance
obtained from the optimized geometry. Transient NOEs were
Boltzmann-averaged over the MM3 conformation maps
calculated for every dissacharide fragment using the same
methodology as for fucobiosides. The resulting NOESY crosspeak volumes showed weak correlation to the experiment, which
encouraged authors to model a reducing end sulfate group as
undissociated rather than as an anion372.
Casset and coworkers examined the potential energy
hypersurface of sucrose using molecular mechanics calculations
in MM3(92) force field interfaced with two different algorithms
for conformational searching (systematic grid-search approach,
and CICADA procedure).
CICADA (Channels In Conformational space Analyzed by
Driver Approach) method drives selected dihedral angles to
explore the low-energy regions and permits full geometry
relaxation. Using the grid-search approach, the relaxed adiabatic
map of sucrose was calculated as a function of the glycosidic
torsion angles, and three families of stable conformers were
identified. The CICADA procedure found all minima and the
low-energy conversion pathways for sucrose in agreement with
those located by the grid-search approach.
Theoretical NOESY volumes were calculated using full
relaxation method from an ensemble-averaged relaxation matrix,
as described earlier373. All accessible conformations derived from
either the grid-search or the CICADA method were taken into
account. Two sets of NOESY volumes were calculated using
averaging methods appropriate for both slow and fast internal
motions. The agreement factors, which are relative deviations
between the calculated and the experimental non-diagonal
400 MHz NOESY volumes, were 0.170 (grid-search, fast
motion), 0.175 (grid-search, slow motion), 0.175 (CICADA, fast
motion), 0.163 (CICADA, slow motion). These values improved
(0.118-0.139) when only intensive NOE peaks were considered.
The study demonstrated the ability of the CICADA method to
reproduce the potential energy surface of a flexible molecule and
therefore to simulate its NOEs159.
Landstrom and Widmalm carried out an atomistic all-atom
MD simulation of the branching region of Aeromonas
salmonicida O-specific polysaccharide, using the β-D-ManpNAc(1→4)[α-D-Glcp-(1→3)]-α-L-Rhap-OMe trisaccharide as a
model, with explicit solvent molecules. The MD simulations with
1 µs duration revealed a dynamic conformational process on the
nanosecond time scale, which had lacked the attention of
researchers. The obtained results emphasized the predictive
power of MD simulations in the studies of biomolecular systems
and explained an unusual NOE due to conformational
exchange143. The MD simulations employed PARM22/SU01,
which is a CHARMM22-type force field modified for
carbohydrates173 and implemented in NAMD 2.6b1. Initial
conditions were prepared by placing the model trisaccharide in a
previously equilibrated cubic water box, followed by energy
minimization and heating. The smooth particle-mesh Ewald
method374 was used to calculate the full electrostatic interaction.
The 500 MHz NOESY volumes for H-2 (Rha) – H-2
(ManNAc) homonuclear interaction were simulated as a function
of mixing time for two conformation states of the above
trisaccharide model in MestreLabs Research Mspin375 using a full
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relaxation-matrix formalism376, and a molecular reorientation
correlation time of 200 ps.
Blundell and coworkers reported the complete resolution and
assignment of nuclei in hyaluronan oligosaccharides with seven
different naturally occurring terminal rings. They simulated the
non-first-order line shape of the H-2VII proton in HA6AN (structure
7 in the original publication) and used this data in spectrum
assignment. GAMMA software377 utilized in the simulation
employed multiple iterative rounds with floating values for 3JH,H
and ∆δ(H-3,H-4) to find the best fit to the intensity data for H-2VII
proton. All five protons within the GlcA ring were used to model
the spin system378.
9. Conclusions
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Based on the literature data discussed in the present review we
compare the scope and performance of various computational
approaches to predict the NMR parameters of carbohydrates.
For a representative view, the accuracy of 13C NMR chemical
shifts calculations by different methods was summarized for two
simple monosaccharides, α- and β-anomeric forms of D-glucose
(Table 7). On average, empirical schemes provide better accuracy
with RMS in the range of 0.07–2.51 ppm (in many cases less than
1 ppm). DFT and ab initio calculations have shown varying
performance with the RMS values varying from 1.75 to
9.81 ppm. The best accuracy was observed for the calculations at
B3PW91/6-31+G(d)//MM+ level (RMS = 1.75 ppm)264 and at
PBE/TZ2p level (RMS = 2.43 ppm)236.
