Glycobiology vol. 21 no. 12 pp. 1541–1553, 2011
doi:10.1093/glycob/cwr036
Advance Access publication on March 24, 2011
REVIEW
Systems glycobiology: biochemical reaction networks
regulating glycan structure and function
Sriram Neelamegham1 and Gang Liu
Department of Chemical and Biological Engineering, and The NY State
Center for Excellence in Bioinformatics and Life Sciences, State University
of New York, Buffalo, NY 14260, USA
Received on November 18, 2010; revised on January 15, 2011; accepted on
March 18, 2011
There is a growing use of bioinformatics based methods in
the field of Glycobiology. These have been used largely to
curate glycan structures, organize array-based experimental data and display existing knowledge of glycosylationrelated pathways in silico. Although the cataloging of vast
amounts of data is beneficial, it is often a challenge to gain
meaningful mechanistic insight from this exercise alone.
The development of specific analysis tools to query the
database is necessary. If these queries can integrate existing knowledge of glycobiology, new insights may be
gained. Such queries that couple biochemical knowledge
and mathematics have been developed in the field of
Systems Biology. The current review summarizes the
current state of the art in the application of computational
modeling in the field of Glycobiology. It provides (i) an
overview of experimental and online resources that can be
used to construct glycosylation reaction networks, (ii)
mathematical methods to formulate the problem including
a description of ordinary differential equation and logicbased reaction networks, (iii) optimization techniques that
can be applied to fit experimental data for the purpose of
model reconstruction and for evaluating unknown model
parameters, (iv) post-simulation analysis methods that
yield experimentally testable hypotheses and (v) a
summary of available software tools that can be used by
non-specialists to perform many of the above functions.
Keywords: in silico simulation / leukocyte–endothelium
interaction / O-glycans / optimization / systems biology
Systems glycobiology
Glycosylation is a common type of post-translational modification. This results in the attachment of carbohydrates to
protein and lipid scaffolds. By some accounts, 50% of all
1
To whom correspondence should be addressed: Tel: +716-645-1200; Fax:
+716-645-3822; e-mail: [email protected]
proteins are glycosylated (Apweiler et al. 1999). Such glycans
participate in a variety of biological processes including
protein folding, cell growth and development, immunity,
anti-coagulation, microbial pathogenesis and cancer metastasis. Alteration of the normal glycosylation machinery can
result in a variety of diseases that are grouped under the
classification “congenital defects of glycosylation” (Freeze
2007; Jaeken and Matthijs 2007).
Although the conventional, reductionist approach of experimentation involves the study of individual proteins and
molecular interactions one-at-a-time, recent advances in experimental methods and knowledge of biochemical processes
enable the study of biological “systems” as a whole. Such
systems-level studies focus on the discovery of “emergent”
properties that arise as a result of multiple, complex molecular
interactions. These interactions are often depicted using biochemical reaction networks, as opposed to single reactions
alone. Both the application of conventional procedures and
newer high-throughput technologies enable the collection of
experimental data that are necessary for systems-level analysis. There is also a keen focus in this field on developing
appropriate mechanistic, quantitative models that can guide
the interpretation of such data. Together, the integration of
experiments and computational modeling has given rise to a
field of research that is termed “Systems Biology”.
Systems Biology approaches have been applied in studies of
metabolic pathways (Orth et al. 2010) and signal transduction
(Aldridge et al. 2006; Janes and Yaffe 2006). Such studies are
fueled by the generation of -omics-based experimental data in
the areas of Genomics, Proteomics, Metabolomics etc.
Corollaries to the Systems Biology concept have emerged in
recent years in other areas including Systems Chemistry that
deals with the emerging properties of interacting chemical
systems and networks, Systems Genetics that examines how
the presence of a variety of interacting genes and molecules
results in complex traits and Systems Physiology that integrates
knowledge of structure–function relationships at the cellular,
tissue and organ levels to explain the behavior of whole living
organism. The recent availability of advanced experimental
methodologies in the area of Glycomics and Glycobiology
promises that advances in the field of Systems Biology will
also impact studies of the Glycome—an emerging field that is
called Systems Glycobiology.
The current article attempts to classify research problems
in the field of Glycobiology that may be amenable to
systems-level analysis and to discuss experimental and
© The Author 2011. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected]
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S Neelamegham and G Liu
computational techniques that can aid such work. The case of
leukocyte adhesion to vascular endothelial cells is used as an
example in many sections since this is a well-studied and important biological interaction in the fields of Glycobiology and
Medicine. Here, leukocyte and endothelial adhesion molecules
belonging to the selectin family bind glycoprotein ligands, and
this initiates a cascade of events that eventually results in the
recruitment of leukocytes to sites of acute and chronic inflammation (McEver and Cummings 1997; Neelamegham 2004;
Sackstein 2009). An overarching goal is to provide background
information that may appeal both to glycobiologists interested
in the application of quantitative analysis and to computational
scientists interested in studying the Glycome.
Glycosylation reaction networks
The overall glycosylation process in mammalian cells is regulated by smaller networks of reactions that may be grouped
into three classes (Figure 1). (i) Metabolic reactions that result
in the formation of sugar nucleotides (uridine diphosphate
galactose, cytidine monophosphate sialic acid etc.). These
reactions, which take place in the cytoplasm and nucleus of
cells, involve various families of enzymes including kinases,
synthases and epimerases. Figure 2A provides a schematic that
gives an overview of this class of biochemical pathways. (ii)
Glycosylation reactions that mediate the addition of glycans to
proteins and lipids. Such reactions, which primarily occur in
the endoplasmic reticulum (ER) and Golgi compartments,
involve primarily the glycosyltransferases and also other
enzyme families like sulfotransferases. For this to occur, sugar
nucleotides generated in the metabolic reactions must be transported to the ER/Golgi. Together, these reactions result in the
construction of glycoproteins, glycosphingolipids, proteoglycans and glycosylphosphatidylinositol-linked protein anchors.
