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Entropy-Enthalpy
Compensation: Role and
Ramifications in Biomolecular
Ligand Recognition and Design
John D. Chodera1 and David L. Mobley2
1
Computational Biology Center, Memorial Sloan-Kettering Cancer Center,
New York, New York 10065; email: [email protected]
2
Department of Chemistry and Pharmaceutical Sciences, University of California, Irvine,
California 92697; email: [email protected]
Annu. Rev. Biophys. 2013. 42:121–42
Keywords
The Annual Review of Biophysics is online at
biophys.annualreviews.org
entropy-enthalpy compensation, isothermal titration calorimetry,
small-molecule ligand engineering
This article’s doi:
10.1146/annurev-biophys-083012-130318
c 2013 by Annual Reviews.
Copyright ⃝
All rights reserved
Abstract
Recent calorimetric studies of interactions between small molecules and
biomolecular targets have generated renewed interest in the phenomenon
of entropy-enthalpy compensation. In these studies, entropic and enthalpic
contributions to binding are observed to vary substantially and in an opposing manner as the ligand or protein is modified, whereas the binding free
energy varies little. In severe examples, engineered enthalpic gains can lead
to completely compensating entropic penalties, frustrating ligand design.
Here, we examine the evidence for compensation, as well as its potential
origins, prevalence, severity, and ramifications for ligand engineering. We
find the evidence for severe compensation to be weak in light of the large
magnitude of and correlation between errors in experimental measurements
of entropic and enthalpic contributions to binding, though a limited form of
compensation may be common. Given the difficulty of predicting or measuring entropic and enthalpic changes to useful precision, or using this information in design, we recommend ligand engineering efforts instead focus on
computational and experimental methodologies to directly assess changes in
binding free energy.
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Contents
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INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ENTROPY-ENTHALPY COMPENSATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
EXPERIMENTAL EVIDENCE FOR COMPENSATION . . . . . . . . . . . . . . . . . . . . . . . .
Entropy-Enthalpy Compensation Appears in Many
Thermodynamic Phenomena. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calorimetric Studies Show Apparent Evidence of Compensation
in Ligand Binding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CRITICAL EXAMINATION OF EXPERIMENTAL EVIDENCE . . . . . . . . . . . . . . . .
ITC Measurements Can Have Large, Underreported Errors in !H and T!S . . . . . .
Correlated Errors in !H and T!S Can Produce Apparent Compensation . . . . . . . . .
A Window Effect Restricting the Range of !G Can Cause
Apparent Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Choice of Standard State Can Alter Entropy-Enthalpy Decomposition . . . . . . . . . . . .
PHYSICAL ORIGIN OF COMPENSATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solvent Reorganization May Be a Ubiquitous Source of Compensation . . . . . . . . . . . .
Conformational Restriction of Bound States Is Not Universally Compensating . . . .
Receptor Flexibility May Be a Source of Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Decomposition of the Free Energy Is Not Unique . . . . . . . . . . . . . . . . . . . . . . . . . . .
RAMIFICATIONS FOR LIGAND ENGINEERING . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Making Inferences About Driving Forces of Binding Can Be Difficult . . . . . . . . . . . . .
True Compensation Can Frustrate Interpretation
of Thermodynamic Signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Designing for Enthalpic Improvements Has Limited Utility . . . . . . . . . . . . . . . . . . . . . .
Designing for Improvements in Affinity Directly Is Likely
To Be More Productive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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124
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127
129
130
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136
137
INTRODUCTION
Entropy-enthalpy
compensation:
the observation that
changes in entropic
and enthalpic
contributions to free
energies appear to
oppose each other
122
In recent years, numerous studies of protein-ligand association invoke some form of entropyenthalpy compensation to explain the observed thermodynamic partitioning of binding free energy
between entropic and enthalpic components (3, 9, 18, 29, 31, 49, 52, 58, 77, 91, 109). A recent metaanalysis of the binding thermodynamics of an aggregated set of ∼100 protein-ligand complexes
selected from the BindingDB database (62), a database of binding data extracted from the literature,
concluded that compensation is “clearly evidenced” (81). Several groups have reported a severe
form of compensation, in which small ligand modifications (such as the introduction of a hydrogen
bond partner) result in a favorable enthalpic gain that is completely offset by an equivalent loss in
entropy, resulting in no net gain in affinity (9, 58, 96). In addition, drug resistance mutations can
apparently cause large, nearly compensatory changes in the enthalpies and entropies of inhibitor
binding, suggesting important changes in the mechanism of ligand recognition (49). In light of
such observations, it has been proposed that entropy-enthalpy compensation should be a major
concern during lead optimization in drug discovery (27, 28, 34, 57, 58, 80, 114).
A pervasive, severe form of entropy-enthalpy compensation would pose obvious problems in
the engineering of high-affinity ligands (34, 80). Complete compensation would mean that modifications made with the intent of improving the enthalpy of interaction (such as the introduction
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of a hydrogen bond donor) would be counterbalanced by unfavorable entropic contributions,
leading to no net gain in affinity. Complete compensation would also imply that modifications
made with the intent of reducing unfavorable entropic contributions to binding (such as the removal of rotatable bonds or the addition of internal ligand constraints) would lead to equivalent
enthalpic penalties, again resulting in no net gain in affinity. Obvious questions arise: Is compensation a real phenomenon? If so, how pervasive is it? And how can we know in advance which
ligands or scaffolds will be difficult to optimize as a result?
Here, we review the concept of entropy-enthalpy compensation and critically evaluate experimental evidence for the existence of this phenomenon, discussing possible alternative explanations.
We also highlight proposed physical mechanisms for compensation and conclude by discussing
implications of this work for rational ligand design.
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ENTROPY-ENTHALPY COMPENSATION
The Gibbs free energy change,1 !G, of a ligand binding reaction can be written as
!G = !H − T!S,
1.
where !H denotes the enthalpic contribution and −T!S the corresponding entropic contribution
to binding. In thermodynamic terms, the enthalpic component quantifies the change in heat
associated with binding, and the entropic component quantifies the change in disorder of the
overall system (including the ligand, receptor, and surrounding solvent).
In ligand binding, the term entropy-enthalpy compensation generally means that a ligand
modification results in a change in the enthalpic contribution to binding, !!H ≡ !H 2 − !H 1 ,
which is partially or fully offset by a similar change in the entropic component of binding, T!!S ≡
(T!S2 ) − (T!S1 ). This implies that !!H and T!!S share the same sign if compensation occurs,
and for a strong form of compensation in which the net change in binding affinity !!G ≈ 0, we
must have !!H ≈ T!!S.
In the literature, evidence of compensation is often presented in the form of a graph in which
T!S is plotted against !H and fit with a linear regression (as in Figure 3b), often with a slope
near unity. Alternatively, the graph may depict !S (rather than T!S) plotted against !H, with
the slope of linear regression—termed the compensation temperature— often ascribed physical
meaning (54, 63, 87).
In the discussion of evidence for compensation, numerous questions have been raised: What
is the origin of this phenomenon? Is this a universal phenomenon in thermodynamics? In ligand
binding? If compensation is not universal, does its appearance in a congeneric series provide some
form of “extrathermodynamic information” about the system that could be exploited? Or is there
a more mundane explanation for why we often see this correlation between enthalpic and entropic
contributions to binding? We attempt to address some of the most provocative aspects of these
questions in the course of this review.
EXPERIMENTAL EVIDENCE FOR COMPENSATION
We begin by reviewing experimental evidence supporting the notion that entropy-enthalpy compensation exists, is pervasive, and can be severe. As many reviews have already been devoted to
this topic (4, 15, 16, 22, 24, 25, 32, 36, 54, 61, 63, 67, 74, 87, 94), we restrict ourselves to a
brief review of experimental evidence for compensation in general before focusing on evidence of
compensation specifically in protein-ligand binding.
1
We refer to standard state quantities (5, 38, 39, 119) throughout, omitting the ◦ superscript for simplicity.
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a
b
c
150
∆G
5
10
kcal mol–1
kcal mol–1
∆H
3
2
1
50
∆H
kcal mol–1
100
4
T∆S
∆G
–10
∆H
T∆S
∆G
0
T∆S
0
–20
0
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0
50
100
Temperature (°C)
–50
20
40
60
80
Temperature (°C)
20
40
60
80
Temperature (°C)
Figure 1
Entropy-enthalpy compensation as a general phenomenon in thermodynamics. Three examples of compensating entropic and
enthalpic contributions to the free energy as a function of temperature in general thermodynamic phenomena. The free energy (!G) of
the process as a function of temperature is shown, along with enthalpic (!H) and entropic (T!S) contributions. (a) Transfer of
neopentane from its neat phase to water (data from figure 3 of Reference 59), (b) myoglobin unfolding (data from table 2 of Reference
65), and (c) protein-protein association (data from figure 3b of Reference 15). In all three cases, !H and T!S change substantially
whereas !G remains almost constant, suggesting substantial entropy-enthalpy compensation.
Entropy-Enthalpy Compensation Appears in Many
Thermodynamic Phenomena
Heat capacity: the
quantity of energy
required to heat a
system to achieve a
fixed increase in
temperature
Thermodynamic
signature: the free
energy of a reaction
along with its enthalpic
(!H) and entropic
(T!S) components
Association constant
(Ka ): for an
equilibrium
two-component
binding reaction
between protein P and
ligand L, Ka =
[PL]/[P][L]
124
Many experiments suggest the existence of a weak form of entropy-enthalpy compensation in
response to the variation of a thermodynamic parameter, such as temperature or pressure. For
example, in the transfer of neopentane from its neat phase to water (depicted in Figure 1a),
the enthalpic and entropic components vary over a large range with temperature but appear to
compensate so that the overall free energy of transfer varies by much less over the same temperature
window (59). Similarly, the unfolding of myoglobin in water (Figure 1b) is accompanied by large
changes in the entropic and enthalpic components but small changes in the overall free energy
of unfolding over a wide range of experimental temperatures (65). Protein-protein association
(Figure 1c) also often demonstrates similar behavior with regard to temperature (15).