Methyl
6-O-(diphenylphospho)-a-D-glucopyranoside
[(PhO)2P(O)-O-6)α-D-Glcp-1OMe ], a sugar derivative with an
uncommon substituent, can serve as a crucial test. Chemical shift
simulation for such a compound is a complicated task both for
density functional theory (due to complex electronic structure)
and for empirical schemes (due to poor representation in
chemical shift databases). A summary of theoretical predictions
by different methods reveals important trends (and excellent
predictive potential for the rest of the molecule (RMS = 0.11 and
0.52 ppm). This difference in accuracy can be accounted for the
rigid structure of a benzene ring and the presence of only a single
stereoisomer with the given atom connectivity, which is a
structural fragment highly populated in the chemical shift
database.
Sucrose disacharide serves as a test of chemical shift
prediction strength of molecules containing glycosidic bonds and
residues poorly populated in chemical shift databases, such as
fructopyranose. Fig. 10 illustrates the results of empirical and
quantum-mechanical calculations. Only GIAO calculation at
B3LYP/6-311G++(2d,2p) level in COSMO water model (Fig.
10C) could accurately predict chemical shifts of carbons
adjascent to a glycosidic bond, while empirical prediction was the
only one to produce a correct order of signals. The accuracy of
quantum mechanical predictions was similar, except for the nonhydroxylated carbon of the fructose residue (F5). The statistical
and performance data of these calculations are summarized in
Table 9.
To conclude, recent outstanding progress in development of
theoretical methods and rapid increase of hardware performance
greatly facilitated the application of computational tools to NMRChemical Society Reviews, 2013, 0, 00–00 | 31
10
15
20
25
45
50
55
60
80
based structural studies of carbohydrates. Nowadays, prediction
of the NMR parameters of mono- and small oligosaccharides
benefit from formalized procedures and became a routine task.
Table 8). DFT calculations at B3LYP level provide reasonable
accuracy for carbohydrate moiety (RMS = 3.28 ppm) and an
unacceptable error for the rest of the molecule (RMS = 5.89
ppm). Changing density functional to PBE improves description
of the non-carbohydrate part of the molecule (RMS = 3.03 ppm),
but shows poor results for a monosaccharide core (RMS = 9.37
ppm), allowing a suggestion that B3LYP is better adopted for
conformationally flexible structures.
An important point for theoretical calculations at density
functional and ab initio levels is a choice of reference. As
summarized in and excellent predictive potential for the rest of
the molecule (RMS = 0.11 and 0.52 ppm). This difference in
accuracy can be accounted for the rigid structure of a benzene
ring and the presence of only a single stereoisomer with the given
atom connectivity, which is a structural fragment highly
populated in the chemical shift database.
Sucrose disacharide serves as a test of chemical shift
prediction strength of molecules containing glycosidic bonds and
residues poorly populated in chemical shift databases, such as
Table 8, noticeable difference in accuracy may be observed upon
changing a reference from benzene (RMS = 9.37, 3.03 ppm) to
ethylene glycol (RMS = 9.31, 4.76 ppm).
Despite the rare nature of the molecule, empirical methods
gave good prediction with RMS deviation being as small as
2.01 ppm using carbohydrate-optimized BIOPSEL algorithm
(and excellent predictive potential for the rest of the molecule
(RMS = 0.11 and 0.52 ppm). This difference in accuracy can be
accounted for the rigid structure of a benzene ring and the
presence of only a single stereoisomer with the given atom
connectivity, which is a structural fragment highly populated in
the chemical shift database.
Sucrose disacharide serves as a test of chemical shift
prediction strength of molecules containing glycosidic bonds and
residues poorly populated in chemical shift databases, such as
fructopyranose. Fig. 10 illustrates the results of empirical and
quantum-mechanical calculations. Only GIAO calculation at
B3LYP/6-311G++(2d,2p) level in COSMO water model (Fig.