Figure 2B–D provides an overview of the reaction pathways
leading to the formation of O-glycans, N-glycans and glycolipids. Figure 2B shows the reactions that lead to the synthesis
of the eight core structures that are common to O-glycans,
labeled core-1 to core-8. It also shows one example of a reaction pathway that can lead to the formation of the sialyl
Lewis-X tetrasaccharide (sLeX) glycan on the mucin core-2
structure. Such sLeX glycans can participate as ligands for the
selectin family of adhesion molecules. This sLeX is defined as
the “system output” in the example discussed in later sections
of this review. Figure 2C shows that an array of high mannose,
hybrid and complex N-glycans can emerge from the combinatorial action of exoglycosidases, chain extending and chain terminating glycosyltransferases. Figure 2D provides an overview
of pathways leading to the formation of glycosphingolipids.
More comprehensive information on these and other pathways
that lead to cellular glycosylation can be found in textbooks in
the field (Varki et al. 2008) and also at the Kyoto Encyclopedia
of Genes and Genomes (KEGG) GLYCAN database (http
://www.genome.jp/kegg/glycan/; Hashimoto et al. 2006). (iii)
Once glycoproteins and glycolipids are formed, various transport mechanisms regulate the distribution of these glycoconjugates in cells, on the cell surface, nucleus and cytoplasm
(Figure 1). There also exist recycling/salvage reactions that
contribute to the synthesis of monosaccharides after the proteolysis of macromolecules.
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Besides the above three groups of reactions that regulate the
synthesis and distribution of glycans, functional reactions in
cells or at the cell surface regulate the effector functions of
glycans. These effector functions include, but are not limited
to, cell adhesion, signaling and apoptosis. Some glycans play
important roles in signaling, like members of the Notch family
(Jafar-Nejad et al. 2010), and this results in regulation of the
cellular transcriptome. Together these complex interactions
regulate cell function. In principle, it is possible to study each
of the modules described in this section as a whole or in part
individually, and then use systems-biology/multiscale
approaches to integrate the information quantitatively. Thus,
even though processes like glycoconjugate mass transport or
salvage can be studied one at a time, these individual steps can
also be integrated into a larger biosynthesis/network model.
Mathematical modeling of biochemical reaction networks
Development of mathematical models to describe glycosylation requires three essential steps (Figure 3). (i) “Biological
information gathering”: this involves the definition of essential
model components like enzymes, substrates and products.
This step catalogs all the constituents of the biochemical
network under study and their connectivity. It relies heavily
on existing knowledge of cell biology and biochemistry, and
analytical tools described below. (ii) “Model formulation”:
this defines the nature of the computer model. This formulation may be based on simple linear algebra and optimization
principles alone if we are interested primarily in the steady
state behavior of the system. It can incorporate ordinary differential equations (ODEs) or Boolean networks when time is a
variable. Depending on the nature of the model formulation
and the specific enzymatic/non-enzymatic processes, then, one
collates appropriate kinetic/thermodynamic/stochastic/optimization parameters associated with the system (e.g. Michaelis
constant KM, dissociation constant Kd and on/off rate constants kon/off ). (iii) “Simulation and post-simulation analysis”:
this is performed in order to simulate the experimental system
in silico (i.e. in the computer) and to determine unknown
model parameters based on fitting experimental data. Since
many different models may attempt to fit one experimental
data set and since each of these can yield large amounts of
time- and concentration-dependent data under varying knockout/chemical treatment conditions, visualization of multidimensional results is important. Thus, network analysis
strategies are applied to consolidate the findings emerging
from complex reaction network simulations and to generate
experimentally testable hypotheses. Wet-lab (experimental)
testing of hypotheses generated by dry-lab (computer) simulations is a critical step for model validation. This leads to the
iterative refinement of model structure and parameters. The
remaining sections of this manuscript describe each of these
steps in some detail.
Biological information gathering: experimental tools
and online resources
The formulation of a quantitative biochemical model is
initiated with the characterization of participating molecules in
Modeling glycosylation processes
Fig. 1. Systems-level view of glycosylation.
the network and the interaction between these components.
More specifically, this information includes (i) molecular
network topology in qualitative aspect and (ii) kinetic data that
provide estimates of model parameters. Often, this knowledge
is gleaned from a large-scale literature review of well-accepted
biological findings. In addition to this, in recent years, a series
of databases have appeared that provide leads for pathway construction by collating data related to the genome, proteome,
interactome and metabolome (reviewed in Ng et al. 2006).
Reaction networks resulting from this step may be described in
XML (eXtensible Markup Language) format, since an increasing number of mathematical models and analysis tools developed in recent years utilize this representation. These modeling
standards allow streamlined documentation and exchange of
model information among research groups. The Systems
Biology Markup Language (SBML; Hucka et al. 2003) and
the Cell Markup Language (CellML; Garny et al. 2008) are
two widely used formats for such representation of biochemical reaction networks. Graphical presentation of models using
System Biology Graphical Notation (SBGN; Le Novere et al.
2009), Molecular Interaction Map (MIM; Kohn et al. 2006) or
other tools can also be beneficial for the accurate transmission
of biological information. MIM diagrams have been used to
represent a wide range of molecular networks. SBGN contains
three levels of diagrams including process diagram, entity
relationships and activity flow diagram, and these are compatible with SBML. Presentation of glycosylation networks using
SBML notation has been initiated (Liu et al. 2008).
XML-based rules/schema to describe carbohydrate structures
in silico have also been defined by several groups (Kikuchi
et al. 2005; Sahoo et al. 2005; Herget et al. 2008). Thus,
attempts to merge developments in computation/systems
biology with experimental research in the field of glycobiology
are underway.
