Excluded volume in protein side-chain packing

The excluded volume occupied by protein side-chains and the requirement of high packing density in the protein interior should severely limit the number of side-chain conformations compatible with a given native backbone. To examine the relationship between side-chain geometry and side-chain packing, we use an all-atom Monte Carlo simulation to sample the large space of side-chain conformations. We study three models of excluded volume and use umbrella sampling to effectively explore the entire space. We find that while excluded volume constraints reduce the size of conformational space by many orders of magnitude, the number of allowed conformations is still large. An average repacked conformation has 20 % of its chi angles in a non-native state, a marked reduction from the expected 67 % in the absence of excluded volume. Interestingly, well-packed conformations with up to 50 % non-native chi angles exist. The repacked conformations have native packing density as measured by a standard Voronoi procedure. Entropy is distributed non-uniformly over positions, and we partially explain the observed distribution using rotamer probabilities derived from the Protein Data Bank database. In several cases, native rotamers that occur infrequently in the database are seen with high probability in our simulation, indicating that sequence-specific excluded volume interactions can stabilize rotamers that are rare for a given backbone. In spite of our finding that 65 % of the native rotamers and 85 % of chi(1) angles can be predicted correctly on the basis of excluded volume only, 95 % of positions can accommodate more than one rotamer in simulation. We estimate that, in order to quench the side-chain entropy observed in the presence of excluded volume interactions, other interactions (hydrophobic, polar, electrostatic) must provide an additional stabilization of at least 0.6 kT per residue in order to single out the native state.     

Determinants of protein side-chain packing.

The problem of protein side-chain packing for a given backbone trace is investigated using 3 different prediction models. The first requires an exhaustive search of all possible combinations of side-chain conformers, using the dead-end elimination theorem. The second considers only side-chain-backbone interactions, whereas the third neglects side-chain-backbone interactions and instead keeps side-chain-side-chain interactions. Predictions of side-chain conformations for 11 proteins using all 3 models show that removal of side-chain-side-chain interactions does not cause a large decrease in the prediction accuracy, whereas the model having only side-chain-side-chain interactions still retains a significant level of accuracy. These results suggest that the 2 classes of interactions, side-chain-backbone and side-chain-side-chain, are consistent with each other and work concurrently to stabilize the native conformations. This is confirmed by analyses of energy spectra of the side-chain conformations derived from the fourth prediction model, the Independent model, which gives almost the same quality of the prediction as the dead-end elimination. The analyses indicate that the 2 classes of interactions simultaneously increase the energy difference between the native and nonnative conformations.     

Side chain burial and hydrophobic core packing in protein folding transition states

A critical step in the folding pathway of globular proteins is the formation of a tightly packed hydrophobic core. Several mutational studies have addressed the question of whether tight packing interactions are present during the rate-limiting step of folding. In some of these investigations, substituted side chains have been assumed to form native-like interactions in the transition state when the folding rates of mutant proteins correlate with their native-state stabilities. Alternatively, it has been argued that side chains participate in nonspecific hydrophobic collapse when the folding rates of mutant proteins correlate with side-chain hydrophobicity. In a reanalysis of published data, we have found that folding rates often correlate similarly well, or poorly, with both native-state stability and side-chain hydrophobicity, and it is therefore not possible to select an appropriate transition state model based on these one-parameter correlations. We show that this ambiguity can be resolved using a two-parameter model in which side chain burial and the formation of all other native-like interactions can occur asynchronously. Notably, the model agrees well with experimental data, even for positions where the one-parameter correlations are poor. We find that many side chains experience a previously unrecognized type of transition state environment in which specific, native-like interactions are formed, but hydrophobic burial dominates. Implications of these results to the design and analysis of protein folding studies are discussed.     