Table 8). An obvious drawback of the specific empirical schemes
is the limitation in the analyzed structures, since BIOPSEL
cannot predict chemical shifts of the aromatic part, while
CASPER lacks the interface for phosphorus-bonded
32 | Chemical Society Reviews, 2013, 0, 00–00
5
30
35
40
65
70
75
85
Nevertheless, in spite of widespread areas of potential
application, the limitations of computational approaches are still
an important issue.
fructopyranose. Fig. 10 illustrates the results of empirical and
quantum-mechanical calculations. Only GIAO calculation at
B3LYP/6-311G++(2d,2p) level in COSMO water model (Fig.
10C) could accurately predict chemical shifts of carbons
adjascent to a glycosidic bond, while empirical prediction was the
only one to produce a correct order of signals. The accuracy of
quantum mechanical predictions was similar, except for the nonhydroxylated carbon of the fructose residue (F5). The statistical
and performance data of these calculations are summarized in
Table 9.
To conclude, recent outstanding progress in development of
theoretical methods and rapid increase of hardware performance
greatly facilitated the application of computational tools to NMRbased structural studies of carbohydrates. Nowadays, prediction
of the NMR parameters of mono- and small oligosaccharides
benefit from formalized procedures and became a routine task.
Nevertheless, in spite of widespread areas of potential
application, the limitations of computational approaches are still
an important issue.
10C) could accurately predict chemical shifts of carbons
adjascent to a glycosidic bond, while empirical prediction was the
only one to produce a correct order of signals. The accuracy of
quantum mechanical predictions was similar, except for the nonhydroxylated carbon of the fructose residue (F5). The statistical
and performance data of these calculations are summarized in
Table 9.
To conclude, recent outstanding progress in development of
theoretical methods and rapid increase of hardware performance
greatly facilitated the application of computational tools to NMRbased structural studies of carbohydrates. Nowadays, prediction
of the NMR parameters of mono- and small oligosaccharides
benefit from formalized procedures and became a routine task.
Nevertheless, in spite of widespread areas of potential
application, the limitations of computational approaches are still
an important issue.
monosaccharides. Empirical algorithms with non-specific
databases demonstrated a good predictive potential for chemical
shifts of the carbohydrate moiety (RMS = 3.14 and 3.83 ppm)
This journal is © The Royal Society of Chemistry 2013
Table 7. Comparison of 13C NMR spectra of α- and β-glucopyranose calculated by various methods in solution or gas phase.
13
Method
(chemical shifts // geometry)
B3LYP/pcJ//B3LYP/6-31G(d,p)
BP86/TZVP//BP86/TZVP
B3LYP/cc-pVTZ//B3LYP/6-31G(d,p)
ONIOM [MP2 : HF/6-311++G(2d,2p)]//
MP2/cc-pVDZ
HF SCF/TZVP//B3LYP/TZVP
B3LYP/TZVP//B3LYP/TZVP
MP2/TZVP//B3LYP/TZVP
ONIOM [MP2 : HF/ 6-311++G(2d,2p)]//
MP2/cc-pVDZ
MP2/TZVP//MP2/TZVP
ONIOM [MP2 : HF/ 6-311++G(2d,2p)]//
MP2/cc-pVDZ
PBE/TZ2p
B3PW91/6-31+G(d)//MM+
HOSE + neural net (ACDLabs 10)
HOSE (MestreNova/ ModGraph)
HOSE (ACDLabs 10)
Incremental (BIOPSEL / BCSDB)
Incremental (CASPER)
30°C, in water
in water