With regard to collating data that can be used for model
synthesis at the gene level, whereas most of the existing
databases are not specifically curated for studies related to the
glycome, databases like Gene Expression Omnibus (GEO;
Boyle 2005), ArrayExpress (Parkinson et al. 2007) and
CIBEX (Ikeo et al. 2003) do contain information relevant
to this field. In addition, the Consortium of Functional
Glycomics
(CFG;
www.functionalglycomics.org)
has
designed a custom Affymetrix array that has improved the
representation of glycosyltransferase genes and related downstream targets, compared with whole-genome microarrays
(Raman et al. 2005). This tool monitors the expression of
2000 human and mouse transcripts relevant to
Glycobiology. In addition to this, efforts have been
undertaken to apply quantitative real-time reverse
transcriptase-polymerase chain reaction (PCR) to monitor glycosyltransferases and related genes in both human (Marathe
et al. 2008; Ito et al. 2009) and mouse (Nairn et al. 2008)
systems. Upon comparing >700 genes using real-time PCR vs
microarray data, Nairn et al. (2008) report greater sensitivity
and dynamic range for their PCR-based approach, particularly
in the case of low-abundance glycan-related transcripts.
Overall, experimental tools are available to interrogate the
effect of system perturbation at the transcript level.
While gene expression measurements can be made rapidly,
the relationship between gene expression and protein
expression is typically non-linear. This is even more complicated in the case of Glycobiology, since glycosyltransferases
catalyze post-translational modifications. Thus, in addition to
the expression levels, quantitation of enzyme activity is
important for model construction. This can be performed for
various families of glycosyltransferases using an array of
carbohydrate acceptors (Taniguchi et al. 2002; Marathe et al.
2008). Data related to enzyme activity, including but not
limited to glycosylation-related processes, are also comprehensive catalogued in the BRENDA (www.brenda-enzymes.org/)
database based on surveying over 79,000 primary literature
(Chang et al. 2009). However, this database suffers from
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S Neelamegham and G Liu
Fig. 2. Overview of selected glycosylation reaction pathways. (A) Biosynthesis and interconversion of monosaccharides. The schematic illustrates biochemical
reactions leading to the formation of activated sugar nucleotides (UDP-Glc, UDP-Gal, UDP-GlcNAc, UDP-GalNAc, UDP-GlcA, UDP-Xyl, GDP-Man,
GDP-Fuc and cytidine monophosphate (CMP)-sialic acid [Neu5Ac and Neu5Gc]) when glucose is the primary energy source. Here, the monosaccharide is
metabolized by a series of kinase and epimerase reactions depicted by arrows to form various activated sugar nucleotides (shown in orange rectangle). Once
sugar nucleotides are formed in the cytosol, they are directed to the ER/golgi where glycosylation takes place. The sugar nucleotide composition of cells along
with the expression and activity of glycosyltransferases, together regulate the cellular glycan signature. Changes to other metabolic reactions like glycolysis
(which consumes Glc-6-P and provides phosphophenolpyruvate (PEP)), respiration (which provides ATP etc.) and salvage pathways (which breakdown
cell-surface glycoconjugates to regenerate monosaccharides) can also regulate the biochemical reaction rates. (B) O-Linked glycosylation. This is initiated by the
attachment of GalNAcα to Ser/Thr residues using enzymes belonging to the ppGalNAcT family. These complex sugars consist of three distinct regions: core,
backbone and non-reducing terminus. GlcNAc and Gal are key β-linked sugars found in the backbone region, whereas Galα, Fucα and NeuAcα2 are generally
located at the non-reducing terminus. Among the eight known core structures in O-glycans, the core-2 structure Galβ1 → 3(GlcNAcβ1 → 6)GalNAcα-Ser/Thr is
prominent in selectin ligands. The synthesis of sLeX (NeuAcα2,3Galβ1,4(Fucα1,3)GlcNAc), the prototypic selectin ligand, attached to a core-2 structure is
shown. (C) N-Linked glycosylation. In the ER, the dolichol oligosaccharide precursor composed of 14 monosaccharides is transferred to Asp residues on the
nascent protein. Trimming of the oligosaccharide by Glcase and α-mannosidase in the ER and Golgi results in high-mannose-type glycans. These can be further
diversified into hybrid (with at least one GlcNAc attached to the mannose core residues) and complex N-glycans (with GlcNAc antennae attached to mannose).
(D) Glycolipid synthesis. This proceeds when glucose or galactose attach to ceramide units to form glucosylceramides (GlcCers) or galactosylceramides
(GalCers). The number of variants of GalCers is limited. GlcCers are diversified by addition of a galactose and additional diversification that results in
Ganglio-series (with 1 or more sialic acids), neolacto-series (common in leukocytes) and their families of glycosylated lipids. Glc, glucose; Fruc, fructose; Gal,
galactose; GlcNAc, N-acetylglucosamine; GalNAc, N-acetylgalactosamine; GlcN, glucosamine; P, phosphate; Xyl, xylose; GlcA, glucuronic acid; PEP,
phosphoenolpyruvate; ATP, adenosine triphosphate; UDP, uridine diphosphate; GDP, guanosine diphosphate; CMP, cytidine monophosphate; OST,
oligosaccharyltransferase. See Varki et al. (2008) for more details on the reaction pathways.
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Modeling glycosylation processes
Fig. 3. Basic steps during model construction.
shortcomings of individual laboratories, since the units used in
publications and the experimental procedures do not follow a
uniform pattern. A second, but smaller, database that is geared
toward computer simulation is called SABIO-RK (System for
the Analysis of Biochemical Pathways - Reaction Kinetics;
Rojas et al. 2007). This information resource collects much of
its data from the KEGG database. Although this system has the
advantage in that its output is in SBML format, data related to
the field of Glycobiology is somewhat limited.
