Side-chain conformational entropy in protein unfolded states

The largest force disfavoring the folding of a protein is the loss of conformational entropy. A large contribution to this entropy loss is due to the side-chains, which are restricted, although not immobilized, in the folded protein. In order to accurately estimate the loss of side-chain conformational entropy that occurs upon folding it is necessary to have accurate estimates of the amount of entropy possessed by side-chains in the ensemble of unfolded states. A new scale of side-chain conformational entropies is presented here. This scale was derived from Monte Carlo computer simulations of small peptide models. It is demonstrated that the entropies are independent of host peptide length. This new scale has the advantage over previous scales of being more precise with low standard errors. Better estimates are obtained for long (e.g., Arg and Lys) and rare (e.g., Trp and Met) side-chains. Excellent agreement with previous side-chain entropy scales is achieved, indicating that further advancements in accuracy are likely to be small at best. Strikingly, longer side-chains are found to possess a smaller fraction of the theoretical maximum entropy available than short side-chains. This indicates that rotations about torsions after chi(2) are significantly affected by side-chain interactions with the polypeptide backbone. This finding invalidates previous assumptions about side-chain-backbone interactions. Proteins 2000;40:443-450.     

Optimization of van der Waals energy for protein side-chain placement and design

Computational determination of optimal side-chain conformations in protein structures has been a long-standing and challenging problem. Solving this problem is important for many applications including homology modeling, protein docking, and for placing small molecule ligands on protein-binding sites. Programs available as of this writing are very fast and reasonably accurate, as measured by deviations of side-chain dihedral angles; however, often due to multiple atomic clashes, they produce structures with high positive energies. This is problematic in applications where the energy values are important, for example when placing small molecules in docking applications; the relatively small binding energy of the small molecule is drowned by the large energy due to atomic clashes that hampers finding the lowest energy state of the docked ligand. To address this we have developed an algorithm for generating a set of side-chain conformations that is dense enough that at least one of its members would have a root mean-square deviation of no more than R Å from any possible side-chain conformation of the amino acid. We call such a set a side-chain cover set of order R for the amino acid. The size of the set is constrained by the energy of the interaction of the side chain to the backbone atoms. Then, side-chain cover sets are used to optimize the conformation of the side chains given the coordinates of the backbone of a protein. The method we use is based on a variety of dead-end elimination methods and the recently discovered dynamic programming algorithm for this problem. This was implemented in a computer program called Octopus where we use side-chain cover sets with very small values for R, such as 0.1 Å, which ensures that for each amino-acid side chain the set contains a conformation with a root mean-square deviation of, at most, R from the optimal conformation. The side-chain dihedral-angle accuracy of the program is comparable to other implementations; however, it has the important advantage that the structures produced by the program have negative energies that are very close to the energies of the crystal structure for all tested proteins.     

Protein design simulations suggest that side-chain conformational entropy is not a strong determinant of amino acid environmental preferences

Loss of side-chain conformational entropy is an important force opposing protein folding and the relative preferences of the amino acids for being buried or solvent exposed may be partially determined by which amino acids lose more side-chain entropy when placed in the core of a protein. To investigate these preferences, we have incorporated explicit modeling of side-chain entropy into the protein design algorithm, RosettaDesign. In the standard version of the program, the energy of a particular sequence for a fixed backbone depends only on the lowest energy side-chain conformations that can be identified for that sequence. In the new model, the free energy of a single amino acid sequence is calculated by evaluating the average energy and entropy of an ensemble of structures generated by Monte Carlo sampling of amino acid side-chain conformations. To evaluate the impact of including explicit side-chain entropy, sequences were designed for 110 native protein backbones with and without the entropy model. In general, the differences between the two sets of sequences are modest, with the largest changes being observed for the longer amino acids: methionine and arginine. Overall, the identity between the designed sequences and the native sequences does not increase with the addition of entropy, unlike what is observed when other key terms are added to the model (hydrogen bonding, Lennard-Jones energies, and solvation energies). These results suggest that side-chain conformational entropy has a relatively small role in determining the preferred amino acid at each residue position in a protein.     