Hydrophobic core fluidity of homologous protein domains: relation of side-chain dynamics to core composition and packing

The side-chain dynamics of methyl groups in two structurally related proteins from the fibronectin type III (fnIII) superfamily, the third fnIII domain from human tenascin (TNfn3) and the tenth fnIII domain from human fibronectin (FNfn10), have been studied by NMR spectroscopy. Side-chain order parameters reveal that the hydrophobic cores of the two proteins have substantially different mobilities. The core of TNfn3 is very dynamic, with exceptionally low order parameters for the most deeply buried residues, while that of FNfn10 is more like those of other proteins which have been studied with this technique, having a relatively rigid core with uniformly distributed dynamics. The unusually dynamic core of TNfn3 appears to be related to its amino acid composition, which makes it more fluid-like. A further explanation for the mobility of the TNfn3 core may be found in the negative correlation between the order parameter and excess packing volume, which shows that the core of TNfn3 is less densely packed and consequently has lower methyl order parameters for its buried residues. Rotameric transitions, presumably facilitated by the lower packing density, appear to make an important contribution to lowering the order parameters, and have been probed by measuring three-bond scalar couplings. Overall, although backbone dynamics is generally similar for proteins with the same topology on a fast time scale (picoseconds to nanoseconds), this study shows that a single fold can accommodate a wide variation in the dynamic properties of its core.     

Effect of hydrophobic core packing on sidechain dynamics

The effect of hydrophobic core packing on sidechain dynamics was analyzed by comparing the dynamics of wild-type (WT) ubiquitin to those of a variant which has seven core mutations. This variant, 1D7, was designed to resemble WT by having a well-packed core of similar volume, and we find that its overall level of dynamics is only subtly different from WT. However, the mutations caused a redistribution in the positions of core residues that are dynamic. This correlates with the tendency of these residues to populate unfavorable rotamers, suggesting that strain from poor sidechain conformations may promote increased flexibility as a mechanism to relieve unfavorable steric interactions. The results demonstrate that even when core volume is conserved, different packing arrangements in mutants can alter dynamic behavior.     

Prediction of protein side-chain conformation by packing optimization

We have developed a rapid and completely automatic method for prediction of protein side-chain conformation, applying the simulated annealing algorithm to optimization of side-chain packing (van der Waals) interactions. The method directly attacks the combinatorial problem of simultaneously predicting many residues' conformation, solving in 8 to 12 hours problems for which the systematic search would require over 10(300) central processing unit years. Over a test set of nine proteins ranging in size from 46 to 323 residues, the program's predictions for side-chain atoms had a root-mean-square (r.m.s.) deviation of 1.77 A overall versus the native structures. More importantly, the predictions for core residues were especially accurate, with an r.m.s. value of 1.25 A overall: 80 to 90% of the large hydrophobic side-chains dominating the internal core were correctly predicted, versus 30 to 40% for most current methods. The predictions' main errors were in surface residues poorly constrained by packing and small residues with greater steric freedom and hydrogen bonding interactions, which were not included in the program's potential function. van der Waals interactions appear to be the supreme determinant of the arrangement of side-chains in the core, enforcing a unique allowed packing that in every case so far examined matches the native structure.     

Hydrophobic core packing and protein design

Over the past few years, we have witnessed exciting advances in protein design. Several groups have reported success in the design of hydrophobic cores, and the principles developed in these studies have been recently applied to the full sequence design of a small protein motif and the design of a catalytically active metal center. These successes suggest that designing large, functional proteins in computero is more feasible than ever before.     

Redesigning the hydrophobic core of a four-helix-bundle protein.

Rationally redesigned variants of the 4-helix-bundle protein Rop are described. The novel proteins have simplified, repacked, hydrophobic cores and yet reproduce the structure and native-like physical properties of the wild-type protein. The repacked proteins have been characterized thermodynamically and their equilibrium and kinetic thermal and chemical unfolding properties are compared with those of wild-type Rop. The equilibrium stability of the repacked proteins to thermal denaturation is enhanced relative to that of the wild-type protein. The rate of chemically induced folding and unfolding of wild-type Rop is extremely slow when compared with other small proteins. Interestingly, although the repacked proteins are more thermally stable than the wild type, their rates of chemically induced folding and unfolding are greatly increased in comparison to wild type. Perhaps as a consequence of this, their equilibrium stabilities to chemical denaturants are slightly reduced in comparison to the wild type.     