Besides gene and protein-level data, structural information
can form a key component for model construction. Both
advances in online tools and analytical methods enable this
approach (Raman et al. 2005; Aoki-Kinoshita 2008;
Mamitsuka 2008; Frank and Schloissnig 2010). In this regard,
repositories of carbohydrate structures have emerged in recent
years including the GlycosuiteDB (Cooper et al. 2003) and
GlycomeDB databases (Ranzinger et al. 2009). The latter
serves as a repository of glycan structure data collected from
existing databases including CarbBank, GLYCOSCIENCES.
de, CFG, KEGG and others. The KEGG GLYCAN (http
://www.genome.jp/kegg/glycan/) database has also manually
cataloged biochemical pathways relevant to glycosylation
(Hashimoto et al. 2006). Finally, efforts are underway to
extend this approach such that functional networks related to
glycans can be dynamically created (Hashimoto et al. 2010).
Analytical tool development for Glycomics research can
greatly benefit Systems Glycobiology. In this regard, although
traditional methods focus on using electrophoresis, chromatography and associated radioactivity-based assays, new families
of high-throughput technologies have been developed for
Glycomics. In particular, MALDI (matrix-assisted laser desorption/ionization), liquid chromatography-mass spectrometry
(MS) and variants of these methods are providing valuable
data on the sites of proteins that are glycosylated and the
profile of carbohydrates attached to specific proteins (Mechref
and Novotny 2009; North et al. 2009; Zaia 2009). Using a
variety of lectin-based purification steps, chemical modification protocols, exoglycosidase digestion methods and
isotope labeling strategies, advances are being made with the
goal of completely characterizing the site-specific nature of
glycosylation. A major challenge remains the limited quantitative data regarding glycosylation that is necessary in order
to account for glycan microheterogeneity. Another limitation
remains the lack of automated programs that can be used to
analyze MS data. Availability of more detailed information on
protein-specific glycan structures may enable systems-level
analysis that incorporates the stochastic nature of the glycan
biosynthesis pathways, and it may explain non-linearities
associated with glycan structure and function.
Other large-scale analytical technologies include microarraybased methods where either lectins, antibodies or carbohydrates are immobilized on substrates (reviewed by Paulson
et al. 2006; Hsu and Mahal 2009). Lectin microarrays consist
of dense spots of immobilized lectins. Fluorescent glycoproteins (Kuno et al. 2009) and cells (Pilobello et al. 2007) are
hybridized with these lectin spots and scanners are used to
monitor binding. Glycan structures associated with proteins/
cells are then inferred based on the known specificity of
lectins. As an alternative to lectins, some investigators have
immobilized carbohydrates on substrates since these can be
used to assay for glycan-binding proteins (Blixt et al. 2004;
Xia et al. 2005). In yet another variant of the same principle,
anti-glycoprotein antibodies have been immobilized on slides
to capture specific glycoproteins. Specific glycan structures on
the captured macromolecule are then assayed using fluorescent
lectins and anti-carbohydrate antibodies (Chen et al. 2007).
Such an approach where antibodies are used to capture glycoproteins onto substrates ( polystyrene beads) and fluorescent
anti-carbohydrate antibodies are used detect glycan structures
has also been extended to a flow cytometry format in order to
detect site-specific glycosylation (Jayakumar et al. 2009).
Model formulation: approaches for in silico simulation
Many different modeling approaches can be applied to study
glycosylation reaction networks. The choice of strategies is
driven by the amount of experimental data available and existing knowledge of biochemistry and also by the project goals
and available expertise (Figure 4A). ODE network models
can be simulated when rich experimental data sets and biochemical knowledge are available. Although this type of modeling is straightforward, a major challenge is that all necessary
rate constants might not be available in literature and this can
hinder mathematical model formulation. Boolean networks
are simulated in the absence of such detailed information. In
this case, the organization of the network is more important
compared with the kinetic details. This is suitable either when
there is insufficient information on overall network structure
and molecular mechanism or when insufficient kinetic and
temporal data exist. Statistical analysis is appropriate when
experimental data are available, but detailed biochemical
knowledge is lacking. This approach is particularly useful for
semi-quantitative grouping of related components in a biochemical reaction network. These three groups of modeling
approaches are described next.
Models based on a set of coupled ODE networks
In this approach, each equation represents a single biological
reaction or process. This type of representation is common in
biological literature, and it has been used to describe cellular
signaling (Aldridge et al. 2006) and glycosylation processes
(described in the next section). This approach is appropriate
(i) when there is only one independent variable (typically
time) and (ii) when the number of reactants is large.
Reactions written here typically emerge from the law of
mass action, which states that the rate of an elemental reaction
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S Neelamegham and G Liu
Fig. 4. Mathematical models. (A) Modeling approach selected depends on the volume of experimental data and biochemical knowledge available. This is a
qualitative, conceptual figure generated using MATLAB. (B) Most reactions in glycosylation systems fall into one of three categories.
(reaction with one transition state) is proportional to the frequency with which the reacting species collide. This, in turn,
depends on the concentration of reactants in the system.
Concentration terms are raised to the power of an arbitrary
reaction order, which typically corresponds to the molecularity of the reaction. Although three different types of reactions are common in the field of glycobiology (Figure 4B),
we discuss the case of the reversible biochemical reaction
with forward and reverse velocities vf and vr, and kinetic rate
constants kf and kr, below:
kf
C ðat time ¼ 0Þ ¼ C0
A þ B O A0 þ B0
kr
net velocity ðvÞ ¼ d½A
¼ vf vr ¼ kf ½A½B kr ½A0 ½B0 dt
The equilibrium constant (Keq) for this equation is Keq = kf/kr
= [A′][B′]/([A][B]). Extending this approach, the velocity of
the ith reaction (vi) follows:
vi ¼ vi;f vi;r ¼ ki;f
m
Y
mf
Cl il ki;r
l¼1
m
Y
mril
Cl
ð1Þ
l¼1
Here, Cl is the concentration of the lth species, and mfil mril
refers to the forward (reverse) reaction order of the ith reaction
with respect to the lth species. For a general system with m
substrates and n reactions, the above equation can be written
in matrix notations as:
dC
¼ aT v
dt
ð2Þ
Here, the vector v consists of n individual reaction velocities, C contains the concentrations of the m reactants
and the m × n matrix α T contains the stoichiometric coefficients for the reaction network. In general, α T describes the
connectivity between individual flux vectors or reaction velocities (v = v1, v2, …, vn) and the time derivative of species
concentration (C = C1, C2, …, Cm). This matrix is typically
a “sparse” matrix, i.e. it contains a large number of zeros.