Because entropy-enthalpy compensation appears in so many different contexts, it has been
proposed by some to be a ubiquitous thermodynamic phenomenon (22, 63). Although a number
of critical reviews have cautioned that the relatively narrow temperature range in which this
behavior is observed can lead to misleading conclusions about the significance of the observed
correlation between enthalpy and entropy (16, 23, 54, 67), the general consensus is that this form of
compensation—in which entropy and enthalpy changes oppose each other in response to changes
in temperature, sometimes called thermodynamic homeostasis—can be a simple consequence of
processes that possess a finite heat capacity !c p (14). Ironically, it is the universality of this form of
compensation that limits its utility, since different classes of interactions cannot be distinguished
on the basis of their thermodynamic signatures alone (15).
Calorimetric Studies Show Apparent Evidence of Compensation
in Ligand Binding
In principle, entropic and enthalpic contributions to ligand binding could be extracted from a
van’t Hoff plot of ln Ka (where Ka is the association constant) as a function of temperature, but
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a
HO
O
O
O
NH
N
NH
O
O
N
R
OH
b
S
H2NO2S
Y
T∆S
–S–CH3
–SO2CH3
–14.87(9)
–14.6(2)
–8.2(2)
–12.1(6)
–6.67(9)
–2.5(2)
–H
–Et
–n-Bu
∆G
∆H
T∆S
–6.35(5)
–6.07(5)
–6.26(5)
–4.5(1)
–3.3(1)
–2.4(1)
1.8(1)
2.7(2)
3.9(2)
X
X
H2NO2S
kcal mol–1
∆H
R group
Cl–
N
c
∆G
CH3
N
R
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N
H
CH3
R group
X
Y
∆∆G
∆∆H
N
NH
1.1(2)
4.2(4)
T∆∆S
3.1(4)
Y
Figure 2
Examples of severe compensation reported in the calorimetry literature. Several cases are shown in which ligand modifications lead to
large changes in the enthalpic and entropic contributions to binding whereas the overall binding free energy remains essentially
unchanged. (a) Severe compensation in HIV-1 protease inhibitors (data from table 1 of Reference 58), (b) para-substituted
benzamidinium trypsin inhibitors binding to trypsin (data from table 1 of Reference 96), and (c) nonpolar ring expansions in
arylsulfonamide trypsin inhibitors (data from table S3 of Reference 91). Quantities in parentheses denote one standard error of least
significant digit.
the challenging nature of these studies has prompted interest in alternative approaches. A van’t
Hoff analysis requires multiple measurements across a wide range of temperatures, which can be
time-consuming and costly and can present technical challenges in data analysis (102). In contrast,
the widespread availability of sensitive modern microcalorimeters has made isothermal titration
calorimetry (ITC) an attractive approach for the study of binding thermodynamics (73, 115). A
single ITC experiment can provide both Ka and !H (and hence also !G and T!S) from a single
experiment (112). As of this writing, BindingDB (62) contains over 1,180 reported ITC measurements of binding thermodynamics, a testament to the widespread popularity of this technique.
Numerous ITC studies have reported claims of entropy-enthalpy compensation. A series of
early measurements of Ca2+ binding to calcium-binding proteins reported that the observed linear
relationship between !H and T!S with a slope of near unity (shown in Figure 3a) was characteristic of entropy-enthalpy compensation, and suggested this might indicate binding was linked to
a folding-like process given the similarity of this correlation to earlier lysozyme unfolding measurements (56). A detailed study of a series of related para-substituted benzamidinium inhibitors
of the serine protease trypsin (such as those shown in Figure 2b) found that nearly all ligands in
the series exhibited entropy-enthalpy compensation in that the free energy of binding remained
almost unchanged despite large observed changes in !H and T!S (96).
In some cases, a severe form of compensation appears to completely negate expected affinity
gains. Freire and colleagues (58) found that introducing a hydrogen bond acceptor into an HIV-1
protease inhibitor (Figure 2a) resulted in a 3.9 kcal mol−1 gain in the enthalpic contribution to
binding, but this gain was completely offset by a corresponding loss in the entropic contribution,
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ITC: isothermal
titration calorimetry
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a
10
15
10
T∆S (kcal mol–1)
T∆S (kcal mol–1)
5
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b
0
–5
5
0
–10
–5
–15
–10
–20
–10
0
–20
∆H (kcal mol–1)
c
4
15
0
d
High-affinity region
10
T∆S (kcal mol–1)
2
T∆S (kcal mol–1)
–10
∆H (kcal mol–1)
0
–2
–4
5
0
–5
–10
–6
Low-affinity region
–15
–15
–10
∆H (kcal mol–1)
–5
–20
–10
0
∆H (kcal mol–1)
Figure 3
Compensation behavior in calorimetry data. All plots show apparent compensation behavior between
enthalpic (!H) and entropic (T!S) components of free energy of binding. (a) Apparent compensation
behavior from isothermal titration calorimetry (ITC) measurements of Ca2+ to calcium-binding proteins
(black circles) with linear fit [red dashed line, slope = 0.92(5), R2 = 0.96(3) by bootstrap] (data from figure 3 of
Reference 56). (b) Meta-analysis of ITC measurements of protein-ligand complexes (circles) selected from the
BindingDB database (62) with linear fit [dashed line, slope = 0.93(3), R2 = 0.91(2) by bootstrap] (data from
figure 1 of Reference 81). (c) Apparent (but fallacious) compensation over a wide range of energies. The
figure shows independent ITC measurements performed in different laboratories using identical samples of
ligand and protein [4-carboxy-benzenesulfonamide (CBS) binding to bovine carbonic anhydrase II] from the
ABRF-MIRG’02 (Molecular Interactions Research Group of the Association of Biomolecular Resource
Facilities) assessment (71). Here reported measurement errors (error bars representing one standard error)
are much smaller than the actual variation among independent measurements (computed from table 3 of
Reference 71). Linear fit denoted by dashed line [slope = 0.99(2), R2 = 0.997(1) by bootstrap].
(d ) Instrumental limitations on binding affinities measurable by ITC generally restrict the measurable range
of !G (but not !H) to the unshaded region, inducing a linear correlation in !H and T!S due to the
window effect as described in the text (data from figure 1 of Reference 72).
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resulting in no net change in affinity. The authors suggested that this was a manifestation of the
cancellation of entropic and enthalpic contributions for forming a hydrogen bond suggested earlier by Dunitz (22), concluding “it is apparent that structuring associated with hydrogen bonding
formation can significantly compensate for any improvement in binding affinity” (58). If plots of
enthalpic and entropic contributions are to be believed, this severe form of compensation may be
pervasive: A meta-analysis of the ITC measurements for a set of ∼100 protein-ligand complexes
selected from the BindingDB database (62) concluded that entropy-enthalpy compensation produced a plot of !H versus T!S that shows a slope of near unity (reproduced as Figure 3b) (81),
suggesting a form of severe compensation in which enthalpic changes are completely offset by
corresponding entropic changes.
Calorimetric studies of a congeneric series of thrombin ligands concluded that competing entropic and enthalpic responses to chemical modifications of the ligand scaffold could be responsible
for apparent nonadditive effects (3). A study of matched pairs of carbonic anhydrase II ligands in
which a five-membered ring is expanded in size by the addition of a fused benzene ring (depicted in
Figure 2c) also demonstrated apparent entropy-enthalpy compensation, attributed by the authors
to solvent ordering effects (91). Recent work has also found that receptor mutations can cause
minimal changes in the overall free energy of binding and minimal structural changes in X-ray or
NMR structures of bound ligands but extreme changes in the enthalpic and entropic contributions
to binding, interpreted as suggesting large changes in the mechanism of binding (49, 52, 109).
Matched pairs: pairs
of ligands that share
some part of their
molecular scaffold
CRITICAL EXAMINATION OF EXPERIMENTAL EVIDENCE
Before we can conclude there is a universal (and possibly severe) thermodynamic effect at work
behind observations of entropy-enthalpy compensation, we must consider other explanations for
the observed effects. Below, we survey some of the most important concerns that have been raised
in the literature.
ITC Measurements Can Have Large, Underreported Errors in !H and T!S
As most evidence for entropy-enthalpy compensation in ligand binding comes from ITC experiments, it is important to understand the sources and magnitude of error in these measurements.
In a typical ITC experiment (shown schematically in Figure 4a), one component of the reaction
(generally the macromolecule) is loaded into a sample cell inside an adiabatic thermal jacket that
ensures minimal heat exchange with the environment. The other component (generally the ligand) is loaded into a syringe inserted into the sample cell. During the course of the experiment,
small quantities of titrant are injected into the sample cell, and the quantity of heat liberated
(or consumed) during each injection is measured by integrating the power that must be applied
to the sample cell to keep the temperature equal to that of a reference cell heated by constant
known power (Figure 4b). A nonlinear fit of the injection heats by a thermodynamic binding
model is used to obtain the thermodynamic parameters Ka (the association constant), !H (the
enthalpy of association), and n (the stoichiometry parameter2 ), from which the free energy of
binding (!G = −k B T ln K a ) and entropic contribution (T!S = !H − !G) are obtained.