In a staphylococcal nuclease mutant the side-chain of a lysine replacing valine 66 is fully buried in the hydrophobic core

The crystal structure of the staphylococcal nuclease mutant V66K, in which valine 66 is replaced by lysine, has been solved at 1.97 A resolution. Unlike lysine residues in previously reported protein structures, this residue appears to bury its side-chain in the hydrophobic core without salt bridging, hydrogen bonding or other forms of electrostatic stabilization. Solution studies of the free energy of denaturation, delta GH2O, show marked pH dependence and clearly indicate that the lysine residue must be deprotonated in the folded state. V66K is highly unstable at neutral pH but only modestly less stable than the wild-type protein at high pH. The pH dependence of stability for V66K, in combination with similar measurements for the wild-type protein, allowed determination of the pKa values of the lysine in both the denatured and native forms. The epsilon-amine of this residue has a pKa value in the denatured state of 10.2, but in the native state it must be 6.4 or lower. The epsilon-amine is thus deprotonated in the folded molecule. These values enabled an estimation of the epsilon-amine's relative change in free energy of solvation between solvent and the protein interior at 5.1 kcal/mol or greater. This implies that the value of the dielectric constant of the protein interior must be less than 12.8. Lysine is usually found with the methylene groups of its side-chain partly buried but is nevertheless considered a hydrophilic surface residue. It would appear that the high pKa value of lysine, which gives it a positive charge at physiological pH, is the primary reason for its almost exclusive confinement to the surface proteins. When deprotonated, this amino acid type can be fully incorporated into the hydrophobic core.     

Energetics of hydrophobic matching in lipid-protein interactions

Lipid chain length modulates the activity of transmembrane proteins by mismatch between the hydrophobic span of the protein and that of the lipid membrane. Relative binding affinities of lipids with different chain lengths are used to estimate the excess free energy of lipid-protein interaction that arises from hydrophobic mismatch. For a wide range of integral proteins and peptides, the energy cost is much less than the elastic penalty of fully stretching or compressing the lipid chains to achieve complete hydrophobic matching. The chain length dependences of the free energies of lipid association are described by a model that combines elastic chain extension with a free energy term that depends linearly on the extent of residual mismatch. The excess free energy densities involved lie in the region of 0.5-2.0 k_BT.nm⁻². Values of this size could arise from exposure of hydrophobic groups to polar portions of the lipid or protein, but not directly to water, or alternatively from changes in tilt of the transmembrane helices that are energetically comparable to those activating mechanosensitive channels. The influence of hydrophobic mismatch on dimerization of transmembrane helices and their transfer between lipid vesicles, and on shifts in chain-melting transitions of lipid bilayers by incorporated proteins, is analyzed by using the same thermodynamic model. Segmental order parameters confirm that elastic lipid chain distortions are insufficient to compensate fully for the mismatch, but the dependence on chain length with tryptophan-anchored peptides requires that the free energy density of hydrophobic mismatch should increase with increasing extent of mismatch.     

Methyl dynamics for understanding hydrophobic core packing of dynamically different motifs of double-stranded RNA binding domain of protein kinase R

Double-stranded RNA binding domains of human protein kinase R (dsRBD-PKR) regulate distinct cellular functions and the fate of an RNA molecule in the cell. This highly homologous domains present in multiple copies in a number of species, exhibit individual and specific functional specificity. Number of NMR and X-ray crystallographic structural studies reveals that such domains take a common alpha-beta-beta-beta-alpha tertiary fold. However, the functional specificities of these domains could be due to the dynamics of the individual amino acid residues, as has been shown earlier in the case of backbone dynamics of 15N-1H of dsRNA binding motifs (dsRBMs) of human protein kinase R (PKR) (Nanduri S, Rahman F, Williams BRG, Qin J. EMBO J 2000;19:5567-5574). To further investigate if the differences in dynamics of the two dsRBMs are restricted to only backbone, or if the side-chain motions are also different to the extent of influencing their packing of the two hydrophobic cores, we have investigated the methyl group dynamics using 13C-methyl relaxation measurements. The results show that the hydrophobic core of dsRBM1 is more tightly packed than dsRBM2, and it seems to undergo less fast scale motions in the subnanosecond regime.     

Genetic algorithm with alternating selection pressure for protein side-chain packing and pK(a) prediction

The prediction of protein side-chain conformation is central for understanding protein functions. Side-chain packing is a sub-problem of protein folding and its computational complexity has been shown to be NP-hard. We investigated the capabilities of a hybrid (genetic algorithm/simulated annealing) technique for side-chain packing and for the generation of an ensemble of low energy side-chain conformations. Our method first relies on obtaining a near-optimal low energy protein conformation by optimizing its amino-acid side-chains. Upon convergence, the genetic algorithm is allowed to undergo forward and “backward” evolution by alternating selection pressures between minimal and higher energy setpoints. We show that this technique is very efficient for obtaining distributions of solutions centered at any desired energy from the minimum. We outline the general concepts of our evolutionary sampling methodology using three different alternating selective pressure schemes. Quality of the method was assessed by using it for protein pK(a) prediction.     