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This is because in typical biological systems, each species/
reactant participates in only a few biochemical reactions.
Biological connectivity identified in α T is based on our
knowledge of biochemistry/biology and also experiments
that verify the existence or the absence of relevant reaction
components, like specific glycosyltransferases or substrates.
For typical biological reaction networks, the number of
reactions (n) exceeds the number of reactants (m), i.e. n >
m. The above equation is typically solved as an initial
value problem with initial conditions:
ð3Þ
In cases where there is more than one independent variable,
e.g. if spatial gradients in reactants or enzymes exist in
addition to time, this modeling approach is extended to
incorporate partial differential equations. In this regard,
although the distribution of glycosylating enzymes varies
within ER/Golgi compartment, glycosylation processes can
still be modeled using ODEs by simulating each Golgi or
ER compartment as a separate well-mixed reactor and by
arranging these compartments in series to simulate the
entire network process.
With regard to the number of reactants, a variety of glycan
structures may occur at a specific protein site if the number of
reactants is low. This phenomenon is termed “microheterogeneity”. Similarly, heterogeneity that results in the presence
or the absence of glycans at a given site is termed “macroheterogeneity”. Due to such heterogeneity, a single protein may
have different molecular weights and function. Although the
extent of heterogeneity can vary depending on the protein/cell
type and specific glycosylation site, the precise mechanism is
not well understood. In this regard, stochastic or probabilistic
models can be used to simulate the distribution of glycans at
a given site. In such computations, in addition to measuring
the mean glycan structure at the site, there is also interest in
generating fluctuation data that can explain heterogeneity.
The coupling of experiments with theory can reveal the
relative contributions of glycosyltransferase expression levels,
substrate
structure,
enzyme
catalysis
rates
and
Modeling glycosylation processes
glycosyltransferase enzyme competition for common substrates in regulating glycan heterogeneity.
Logic-based models and related network analysis
Logic-based models use “gates” and “truth tables” to specify
interactions between model species. In this case, the reaction
networks are represented by a directed graph, where the nodes
represent individual reactants/species and edges denote the
connectivity. The m species in this reaction network are
denoted Sj ( j = 1, …, m), and they are said to have a concentration Cj. In the case of Boolean (two-state) networks, Cj is 1
if it exists (ON) and 0 if it does not (OFF). Figure 5 presents
an example of such a network. Here, the conventional reaction
pathway shown in Figure 5A is represented in Boolean
network notation in Figure 5B. Boolean transfer functions
represented on each edge contains “gate” information. These
are typically the three logic operators “not”, “and” and “or”
or derivatives of these. The future state of the nodes (S*, at
time t + 1) is determined based on the current state (S, at time
t) and the Boolean transfer functions as shown in Figure 5C.
Due to the nature of the state diagram, Boolean networks typically achieve a stationary or recurring state that are together
referred to as “dynamic attractors”. This is illustrated in
Figure 5D, where following an increase at intermediate times,
S4 settles to the basal level.
Although Boolean network models are straightforward to
simulate, they provide only limited information regarding
network dynamics when all species are updated synchronously at each time point, as in Figure 5. It also does not
allow simulation of processes that may proceed at different
time scales, e.g. changes in gene expression and glycan synthesis. In order to better understand the dynamics of the
network, thus various strategies have been developed to diversify the network output. The goal of this exercise is to obtain
an understanding of the average behavior of each model
element. Strategies implement to achieve this end include the
updating of node concentrations asynchronously, i.e. each
node is updated either in a random sequence or at selected
time intervals. In addition, variants of the classical Boolean
network have appeared like the threshold Boolean network
and piecewise linear systems that allow definition of more
complex logic operators (Albert and Wang 2009). In addition,
multistate and fuzzy logic models have emerged that allow
Fig. 5. Boolean network. (A) Conventional representation of a small reaction
system. (B) Representation of the same system as in (A) using logic gates.
(C) Statements derived from the logic-gate diagram in (B). (D) Simulation
of the network described in (C) using synchronous updating of species
concentration. As seen, while S1 is available initially, it is suppressed by the
formation of S4. S4 subsequently decreases to basal levels at time = 5.
additional states to be populated, in addition to the ON/OFF
(1/0) state (Morris et al. 2010). By incorporating these concepts, logic-based models aim to generate temporal behavior
without detailed kinetic information. Logic-based models
have found wide application in systems describing regulatory
networks and signaling cascades. The application of this
approach to studies of glycosylation pathways is anticipated.
Statistical analysis methods
“Data-driven models” constitute a collection of statistical
tools that enable analysis of experimental data collected using
high-throughput proteomic methods. The advantage of this
approach is that models can be established using this
approach, even when mechanistic knowledge of a particular
pathway is sparse. Many of the modeling concepts used in
this method are analogous to techniques previously developed
for analysis of DNA microarray data (Janes and Yaffe 2006).
This includes techniques like hierarchical clustering, principal
component analysis and partial least-square methods. In
addition to analyzing raw experimental data these same techniques can also be applied to consolidate the findings emerging from in silico simulations of glycosylation reaction
networks.
Prior models of glycosylation reaction networks
Attempts have been initiated to create computational models
that can resolve the complex nature of the glycosylation processes. The number of such approaches is few compared with
other fields that study cell signaling or metabolic pathways.
Most of these models focus on N-linked glycosylation
(Shelikoff et al. 1996; Umana and Bailey 1997; Krambeck
and Betenbaugh 2005; Hossler et al. 2007; Lau et al. 2007).