70°C, in water
25°C, in water
5
10
15
20
C NMR spectrum of D-Glcp a,c, ppm
Notes and reference
RMS error
b,c
, ppm
Non-empirical methods
104.74 82.14 83.96 79.55 81.89 70.10 (α)
108.59 85.01 86.00 79.23 86.58 70.18 (β)
103.16 79.17 81.03 74.10 79.53 65.28
101.45 79.34 81.01 75.25 79.70 66.36 (α)
9.81 (α)
9.68 (β)
6.81 (α)
6.70 (α)
102.88 79.37 79.65 80.59 76.55 70.37 (β)
6.28 (β)
86.52 67.63 69.34 63.24 68.58 57.19 (α)
100.06 77.88 79.77 72.60 77.91 64.23 (α)
99.95 77.70 79.51 72.15 77.32 64.09 (α)
102.93 79.18 80.15 74.83 80.28 66.88 (β)
5.37 (α)
5.12 (α)
4.87 (α)
4.50 (β)
for α-D-Glcp 4C1 276
99.61 77.37 78.61 71.73 75.59 63.88 (α)
102.61 78.95 80.09 71.25 79.60 62.84 (β)
4.25 (α)
3.39 (β)
for α-D-Glcp 4C1 276
for β-D-Glcp 4C1 G- 263
94.47 73.45 77.42 73.23 75.46 63.25 (α)
91.6 70.6 72.3 72.1 70.4 63.9 (α)
94.8 74.6 74.6 72.4 74.6 63.5 (β)
2.43 (α)
1.75 (α)
1.83 (β)
Empirical methods
95.33 74.67 76.68 70.71 76.66 62.10 (α)
95.33 74.67 76.68 70.71 76.66 62.10 (β)
95.54 74.73 74.52 70.41 76.24 62.11 (α)
95.54 74.73 74.52 70.41 76.24 62.11 (β)
95.56 73.08 73.73 70.13 74.93 62.38 (α)
95.56 73.08 73.73 70.13 74.93 62.38 (β)
93.3 72.7 74.0 70.9 73.2 61.9 (α)
97.1 75.4 77.0 70.9 77.2 62.1 (β)
92.99 72.47 73.78 70.71 72.37 61.84 (α)
96.84 75.20 76.76 70.71 76.76 61.84 (β)
Experimental data
92.77 72.15 73.43 70.32 72.10 61.27 (α)
96.59 74.81 76.43 70.27 76.61 61.42 (β)
93.3 72.7 74.0 70.9 72.7 61.9 (α)
97.1 75.4 77.0 70.9 77.2 62.1 (β)
92.99 72.47 73.78 70.71 72.37 61.84 (α)
96.84 75.20 76.76 70.71 76.76 61.84 (β)
92.9 72.5 73.8 70.6 72.3 61.6 (α)
96.7 75.1 76.7 70.6 76.8 61.7 (β)
92.48 71.87 73.15 70.04 71.82 60.99 (α)
93.3 73.1 74.4 71.2 72.9 62.4 (α)
a
Signals are in the order of atom enumeration (C1-C6)
b
RMS error was calculated against the experimental spectrum averaged from six listed sources.
c
Anomeric configurations are in parentheses.
2.51 (α)
0.65 (β)
2.15 (α)
1.09 (β)
1.55 (α)
1.78 (β)
0.42 (α)
0.30 (β)
0.08 (α)
0.07 (β)
260
for α-D-Glcp 4C1 276
gas phase, averaged through
conformers254
for β-D-Glcp 4C1 T 263
for β-D-Glcp 4C1 G+ 263
normalized against ethylenglycol236
264
required manual setting of geometry
d
results for α- and β-glucose were
the same.
required manual setting of geometry
d
reported accuracy was “best” (mark
4 of 0..4)114
reported expected error was 0.00 117
260
112
119
318
254
379
d
ACDLabs could not properly minimize the geometry starting from the template “Glc”. Prior to calculation, the starting geometry of α- and β-Glcp was
manually set with subsequent built-in MM2 minimization. Results for α- and β-glucose in water were the same.
and excellent predictive potential for the rest of the molecule
(RMS = 0.11 and 0.52 ppm). This difference in accuracy can be
accounted for the rigid structure of a benzene ring and the
presence of only a single stereoisomer with the given atom
connectivity, which is a structural fragment highly populated in
the chemical shift database.
Sucrose disacharide serves as a test of chemical shift
prediction strength of molecules containing glycosidic bonds and
residues poorly populated in chemical shift databases, such as
fructopyranose. Fig. 10 illustrates the results of empirical and
quantum-mechanical calculations. Only GIAO calculation at
B3LYP/6-311G++(2d,2p) level in COSMO water model (Fig.