Angular variances for internal bond rotations of side chains in GXG-based tripeptides derived from (13)C-NMR relaxation measurements: Implications to protein folding

The study of backbone and side-chain internal motions in proteins and peptides is crucial to having a better understanding of protein/peptide "structure" and to characterizing unfolded and partially folded states of proteins and peptides. To achieve this, however, requires establishing a baseline for internal motions and motional restrictions for all residues in the fully, solvent-exposed "unfolded state." GXG-based tripeptides are the simpliest peptides where residue X is fully solvent exposed in the context of an actual peptide. In this study, a series of GXG-based tripeptides has been synthesized with X being varied to include all twenty common amino acid residues. Proton-coupled and -decoupled (13)C-nmr relaxation measurements have been performed on these twenty tripeptides and various motional models (Lipari-Szabo model free approach, rotational anisotropic diffusion, rotational fluctuations within a potential well, rotational jump model) have been used to analyze relaxation data for derivation of angular variances and motional correlation times for backbone and side-chain chi(1) and chi(2) bonds and methyl group rotations. At 298 K, backbone motional correlation times range from about 50 to 85 ps, whereas side-chain motional correlation times show a much broader spread from about 18 to 80 ps. Angular variances for backbone phi,psi bond rotations range from 11 degrees to 23 degrees and those for side chains vary from 5 degrees to 24 degrees for chi(1) bond rotations and from 5 degrees to 27 degrees for chi(2) bond rotations. Even in these peptide models of the "unfolded state," side-chain angular variances can be as restricted as those for backbone and beta-branched (valine, threonine, and isoleucine) and aromatic side chains display the most restricted motions probably due to steric hinderence with backbone atoms. Comparison with motional data on residues in partially folded, beta-sheet-forming peptides indicates that side-chain motions of at least hydrophobic residues are less restricted in the partially folded state, suggesting that an increase in side-chain conformational entropy may help drive early-stage protein folding. Copyright 1999 John Wiley & Sons, Inc.     

Retention of Conformational Entropy upon Calmodulin Binding to Target Peptides Is Driven by Transient Salt Bridges

Calmodulin (CaM) is a highly flexible calcium-binding protein that mediates signal transduction through an ability to differentially bind to highly variable binding sequences in target proteins. To identify how binding affects CaM motions, and its relationship to conformational entropy and target peptide sequence, we have employed fully atomistic, explicit solvent molecular dynamics simulations of unbound CaM and CaM bound to five different target peptides. The calculated CaM conformational binding entropies correlate with experimentally derived conformational entropies with a correlation coefficient R² of 0.95. Selected side-chain interactions with target peptides restrain interhelical loop motions, acting to tune the conformational entropy of the bound complex via widely distributed CaM motions. In the complex with the most conformational entropy retention (CaM in complex with the neuronal nitric oxide synthase binding sequence), Lys-148 at the C-terminus of CaM forms transient salt bridges alternating between Glu side chains in the N-domain, the central linker, and the binding target. Additional analyses of CaM structures, fluctuations, and CaM-target interactions illuminate the interplay between electrostatic, side chain, and backbone properties in the ability of CaM to recognize and discriminate against targets by tuning its conformational entropy, and suggest a need to consider conformational dynamics in optimizing binding affinities.     