The various sources of error contributing to an ITC measurement are now well understood (1,
17, 44, 68, 92, 97–101, 103–106). Despite this, the errors or uncertainties of ITC measurements
are consistently underreported (71, 106). In the most striking illustration of this, a large-scale
interlaboratory assessment by the Molecular Interactions Research Group of the Association
2
The stoichiometry or site parameter n has been shown to also include contributions from errors in the stated sample cell
volume (99), macromolecule concentration (100), and macromolecule purity.
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a
b
Syringe
0
μW
–2
–4
Temperature
differential
sensor
0
Reference
cell
Sample
cell
Heater
(constant power)
Heater
(power controlled
by temperature
differential)
Thermal jacket
20
40
60
80
100
120
2.0
2.5
3.0
Time (min)
0
kJ (mole of injectant)–1
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–6
–10
–20
–30
–40
–50
0.0
0.5
1.0
1.5
Molar ratio
Figure 4
Typical isothermal titration calorimetry (ITC) experimental configuration and data. (a) A typical experimental configuration for
power-compensating ITC. (b) Typical data from an ITC experiment showing applied power as a function of time (top) and integrated
heats of injection with fit to thermodynamic parameters (bottom) (reproduced from figure 2 of Reference 15, with permission).
of Biomolecular Resource Facilities (ABRF-MIRG’02) (71) distributed identical samples of ligand and protein for a standard 1:1 association reaction—4-carboxy-benzenesulfonamide (CBS)
binding to bovine carbonic anhydrase II (CAII)—to 14 different member laboratories with ITC
expertise, asking them to report measurements of Ka and !H. These measurements, conducted
independently by different laboratories, are a true assessment of the accuracy of the technique.
Both the reported affinities and the enthalpies of binding reflected a standard deviation over independent measurements (which reflects the standard error of an individual experiment) of ∼24%,
with reported enthalpies of binding spanning a 10.7 kcal mol−1 range (1, 71, 106). Although each
group also reported standard errors of the thermodynamic parameters, the reported errors nearly
universally underestimated the true error (reflected in the interlaboratory variation) by one to two
orders of magnitude (71, 106).
The main source of measurement error was found to be a failure to accurately quantitate the ligand (titrant) concentration used in the experiment (71, 106). Although errors in the macromolecule
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concentration are absorbed into a site parameter n in standard ITC data fitting procedures (100),
these procedures generally assume the ligand concentration is known exactly, so an error of 10% in
the ligand concentration will directly lead to errors of 10% in Ka and !H (100, 106). Unfortunately,
the errors reported by standard analysis packages in the parameter fit reflect only the uncertainty
in the nonlinear fit, completely omitting the effect of concentration uncertainties (106).
Although some groups report standard deviations over repeated measurements as estimates of
measurement error, if these measurements are performed using the same ligand stock solution,
this error neglects the contribution from the uncertainty in the ligand stock concentration. While
good analytical laboratory practice can consistently achieve 2% accuracies in titrant concentration,
the ABRF-MIRG’02 study found that concentration errors are more typically ∼10%, limiting the
overall accuracy of ITC measurements to at least 10% even if there is no measurement error during
titration (71). It is certainly possible to achieve higher accuracies with ITC measurements if great
care is exercised throughout all precision-limiting steps, and if characterized titrant concentration
errors can be included during data analysis (105, 106). However, a publication lacking specific,
documented evidence of both of these critical steps must be assumed to suffer from the same
degree of error in Ka and !H found in the ABRF-MIRG’02 assessment, as there is no evidence
better precision has been achieved.
Correlated Errors in !H and T!S Can Produce Apparent Compensation
Because calorimetry directly determines Ka and !H from nonlinear fitting to the injection heats,
!G and T!S are not independently extracted, but rather computed from these quantities. How
do typical errors observed in ITC measurements propagate into these quantities? A typical error
of ∼20% in Ka translates into a rather small absolute error in !G—about 0.1 kcal mol−1 —because
of the logarithmic dependence of !G on Ka through the relationship !G = −kB T ln Ka .3 For
the CBS-CAII binding reaction4 considered in the ABRF-MIRG’02 study, the root-mean-square
(RMS) error in !G was only 0.13 kcal mol−1 , a relative error of only ∼1.6%. Compared with a
2.5 kcal mol−1 error in !H (∼23%), the error in !G is negligible. When the entropic contribution
to binding −T!S = !G − !H is computed, the uncertainty in !H dominates (as the correlation
between !H and Ka is negligible here; 105), resulting in an equal and opposite error in T!S.
This fact immediately suggests a critical issue: While typical ITC measurements can give reliable
free energies of binding, apparent entropy-enthalpy compensation can arise from the large, equal,
and opposite errors in the enthalpic and entropic contributions computed from the nonlinear fit.
Thus, compensation may appear even when none exists!
Indeed, this is precisely what is observed in the ABRF-MIRG’02 dataset. Figure 3c depicts
the enthalpic and entropic components of independent measurements made for the same proteinligand binding reaction of CBS binding to CAII, conducted with identical source material. The
striking similarity of this plot to panels a and b of Figure 3—which purport to show experimental
evidence of the existence of entropy-enthalpy compensation—cannot be avoided. Figure 3c is
not evidence of compensation, since the data comes from repeated measurements by different
laboratories using identical samples of protein and ligand. We are left with no conclusion except
that it is meaningless to plot !H and T!S versus one another because of their large correlated
errors, unless extreme care is taken to minimize, quantify, and propagate these errors.
Although correlations between enthalpies and entropies computed from the same experimental
data have been pointed out repeatedly in the literature, this issue still appears to not be widely
3
4
Nonlinear fitting:
a numerical technique
used to determine the
parameters of a
nonlinear equation by
matching to data,
often with associated
error bars
Relative error:
the ratio of a standard
error of some quantity
to the estimate or
actual value of the
quantity, often
expressed as a
percentage
Root-mean-square
(RMS) error: often
computed as the
standard deviation
among independent
experiments, and an
indicator of the
standard error
expected from a single
experiment
Straightforward first-order Taylor series error propagation gives δ!G = k B T |δ K a /K a |.
Using !G = 8.24 ± 0.02 kcal mol−1 and !H = −11.11 ± 0.04 kcal mol−1 from Reference 106.
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appreciated. Exner (23) and contemporaries (67, 74, 75) pointed out how similar problems can lead
to erroneous interpretation of activation energetics in kinetic studies. Apparent linear correlation
between !H and T!S is often still presented as evidence of compensation (81) despite Exner’s
aptly named follow-up, “How to Get Wrong Experimental Results from Good Experimental Data:
A Survey of Incorrect Applications of Regression” (24). In view of these issues, several subsequent
studies have attempted to control for the effects of statistical correlation and errors and test for
remaining correlations. This work generally concluded that there is some residual correlation
between entropy and enthalpy, but it falls far short of severe compensation (29, 72, 108).
In summary, whereas !G can be measured robustly and to good precision by standard laboratory practices, !H can be subject to errors in excess of 20% unless extraordinary care is taken,
resulting in comparably large correlated errors in T!S. Thus, even repeated measurements of
!H and T!S for the same system can show apparent entropy-enthalpy compensation if plotted
against each other.
A Window Effect Restricting the Range of !G Can Cause
Apparent Compensation
Apparent correlation between !H and T!S can also arise because measured values of !G tend
to occupy a restricted range whereas !H (and hence T!S) can vary over a much wider range—a
phenomenon sometimes termed the window effect (15, 22, 24, 25, 29, 72, 87, 93, 94). Sharp (87)
illustrated this in a simple graphical way. He chose random enthalpies drawn from the range of
reported !H values, then computed corresponding T!S values from !H based on the experimental !G values. Plotting the resulting !H and T!S pairs showed a strong correlation essentially
indistinguishable from the purported calorimetric evidence of compensation shown in Figure 3a.
Why are free energies small in magnitude, whereas enthalpies can be large? Several explanations
have been put forth.
Instrumental limitations. Experimental constraints of ITC generally limit measurable binding
affinities to a range in which the calorimetric constant c ≡ K a [M 0 ] is restricted to 1 < c < 1,000
(115). This restriction naturally appears to induce a linear correlation between enthalpic and
entropic contributions to binding (72) (Figure 3d). Although protocols for measuring thermodynamic parameters for tight-binding (111) or weak-binding (104) ligands have been developed,
the vast majority of calorimetric measurements do not make use of these techniques, effectively
restricting the bulk of available measurements to a narrow range of !G (72).
Data selection bias. Several claims of evidence for compensation examine the !!H and T!!S
of matched pairs of ligands (91, 110), but it has been cautioned that data selection bias can lead
to the appearance of compensation, noncompensation, or even anticompensation, depending on
how the pairing was selected (25, 36).
Publication bias. Useful or interesting biomolecular ligands have affinities within a relatively
narrow range. For example, good initial hits from high-throughput screening efforts might have
dissociation constants (Kd ) in the millimolar to micromolar range and good lead compounds in
the micromolar to nanomolar range. Enthalpies (and hence entropies) have no such expectations
or restrictions placed on them. Indeed, examination of affinities compiled from publications into
a public pKi database (not necessarily determined calorimetrically, so free of ITC measurement
limitations) shows the central 95% of reported pKi values (in a curated set of 7,667 measurements)
span a range of roughly 6.5–15.2 kcal mol−1 in equivalent binding free energy (53) (Figure 6a).
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The distribution also shows significant skew toward stronger binders, suggesting that apparent
inhibition constants of tight-binding molecules are reported more frequently (53) (Figure 6a).