The model by Umana and Bailey (1997) examines N-linked
glycosylation based on experimentally determined rate constants, but it does not attempt to relate model output with
experimentally determined glycan distribution. Krambeck and
Betenbaugh (2005) make this comparison with experimental
data. Their most recent effort (Krambeck et al. 2009) attempts
to match matrix-assisted laser desorption/ionization time-offlight (MALDI-TOF) mass spectrometer (MS) data of normal
and leukemic monocytes by varying the rate constants of 19
enzymes that participate in N-glycan biosynthesis. In another
extension of this concept, Hossler et al. (2007) simulated
N-glycan biosynthesis pathways in two reactor configurations
that simulate either glycoprotein movement across the Golgi
(four continuous stirred-tank reactors in series) or cisternal
maturation and vesicular transport (four plug flow reactors in
series). These investigators also define hypothetical conditions
where glycan micro-heterogeneity may be minimized. In a
rigorous investigation, Lau et al. (2007) combine experiments
with theory to demonstrate that the production of branched
tri- and tetra-antennary N-glycans is ultrasensitive to hexosamine flux. By integrating a set of component models during
analysis, these authors also demonstrate that the number and
degree of branched N-glycans regulate cell-surface glycoprotein levels, cell growth and arrest function. These results
have implications for salvage pathways and disorders that can
be treated through salvage. Other attempts to apply
1547
S Neelamegham and G Liu
mathematical modeling in the field of glycobiology focus on
a limited set of reactions and not entire reaction networks
(Monica et al. 1997; Bieberich and Yu 1999; Gerken 2004).
While these previous papers focus on N-glycan biosynthesis, we developed the first reaction network for modeling
O-linked glycosylation (Liu et al. 2008; Figure 6). The goal of
this study was to determine: (i) the rate limiting steps regulating the formation of O-glycans on P-selectin glycoprotein
ligand (PSGL)-1 since these carbohydrates play an important
role in mediating selectin-mediated leukocyte-endothelium
adhesion during inflammation; and (ii) the extent to which
computer simulations of O-glycosylation networks can fit
experimentally derived glycan distribution data. To test this
possibility, we gleaned experimental data on the distribution of
O-glycans of PSGL-1 from literature (Aeed et al. 1998). By
varying the rate constants and reaction pathway structure in the
in silico O-glycosylation model, we then attempts to match
the output of the computer model (Liu et al. 2008) with that of
the measured experimental data (Aeed et al. 1998). The
primary system output of this reaction network is the sLeX
glycan (shown in Figure 6). The model parameters include five
glycosyltransferase lumped rate constants, ki (these are the
fitted unknowns). The in silico estimates of glycosyltransferase
rate constants (Liu et al. 2008) were then compared with
wet-lab experiments that measured these same enzyme activities (Marathe et al. 2008), and this confirmed that the in silico
modeling approach was appropriate. For illustrative purposes,
this example is further elaborated upon in the remaining portions of this manuscript.
Simulation and optimization: reaction rate constants
and model structure
Whether Glycomics data come from conventional experiments
or from high-throughput datasets, fitting model parameters to
experimental data is a challenge (Banga 2008). In this regard,
there are two problems here that are not clearly separable:
(i) finding a suitable model structure that is appropriate for the
experiment; and (ii) determining model parameters that fit this
“suitable model”. We consider the second problem first since
this is more tractable.
Global and local optimization to define reaction rate
constants
The goal here is to minimize the objective or cost function
f(k), which is a measure of the error between model simulation results (“dry data”) and biological experimental data
(“wet data”). In our example, simulation and experimental
data represent glycan distribution data (Figure 6), the difference between which is minimized by varying the rate constants ki:
argminki [½0;1 ð f ðkÞÞ or argminki [½0;1 j simulation result½k
experiment data½k j
ð4Þ
Due to the nature of the reactions (Figure 4B), the optimization
problem
is
inherently
non-linear,
with
possible
1548
differential-algebraic constraints. Solution can be attempted
using either local or global optimization methods. Local
methods determine solutions in the proximity of the starting
guess. Global search algorithms span the entire parameter
space and these are suitable when multiple solutions may exist.
Due to this nature, global optimization methods are computationally expensive, and they converge more slowly compared
with local optimization methods. Determination of the ideal
solution cannot be guaranteed using global optimization routines. Taking this into consideration, our approach is to
perform global optimization (genetic algorithm) first to find
the neighborhood of the solution, and then to use local minimization (quasi-Newton method) to converge to the precise
solution (Liu et al. 2008). This methodology is termed
“hybrid-genetic algorithm”.
Genetic algorithm is a global optimization procedure that is
inspired by Darwinian evolution. It includes many features
that are common to natural inheritance like cross-over which
is expected when there is genetic recombination, mutations
that can occur naturally with some frequency and selection
that aims to preserve the fittest species. In these calculations,
in the first step, several sets of “parent” rate constants are
generated at random, such that each set satisfies the constraints of the solution space. In our previous work that had
five unknown rate constants (Liu et al. 2008), thus we generated 50 sets of “parent rate constants”. Each of these sets is
denoted by the array k, and it represents an initial guess for
the solution of the optimization problem. The fitness of each
of these “parents” is evaluated using the objective/cost function [Eq. (4)]. In the next iteration, although a few (say four)
of the fittest or “elite” parents with the smallest objective
function are preserved or “selected”, the remaining k arrays
are regenerated by either “crossing/mixing” rate constants
among the parent sets and/or by generating additional diversity by randomly perturbing or “mutating” selected constants.
The fitness of the new generation is then evaluated and the
selection, cross-over and mutation steps are repeated again to
refine the “elite” parents. This procedure is repeated a
number of times. In general, the “elite” parents converge
quite rapidly in the first few iterations, whereas the subsequent refinement of the solution proceeds quite slowly.
Besides genetic algorithms, other techniques that can be used
for solution of the global optimization problem include simulated annealing (Wolkenhauer 2007; Song et al. 2010) and
other evolutionary programming methods (Moles et al. 2003;
Patil et al. 2005).