Side-chain flexibility in protein-ligand binding: the minimal rotation hypothesis

The goal of this work is to learn from nature about the magnitudes of side-chain motions that occur when proteins bind small organic molecules, and model these motions to improve the prediction of protein-ligand complexes. Following analysis of protein side-chain motions upon ligand binding in 63 complexes, we tested the ability of the docking tool SLIDE to model these motions without being restricted to rotameric transitions or deciding which side chains should be considered as flexible. The model tested is that side-chain conformational changes involving more atoms or larger rotations are likely to be more costly and less prevalent than small motions due to energy barriers between rotamers and the potential of large motions to cause new steric clashes. Accordingly, SLIDE adjusts the protein and ligand side groups as little as necessary to achieve steric complementarity. We tested the hypothesis that small motions are sufficient to achieve good dockings using 63 ligands and the apo structures of 20 different proteins and compared SLIDE side-chain rotations to those experimentally observed. None of these proteins undergoes major main-chain conformational change upon ligand binding, ensuring that side-chain flexibility modeling is not required to compensate for main-chain motions. Although more frugal in the number of side-chain rotations performed, this model substantially mimics the experimentally observed motions. Most side chains do not shift to a new rotamer, and small motions are both necessary and sufficient to predict the correct binding orientation and most protein-ligand interactions for the 20 proteins analyzed.     

Rational Design and Biophysical Characterization of Thioredoxin-Based Aptamers: Insights into Peptide Grafting

Peptide aptamers are simple structures, often made up of a single-variable peptide loop constrained within a constant scaffold protein. Aptamers were rationally designed by inserting peptides into a solvent-exposed loop on thioredoxin (Trx). They were designed to interact with the proteins elongation initiation factor 4E (eIF4E) and mouse double minute 2 (MDM2) and were then validated by competitive fluorescence anisotropy experiments. The constructed aptamers interacted with eIF4E and MDM2 with apparent K_d values of 1.25 ± 0.06 μM and 0.09 ± 0.01 μM, respectively, as determined by isothermal titration calorimetry (ITC). The MDM2 aptamer (SuperTIP) interacted ∼ 2-fold more tightly with MDM2 than the free linear peptide (12.1 peptide), while the eIF4E aptamer elongation initiation factor 4GI-SG interacted ∼ 5-fold less strongly than the free linear peptide (elongation initiation factor 4GI). These differences in binding with respect to each aptamer's free peptide reveal that there are more factors involved than just constraining a peptide in a scaffold that lead to tighter binding. ITC studies of aptamer interactions reveal an enthalpic component more favorable than that for the free linear peptides, as well as a larger unfavorable entropic component. These results indicated that stapling of the free peptide in the scaffold increases the favorable enthalpy of the interaction with the target protein. Thermostability studies also revealed that peptide insertion significantly destabilized the Trx scaffold by ∼ 27 °C. It is this destabilization that leads to an increase in the flexibility of the Trx scaffold, which presumably is lost upon the aptamer's interaction with the target protein and is the cause of the increase in unfavorable entropy in the ITC studies. The precise origin of the enthalpic effect was further studied using molecular dynamics for the MDM2-SuperTIP system, which revealed that there were also favorable electrostatic interactions between the Trx scaffold and the MDM2 protein itself, as well as with the inserted peptide. This work reveals that any increase in the binding affinity of an aptamer over a free peptide is dependent on the increase in the favorable enthalpy of binding, which is ideally caused by stapling of the peptide or by additional interactions between the aptamer protein and its target. These need to be sufficient to compensate for the destabilization of the scaffold by peptide insertion. These observations will be useful in future aptamer designs.     

Alternate Binding Modes for a Ubiquitin-SH3 Domain Interaction Studied by NMR Spectroscopy

Surfaces of many binding domains are plastic, enabling them to interact with multiple targets. An understanding of how they bind and recognize their partners is therefore predicated on characterizing such dynamic interfaces. Yet, these interfaces are difficult to study by standard biophysical techniques that often ‘freeze’ out conformations or that produce data averaged over an ensemble of conformers. In this study, we used NMR spectroscopy to study the interaction between the C-terminal SH3 domain of CIN85 and ubiquitin that involves the ‘classical’ binding sites of these proteins. Notably, chemical shift titration data of one target with another and relaxation dispersion data that report on millisecond time scale exchange processes are both well fit to a simple binding model in which free protein is in equilibrium with a single bound conformation. However, dissociation constants and chemical shift differences between free and bound states measured from both classes of experiment are in disagreement. It is shown that the data can be reconciled by considering three-state binding models involving two distinct bound conformations. By combining titration and dispersion data, kinetic and thermodynamic parameters of the three-state binding reaction are obtained along with chemical shifts for each state. A picture emerges in which one bound conformer has increased entropy and enthalpy relative to the second and chemical shifts similar to that of the free state, suggesting a less packed interface. This study provides an example of the interplay between entropy and enthalpy to fine-tune molecular interactions involving the same binding surfaces.     