Fundamental physical limitations of affinity. It is also possible that a fundamental physical
limitation restricts the affinities accessible by ligands, possibly even due to the existence of real
entropy-enthalpy compensation that is inescapable at high affinities (85). Indeed, it has been
speculated for some time that thermodynamic factors limit the maximum affinity achievable for
noncovalent ligands of macromolecular targets, though the exact nature of these factors remains
uncertain (55).
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Choice of Standard State Can Alter Entropy-Enthalpy Decomposition
In order to standardize reporting, binding free energies are typically expressed with respect to
a standard state and presented as standard binding free energies (5, 38, 39, 119). Because the
association constant K a = [P L]/[P][L] has units of inverse concentration, a choice of units and
standard concentration C0 must be made in order to convert this to a unitless quantity K a◦ = K a C0
and obtain a standard binding free energy !G◦ = −k B T ln K a◦ .
Although the standard concentration C0 is in principle arbitrary, convention is to report !G◦
values where concentrations are expressed in terms of molarity and C0 is taken to be 1 M. This
choice has certain advantages, in that it removes the translational component of the entropy from
the standard entropy of binding !S◦ (5). Whereas changing the choice of concentration units
or standard concentration C0 would not affect relative differences in enthalpies or entropies of
binding, it could indeed affect the enthalpic and entropic components of a single binding affinity
measurement, necessitating care in the handling and interpretation of thermodynamic signatures.
PHYSICAL ORIGIN OF COMPENSATION
If some degree of entropy-enthalpy compensation is possible, what physical mechanism might
underlie this phenomenon? Numerous mechanisms have been proposed (10, 32, 33, 42, 58, 77–
80, 86, 109, 113), and we highlight some of the most popular proposals.
Solvent Reorganization May Be a Ubiquitous Source of Compensation
Numerous groups have suggested that solvent reorganization on binding could be responsible
for compensation behavior. Lumry & Rajender (63) suggested compensation behavior was a fundamental property of processes occurring in water. A statistical mechanical model of solvent
reorganization attempts to demonstrate how nearly all reactions in solvent should lead to compensation behavior (43). A two-state model of water (in which hydrogen bonds are either broken
or unbroken) has also been shown to lead to severe compensation in hydrophobic hydration (60).
Conformational Restriction of Bound States Is Not Universally Compensating
The simplest physical picture one might propose is that increasing favorable protein-ligand interactions in the bound state might cause additional conformational restriction of the bound ligand,
narrowing or restricting the populations of the energy wells in the bound state and diminishing its conformational entropy, thus causing the entropy change upon binding to become more
unfavorable (22, 58, 85). Although this makes some intuitive sense, it does not appear to be a universal cause of compensation. Consider, for example, the idealized protein-ligand binding reaction
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4
a
0
–2
b
c
–4
–6
–8
–10
0
–2
–4
–2.5
–3
–6
0
2
4
6
r (Å)
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T∆S (kcal mol–1)
–2
F(r) (kcal mol–1)
U(r) (kcal mol–1)
2
–8
0
2
4
6
–3.5
–10
r (Å)
–8
–6
–4
–2
0
∆H (kcal/mol)
Figure 5
A simple model system illustrating weak entropy-enthalpy compensation. An idealized protein and ligand interact via a Morse potential
that is strengthened or weakened to simulate ligand modifications. (a) Intermolecular Morse potential U (r) = De [1 − e −a(r−r0 ) ]2 , with
r0 = 2.8 Å, a = 1/(0.5 Å), and well depth De varying from 2 to 10 kcal mol−1 . (b) Potential of mean force F (r) = U (r) − k B T ln 4πr 2
between protein and ligand as a function of intermolecular distance r for temperature T = 25C. (c) Standard entropic (T!S) and
enthalpic (!H) contributions to the binding free energy for different well depths De , computed from classical statistical mechanics.
Note that, although some entropy-enthalpy compensation is apparent, it is not linear or severe.
depicted in Figure 5, in which a spherically symmetric ligand interacts with a protein partner via
a Morse potential in r (Figure 5a). Because of the three-dimensional nature of space, the free
energy along the protein-ligand separation coordinate r has a well-defined separation between
bound and unbound states (Figure 5b). When the protein-ligand interaction is modulated to make
the bound well depth deeper, the free energy of binding becomes more favorable in a manner that
is almost linear with the enthalpy due to the simplicity of the system. When the decomposition
into entropic and enthalpic components is examined (Figure 5c), some compensation between
entropy and enthalpy is evident, but this compensation is very weak and certainly does not achieve
the slope of unity expected from severe compensation. In fact, the maximum slope attained is
near the weakest enthalpies (and hence free energies) of binding, the opposite of what is observed
experimentally when severe compensation is claimed for very tight binders (58).
Although this simple numerical model does not rule out the conformational restriction mechanism of compensation for all simple models, it suggests this mechanism cannot cause universal
compensation. Related models with different parameter choices do demonstrate the potential for
near-complete compensation in a very narrow range of interaction energies (22, 85), and other
theoretical treatments of weak association find that both compensation and noncompensation
behaviors can be observed (32).
Host-guest system:
a pair of small organic
molecules with high
affinity for each other,
where the larger
“host” often physically
encapsulates a smaller
“guest” molecule
132
Receptor Flexibility May Be a Source of Compensation
A simple model of a ligand associating with a flexible macromolecule demonstrates how the free
energy change on perturbation of the ligand or protein can be small, but larger (and equal) compensating changes in entropy and enthalpy can occur (77, 79). Detailed atomistic investigation of
a simple host-guest system found no correlation between the depth of an energy well and its narrowness, though an accurate accounting of the changes in the widths of energy wells upon binding
was essential to reproducing experimental binding free energies (10). Subsequent investigations
of a different set of host-guest systems revealed that compensation can be overcome by extremely
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tight-fitting guest molecules that appear to make up losses in conformational flexibility through
liberating hydrating solvent molecules (80).
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The Decomposition of the Free Energy Is Not Unique
Another complication is that the decomposition of free energy changes into entropic and enthalpic
contributions is not necessarily unique. In computational studies, the resolution of the model
employed (i.e., the choice of which degrees of freedom are explicitly represented and which
are implicitly modeled) can modulate the entropic and enthalpic components of thermodynamic
processes, even if the overall free energy is preserved (82). For example, a recent study of model
ligand-cavity association with atomistic and coarse-grained potentials found that, whereas the
overall free energy as a function of intermolecular distance was robust to model resolution, the
entropic and enthalpic contributions were not (2). Surprisingly, the experimental interpretation of
entropy and enthalpy can also depend on the measurement technique or definition of the bound
state, even when the binding free energy is robust to this choice (78).
RAMIFICATIONS FOR LIGAND ENGINEERING
Making Inferences About Driving Forces of Binding Can Be Difficult
Recent proposals suggest enthalpic and entropic contributions to binding should play a key role
in guiding ligand design (27–29, 34, 57, 58). But is there real practical value to this information?
Assuming enthalpic and entropic contributions could be accurately measured, do these contributions to binding give us additional insight? And is this insight useful in making engineering
decisions?
Biophysicists have numerous rules of thumb regarding the thermodynamic signatures of elementary molecular interactions: Hydrogen bonds are enthalpically driven, hydrophobic association is entropically driven, liberating waters from a binding site increases entropy, sterically
constraining a ligand by eliminating rotatable bonds reduces the entropy of the unbound state,
and so on (50). However, the statistical mechanics governing the behavior of the system makes
no such distinction between enthalpy and entropy, nor do these elementary interactions necessarily act in an additive manner. The fundamental quantity modulated by changes to a ligand is
the potential energy of the system, U(x), where x denotes the microscopic configuration of the
system (including receptor, ligand, and surrounding solvent degrees of freedom). At equilibrium,
the distribution of configurations observed within a specific volume of the cell or test tube is given
by the Boltzmann distribution (20),
ρ(x) ∝ e −(U (x)+ p V (x))/kB T ,
2.
where kB is the Boltzmann constant, T is the temperature, p is pressure, and V (x) is the instantaneous volume of the entire system, including solvent. The entropy and enthalpy are not
fundamental quantities, but rather both are functions of the microscopic distribution,
!
H ≡ d x[ U (x)ρ(x) + p V (x)]
!
3.
d x ρ(x) ln ρ(x).
ST ≡ −k B T
Here, the enthalpy term includes a term also depending on pV(x), the product of the pressure
and volume; normally, at standard temperature and pressure this contribution is insignificant. In
any case, because both entropy and enthalpy depend on the microscopic probability distribution
ρ(x), any perturbation to U(x) resulting from a ligand modification will in general perturb both
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the enthalpy and the entropy. That is, entropy and enthalpy are inherently intertwined, and
modifications that change only one but not the other are the exception, not the rule. Thus, these
rules of thumb fail to hold up when specific examples are scrutinized (50).
Furthermore, determining how to make useful modifications based on entropic and enthalpic
patterns in a ligand series is not straightforward. Even rationalizing the enthalpic and entropic
behavior in an extremely simple host-guest system—such as Ca2+ binding to simple organic chelating agents related to EDTA—appears hopelessly complex (13). In the Ca2+ :EDTA complexation
example (13), the authors find that increasing the number of chelating arms of the host—strongly
opposed by conformational entropy—increases the affinity. Without a model that includes favorable entropic contributions as chelating arms are added, the authors conclude in frustration that
it is impossible to construct a simple self-consistent model of binding for this ligand series (13).