Alignment of protein sequences using the hydrophobic core scores

Making an alignment of the amino acid sequences is an essential step in the prediction of an unknown protein structure by model building from the known structure of a protein of the same family. To improve the accuracy of the alignments, we introduced the concept of hydrophobic core scores, which restrains putting insertions/deletions in the hydrophobic core regions of the protein. Eight pairs of protein sequences were aligned by this method, and the quality of the alignments were assessed by reference to those obtained by the structural superposition. The introduction of the hydrophobic core scores derived from the knowledge of the tertiary structure of one of each pair resulted in an improvement of the accuracy of the alignments. The quality of the alignment was found to depend on the homology of the protein sequences.     

Validation of NMR side-chain conformations by packing calculations

The precision and accuracy of protein structures determined by nuclear magnetic resonance (NMR) spectroscopy depend on the completeness of input experimental data set. Typically, rather than a single structure, an ensemble of up to 20 equally representative conformers is generated and routinely deposited in the Protein Database. There are substantially more experimentally derived restraints available to define the main-chain coordinates than those of the side chains. Consequently, the side-chain conformations among the conformers are more variable and less well defined than those of the backbone. Even when a side chain is determined with high precision and is found to adopt very similar orientations among all the conformers in the ensemble, it is possible that its orientation might still be incorrect. Thus, it would be helpful if there were a method to assess independently the side-chain orientations determined by NMR. Recently, homology modeling by side-chain packing algorithms has been shown to be successful in predicting the side-chain conformations of the buried residues for a protein when the main-chain coordinates and sequence information are given. Since the main-chain coordinates determined by NMR are consistently more reliable than those of the side-chains, we have applied the side-chain packing algorithms to predict side-chain conformations that are compatible with the NMR-derived backbone. Using four test cases where the NMR solution structures and the X-ray crystal structure of the same protein are available, we demonstrate that the side-chain packing method can provide independent validation for the side-chain conformations of NMR structures. Comparison of the side-chain conformations derived by side-chain packing prediction and by NMR spectroscopy demonstrates that when there is agreement between the NMR model and the predicted model, on average 78% of the time the X-ray structure also concurs. While the side-chain packing method can confirm the reliable residue conformations in NMR models, more importantly, it can also identify the questionable residue conformations with an accuracy of 60%. This validation method can serve to increase the confidence level for potential users of structural models determined by NMR.     

Fragment complementation studies of protein stabilization by hydrophobic core residues

Interactions that stabilize the native state of a protein have been studied by measuring the affinity between subdomain fragments with and without site-specific residue substitutions. A calbindin D(9k) variant with a single CNBr cleavage site at position 43 between its two EF-hand subdomains was used as a starting point for the study. Into this variant were introduced 11 site-specific substitutions involving hydrophobic core residues at the interface between the two EF-hands. The mutants were cleaved with CNBr to produce wild-type and mutated single-EF-hand fragments: EF1 (residues 1--43) and EF2 (residues 44--75). The interaction between the two EF-hands was studied using surface plasmon resonance (SPR) technology, which follows the rates of association and dissociation of the complex. Wild-type EF1 was immobilized on a dextran matrix, and the wild-type and mutated versions of EF2 were injected at several different concentrations. In another set of experiments, wild-type EF2 was immobilized and wild-type or mutant EF1 was injected. Dissociation rate constants ranged between 1.1 x 10(-5) and 1.0 x 10(-2) s(-1) and the association rate constants between 2 x 10(5) and 4.0 x 10(6) M(-1) s(-1). The affinity between EF1 and EF2 was as high as 3.6 x 10(11) M(-1) when none of them was mutated. For the 11 hydrophobic core mutants, a strong correlation (r = 0.999) was found between the affinity of EF1 for EF2 and the stability toward denaturation of the corresponding intact protein. The observed correlation implies that the factors governing the stability of the intact protein also contribute to the affinity of the bimolecular EF1-EF2 complex. In addition, the data presented here show that interactions among hydrophobic core residues are major contributors both to the affinity between the two EF-hand subdomains and to the stability of the intact domain.     