10C) could accurately predict chemical shifts of carbons
adjascent to a glycosidic bond, while empirical prediction was the
This journal is © The Royal Society of Chemistry 2013
25
30
only one to produce a correct order of signals. The accuracy of
quantum mechanical predictions was similar, except for the nonhydroxylated carbon of the fructose residue (F5). The statistical
and performance data of these calculations are summarized in
Table 9.
To conclude, recent outstanding progress in development of
theoretical methods and rapid increase of hardware performance
greatly facilitated the application of computational tools to NMRbased structural studies of carbohydrates. Nowadays, prediction
of the NMR parameters of mono- and small oligosaccharides
benefit from formalized procedures and became a routine task.
Nevertheless, in spite of widespread areas of potential
application, the limitations of computational approaches are still
an important issue.
Chemical Society Reviews, 2013, 0, 00–00 | 33
Table 8. Prediction of 13C NMR chemical shifts (in ppm) for (PhO)2P(O)-O-6)α-D-Glcp-1OMe using different methods.
Method
Software
Chemical shifts of (PhO)2P(O)-O-6)α-D-Glcp-1OMe
RMS
error b
Me
i-Ph
o-Ph m-Ph p-Ph Glc Other
part atoms
54.61 157.72, 120.08, 129.31, 124.39, 9.37 3.03
158.47 119.18 128.89 122.96
C1
C2
C3
C4
C5
C6
PRIRODAa 380,
normalized against
benzene (default)
PRIRODAa 380,
normalized against
ethylene glycol
Gaussian 03 135
106.32
76.67
79.97
74.38
74.60
50.63
72.60
75.90
70.31
70.53
46.56
50.54
116.01, 125.24, 119.61 9.31
154.02 115.11 124.82
4.76
102.25
98.02
72.42
74.11
77.16
69.90
69.31
55.20
145.25 114.95 122.55 118.02 3.28
5.89
Mestre Nova a 73, 76
103.31
72.66
74.67
70.79
75.08
66.89
55.81
151.31 120.53 130.07 126.15 3.83
0.52
ACDLabs
BIOPSEL 113, 115
102.44
99.3
0.11
-
CASPER 116, 121
Experiment in CDCl3 268
95.51
71.84 75.90 69.94 72.85 67.38 55.50 150.60 120.10 129.80 125.50 3.14
72.7
74.0
70.9
72.7
66.9
no output
2.01
poor accuracy reported с
no output (P-linked sugars are not supported)
71.88 73.92 69.63 70.29 68.22 55.27 150.45 120.12 129.84 125.52 0
PBE/TZ2p
(geometry, NMR)
236
B3LYP/ 6-31G(d)
(geometry, NMR)
268
HOSE and its
variations
a 68, 381
Incremental at
residual level
0
a
Starting geometry was obtained by MM2, then re-optimized in the specified software.
RMS was calculated against experimental data in CDCl3.
c
BIOPSEL reported the calculation accuracy as poor (mark 1 of 0..4) for a saccharide part and as 0 of 0..4 for a non-saccharide part.
b
5
10
15
35
Empirical schemes are easy to use and provide good accuracy
for compounds possessing a widespread structural motif, while
the performance for molecules with atypical substituents (not
parameterized for) or with an unexpected secondary structure can
be poor. Further extension of databases and algorithmic
improvements are expected to enhance the application of
empirical algorithms.
In contrast to the empirical methods, DFT and ab initio
calculations should be suitable for computational predictions of
the NMR parameters for any carbohydrate structures and
substituents from the first principles. A careful selection of the
theory levels used for geometry optimization and NMR
calculation allows achievement of reasonable accuracy for small
systems (monosaccharides). An outstanding advantage of DFT
and ab initio calculations is the ability to predict the NMR
20
25
30
parameters other than chemical shifts. Particularly, its successful
applications for the prediction of spin-spin coupling constants,
relaxation rates, NOEs, chemical shifts in atypical solvents, and
conformation-specific NMR parameters have been reported.