Thermodynamics of GTP and GDP Binding to Bacterial Initiation Factor 2 Suggests Two Types of Structural Transitions

During initiation of messenger RNA translation in bacteria, the GTPase initiation factor (IF) 2 plays major roles in the assembly of the preinitiation 30S complex and its docking to the 50S ribosomal subunit leading to the 70S initiation complex, ready to form the first peptide bond in a nascent protein. Rapid and accurate initiation of bacterial protein synthesis is driven by conformational changes in IF2, induced by GDP-GTP exchange and GTP hydrolysis. We have used isothermal titration calorimetry and linear extrapolation to characterize the thermodynamics of the binding of GDP and GTP to free IF2 in the temperature interval 4-37 °C. IF2 binds with about 20-fold and 2-fold higher affinity for GDP than for GTP at 4 and 37 °C, respectively. The binding of IF2 to both GTP and GDP is characterized by a large heat capacity change (− 868 ± 25 and − 577 ± 23 cal mol^− 1 K^− 1, respectively), associated with compensatory changes in binding entropy and enthalpy. From our data, we propose that GTP binding to IF2 leads to protection of hydrophobic amino acid residues from solvent by the locking of switch I and switch II loops to the γ-phosphate of GTP, as in the case of elongation factor G. From the large heat capacity change (also upon GDP binding) not seen in the case of elongation factor G, we propose the existence of yet another type of conformational change in IF2, which is induced by GDP and GTP alike. Also, this transition is likely to protect hydrophobic groups from solvent, and its functional relevance is discussed.     

A protocol for CABS-dock protein–peptide docking driven by side-chain contact information

Background

The characterization of protein–peptide interactions is a challenge for computational molecular docking. Protein–peptide docking tools face at least two major difficulties: (1) efficient sampling of large-scale conformational changes induced by binding and (2) selection of the best models from a large set of predicted structures. In this paper, we merge an efficient sampling technique with external information about side-chain contacts to sample and select the best possible models.

Methods

In this paper we test a new protocol that uses information about side-chain contacts in CABS-dock protein–peptide docking. As shown in our recent studies, CABS-dock enables efficient modeling of large-scale conformational changes without knowledge about the binding site. However, the resulting set of binding sites and poses is in many cases highly diverse and difficult to score.

Results

As we demonstrate here, information about a single side-chain contact can significantly improve the prediction accuracy. Importantly, the imposed constraints for side-chain contacts are quite soft. Therefore, the developed protocol does not require precise contact information and ensures large-scale peptide flexibility in the broad contact area.

Conclusions

The demonstrated protocol provides the extension of the CABS-dock method that can be practically used in the structure prediction of protein–peptide complexes guided by the knowledge of the binding interface.

     

Association entropy in adsorption processes

The association of two species to form a bound complex, e.g., the binding of a ligand to a protein or the adsorption of a peptide on a lipid membrane, involves an entropy loss, reflecting the conversion of free translational and rotational degrees of freedom into bound motions. Previous theoretical estimates of the standard entropy change in bimolecular binding processes, DeltaS(o), have been derived from the root-mean-square fluctuations in protein crystals, suggesting DeltaS(o) approximately -50 e.u., i.e., TDeltaS degrees approximately -25 kT = -15 kcal/mol. In this work we focus on adsorption, rather than binding processes. We first present a simple statistical-thermodynamic scheme for calculating the adsorption entropy, including its resolution into translational and rotational contributions, using the known distance-orientation dependent binding (adsorption) potential. We then utilize this scheme to calculate the free energy of interaction and entropy of pentalysine adsorption onto a lipid membrane, obtaining TDeltaS(o) approximately -1.7 kT approximately -1.3 kcal/mol. Most of this entropy change is due to the conversion of one free translation into a bound motion, the rest arising from the confinement of two rotational degrees of freedom. The smaller entropy loss in adsorption compared to binding processes arises partly because a smaller number of degrees of freedom become restricted, but mainly due to the fact that the binding potential is much "softer."     