Once we identify the vicinity of the global solution
space, local optimization strategies can be used to rapidly
refine the solution. These methods typically focus on the
gradient of the function (f(k)) in the vicinity of the starting
guess. Based on the gradient, the calculation steps the rate
constant k in order to minimize the objective function until
the convergence criteria are met. A common local optimizer
is the iterative Newton method. According to this, if the
function f(k) is twice differentiable, the sequence of k can
be refined by:
k ðnþ1Þ ¼ k ðnÞ f 0 ðk ðnÞ Þ
f 00 ðk ðnÞ Þ
Modeling glycosylation processes
Fig. 6. O-Glycosylation reaction network. (A) The single compartment O-linked glycosylation model for the synthesis of sLeX-type structures in human
leukocyte. The core-2 trisaccharide (Galβ1,3(GlcNAcβ1,6)GalNAcα-, species S1) is input into a well-mixed reactor that contains five enzyme activities labeled
E1–5 (corresponding to GalT, two SialylTs, GlcNAcT and FucT). The rate constant values of these five rate constants are the unknowns. sLeX-type structures are
generated on species S14 and S17 (red box). Glycan distribution generated by computer modeling is compared with experimental data by optimizing both model
structure and enzyme rate constants (E1–5). (B) Eight hundred thirty-seven subset models were generated by deleting one or more species and associated reactions
in the master pathway shown in (A). Hybrid-genetic algorithm was used to fit each of these models. Superior models have smaller fitness functions. The master
pathway containing all reactions does not converge to experimental data as well as many of the subset models.
The above scheme can be generalized in higher order
matrix form by writing
kðnþ1Þ ¼ kðnÞ Hðk ðnÞ Þ1 rf ðk ðnÞ Þ where Hij ¼
@2f
ð5Þ
@xi @xj
Other variants of local optimization routines exist including
the quasi-Newton method, conjugate gradient method and
steepest descent method (Ashyraliyev et al. 2008). The
precise choice of local optimization programs used depends
on the nature of the problem.
Subset modeling to define model structure
The uncertainty of glycosylation models not only lies in the
large parameter space, but also in the variation of the structure
of the kinetic model. Estimation of network structure is
termed “model reconstruction”. A heuristic approach to optimizing the network involves identifying all possible models
fitting the experimental data and then extract the common features among the best data-fitted networks. This concept has
been applied in our study of O-linked glycosylation (Liu et al.
2008). Here, an algorithm is proposed to generate a number
of potential reaction networks using a concept called “subset
modeling”. In this approach, individual species and associated
reactions in the master pathway (which contains all possible
reactions and species) are deleted sequentially. Either one or
more than one species is deleted for a single simulation to
generate subsets of the master pathway. The hybrid-genetic
algorithm method described in the preceding section is then
applied to fit experimental data to the model. The suitability
of the subset models is evaluated based on its ability to
minimize the f(k). Such analysis results in the ranking of
“subset models” based on fitness function. Fitness function
for 837 subset models is shown in Figure 6B. As seen, the
fitness function for the various models varies over a wide
range. Also, fitness of the master pathway which contains all
possible biochemical reactions is poor compared with the
subset pathways that contain only a fraction of all possible
reactions.
Clustering analysis and principal component analysis can
be performed to sets of pathways which display fitness function values in a narrow range (Liu et al. 2008). This can be
used to quantify the relative contributions of specific network
components to system output.
Post-simulation analysis: hypothesis generation
The ultimate goal of simulation programs is to define the
“design principles” of nature. However, with the large number
of calculations that are possible and the number of model
equations and parameters, it is challenging to define intrinsic
and dynamic network properties. Post-simulation analysis
methods like sensitivity analysis and bifurcation analysis are
thus necessary to define the emergent system properties
including their robustness, fragility, oscillation, bistability and
modularity. Such post-simulation analysis methods can also
aid the generation of experimental hypothesis and guide
model validation. In this regard, robustness measures the
ability of a system to maintain cellular function at a given
level even in the face of perturbation and evolution (Kitano
2004; Stelling et al. 2004). Oscillation describes the ability of
a system to swing between two equilibrium states or fluctuate
around a particular value (Reinke and Gatfield 2006; Pigolotti
et al. 2007). Bistability refers to the ability of living cells to
move from one state to another abruptly in a switch-like
manner (Ferrell 2002; Dubnau and Losick 2006; Lau et al.
2007). System network modularity describes the ability of a
module or set of biochemical reactions to function as one unit
irrespective of the external connections (Sauro 2008; Kim
et al. 2009). Selected post-simulation analysis methods are
briefly discussed next.
Sensitivity analysis
Sensitivity analysis, also called parametric sensitivity analysis,
is a perturbation method that quantifies the changes in system
output in response to a small change in system parameter.
System parameter defined here cannot only include the individual reaction rate constants or other kinetic coefficient such
as Vm and Km, but they may also include pathway structure
1549
S Neelamegham and G Liu
and initial concentrations of reacting molecules. System
output includes individual species concentration, reaction velocity or functions of interest, e.g. biological oscillation period
and amplitude. In the case of our simulations (Liu et al.
2008), we define the sensitivity coefficient based on the
glycan sLeX which we define to be the system output. The
system parameter considered was the glycosyltransferase rate
constant, ki, i.e. we evaluate ∂[sLeX]/∂ki. Normalizing this
coefficient is appropriate when comparing the large numbers
of parameter sensitivities and for the identification of prominent factors in a complex parameter space. Thus, the scaled
sensitivity coefficient is defined as:
Wij ¼
ki @½sLeX ½sLeX @ki
ð6Þ
Among the methodologies applied to evaluate sensitivity
coefficients, the simplest one is the finite difference method
(Hornberg et al. 2005; Liu et al. 2005; Wang et al. 2008),
which is used to quantify local sensitivities. Here, the
response of system output is simulated by manually varying
the interested parameter within a small range while holding
other parameters at a fixed value. The advantage of this
approach is that no other complicated sensitivity equations are
required. Another common method to evaluate local sensitivity coefficients is called the “direct differential method”
(Liu et al. 2005). The sensitivity coefficients here can be
described in terms of sensitivity equations resulting from the
differentiation of kinetic ODEs with respect to the system parameters. In this case, sensitivity coefficients are obtained, by
simultaneously solving both the sensitivity and kinetic ODEs
(Liu et al. 2005). Although the above methods are
conceptually straightforward, these techniques can become
computationally expensive with increasing the size of the
reaction network and the number of system parameters.