Protein side-chain packing problem: a maximum edge-weight clique algorithmic approach

"Protein Side-chain Packing" has an ever-increasing application in the field of bio-informatics, dating from the early methods of homology modeling to protein design and to the protein docking. However, this problem is computationally known to be NP-hard. In this regard, we have developed a novel approach to solve this problem using the notion of a maximum edge-weight clique. Our approach is based on efficient reduction of protein side-chain packing problem to a graph and then solving the reduced graph to find the maximum clique by applying an efficient clique finding algorithm developed by our co-authors. Since our approach is based on deterministic algorithms in contrast to the various existing algorithms based on heuristic approaches, our algorithm guarantees of finding an optimal solution. We have tested this approach to predict the side-chain conformations of a set of proteins and have compared the results with other existing methods. We have found that our results are favorably comparable or better than the results produced by the existing methods. As our test set contains a protein of 494 residues, we have obtained considerable improvement in terms of size of the proteins and in terms of the efficiency and the accuracy of prediction.     

Step-wise formation of helical structure and side-chain packing in a peptide from scorpion neurotoxin support hierarchic model of protein folding

The mechanism of protein folding has been the subject of extensive investigation during the last decade, both because of its academic challenge and because of its relation to many diseases which are known to occur due to misfolding of proteins. In this context, we report here a systematic investigation on the step-wise formation of a helical structure by the addition of hexafluoroacetone, in a 14-residue peptide derived from a part of the scorpion neurotoxin protein. The NMR and circular dichroism results indicate that the peptide has an inherent propensity for helix formation and this is limited to the internal few residues in aqueous solution. With the addition of the fluorosolvent, the helical content progressively increases and spans the whole sequence. This is accompanied by concomitant packing of the side chains. These results provide support to the so-called hierarchic model of protein folding which dictates that the local sequence determines the secondary structures in the protein and the side chains play an important role in this process.     

Non-randomness in side-chain packing: the distribution of interplanar angles

We analyze the distributions of interplanar angles between interacting side chains with well-defined planar regions, to see whether these distributions correspond to random packing or alternatively show orientational preferences. We use a non-homologous set of 79 high-resolution protein chain structures to show that the observed distributions are significantly different from the sinusoidal one expected for random packing. Overall, we see a relative excess of small angles and a paucity of large interplanar angles; the difference between the expected and observed distributions can be described as a shift of 5% of the interplanar angles from large (≥60°) to small (<30°) values. By grouping the residue pairs into categories based on chemical similarity, we find that some categories have very non-sinusoidal interplanar angle distributions, whereas other categories have distributions that are close to sinusoidal. For a few categories, observed deviations from a sinusoidal distribution can be explained by the electrostatic anisotropy of the isolated pair potential energy. In other cases, the observed distributions reflect the longer range effects of different possible interaction geometries. In particular, geometries that disrupt external hydrogen bonding are disfavored. Proteins 29:370–380, 1997. © 1997 Wiley-Liss, Inc.     

Increasing sequence diversity with flexible backbone protein design: the complete redesign of a protein hydrophobic core

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Highlights? Flexible backbone design has been used to mutate every position in a protein core ? The redesign is hyperthermostable (melting temperature >140°C) ? An NMR structure and an X-ray structure closely match the design model ? Designed backbone perturbations were accurately recapitulated     

Crosstalk between the protein surface and hydrophobic core in a core-swapped fibronectin type III domain

Two homologous fibronectin type III (fnIII) domains, FNfn10 (the 10th fnIII domain of human fibronectin) and TNfn3 (the third fnIII domain of human tenascin), have essentially the same backbone structure, although they share only ∼ 24% sequence identity. While they share a similar folding mechanism with a common core of key residues in the folding transition state, they differ in many other physical properties. We use a chimeric protein, FNoTNc, to investigate the molecular basis for these differences. FNoTNc is a core-swapped protein, containing the “outside” (surface and loops) of FNfn10 and the hydrophobic core of TNfn3. Remarkably, FNoTNc retains the structure of the parent proteins despite the extent of redesign, allowing us to gain insight into which components of each parent protein are responsible for different aspects of its behaviour. Naively, one would expect properties that appear to depend principally on the core to be similar to TNfn3, for example, the response to mutations, folding kinetics and side-chain dynamics, while properties apparently determined by differences in the surface and loops, such as backbone dynamics, would be more like FNfn10. While this is broadly true, it is clear that there are also unexpected crosstalk effects between the core and the surface. For example, the anomalous response of FNfn10 to mutation is not solely a property of the core as we had previously suggested.