Ligand-dependent dynamics and intramolecular signaling in a PDZ domain

Allosteric communication is a fundamental process that proteins use to propagate signals from one site to functionally important distal sites. Although allostery is usually associated with multimeric proteins and enzymes, “long-range” communication may be a fundamental property of proteins. In some cases, communication occurs with minimal structural change. PDZ (post-synaptic density-95/discs large/zonula occludens-1) domains are small, protein-protein binding modules that can use multiple surfaces for docking diverse molecules. Furthermore, these domains have long-range energetic couplings that link the ligand-binding site to distal regions of the structure. Here, we show that allosteric behavior in a representative member of the PDZ domain family may be directly detected using side-chain methyl dynamics measurements. The changes in side-chain dynamics parameters in the second PDZ domain from the human tyrosine phosphatase 1E (hPTP1E) were determined upon binding a peptide target. Long-range dynamic effects were detected that correspond to previously observed pair-wise energetic couplings. These results provide one of the first experimental examples for the potential role of ps-ns timescale dynamics in propagating long-range signals within a protein, and reinforce the idea that dynamic fluctuations in proteins contribute to allosteric signal transduction.     

Unique example of amyloid aggregates stabilized by main chain H-bond instead of the steric zipper: molecular dynamics study of the amyloidogenic segment of amylin wild-type and mutants

Most proteins do not aggregate while in their native functional states. However, they may be disturbed from their native conformation by certain change in the environment, and form unwanted oligomeric or polymeric aggregates. Recent experimental data demonstrate that soluble oligomers of amyloidogenic proteins are responsible for amyloidosis and its cytotoxicity. Human islet amyloid polypeptide (IAPP or amylin) is a 37-residue hormone found as fibrillar deposits in pancreatic extracts of nearly all type II diabetics. In this study we performed in silico mutation analysis to examine the stability of the double layer five strand aggregates formed by heptapeptide NNFGAIL segment from amyline peptide. This segment is one of the shortest fragments that can form amyloid fibrils similar to those formed by the full length peptide. The mutants obtained by single glycine replacement were also studied to investigate the specificity of the dry self-complementary interface between the neighboring β-sheet layers. The molecular dynamics simulations of the aggregates run for 20 ns at 330 K, the degree of the aggregate disassembly was investigated using several geometry analysis tools: the root mean square deviations of the C_α atoms, root mean square fluctuations per residue, twist angles, interstrand distances, fraction of the secondary structure elements, and number of H-bonds. The analysis shows that most mutations make the aggregates unstable, and their stabilities were dependent to a large extent on the position of replaced residues. Our mutational simulations are in agreement with the pervious experimental observations. We also used free binding energy calculations to determine the role of different components: nonpolar effects, electrostatics and entropy in binding. Nonpolar effects remained consistently more favorable in wild type and mutants reinforcing the importance of hydrophobic effects in protein-protein binding. While entropy systematically opposed binding in all cases, there was no clear trend in the entropy difference between wildtype and glycine mutants. Free energy decomposition shows residues situated at the interface were found to make favorable contributions to the peptide-peptide association. The study of the wild type and mutants in an explicit solvent could provide valuable insight into the future computer guided design efforts for the amyloid aggregation inhibitor.     