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True Compensation Can Frustrate Interpretation
of Thermodynamic Signatures
Ironically, real compensating enthalpic and entropic contributions can actually obscure the true
driving forces of ligand association, complicating the interpretation of thermodynamic signatures
from reliable calorimetry experiments. For example, a recent computational study of the association of a spherical hydrophobic ligand with a hemispherical cavity found that association was
thermodynamically favorable but enthalpically driven, rather than entropically driven as one would
expect in hydrophobic association (86). It was postulated that this effect was due to a net-favorable
enthalpy of liberated water making additional hydrogen bonds upon returning to the bulk (86),
but an alternative explanation is more likely: Entropy-enthalpy compensation in reorganizing water hydrogen bonds to accommodate newly liberated waters gives almost perfect compensation,
resulting in a process that is net neutral in free energy (42). The true driving force is therefore the
increase in configurational-translational entropy of water due to the burial of hydrophobic surface
area (an entropically dominant effect), but this effect is masked due to the larger magnitude of the
hydrogen bond reorganization event (42).
Thus, interpreting fundamental driving forces can be highly nontrivial because numerous effects contribute to observed enthalpies and entropies of binding. Other observations support this
conclusion. For example, a joint calorimetric and X-ray study of a congeneric series of trypsin ligands found that, despite having nearly identical thermodynamic profiles, many ligands have different binding modes, highlighting the difficulty of drawing useful conclusions about the mechanism
of binding from thermodynamic profiles (9). In another system, the opposite was found to be the
case: Vastly different thermodynamic profiles resulted from essentially invisible (sub-Angstrom)
differences in binding geometry (113). Similarly, computational work recently found that even
small protein conformational changes can lead to markedly different thermodynamic profiles for
binding of the same ligand (26).
Designing for Enthalpic Improvements Has Limited Utility
Computer-aided schemes for rational ligand design that go beyond simple molecular visualization
[such as virtual screening (89) and end point simulation methods (95)] rely heavily on the estimation
of binding enthalpies. However, the optimization of binding interactions by this route presents
many challenges that may explain its limited success (83). Precise computation of the enthalpy of
association is inherently difficult because of simple statistics; in effect, its estimation requires taking
a small difference in the means of two distributions that are orders of magnitude broader than
the difference between their means. Estimating the enthalpy of transfer by molecular simulation
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10
a
5
3,500
∆G (kcal mol–1)
3,000
Occurrences
b
2,500
2,000
1,500
Others
Aldose reductase
HIV-1 protease
Renin
0
−5
−10
1,000
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−15
500
0
−15
−10
∆G (kcal mol–1)
−5
−20
−60
−40
−20
0
20
∆H (kcal mol–1)
Figure 6
Distribution of published binding free energies and correlation with enthalpy. (a) Distribution of binding free energies computed from
ChEMBL pKi activity data (data from figure 4 of Reference 53). (b) Poor correlation of enthalpy (!H) with free energy (!G) of binding
from meta-analysis of isothermal titration calorimetry (ITC) measurements selected from the BindingDB database (62) (all ITC
measurements from the BindingDB as of this writing are shown in a manner similar to that in figure 2a of Reference 81). Whereas
aldose reductase and HIV-1 protease show some correlation between enthalpy and the free energy of binding, correlation is generally
poor for other systems, such as renin, and enthalpies span a much broader range than free energies.
thus requires extremely long simulations to ensure that the mean enthalpies of the initial and final
states are estimated with sufficient precision to compute a reliable average enthalpy difference
(45). Computation of entropies is similarly difficult (90).
These issues have presented difficulties for so-called end point methods that attempt to estimate the free energy of binding by computing separate estimates of the enthalpic and entropic
contributions (40, 47, 95). As an alternative, docking and rescoring approaches (41) assume that
only the neighborhood of a single minimum energy configuration contributes to the enthalpy of
binding, which introduces additional error into the computed enthalpies of interaction (84).
Worse yet, it appears that enthalpies—even if they can be accurately predicted—are only weakly
correlated with binding free energies. The earliest calorimetric measurements of protein–small
molecule interactions hinted that enthalpies are not necessarily predictive of binding free energies
(6). This observation has been confirmed by recent large-scale calorimetric database assessments
(Figure 6b), with a few notable exceptions (81): HIV-1 protease and aldose reductase appear to
show weak correlation between enthalpies and free energies of binding, which may explain why
rational drug design and virtual screening efforts have found unusually high success rates in these
targets (30, 46, 116). This poor correlation does not appear to be due to the complexity of the
binding landscape, as even simple host-guest systems appear to show poor correlation between
enthalpies and free energies of binding (10).
Poor correlation between enthalpies and free energies of binding also may explain why end
point methods have a great deal of difficulty with most protein targets. These methods must either
employ a crude model of ligand entropy with poor accuracy and convergence properties (40, 47,
90) or ignore differences in ligand binding entropies altogether and assume enthalpies alone are
www.annualreviews.org • Entropy-Enthalpy Compensation
Small molecule:
generally an organic
compound of low
molecular weight
(<800 Da), often
having drug-like
properties
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predictive of affinity, a point contested by both experimental (9, 52) and computational (10) studies
(also recently reviewed in Reference 50).
In summary, even if it was possible to accurately predict specific interactions that would yield desired enthalpy changes, it seems unclear that doing so would actually yield corresponding improvements in binding affinity. Furthermore, accurate estimation of changes in binding enthalpy seems
beyond the reach of current methods and, as we will see, can be difficult to validate experimentally.
Designing for Improvements in Affinity Directly Is Likely
To Be More Productive
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Through steady progress in computer simulation techniques, protein-ligand binding free energies
can now be computed directly, without relying on separately estimating enthalpic and entropic
components. This avoids difficulties in dealing with the large and often correlated errors and near
cancellations in separate estimates of entropy and enthalpy. Alchemical methods in particular (7,
11, 19, 37, 39, 107) directly compute the free energy of decoupling the ligand from its environment.
These techniques, originally introduced nearly three decades ago (107), have advanced to the point
where both the binding !G of individual ligands and the binding !!G of ligand modifications
can be calculated precisely (11, 19, 37). There are reported cases in which ligand binding free
energies have been computed or predicted with errors of 1–2 kcal mol−1 (8, 35, 70) for wellbehaved systems where protein conformational changes are minimal. Alternative approaches can
compute free energies of binding of even large, charged ligands by estimating the free energy for
direct ligand dissociation along an unbinding pathway (117).
Moreover, the computational effort required to compute precise estimates of free energy differences is often orders of magnitude less than that required to compute enthalpy differences to
the same precision, even for simple solvated systems (45). Slow protein conformational changes
(69) and changes in protonation (21) or tautomeric states (66) still pose a challenge for these calculations. However, these same challenges plague estimation of enthalpies, and binding free energy
calculations, unlike enthalpy calculations, give correct estimates of affinity when these issues are
handled properly, at least to the accuracy achievable by the force field. Computations of binding
free energy also have the advantage of being validated more easily against experimental data, due
to the small error in typical calorimetrically determined binding free energies (0.1 kcal mol−1 )
compared to enthalpies (2.0 kcal mol−1 )5 . Public databases from other experimental techniques
are also more plentiful and trustworthy if only free energies of binding are of interest; a recent
analysis of public pKi data found the effective RMS error to be ∼0.75 kcal mol−1 (53)6 .
How can these computational tools be useful in design? Historically, standard practice in
ligand engineering has been to propose, synthesize, and test small, synthetically feasible modifications, such as introducing additional hydrogen bonding partners, improving steric complementarity, or reducing ligand conformational flexibility. However, improvements in computational
power and software have now made it feasible to computationally evaluate proposed modifications
to these compounds prior to synthesis and testing (48, 88, 118). Looking forward, it is not hard
to foresee computational schemes being routinely used to propose modifications likely to lead to
5
To obtain these typical error estimates, we used the standard deviation among independent experimental ITC measurements
from Reference 71, ∼20% in both Ka and !H. This gives an RMS error in !G of kT ln 1.2 ≈ 0.1 kcal mol−1 for T ≈ 298 K.
The error in !H was estimated from the RMS average error assuming the distribution of enthalpies in the BindingDB (62)
was representative.
6
Reference 53 quotes a standard deviation of 0.54 pKi units, which we convert to free energy !G = kT ln 10pK i assuming
T ≈ 298 K.
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affinity improvements, decoupling this process from human intuition altogether. Inklings of this
future already exist: Simulation techniques such as multisite lambda dynamics (51) and Monte
Carlo–based methods (64, 76) allow the evaluation of many potential changes within a single simulation. Clever schemes involving the postprocessing of simulations of nonchemical species (12)
also show promise for automatically proposing chemical derivatives leading to enhanced affinity
or selectivity.
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CONCLUSIONS
Overall, we fail to find conclusive evidence for a pervasive form of entropy-enthalpy compensation,
nor do we find a universal physical explanation which would be expected to routinely yield such
compensation. Rather, we find substantial evidence that large uncertainties in enthalpy measurements can yield apparent (but false) entropy-enthalpy compensation. These large uncertainties
can arise from factors such as titrant concentration errors, which are in many cases not taken into
account in reporting the error of calorimetric results. Enthalpies are also particularly difficult to
estimate computationally, and experimentally correlate only poorly with free energies of binding.
On the whole, we believe this work lends support to the idea of attempting to design ligands on the
basis of free energy considerations alone, rather than attempting to design separately for enthalpy
or entropy while factoring in the possibility of entropy-enthalpy compensation.
SUMMARY POINTS
1. While a weak form of entropy-enthalpy compensation is likely common, evidence of a
severe or pervasive form of compensation is poor.
2. Measurement and calculation of enthalpies and entropies is more difficult than measuring
or computing free energies.
3. Entropic and enthalpic contributions are difficult to interpret and are unlikely to be useful
in rational ligand design.
4. When intuition fails in proposing modifications that lead to affinity gains, schemes that
compute binding free energies directly are poised to be of high utility.