Finally, we anticipate a rapid progress in application of DFT
and ab initio calculations for prediction of the NMR parameters
of carbohydrates with more dedicated impact on everyday
practical needs in experimental structure determination. At the
same time, empirical correlations are still in use for routine NMR
predictions and for glycans built up of three and more sugar
residues, since right now it is too early to expect superior
performance of DFT calculations in all aspects of carbohydrate
structure analysis.
Table 9. The performance of empirical and density functional prediction of 13C NMR spectrum of sucrose. a
Parameters
BCSDB/BIOPSEL b 114
(empirical)
GIAO at
PBE/TZ2p level c 236
GIAO at
B3LYP/6-311G(2d,p) level c
COSMO / GIAO at
B3LYP/6-311G++(2d,2p) level d
RMS, ppm
2.6
5.4
4.6
3.9
Linear correlation
0.994
0.981
0.953
0.981
Calculation time e
<0.1 sec
29 min
12.5 hours
67.8 hours
a
Reference experimental data are from the 13C NMR spectrum at 25°C in D2O.
b
Used chemical shift database is dedicated to water solutions of carbohydrates.
c
The spectrum was normalized against chemical shifts of ethylene glycol (were 63.4 ppm in CDCl3 379). The geometry was optimized in the same basis
set.
40
d
The calculations were carried out in COSMO water model. The geometry was optimized in the same basis set. The spectrum was normalized against
ethylene glycol in CDCl3 (63.4 ppm379), while normalization against ethylene glycol in D2O (67.3 ppm379) gave an RMS error of 7.4 ppm.
e
Performance data were obtained on a personal computer with Intel Core 2 quad-core processor running at 3.0 GHz.
This journal is © The Royal Society of Chemistry 2013
Chemical Society Reviews, 2013, 0, 00–00 | 34
5
Fig. 10. Deviation of 13C chemical shifts of sucrose disaccharide predicted by different methods versus experimental spectrum. Dashed lines represent
correlations between signals. Black values (A) were predicted empirically using an incremental schema. Experimental spectrum (B) was recorded at 25°C
in D2O. Signal assignment is denoted by F (fructose residue) or G (glucose residue) symbol and the carbon number. Red values (C) were calculated at
PBE/TZ2p level, and green values (D) were calculated at B3LYP/6-311G++(2d,2p) level using COSMO water model. See calculation details in Table 9.
10. Abbreviations
10
15
20
Force fields in italic.
QM theory levels in bold.
QM functionals and basis sets in bold-italic.
3D
– three-dimensional
3D HOSE – enhanced HOSE that utilizes stereochemistry
information
AMBER – assisted model building with energy refinement
B3LYP
– Becke three-parameter with Lee-Yang-Parr
B3PW91 – Becke three-parameter with Perdew-Wang 91
BD,
BD(T),
BD(TQ) – Brückner energies (including doubles, triples
and quadruples)
This journal is © The Royal Society of Chemistry 2013
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35
BPT
CCS,
CCSD,
CCSDT
– bond polarization theory
– coupled cluster methods (including singles,
doubles and triples)
CHARMM – chemistry at Harvard macromolecular mechanics
CHF
- coupled Hartree-Fock
CI
– configuration interaction
CICADA – channels in conformational space analyzed by
driver approach
COSMO – conductor-like screening model
COSMOS – computer simulations of molecular structures
CPCM
– conductor-like polarizable continuum model
CP/MAS - cross-polarization / magic angle spinning
CS
– (isotropic) chemical shift
CSS
– chemical shift surface
Chemical Society Reviews, 2013, 0, 00–00 | 35
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10
15
20
25
30
35
40
CST
CSFF
CSGT
IGAIM
DFT
DFT-D
– chemical shielding tensor
– carbohydrate solution force field
– continuous set of gauge transformations
– individual gauges for atoms in molecules
– density functional theory