Therefore, adjoint methods (Cao et al. 2003) or Greens function methods (Hwang et al. 1978; Nikolaev et al. 2007) have
been applied to reduce computation time. These methods
involve solution of the adjoint sensitivity ODE or Greens
function equation associated with the kinetic equation. In
comparison with the direct methods, the latter techniques are
better suited for cases where the sensitivities of complex
system variables have to be evaluated with respect to all
system parameters (Rabitz et al. 1983).
Besides evaluating the effect of system perturbation, sensitivity analysis has also been widely used to quantify the
robustness of complex biological systems. Parameters and
components that are very sensitive to parametric variations
can introduce fragility into the system and typically these are
not natural properties of the biological system. Although
robustness evaluates the overall response of network to perturbation, modularity involves similar analysis of small sections
of the larger networks. Sensitivity analysis applied to these
modules combined with flux analysis can define non-essential
reaction (i.e. reaction with both smaller flux and sensitivity)
in a system (Liu et al. 2005). Deletion of these non-essential
reactions that only display weak effects on system output
enables model reduction. Simplified models emerging from
1550
such analysis reveal the “design principles” of biochemical
reaction networks.
Bifurcation analysis
Although sensitivity analysis offers quantitative insight
regarding the dependency of system dynamics on parameters,
bifurcation analysis applied on ODE network models is more
focused on qualitatively understanding how the system steady
states are affected by system parameters. The states of the biological systems can be stable, unstable or oscillatory. In the
parameter space, the point at which the system states shift
from one category to another is defined as the “bifurcation
point”. At bifurcation points, where the network undergoes a
qualitative change, a stable steady state solution may transit to
an unstable state or vice versa. During such analysis, bifurcation diagrams display the equilibrium or periodic states of a
system as a function of the bifurcation parameter. Four
common types of local bifurcations defined in such analysis
include saddle-node, transcritical, pitchfork and hopf bifurcations. Among these, saddle-node and hopf bifurcations are
common in studies involving cell signaling (Xiong and Ferrell
2003; Bagci et al. 2006), cell cycle regulation (Tyson et al.
2003) and gene regulation networks (Ozbudak et al. 2004).
Detailed bifurcation analysis of glycosylation pathways has
not been performed thus far. However, based on similar analysis performed for cell signaling pathways like the mitogenactivated protein kinase (MAP-kinase) signaling network
(Bhalla et al. 2002; Angeli et al. 2004; Markevich et al.
2004), one would expect that the application of the
Michaelis–Menten equation, the presence of non-linearities
due to a large number of reactants and products, positive and/
or double-negative feedback loops in glycosylation pathways
may lead to bistability in at least some reaction pathways. As
shown previously for the MAP-kinase pathway (Qiao et al.
2007), models at different regions of the parameters space
may display oscillation and bistability behavior in non-linear
systems.
Software resources
With the maturation of the field of Systems Biology, detailed
development of simulation code is not necessary in most
instances. This is because, there are currently well over a 100
software packages (listed at www.sbml.org) that can be used
to perform most simulation and post-simulation analysis.
Many of these programs focus on the simulation and analysis
of ODE reaction networks, for general purpose or specialized
functions. E-cell (Tomita et al. 1999), Copasi (Hoops et al.
2006), Virtual Cell (Schaff and Loew 1999) and Cell
Designer (Funahashi et al. 2008) provide a variety of functions including friendly user interfaces for model input, parameter estimation, model simulation and analysis. They may
also offer the capability of other functions such as stochastic
simulation or partial differentiation equation solvers. SBML
editor (Rodriguez et al. 2007) provides functions for input
and editing of SBML files directly in a standalone package.
IBRENA (Liu and Neelamegham 2008) provides multiple
model analysis techniques including both forward and adjoint
sensitivity analysis methods and principal component
Modeling glycosylation processes
analysis. SBML-SAT (Zi and Klipp 2006) offers several
global sensitivity analysis algorithms and robustness analysis.
XPP-AUTO (Ermentrout 2002) and bifurcation discovery tool
(Chickarmane et al. 2005) can be used for bifurcation analysis
of ODE systems.
Conclusion
The advancement of analytical tools in the field of Glycomics
is providing new opportunities for the integration of experiments with computer modeling. Such systems-level coupling
of experiments with theory can reveal the design principles
and emergent properties of glycosylation systems. They can
help establish novel quantitative and mechanistic links
between gene expression, protein expression, enzyme activity,
carbohydrate structure and glycoconjugate function. Beyond
uncovering novel Biochemistry and explaining previous
experimental/natural observations in quantitative detail, predictions on the possible outcomes of system perturbation on
cell function are also a likely outcome, and this can have
clinical significance.
Funding
This work was supported by NIH (HL63014) and a grant
from the NY State Stem Cell Foundation.
Conflict of interest
None declared.
Abbreviation
ER, endoplasmic reticulum; KEGG, Kyoto Encyclopedia of
Genes and Genomes; MALDI-TOF, matrix-assisted laser desorption/ionization-time-of-flight; MAP, mitogen-activated
protein; MIM, Molecular Interaction Map; MS, mass spectrometry; ODE, ordinary differential equation; PCR, polymerase chain reaction; PSGL, P-selectin glycoprotein ligand;
SBGN, System Biology Graphical Notation; SBML, Systems
Biology Markup Language; sLeX, sialyl Lewis-X; XML,
eXtensible Markup Language.
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