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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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     

Mutations in the hydrophobic core and in the protein-RNA interface affect the packing and stability of icosahedral viruses.

The information required for successful assembly of an icosahedral virus is encoded in the native conformation of the capsid protein and in its interaction with the nucleic acid. Here we investigated how the packing and stability of virus capsids are sensitive to single amino acid substitutions in the coat protein. Tryptophan fluorescence, bis-8-anilinonaphthalene-1-sulfonate fluorescence, CD and light scattering were employed to measure urea- and pressure-induced effects on MS2 bacteriophage and temperature sensitive mutants. M88V and T45S particles were less stable than the wild-type forms and completely dissociated at 3.0 kbar of pressure. M88V and T45S mutants also had lower stability in the presence of urea. We propose that the lower stability of M88V particles is related to an increase in the cavity of the hydrophobic core. Bis-8-anilinonaphthalene-1-sulfonate fluorescence increased for the pressure-dissociated mutants but not for the urea-denatured samples, indicating that the final products were different. To verify reassembly of the particles, gel filtration chromatography and infectivity assays were performed. The phage titer was reduced dramatically when particles were treated with a high concentration of urea. In contrast, the phage titer recovered after high-pressure treatment. Thus, after pressure-induced dissociation of the virus, information for correct reassembly was preserved. In contrast to M88V and T45S, the D11N mutant virus particle was more stable than the wild-type virus, in spite of it also possessing a temperature sensitive growth phenotype. Overall, our data show how point substitutions in the capsid protein, which affect either the packing or the interaction at the protein-RNA interface, result in changes in virus stability.     

Fine structure analysis of a protein folding transition state; distinguishing between hydrophobic stabilization and specific packing

Developing a detailed understanding of the structure and energetics of protein folding transition states is a key step in describing the folding process. The phi-value analysis approach allows the energetic contribution of side-chains to be mapped out by comparing wild-type with individual mutants where conservative changes are introduced. Studies where multiple substitutions are made at individual sites are much rarer but are potentially very useful for understanding the contribution of each element of a side-chain to transition state formation, and for distinguishing the relative importance of specific packing versus hydrophobic interactions. We have made a series of conservative mutations at multiple buried sites in the N-terminal domain of L9 in order to assess the relative importance of specific side-chain packing versus less specific hydrophobic stabilization of the transition state. A total of 28 variants were prepared using both naturally occurring and non-naturally occurring amino acids at six sites. Analysis of the mutants by NMR and CD showed no perturbation of the structure. There is no correlation between changes in hydrophobicity and changes in stability. In contrast, there is excellent linear correlation between the hydrophobicity of a side-chain and the log of the folding rate, ln(k(f)). The correlation between ln(k(f)) and the change in hydrophobicity holds even for substitutions that change the shape and/or size of a side-chain significantly. For most sites, the correlation with the logarithm of the unfolding rate, ln(k(u)), is much worse. Mutants with more hydrophobic amino acid substitutions fold faster, and those with less hydrophobic amino acid substitutions fold slower. The results show that hydrophobic interactions amongst core residues are an important driving force for forming the transition state, and are more important than specific tight packing interactions. Finally, a number of substitutions lead to negative phi-values and the origin of these effects are described.     

Redesigning the hydrophobic core of a model beta-sheet protein: destabilizing traps through a threading approach

An off-lattice 46-bead model of a small all-beta protein has been recently criticized for possessing too many traps and long-lived intermediates compared with the folding energy landscape predicted for real proteins and models using the principle of minimal frustration. Using a novel sequence design approach based on threading for finding beneficial mutations for destabilizing traps, we proposed three new sequences for folding in the beta-sheet model. Simulated annealing on these sequences found the global minimum more reliably, indicative of a smoother energy landscape, and simulated thermodynamic variables found evidence for a more cooperative collapse transition, lowering of the collapse temperature, and higher folding temperatures. Folding and unfolding kinetics were acquired by calculating first-passage times, and the new sequences were found to fold significantly faster than the original sequence, with a concomitant lowering of the glass temperature, although none of the sequences have highly stable native structures. The new sequences found here are more representative of real proteins and are good folders in the T(f) > T(g) sense, and they should prove useful in future studies of the details of transition states and the nature of folding intermediates in the context of simplified folding models. These results show that our sequence design approach using threading can improve models possessing glasslike folding dynamics.     