Protein surface roughness accounts for binding free energy of Plasmepsin II‐ligand complexes

The calculation of absolute binding affinities for protein‐inhibitor complexes remains as one of the main challenges in computational structure‐based ligand design. The present work explored the calculations of surface fractal dimension (as a measure of surface roughness) and the relationship with experimental binding free energies of Plasmepsin II complexes. Plasmepsin II is an attractive target for novel therapeutic compounds to treat malaria. However, the structural flexibility of this enzyme is a drawback when searching for specific inhibitors. Concerning that, we performed separate explicitly solvated molecular dynamics simulations using the available high‐resolution crystal structures of different Plasmepsin II complexes. Molecular dynamics simulations allowed a better approximation to systems dynamics and, therefore, a more reliable estimation of surface roughness. This constitutes a novel approximation in order to obtain more realistic values of fractal dimension, because previous works considered only x‐ray structures. Binding site fractal dimension was calculated considering the ensemble of structures generated at different simulation times. A linear relationship between binding site fractal dimension and experimental binding free energies of the complexes was observed within 20 ns. Previous studies of the subject did not uncover this relationship. Regression model, coined FD model, was built to estimate binding free energies from binding site fractal dimension values. Leave‐one‐out cross‐validation showed that our model reproduced accurately the absolute binding free energies for our training set (R² = 0.76; <|error|> =0.55 kcal/mol; SD_error = 0.19 kcal/mol). The fact that such a simple model may be applied raises some questions that are addressed in the article.     

Highly stable binding proteins derived from the hyperthermophilic Sso7d scaffold

We have shown that highly stable binding proteins for a wide spectrum of targets can be generated through mutagenesis of the Sso7d protein from the hyperthermophilic archaeon Sulfolobus solfataricus. Sso7d is a small (∼ 7 kDa, 63 amino acids) DNA-binding protein that lacks cysteine residues and has a melting temperature of nearly 100 °C. We generated a library of 10⁸ Sso7d mutants by randomizing 10 amino acid residues on the DNA-binding surface of Sso7d, using yeast surface display. Binding proteins for a diverse set of model targets could be isolated from this library; our chosen targets included a small organic molecule (fluorescein), a 12 amino acid peptide fragment from the C-terminus of β-catenin, the model proteins hen egg lysozyme and streptavidin, and immunoglobulins from chicken and mouse. Without the application of any affinity maturation strategy, the binding proteins isolated had equilibrium dissociation constants in the nanomolar to micromolar range. Further, Sso7d-derived binding proteins could discriminate between closely related immunoglobulins. Mutant proteins based on Sso7d were expressed at high yields in the Escherichia coli cytoplasm. Despite extensive mutagenesis, Sso7d mutants have high thermal stability; five of six mutants analyzed have melting temperatures > 89 °C. They are also resistant to chemical denaturation by guanidine hydrochloride and retain their secondary structure after extended incubation at extreme pH values. Because of their favorable properties, such as ease of recombinant expression, and high thermal, chemical and pH stability, Sso7d-derived binding proteins will have wide applicability in several areas of biotechnology and medicine.     

Molecular crowding inhibits intramolecular breathing motions in proteins

In aqueous solution some proteins undergo large-scale movements of secondary structures, subunits or domains, referred to as protein “breathing”, that define a native-state ensemble of structures. These fluctuations are sensitive to the nature and concentration of solutes and other proteins and are thereby expected to be different in the crowded interior of a cell than in dilute solution. Here we use a combination of wide angle X-ray scattering (WAXS) and computational modeling to derive a quantitative measure of the spatial scale of conformational fluctuations in a protein solution. Concentration-dependent changes in the observed scattering intensities are consistent with a model of structural fluctuations in which secondary structures undergo rigid-body motions relative to one another. This motion increases with decreasing protein concentration or increasing temperature. Analysis of a set of five structurally and functionally diverse proteins reveals a diversity of kinetic behaviors. Proteins with multiple disulfide bonds exhibit little or no increase in breathing in dilute solutions. The spatial extent of structural fluctuations appears highly dependent on both protein structure and concentration and is universally suppressed at very high protein concentrations.     

