Binding Entropy Can Be Predicted by Crystallographic Ensembles
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Curated by eLife
eLife Assessment
This study provides a useful demonstration that, at least for the systems examined, aspects of the entropic contribution to protein-ligand binding can be inferred directly from crystallographic data. In doing so, it strengthens a view of crystal structures as heterogeneous ensembles that are amenable to statistical-mechanical analysis rather than purely static models. The analytical approaches are carefully developed and transparently discussed, with thoughtful consideration of both successful and less effective methods, lending solid support to the central conclusions. However, because the analysis is based on a relatively small and narrowly sampled set of protein-ligand complexes, the generality of these findings remains speculative and will require broader validation.
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Abstract
Protein-ligand binding is governed by free energy, comprising both enthalpic and entropic contributions. Yet structural interpretations of binding thermodynamics have predominantly focused on enthalpic interactions, largely neglecting entropy because it is difficult to quantify from static structural models. Here, we developed multiconformer ensemble models to analyze high-resolution X-ray crystallography structures and estimate both protein and solvent conformational entropies. These ensemble models successfully predicted experimental binding entropies measured by isothermal titration calorimetry for over 70 protein-ligand pairs across 12 proteins, revealing a strong linear correlation. Protein entropy, estimated using crystallographic order parameters that capture both harmonic and anharmonic motion, correlates linearly with experimental binding entropy. Incorporating resolution-corrected differences in water-molecule counts substantially improves predictions, demonstrating that protein and solvent contributions must be considered jointly. Analysis of water-protein hydrogen bonding networks partially explains entropic differences across complexes. These results establish that crystallographic ensembles can quantify binding entropy, enabling explicit entropic considerations in structure-based studies of molecular recognition for both functional analysis and drug design.
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eLife Assessment
This study provides a useful demonstration that, at least for the systems examined, aspects of the entropic contribution to protein-ligand binding can be inferred directly from crystallographic data. In doing so, it strengthens a view of crystal structures as heterogeneous ensembles that are amenable to statistical-mechanical analysis rather than purely static models. The analytical approaches are carefully developed and transparently discussed, with thoughtful consideration of both successful and less effective methods, lending solid support to the central conclusions. However, because the analysis is based on a relatively small and narrowly sampled set of protein-ligand complexes, the generality of these findings remains speculative and will require broader validation.
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Reviewer #1 (Public review):
Summary:
The authors show that if they generate a weighted multi-conformer ensemble of structural models to fit crystallographic electron density data, the application of statistical mechanical methodologies to that ensemble can provide reasonable estimates of configurational entropy terms related to protein-ligand binding.
Strengths:
A fair range of proteins (12) and ligands (70) is included in the study. The analytical methodologies are well described. Both successful and less successful analytical approaches are discussed, and the latter are frequently as insightful as the former.
Weaknesses:
Compared to the universe of protein-ligand complexes, this dataset is inevitably very limited, so the generality of the observations made here remains speculative. Though a fair range of proteins is studied, the …
Reviewer #1 (Public review):
Summary:
The authors show that if they generate a weighted multi-conformer ensemble of structural models to fit crystallographic electron density data, the application of statistical mechanical methodologies to that ensemble can provide reasonable estimates of configurational entropy terms related to protein-ligand binding.
Strengths:
A fair range of proteins (12) and ligands (70) is included in the study. The analytical methodologies are well described. Both successful and less successful analytical approaches are discussed, and the latter are frequently as insightful as the former.
Weaknesses:
Compared to the universe of protein-ligand complexes, this dataset is inevitably very limited, so the generality of the observations made here remains speculative. Though a fair range of proteins is studied, the dynamic range in the binding affinity data is limited. The practical utility of the approach is never really commented on.