– density functional theory with distancedependent dispersive term
DPCM
– dielectric polarizable continuum model
DSO
- diamagnetic spin orbit (term)
FC
- Fermi contact (term)
FF-DPT - finite-field double perturbation theory
GIAO
– gauge-including atomic orbital
GIPAW – gauge-including projector augmented-wave
GLYCAM – glycan molecular mechanics force field
GROMOS – Groningen molecular simulation
HOSE
– hierarchical organization of spherical environments
HF
– Hartree-Fock
IGLO
– individual gauge for localized orbitals
LANL2DZ – Los Alamos national laboratory 2-double-z
LD
- locally dense
MAD
– mean absolute deviation
MCD
– mode-coupling diffusion
MD
– molecular dynamics
MM2, MM3 – molecular mechanics
MNDO
– modified neglect of differential overlap
MPx
– Møller–Plesset perturbation theory at order x
NMR
– nuclear magnetic resonance
NOE
– nuclear Overhauser effect
ONIOM – our own n-layer integrated molecular orbital and
molecular mechanics approach
OPLS-AA – optimized potentials for liquid simulations - allatom
PBE
– Perdew-Burke-Ernzerhof
PCM
– polarizable continuum model
PHLB
– Palma-Himmel-Liang-Brady
PSO
-paramagnetic spin orbit (term)
QCISD,
QCISD(T),
QCISD(TQ) – quadratic configuration interaction
RAI
– recoupling of anisotropy information
RMS
– root mean square
SCF
– self-consistent field
SD
-spin dipolar (term)
TIP3P
– transferable intermolecular potential, 3 point
60
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36 | Chemical Society Reviews, 2013, 0, 00–00
– lyxose
– ribose
- tetramethylsilane
– xylose
11. Acknowledgements
65
70
This review was written in the framework of development of the
NMR prediction engine of Carbohydrate Structure Database
funded by Russian Foundation for Basic Research, grants 05-0790099 and 04-12-00324.
Authors thank Prof. Y.A. Knirel and Prof. A.S. Shashkov for
critical reading.
12. References
1.
2.
75
80
85
3.
4.
5.
6.
7.
8.
9.
10.
11.
90
12.
13.
14.
95
15.
100
16.
17.
18.
19.
45
Compound names used in the review:
2HOMe-THP
- 2-hydroxymethyltetrahydropyran
2-deoxy-eryPen
– 2-deoxy-erythropentose
Ara
– arabinose
DMSO
– dimethylsulphoxide
Gal
– galactose
GalNAc
- 2-acetamido-2-deoxygalactose
Glc
– glucose
GlcNAc
- 2-acetamido-2-deoxyglucose
Ery
– erythrose
Fuc
– fucose
Ido
– idose
IdopA2S
– 2-sulpho-iduronic acid
Lyx
Rib
TMS
Xyl
105
20.
21.
22.
23.
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Chemical Society Reviews, 2013, 0, 00–00 | 43
Philip Toukach (Ph.D. 2001, associate professor rank 2010) has been
Senior Scientist at Zelinsky Institute of Organic Chemistry (since 2005),
International Scientist of the Year (2004), Guest Scientist at Borstel
Biochemical Research Center (2005-2007) and German Cancer Research center
(2008-2011), Associate Professor at Moscow Academy of Fine Chemical
Technology (since 2008). His major scientific interests are carbohydrate
databases and NMR-based carbohydrate structure prediction. Further
information can be found at his web-site http://toukach.ru/nmr.htm
Valentine Ananikov (Ph.D. 1999; Habilitation 2003) was appointed
Professor and Laboratory Head at Zelinsky Institute of Organic Chemistry
(2005), Elected Member of Russian Academy of Sciences (2008) and
Professor of Chemistry Department of Moscow State University (2012). He
was a recipient of the Russian State Prize for Outstanding Achievements in
Science and Technology (2004), an Award of the Science Support Foundation
(2005), a Medal of the Russian Academy of Sciences (2000), Liebig Lecturer
by German Chemical Society (2010), and Balandin Prize (2010). International
Advisory Boards membership: Advanced Synthesis & Catalysis,
Organometallics and Chemistry An Asian Journal.
44 | Chemical Society Reviews, 2013, 0, 00–00
This journal is © The Royal Society of Chemistry 2013