DISCLOSURE STATEMENT
The authors are not aware of any affiliations, memberships, funding, or financial holdings that
might be perceived as affecting the objectivity of this review.
ACKNOWLEDGMENTS
J.D.C. was supported by a QB3-Berkeley Distinguished Postdoctoral Fellowship during part of
the period in which this manuscript was written. D.L.M. acknowledges funding from the National Institutes of Health (1R15GM096257-01A1) and start-up funding from the University
of California, Irvine. J.D.C. is grateful to Dr. Kim Branson (Hessian Informatics), Dr. Gregory R. Bowman (UCB), Dr. Sarah E. Boyce (Gilead), Dr. Phillip L. Geissler (UCB), Dr. Brian
K. Shoichet (UCSF), Dr. Joel Tellinghuisen (Vanderbilt), and Dr. Veena Thomas (Stanford)
for stimulating discussions on this topic, and to Dr. Gavin Crooks (LBNL) and Dr. Anthony
Nicholls (OpenEye Software) for a critical reading of the manuscript. Dr. Michael K. Gilson and
Dr. Tiqing Liu (UCSD) also provided valuable assistance with BindingDB. GraphClick (Arizona
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Software) was used in data extraction for the generation of many of the figures presented in this
manuscript.
LITERATURE CITED
Annu. Rev. Biophys. 2013.42:121-142. Downloaded from www.annualreviews.org
by 66.108.94.177 on 05/14/13. For personal use only.
1. Baranauskiene L, Petrikaite V, Matuliene J, Matulis D. 2009. Titration calorimetry standards and the
precision of isothermal titration calorimetry data. Int. J. Mol. Sci. 10:2752–62
2. Baron R, Molinero V. 2012. Water-driven cavity-ligand binding: comparison of thermodynamic signatures from coarse-grained and atomic-level simulations. J. Chem. Theory Comput. 7:3696–704
3. Baum B, Muley L, Smolinski M, Heine A, Hangauer D, Klebe G. 2010. Non-additivity of functional
group contributions in protein ligand binding: a comprehensive study by crystallography and isothermal
titration calorimetry. J. Mol. Biol. 397:1042–54
4. Beasley JR, Doyle DF, Chen L, Cohen DS, Fine BR, Pielak GJ. 2002. Searching for quantitative entropyenthalpy compensation among protein variants. Proteins 49:398–402
5. Bennaim A. 1978. Standard thermodynamics of transfer: uses and misuses. J. Phys. Chem. 82:792–803
6. Böhm H, Klebe G. 1996. What can we learn from molecular recognition in protein-ligand complexes
for the design of new drugs? Angew. Chem. Int. Ed. Engl. 35:2588–614
7. Boresch S, Tettinger F, Leitgeb M, Karplus M. 2005. Absolute binding free energies: a quantitative
approach for their calculation. J. Phys. Chem. B 107:9535–51
8. Boyce SE, Mobley DL, Rocklin GJ, Graves AP, Dill KA, Shoichet BK. 2009. Predicting ligand binding
affinity with alchemical free energy methods in a polar model binding site. J. Mol. Biol. 394:747–63
9. Brandt T, Holzmann N, Muley L, Khayat M, Wegscheid-Gerlach C, et al. 2011. Congeneric but still
distinct: how closely related trypsin ligands exhibit different thermodynamic and structural properties.
J. Mol. Biol. 405:1170–87
10. Chang CE, Gilson MK. 2004. Free energy, entropy, and induced fit in host-guest recognition: calculations with the second-generation mining minima algorithm. J. Am. Chem. Soc. 126:13156–64
11. Chodera JD, Mobley DL, Shirts MR, Dixon RW, Branson K, Pande VS. 2011. Alchemical free energy
methods for drug discovery: progress and challenges. Curr. Opin. Struct. Biol. 21:150–60
12. Christ CD, van Gunsteren WF. 2008. Multiple free energies from a single simulation: extending enveloping distribution sampling to nonoverlapping phase-space distributions. J. Chem. Phys. 128:174112
13. Christensen T, Gooden DM, Kung JE, Toone EJ. 2003. Additivity and the physical basis of multivalency
effects: a thermodynamic investigation of the calcium EDTA interaction. J. Am. Chem. Soc. 125:7357–66
14. Cooper A. 2011. Microcalorimetry of heat capacity and volumetric changes in biomolecular
interactions—the link to solvation? J. Therm. Anal. Calorim. 104:69–73
15. Cooper A, Johnson CM, Lakey JH, Nöllmann M. 2001. Heat does not come in different colours: entropyenthalpy compensation, free energy windows, quantum confinement, pressure perturbation calorimetry,
solvation and the multiple causes of heat capacity effects in biomolecular interactions. Biophys. Chem.
93:215–30
16. Cornish-Bowden A. 2002. Enthalpy-entropy compensation: a phantom phenomenon. J. Biosci. 27:121–
26
17. de Rivera M, Socorro F. 2005. Baseline changes in an isothermal titration microcalorimeter. J. Therm.
Anal. Calorim. 80:769–73
18. Delorbe JE, Clements JH, Whiddon BB, Martin SF. 2010. Thermodynamic and structural effects of
macrocyclic constraints in protein-ligand interactions. ACS Med. Chem. Lett. 1:448–52
19. Deng Y, Roux B. 2009. Computations of standard binding free energies with molecular dynamics simulations. J. Phys. Chem. B 113:2234–46
20. Dill KA, Bromberg S. 2003. Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology.
New York: Garland Science
21. Donnini S, Villa A, Groenhof G, Mark AE, Wierenga RK, Juffer AH. 2009. Inclusion of ionization states
of ligands in affinity calculations. Proteins 76:138–50
22. Dunitz JD. 2003. Win some, lose some: enthalpy-entropy compensation in weak intermolecular interactions. Chem. Biol. 2:709–12
138
Chodera
·
Mobley
Annu. Rev. Biophys. 2013.42:121-142. Downloaded from www.annualreviews.org
by 66.108.94.177 on 05/14/13. For personal use only.
BB42CH06-Chodera
ARI
3 April 2013
1:57
23. Exner O. 1964. Concerning the isokinetic relationship. Nature 201:488–90
24. Exner O. 1997. How to get wrong results from good experimental data: a survey of incorrect applications
of regression. J. Phys. Org. Chem. 10:797–813
25. Exner O. 2000. Entropy-enthalpy compensation and anticompensation: solvation and ligand binding.
Chem. Commun. 2000:1655–56
26. Fenley AT, Muddana HS, Gilson MK. 2012. Entropy-enthalpy transduction caused by conformational
shifts can obscure the forces driving protein-ligand binding. Proc. Natl. Acad. Sci. USA 109:20006–11
27. Ferenczy GG, Keserü GM. 2010. Enthalpic efficiency of ligand binding. J. Chem. Inf. Model. 50:1536–41
28. Ferenczy GG, Keserü GM. 2010. Thermodynamics guided lead discovery and optimization. Drug Discov.
Today 15:919–32
29. Ferrante A, Gorski J. 2012. Enthalpy-entropy compensation and cooperativity as thermodynamic epiphenomena of structural flexibility in ligand-receptor interactions. J. Mol. Biol. 417:454–67
30. Ferrari AM, Degliesposti G, Sgobba M, Rastelli G. 2007. Validation of an automated procedure for the
prediction of relative free energies of binding on a set of aldose reductase inhibitors. Bioorg. Med. Chem.
15:7865–77
31. Fisher HF. 2012. Detecting “silent” allosteric coupling. Methods Mol. Biol. 796:71–96
32. Ford DM. 2005. Enthalpy-entropy compensation is not a general feature of weak association. J. Am.
Chem. Soc. 127:16167–70
33. Forrey C, Douglas JF, Gilson MK. 2012. The fundamental role of flexibility on the strength of molecular
binding. Soft Matter 8:6385–92
34. Freire E. 2008. Do enthalpy and entropy distinguish first in class from best in class? Drug Discov. Today
13:869–74
35. Fujitani H, Tanida Y, Ito M, Jayachandran G, Snow C, et al. 2005. Direct calculation of the binding free
energies of FKBP ligands. J. Chem. Phys. 123:084108
36. Gallicchio E, Kubo MM, Levy RM. 1998. Entropy-enthalpy compensation in solvation and ligand
binding revisited. J. Am. Chem. Soc. 120:4526–27
37. Gallicchio E, Levy RM. 2011. Advances in all atom sampling methods for modeling protein-ligand
binding affinities. Curr. Opin. Struct. Biol. 21:161–66
38. General IJ. 2010. A note on the standard state’s binding free energy. J. Chem. Theory Comput. 6:2520–24
39. Gilson MK, Given J, Bush B, McCammon J. 1997. The statistical-thermodynamic basis for computation
of binding affinities: a critical review. Biophys. Chem. 72:1047–69
40. Gohlke H, Case DA. 2004. Converging free energy estimates: MM-PB(GB)SA studies on the proteinprotein complex Ras-Raf. J. Comput. Chem. 25:238–50
41. Graves AP, Shivakumar DM, Boyce SE, Jacobson MP, Case DA, Shoichet BK. 2008. Rescoring docking
hit lists for model cavity sites: predictions and experimental testing. J. Mol. Biol. 377:914–34
42. Graziano G. 2012. Molecular driving forces of the pocket-ligand hydrophobic association. Chem. Phys.
Lett. 533:95–99
43. Grunwald E, Steel C. 1995. Solvent reorganization and thermodynamic enthalpy-entropy compensation.
J. Am. Chem. Soc. 117:5687–92
44. Hansen LD, Fellingham GW, Russell DJ. 2011. Simultaneous determination of equilibrium constants
and enthalpy changes by titration calorimetry: methods, instruments, and uncertainties. Anal. Biochem.