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Reviewer #2 (Public review):
The manuscript by Miller and Wankowicz (M&W) develops a crystallographic approach to predict the contribution of protein conformational entropy to the total binding entropy using multi-conformer ensemble models. The approach loosely follows the path developed by Wand using NMR relaxation methods. Their approach is to generate local crystallographic order parameters (analogous to NMR order parameters) to estimate protein conformational entropy and then combine this with statements about water entropy. The static view of the ensemble is perhaps easier to grasp, with respect to entropy, than the NMR-based dynamical view. This approach is potentially ground-breaking and of great importance given the ease, relative to NMR, with which the source data can be obtained. However, the approach has several deficiencies, …
Reviewer #2 (Public review):
The manuscript by Miller and Wankowicz (M&W) develops a crystallographic approach to predict the contribution of protein conformational entropy to the total binding entropy using multi-conformer ensemble models. The approach loosely follows the path developed by Wand using NMR relaxation methods. Their approach is to generate local crystallographic order parameters (analogous to NMR order parameters) to estimate protein conformational entropy and then combine this with statements about water entropy. The static view of the ensemble is perhaps easier to grasp, with respect to entropy, than the NMR-based dynamical view. This approach is potentially ground-breaking and of great importance given the ease, relative to NMR, with which the source data can be obtained. However, the approach has several deficiencies, only some of which are noted by the authors.
Like the initial Wand approach (Frederick et al Nature, 2007), M&W develop a simple counting relationship between members of the ensemble and a statement about conformational entropy. For reasons that are not clear, M&W utilize "per residue" scaling, which was initially introduced by Wand but later discarded for the more physically meaningful "per torsion angle" scaling. As noted in the Nature 2007 paper, this assumes uncorrelated occupancy. The current Wand approach (Caro et al PNAS, 2017) subsumes correlated occupancy and potentially incomplete sampling of the ensemble into an empirically determined scaling parameter (sd). This is likely a major contributor to the mysterious 1/4 scaling factor that is introduced. It is not clear to me how discrete conformational states are counted from the qFit models. Using the B-factor, as opposed to a thermal factor, to account for motion in a rotamer well seems suspect. With some irony, M&W only look at chi-1 rotamers in distinct contrast to the NMR approach, which looks at the end of the side chain, which captures the entire disorder. On the other hand, the crystallographic approach "sees" all side chains, whereas the NMR approach, as currently rendered, looks only at methyl-bearing side chains and requires coupling to neighbors to report on all side chains (see Kasinath JACS 2013 and Wand & Sharp ARB 2018).
Nevertheless, as noted by Nature 2007, the fact that a linear relationship is seen between the apparent conformational entropy and total binding entropy suggests that the former is a major component of the latter. It also reinforces the idea that dSrt is constant for higher affinity complexes, i.e., residual rigid-body motion of protein relative to ligand is limited (a conclusion reached in PNAS 2017) but not mentioned. This is an important result.
The classic hydrophobic effect is potentially a significant component of total binding entropy. Here, the manuscript falls flat by focusing on crystallographically resolved waters. As shown in site-resolved detail (Nucci et al, NSMB 2011 and others), hydration water has a range of residual motion (entropy) that will modulate contributions to water entropy upon displacement from an interface. A very clear example of the potential for large contributions was demonstrated in the wet interface of a barnase-DNA complex (PNAS 2017). The fact that the classic dASA treatment failed, I think, points to problems elsewhere in the approach.
I note that the range of ligand types explored by M&W is quite limited as compared to PNAS 2017, making generalization somewhat difficult (see Wand Cur. Opin. Struct. Biol, 2013 for why this is important). Finally, it is disappointing that the authors chose not to examine systems common to PNAS 2017, making direct comparison to the NMR method impossible.
In summary, this manuscript sets the field in a new direction. It is a first serious look at conformational entropy using crystallographic approaches. If fully validated, this approach would permit an explosion of insight since the crystallography is now straightforward, very fast and capable of approaching larger systems, relative to the NMR approach. However, there are missing quantitative elements represented by a formal relationship that is fitted by the data. I do not think this is a fatal flaw for this manuscript, however. If the supplementary material is improved for clarity and completeness (e.g, include tables of thermodynamic data; conformer analysis; B-factors) such that all figures could be independently reproduced and therefore analyzed in different ways, and the comments made above are addressed, if not resolved, then I think this manuscript could become a keystone for this new direction.
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