Exposure of hydrophobic core in human prion protein pathogenic mutant H187R

Pathogenesis studies have revealed that H187R mutation of human prion protein (huPrP) is related to GSS type of TSE diseases. Its pathogenic mechanism is still unclear. We here studied the globular domain of this mutant protein by molecular dynamics simulations. Compared to the wide-type protein, the mutant has similar dynamics and stability profiles in our simulation. Conformational rearrangements are concentrated around the mutation site, due to the introduction the positively charged side chain of Arg187. The strong electrostatic repulsion between Arg156 and Arg187 drives both side chains away from their original positions, leaving its hydrophobic core to be solvent accessible. Such a unfavorable conformational change may destabilize the mutant protein and make it more susceptible to unfolding.     

Energetics of protein folding

The energetics of protein folding determine the 3D structure of a folded protein. Knowledge of the energetics is needed to predict the 3D structure from the amino acid sequence or to modify the structure by protein engineering. Recent developments are discussed: major factors are reviewed and auxiliary factors are discussed briefly. Major factors include the hydrophobic factor (burial of non-polar surface area) and van der Waals interactions together with peptide hydrogen bonds and peptide solvation. The long-standing model for the hydrophobic factor (free energy change proportional to buried non-polar surface area) is contrasted with the packing-desolvation model and the approximate nature of the proportionality between free energy and apolar surface area is discussed. Recent energetic studies of forming peptide hydrogen bonds (gas phase) are reviewed together with studies of peptide solvation in solution. Closer agreement is achieved between the 1995 values for protein unfolding enthalpies in vacuum given by Lazaridis-Archontis-Karplus and Makhatadze-Privalov when the solvation enthalpy of the peptide group is taken from electrostatic calculations. Auxiliary factors in folding energetics include salt bridges and side-chain hydrogen bonds, disulfide bridges, and propensities to form alpha-helices and beta-structure. Backbone conformational entropy is a major energetic factor which is discussed only briefly for lack of knowledge.     

Core side-chain packing and backbone conformation in Lpp-56 coiled-coil mutants

Native proteins exhibit precise geometric packing of atoms in their hydrophobic interiors. Nonetheless, controversy remains about the role of core side-chain packing in specifying and stabilizing the folded structures of proteins. Here we investigate the role of core packing in determining the conformation and stability of the Lpp-56 trimerization domain. The X-ray crystal structures of Lpp-56 mutants with alanine substitutions at two and four interior core positions reveal trimeric coiled coils in which the twist of individual helices and the helix-helix spacing vary significantly to achieve the most favored superhelical packing arrangement. Introduction of each alanine "layer" into the hydrophobic core destabilizes the superhelix by 1.4 kcal mol(-1). Although the methyl groups of the alanine residues pack at their optimum van der Waals contacts in the coiled-coil trimer, they provide a smaller component of hydrophobic interactions than bulky hydrophobic side-chains to the thermodynamic stability. Thus, specific side-chain packing in the hydrophobic core of coiled coils are important determinants of protein main-chain conformation and stability.     

Replacement of staphylococcal nuclease hydrophobic core residues with those from thermophilic homologues indicates packing is improved in some thermostable proteins

The importance of tight hydrophobic core packing in stabilizing proteins found in thermophilic organisms has been vigorously disputed. Here, portions of the cores found in three thermophilic homologues were transplanted into the core of staphylococcal nuclease, a protein of modest stability. Packing of the core was evaluated by comparing interaction energy of the three mutants to the comprehensive mutant library built up previously at these same sites in staphylococcal nuclease. It was found that the interaction energy of one thermophilic sequence is extraordinarily favorable and the interaction energies of other two transplanted thermophilic sequences are good, comparable to the interaction energies of mutant cores based on cores found in mesophilic homologues. As expected when transferring just a portion of the core sequence, the mutant proteins were destabilized overall relative to wild-type staphylococcal nuclease. The overall conclusion is that improvement of packing interactions is a mechanism to confer stability employed in some proteins from thermophiles, but not all.