409:220–29
45. Hess B, van der Vegt NFA. 2006. Hydration thermodynamic properties of amino acid analogues: a
systematic comparison of biomolecular force fields and water models. J. Phys. Chem. B 110:17616–26
46. Holloway MK, Wai JM, Halgren TA, Fitzgerald PMD, Vacca JP, et al. 1995. A priori prediction of
activity for HIV-1 protease inhibitors employing energy minimization in the active site. J. Med. Chem.
38:305–17
47. Hou T, Wang J, Li Y, Wang W. 2011. Assessing the performance of the MM/PBSA and MM/GBSA
methods. 1. The accuracy of binding free energy calculations based on molecular dynamics simulations.
J. Chem. Inf. Model. 51:69–82
48. Jorgensen WL. 2009. Progress and issues for computationally guided lead discovery and optimization.
In Drug Design: Structure- and Ligand-Based Approaches, ed. KM Merz, D Ringe, CH Reynolds, pp. 1–14.
Cambridge, UK: Cambridge Univ. Press
www.annualreviews.org • Entropy-Enthalpy Compensation
139
ARI
3 April 2013
1:57
49. King NM, Prabu-Jeyabalan M, Bandaranayake RM, Nalam MNL, Nalivaika EA, et al. 2012. Extreme
entropy-enthalpy compensation in a drug-resistant variant of HIV-1 protease. ACS Chem. Biol. 7:1536–46
50. Klebe G. 2011. On the validity of popular assumptions in computational drug design. J. Cheminform.
3:O18
51. Knight JL, Brooks CL III. 2011. Multisite λ dynamics for simulated structure–activity relationship
studies. J. Chem. Theory Comput. 7:2728–39
52. Koch C, Heine A, Klebe G. 2011. Tracing the detail: how mutations affect binding modes and thermodynamic signatures of closely related aldose reductase inhibitors. J. Mol. Biol. 406:700–12
53. Kramer C, Kalliokoski T, Gedeck P, Vulpetti A. 2012. The experimental uncertainty of heterogeneous
public Ki data. J. Med. Chem. 55:5165–73
54. Krug RR, Hungter WG, Grieger RA. 1976. Statistical interpretation of enthalpy-entropy compensation.
Nature 261:566–67
55. Kuntz ID, Chen K, Sharp KA, Kollman PA. 1999. The maximal affinity of ligands. Proc. Natl. Acad. Sci.
USA 96:9997–10002
56. Kurioki R, Nitta K, Yutani K. 1992. Thermodynamic changes in the binding of Ca2+ to a mutant human
lysozyme (D86/92): enthalpy-entropy compensation observed upon Ca2+ binding to proteins. J. Biol.
Chem. 267:24297–301
57. Ladbury JE, Klebe G, Freire E. 2010. Adding calorimetric data to decision making in lead discovery: a
hot tip. Nat. Rev. Drug Discov. 9:23–27
58. Lafont V, Armstrong AA, Ohtaka H, Kiso Y, Mario Amzel L, Freire E. 2007. Compensating enthalpic
and entropic changes hinder binding affinity optimization. Chem. Biol. Drug Discov. 69:413–22
59. Lee B. 1991. Solvent reorganization contribution to the transfer thermodynamics of small nonpolar
molecules. Biopolymers 31:993–1008
60. Lee B, Graziano G. 1996. A two-state model of hydrophobic hydration that produces compensating
enthalpy and entropy changes. J. Am. Chem. Soc. 118:5163–68
61. Leffler JE. 1955. The enthalpy-entropy relationship and its implications for organic chemistry. J. Org.
Chem. 20:1202–31
62. Liu T, Lin Y, Wen X, Jorissen RN, Gilson MK. 2007. BindingDB: a web-accessible database of experimentally determined protein-ligand binding affinities. Nucleic Acids Res. 35:D198–201
63. Lumry R, Rajender S. 1970. Enthalpy-entropy compensation phenomena in water solutions of proteins
and small molecules: a ubiquitous property of water. Biopolymers 9:1125–227
64. Lyubartsev AP, Martsinovski AA, Shevkunov SV, Vorontsov-Velyaminov PN. 1992. New approach to
Monte Carlo calculation of the free energy: method of expanded ensembles. J. Chem. Phys. 96:1776–83
65. Makhatadze GI, Privalov PL. 1994. Hydration effects in protein unfolding. Biophys. Chem. 51:291–309
66. Martin YC. 2009. Let’s not forget tautomers. J. Comput. Aid. Mol. Des. 23:693–704
67. McGregor R, Milićević B. 1966. On the enthalpy-entropy relationship. Nature 211:523–25
68. Mizoue LS, Tellinghuisen J. 2004. The role of backlash in the “first injection anomaly” in isothermal
titration calorimetry. Anal. Biochem. 326:125–27
69. Mobley DL. 2012. Let’s get honest about sampling. J. Comput. Aid. Mol. Des. 26:93–95
70. Mobley DL, Graves AP, Chodera JD, McReynolds AC, Shoichet BK, Dill KA. 2007. Predicting absolute
ligand binding free energies to a simple model site. J. Mol. Biol. 371:1118–34
71. Myszka DG, Abdiche YN, Arisaka F, Byron O, Eisenstein E, et al. 2009. The ABRF-MIRG’02 study:
assembly state, thermodynamic, and kinetic analysis of an enzyme/inhibitor interaction. J. Biomol. Tech.
14:247–69
72. Olsson TSG, Ladbury JE, Pitt WR, Williams MA. 2011. Extent of enthalpy-entropy compensation in
protein-ligand interactions. Protein Sci. 20:1607–18
73. Peters WB, Frasca V, Brown RK. 2009. Recent developments in isothermal titration calorimetry label
free screening. Comb. Chem. High Throughput Screen. 12:772–90
74. Petersen RC. 1964. Linear relationship between enthalpy and entropy of activation. J. Org. Chem.
29:3133
75. Petersen RC, Markgraf JH, Ross SD. 1961. Solvent effects in decomposition of 1,1′ -diphenylazoethane
and 2,2′ -azobis-(2-methylpropionitrile). J. Am. Chem. Soc. 83:3819–23
Annu. Rev. Biophys. 2013.42:121-142. Downloaded from www.annualreviews.org
by 66.108.94.177 on 05/14/13. For personal use only.
BB42CH06-Chodera
140
Chodera
·
Mobley
Annu. Rev. Biophys. 2013.42:121-142. Downloaded from www.annualreviews.org
by 66.108.94.177 on 05/14/13. For personal use only.
BB42CH06-Chodera
ARI
3 April 2013
1:57
76. Pitera JW, Kollman PA. 2000. Exhaustive mutagenesis in silico: multicoordinate free energy calculations
on proteins and peptides. Proteins 41:385–97
77. Qian H. 1998. Entropy-enthalpy compensation: conformational fluctuation and induced-fit. J. Chem.
Phys. 109:10015–17
78. Qian H. 2006. An asymptotic comparative analysis of the thermodynamics of non-covalent association.
J. Math. Biol. 52:277–89
79. Qian H, Hopfield JJ. 1996. Entropy-enthalpy compensation: perturbation and relaxation in thermodynamic systems. J. Chem. Phys. 105:9292–98
80. Rekharsky MV, Mori T, Yang C, Ko YH, Selvapalam N, et al. 2007. A synthetic host-guest system
achieves avidin-biotin affinity by overcoming enthalpy-entropy compensation. Proc. Natl. Acad. Sci. USA
104:20737–42
81. Reynolds CH, Holloway MK. 2011. Thermodynamics of ligand binding and efficiency. ACS Med. Chem.
Lett. 2:433–37
82. Rudzinski JF, Noid WG. 2011. Coarse-graining entropy, forces, and structures. J. Chem. Phys.
135:214101
83. Schneider G. 2010. Virtual screening: an endless staircase? Nat. Rev. Drug Discov. 9:273–76
84. Scior T, Bender A, Tresadern G, Medina-Franco JL, Martı́nez-Mayorga K, et al. 2012. Recognizing
pitfalls in virtual screening: a critical review. J. Chem. Inf. Model. 52:867–81
85. Searle MS, Westwell MS, Williams DH. 1995. Application of a generalised enthalpy-entropy relationship
to binding co-operativity and weak associations in solution. J. Chem. Soc. Perkin Trans. 2:141–51
86. Setny P, Baron R, McCammon JA. 2010. How can hydrophobic association be enthalpy driven? J. Chem.
Theory Comput. 6:2866–71
87. Sharp K. 2001. Entropy-enthalpy compensation: fact or artifact? Protein Sci. 10:661–67
88. Shirts MR. 2012. Best practices in free energy calculations for drug design. Methods Mol. Biol. 819:425–67
89. Shoichet BK. 2004. Virtual screening of chemical libraries. Nature 432:862–65
90. Singh N, Warshel A. 2010. A comprehensive examination of the contributions to the binding entropy
of protein-ligand complexes. Proteins 78:1724–35
91. Snyder PW, Mecinovic J, Moustakas DT, Thomas SW 3rd, Harder M, et al. 2011. Mechanism of the
hydrophobic effect in the biomolecular recognition of arylsulfonamides by carbonic anhydrase. Proc.