Conformer selection and induced fit in flexible backbone protein-protein docking using computational and NMR ensembles

Accommodating backbone flexibility continues to be the most difficult challenge in computational docking of protein-protein complexes. Towards that end, we simulate four distinct biophysical models of protein binding in RosettaDock, a multiscale Monte-Carlo-based algorithm that uses a quasi-kinetic search process to emulate the diffusional encounter of two proteins and to identify low-energy complexes. The four binding models are as follows: (1) key-lock (KL) model, using rigid-backbone docking; (2) conformer selection (CS) model, using a novel ensemble docking algorithm; (3) induced fit (IF) model, using energy-gradient-based backbone minimization; and (4) combined conformer selection/induced fit (CS/IF) model. Backbone flexibility was limited to the smaller partner of the complex, structural ensembles were generated using Rosetta refinement methods, and docking consisted of local perturbations around the complexed conformation using unbound component crystal structures for a set of 21 target complexes. The lowest-energy structure contained > 30% of the native residue-residue contacts for 9, 13, 13, and 14 targets for KL, CS, IF, and CS/IF docking, respectively. When applied to 15 targets using nuclear magnetic resonance ensembles of the smaller protein, the lowest-energy structure recovered at least 30% native residue contacts in 3, 8, 4, and 8 targets for KL, CS, IF, and CS/IF docking, respectively. CS/IF docking of the nuclear magnetic resonance ensemble performed equally well or better than KL docking with the unbound crystal structure in 10 of 15 cases. The marked success of CS and CS/IF docking shows that ensemble docking can be a versatile and effective method for accommodating conformational plasticity in docking and serves as a demonstration for the CS theory—that binding-competent conformers exist in the unbound ensemble and can be selected based on their favorable binding energies.     

Determination of Ensemble-Average Pairwise Root Mean-Square Deviation from Experimental B-Factors

Root mean-square deviation (RMSD) after roto-translational least-squares fitting is a measure of global structural similarity of macromolecules used commonly. On the other hand, experimental x-ray B-factors are used frequently to study local structural heterogeneity and dynamics in macromolecules by providing direct information about root mean-square fluctuations (RMSF) that can also be calculated from molecular dynamics simulations. We provide a mathematical derivation showing that, given a set of conservative assumptions, a root mean-square ensemble-average of an all-against-all distribution of pairwise RMSD for a single molecular species, <RMSD²>^1/2, is directly related to average B-factors (<B>) and <RMSF²>^1/2. We show this relationship and explore its limits of validity on a heterogeneous ensemble of structures taken from molecular dynamics simulations of villin headpiece generated using distributed-computing techniques and the Folding@Home cluster. Our results provide a basis for quantifying global structural diversity of macromolecules in crystals directly from x-ray experiments, and we show this on a large set of structures taken from the Protein Data Bank. In particular, we show that the ensemble-average pairwise backbone RMSD for a microscopic ensemble underlying a typical protein x-ray structure is ∼1.1 Å, under the assumption that the principal contribution to experimental B-factors is conformational variability.     

Improved side-chain modeling for protein-protein docking

Success in high-resolution protein-protein docking requires accurate modeling of side-chain conformations at the interface. Most current methods either leave side chains fixed in the conformations observed in the unbound protein structures or allow the side chains to sample a set of discrete rotamer conformations. Here we describe a rapid and efficient method for sampling off-rotamer side-chain conformations by torsion space minimization during protein-protein docking starting from discrete rotamer libraries supplemented with side-chain conformations taken from the unbound structures, and show that the new method improves side-chain modeling and increases the energetic discrimination between good and bad models. Analysis of the distribution of side-chain interaction energies within and between the two protein partners shows that the new method leads to more native-like distributions of interaction energies and that the neglect of side-chain entropy produces a small but measurable increase in the number of residues whose interaction energy cannot compensate for the entropic cost of side-chain freezing at the interface. The power of the method is highlighted by a number of predictions of unprecedented accuracy in the recent CAPRI (Critical Assessment of PRedicted Interactions) blind test of protein-protein docking methods.