Natl. Acad. Sci. USA 108:17889–94
92. Socorro F, de La Nuez I, Alvarez L, de Rivera M. 2004. Effect of a stirring process in an isothermal
titration microcalorimeter. Thermochim. Acta 420:163–67
93. Starikov EB, Nordén B. 2007. Enthalpy-entropy compensation: a phantom or something useful? J. Phys.
Chem. B 111:14431–35
94. Starikov EB, Nordén B. 2012. Entropy-enthalpy compensation as a fundamental concept and analysis
tool for systematical experimental data. Chem. Phys. Lett. 538:118–20
95. Swanson JMJ, Henchman RH, McCammon JA. 2004. Revisiting free energy calculations: a theoretical
connection to MM/PBSA and direct calculation of the association free energy. Biophys. Chem. 86:67–74
96. Talhout R, Villa A, Mark AE, Engberts JBFN. 2003. Understanding binding affinity: a combined isothermal titration calorimetry/molecular dynamics study of the binding of a series of hydrophobically modified
benzamidinium chloride inhibitors to trypsin. J. Am. Chem. Soc. 125:10570–79
97. Tellinghuisen J. 2003. A study of statistical error in isothermal titration calorimetry. Anal. Biochem.
321:79–88
98. Tellinghuisen J. 2004. Statistical error in isothermal titration calorimetry. Methods Enzymol. 383:245–82
99. Tellinghuisen J. 2004. Volume errors in isothermal titration calorimetry. Anal. Biochem. 333:405–6
100. Tellinghuisen J. 2005. Optimizing experimental parameters in isothermal titration calorimetry. J. Phys.
Chem. B 109:20027–35
101. Tellinghuisen J. 2005. Statistical error in isothermal titration calorimetry: variance function estimation
from generalized least squares. Anal. Biochem. 343:106–15
102. Tellinghuisen J. 2006. Van’t Hoff analysis of K◦ (T ): how good. . .or bad? Biophys. Chem. 120:114–20
103. Tellinghuisen J. 2007. Optimizing experimental parameters in isothermal titration calorimetry: variable
volume procedures. J. Phys. Chem. B 111:11531–37
www.annualreviews.org • Entropy-Enthalpy Compensation
141
ARI
3 April 2013
1:57
104. Tellinghuisen J. 2008. Isothermal titration calorimetry at very low c. Anal. Biochem. 373:395–97
105. Tellinghuisen J. 2012. Designing isothermal titration calorimetry experiments for the study of 1:1 binding: problems with the “standard protocol”. Anal. Biochem. 424:211–20
106. Tellinghuisen J, Chodera JD. 2011. Systematic errors in isothermal titration calorimetry: concentrations
and baselines. Anal. Biochem. 414:297–99
107. Tembe BL, McCammon JA. 2001. Ligand receptor interactions. Comput. Chem. 8:281–83
108. Tomlinson E. 1983. Enthalpy-entropy compensation analysis of pharmaceutical, biochemical and biological systems. Int. J. Pharm. 13:115–44
109. Tzeng SR, Kalodimos CG. 2012. Protein activity regulation by conformational entropy. Nature 488:236–
40
110. Varadarajan R, Connelly PR, Sturtevant JM, Richards FM. 1992. Heat capacity changes for proteinpeptide interactions in the ribonuclease S system. Biochemistry 31:1421–26
111. Velázquez-Campoy A, Freire E. 2006. Isothermal titration calorimetry to determine association constants
for high-affinity ligands. Nat. Protoc. 1:186–91
112. Velázquez-Campoy A, Ohtaka H, Nezami A, Muzammil S, Freire E. 2004. Isothermal titration calorimetry. Curr. Protoc. Cell Biol. 17.8.1:1–24
113. Ward JM, Gorenstein NM, Tian J, Martin SF, Post CB. 2010. Constraining binding hot spots: NMR
and molecular dynamics simulations provide a structural explanation for enthalpy-entropy compensation
in SH2-ligand binding. J. Am. Chem. Soc. 132:11058–70
114. Whitesides GM, Snyder PW, Moustakas DT, Mirica KA. 2008. Designing ligands to bind tightly to
proteins. In Physical Biology: From Atoms to Medicine, ed. AH Zewail, pp. 189–215. Singapore: World
Scientific
115. Wiseman T, Williston S, Brandts JF, Lin LN. 1989. Rapid measurement of binding constants and heats
of binding using a new titration calorimeter. Anal. Biochem. 179:131–37
116. Wlodawer A, Vondrasek J. 1998. Inhibitors of HIV-1 protease: a major success of structure-assisted drug
design. Annu. Rev. Biophys. Biomol. Struct. 27:249–84
117. Woo HJ, Roux B. 2005. Calculation of absolute protein-ligand binding free energy from computer
simulations. Proc. Natl. Acad. Sci. USA 102:6825–30
118. Zeevaart JG, Wang L, Thakur VV, Leung CS, Tirado-Rives J, et al. 2008. Optimization of azoles
as anti-human immunodeficiency virus agents guided by free-energy calculations. J. Am. Chem. Soc.
130:9492–99
119. Zhou HX, Gilson MK. 2009. Theory of free energy and entropy in noncovalent binding. Chem. Rev.
109:4092–107
Annu. Rev. Biophys. 2013.42:121-142. Downloaded from www.annualreviews.org
by 66.108.94.177 on 05/14/13. For personal use only.
BB42CH06-Chodera
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Contents
Annual Review of
Biophysics
Volume 42, 2013
Doing Molecular Biophysics: Finding, Naming, and Picturing Signal
Within Complexity
Jane S. Richardson and David C. Richardson ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 1
Structural Biology of the Proteasome
Erik Kish-Trier and Christopher P. Hill ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣29
Common Folds and Transport Mechanisms of Secondary
Active Transporters
Yigong Shi ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣51
Coarse-Graining Methods for Computational Biology
Marissa G. Saunders and Gregory A. Voth ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣73
Electrophysiological Characterization of Membrane
Transport Proteins
Christof Grewer, Armanda Gameiro, Thomas Mager, and Klaus Fendler ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣95
Entropy-Enthalpy Compensation: Role and Ramifications in
Biomolecular Ligand Recognition and Design
John D. Chodera and David L. Mobley ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 121
Molecular Mechanisms of Drug Action: An Emerging View
James M. Sonner and Robert S. Cantor ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 143
The Underappreciated Role of Allostery in the Cellular Network
Ruth Nussinov, Chung-Jung Tsai, and Buyong Ma ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 169
Structural Insights into the Evolution of the Adaptive Immune System
Lu Deng, Ming Luo, Alejandro Velikovsky, and Roy A. Mariuzza ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 191
Molecular Mechanisms of RNA Interference
Ross C. Wilson and Jennifer A. Doudna ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 217
Molecular Traffic Jams on DNA
Ilya J. Finkelstein and Eric C. Greene ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 241
vii
BB42-Frontmatter
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Advances, Interactions, and Future Developments in the CNS, Phenix,
and Rosetta Structural Biology Software Systems
Paul D. Adams, David Baker, Axel T. Brunger, Rhiju Das, Frank DiMaio,
Randy J. Read, David C. Richardson, Jane S. Richardson,
and Thomas C. Terwilliger ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 265
Considering Protonation as a Posttranslational Modification
Regulating Protein Structure and Function
André Schönichen, Bradley A. Webb, Matthew P. Jacobson, and Diane L. Barber ♣ ♣ ♣ ♣ ♣ 289
Annu. Rev. Biophys. 2013.42:121-142. Downloaded from www.annualreviews.org
by 66.108.94.177 on 05/14/13. For personal use only.
Energy Functions in De Novo Protein Design: Current Challenges
and Future Prospects
Zhixiu Li, Yuedong Yang, Jian Zhan, Liang Dai, and Yaoqi Zhou ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 315
Quantitative Modeling of Bacterial Chemotaxis: Signal Amplification
and Accurate Adaptation
Yuhai Tu ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 337
Influences of Membrane Mimetic Environments on Membrane
Protein Structures
Huan-Xiang Zhou and Timothy A. Cross ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 361
High-Speed AFM and Applications to Biomolecular Systems
Toshio Ando, Takayuki Uchihashi, and Noriyuki Kodera ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 393
Super-Resolution in Solution X-Ray Scattering and Its Applications to
Structural Systems Biology
Robert P. Rambo and John A. Tainer ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 415
Molecular Basis of NF-κB Signaling
Johanna Napetschnig and Hao Wu ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 443
Regulation of Noise in Gene Expression
Alvaro Sanchez, Sandeep Choubey, and Jane Kondev ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 469
Evolution in Microbes
Edo Kussell ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 493
Protein Structure Determination by Magic-Angle Spinning Solid-State
NMR, and Insights into the Formation, Structure, and Stability of
Amyloid Fibrils
Gemma Comellas and Chad M. Rienstra ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 515
Structural Studies of RNase P
Alfonso Mondragón ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 537
On the Universe of Protein Folds
Rachel Kolodny, Leonid Pereyaslavets, Abraham O. Samson, and Michael Levitt ♣ ♣ ♣ ♣ ♣ ♣ 559
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Torque Measurement at the Single-Molecule Level
Scott Forth, Maxim Y. Sheinin, James Inman, and Michelle D. Wang ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 583
Modeling Gene Expression in Time and Space
Pau Rué and Jordi Garcia-Ojalvo ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 605
Mechanics of Dynamin-Mediated Membrane Fission
Sandrine Morlot and Aurélien Roux ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 629
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Nanoconfinement and the Strength of Biopolymers
Tristan Giesa and Markus J. Buehler ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 651
Solid-State NMR of Nanomachines Involved in Photosynthetic
Energy Conversion
A. Alia, Francesco Buda, Huub J.M. de Groot, and Jörg Matysik ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 675
Index
Cumulative Index of Contributing Authors, Volumes 38–42 ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ 701
Errata
An online log of corrections to Annual Review of Biophysics articles may be found at
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Contents
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