A new approach to the design of uniquely folded thermally stable proteins

A new computer program (CORE) is described that predicts core hydrophobic sequences of predetermined target protein structures. A novel scoring function is employed, which for the first time incorporates parameters directly correlated to free energies of unfolding (deltaGu), melting temperatures (Tm), and cooperativity. Metropolis-driven simulated annealing and low-temperature Monte Carlo sampling are used to optimize this score, generating sequences predicted to yield uniquely folded, stable proteins with cooperative unfolding transitions. The hydrophobic core residues of four natural proteins were predicted using CORE with the backbone structure and solvent exposed residues as input. In the two smaller proteins tested (Gbeta1, 11 core amino acids; 434 cro, 10 core amino acids), the native sequence was regenerated as well as the sequence of known thermally stable variants that exhibit cooperative denaturation transitions. Previously designed sequences of variants with lower thermal stability and weaker cooperativity were not predicted. In the two larger proteins tested (myoglobin, 32 core amino acids; methionine aminopeptidase, 63 core amino acids), sequences with corresponding side-chain conformations remarkably similar to that of native were predicted.     

De novo design of the hydrophobic cores of proteins.

We have developed and experimentally tested a novel computational approach for the de novo design of hydrophobic cores. A pair of computer programs has been written, the first of which creates a "custom" rotamer library for potential hydrophobic residues, based on the backbone structure of the protein of interest. The second program uses a genetic algorithm to globally optimize for a low energy core sequence and structure, using the custom rotamer library as input. Success of the programs in predicting the sequences of native proteins indicates that they should be effective tools for protein design. Using these programs, we have designed and engineered several variants of the phage 434 cro protein, containing five, seven, or eight sequence changes in the hydrophobic core. As controls, we have produced a variant consisting of a randomly generated core with six sequence changes but equal volume relative to the native core and a variant with a "minimalist" core containing predominantly leucine residues. Two of the designs, including one with eight core sequence changes, have thermal stabilities comparable to the native protein, whereas the third design and the minimalist protein are significantly destabilized. The randomly designed control is completely unfolded under equivalent conditions. These results suggest that rational de novo design of hydrophobic cores is feasible, and stress the importance of specific packing interactions for the stability of proteins. A surprising aspect of the results is that all of the variants display highly cooperative thermal denaturation curves and reasonably dispersed NMR spectra. This suggests that the non-core residues of a protein play a significant role in determining the uniqueness of the folded structure.     

Conserved residue clustering and protein structure prediction

Protein residues that are critical for structure and function are expected to be conserved throughout evolution. Here, we investigate the extent to which these conserved residues are clustered in three-dimensional protein structures. In 92% of the proteins in a data set of 79 proteins, the most conserved positions in multiple sequence alignments are significantly more clustered than randomly selected sets of positions. The comparison to random subsets is not necessarily appropriate, however, because the signal could be the result of differences in the amino acid composition of sets of conserved residues compared to random subsets (hydrophobic residues tend to be close together in the protein core), or differences in sequence separation of the residues in the different sets. In order to overcome these limits, we compare the degree of clustering of the conserved positions on the native structure and on alternative conformations generated by the de novo structure prediction method Rosetta. For 65% of the 79 proteins, the conserved residues are significantly more clustered in the native structure than in the alternative conformations, indicating that the clustering of conserved residues in protein structures goes beyond that expected purely from sequence locality and composition effects. The differences in the spatial distribution of conserved residues can be utilized in de novo protein structure prediction: We find that for 79% of the proteins, selection of the Rosetta generated conformations with the greatest clustering of the conserved residues significantly enriches the fraction of close-to-native structures.     

Progress and challenges in high-resolution refinement of protein structure models

Achieving atomic level accuracy in de novo structure prediction presents a formidable challenge even in the context of protein models with correct topologies. High-resolution refinement is a fundamental test of force field accuracy and sampling methodology, and its limited success in both comparative modeling and de novo prediction contexts highlights the limitations of current approaches. We constructed four tests to identify bottlenecks in our current approach and to guide progress in this challenging area. The first three tests showed that idealized native structures are stable under our refinement simulation conditions and that the refinement protocol can significantly decrease the root mean square deviation (RMSD) of perturbed native structures. In the fourth test we applied the refinement protocol to de novo models and showed that accurate models could be identified based on their energies, and in several cases many of the buried side chains adopted native-like conformations. We also showed that the differences in backbone and side-chain conformations between the refined de novo models and the native structures are largely localized to loop regions and regions where the native structure has unusual features such as rare rotamers or atypical hydrogen bonding between beta-strands. The refined de novo models typically have higher energies than refined idealized native structures, indicating that sampling of local backbone conformations and side-chain packing arrangements in a condensed state is a primary obstacle.     

Knowledge-based potential defined for a rotamer library to design protein sequences

A knowledge-based potential for a rotamer library was developed to design protein sequences. Protein side-chain conformations are represented by 56 templates. Each of their fitness to a given structural site-environment is evaluated by a combined function of the three knowledge-based terms, i.e. two-body side-chain packing, one-body hydration and local conformation. The number of matches between the native sequence and the structural site-environment in the database and that of the virtually settled mismatches, counted in advance, were transformed into the energy scores. In the best-14 test (assessment for the reproduction ability of the native rotamer on its structural site within a quarter of 56 fitness rank positions), the structural stability analysis on mutants of human and T4 lysozymes and the inverse-folding search by a structure profile against the sequence database, this function performs better than the function deduced with the conventional normalization and our previously developed function. Targeting various structural motifs, de novo sequence design was conducted with the function. The sequences thus obtained exhibit reasonable molecular masses and hydrophobic/hydrophilic patterns similar to the native sequences of the target and act as if they were the homologs to the target proteins in BLASTP search. This significant improvement is discussed in terms of the reference state for normalization and the crucial role of short-range repulsion to prohibit residue bumps.     

Analysis of anisotropic side-chain packing in proteins and application to high-resolution structure prediction

pi-pi, Cation-pi, and hydrophobic packing interactions contribute specificity to protein folding and stability to the native state. As a step towards developing improved models of these interactions in proteins, we compare the side-chain packing arrangements in native proteins to those found in compact decoys produced by the Rosetta de novo structure prediction method. We find enrichments in the native distributions for T-shaped and parallel offset arrangements of aromatic residue pairs, in parallel stacked arrangements of cation-aromatic pairs, in parallel stacked pairs involving proline residues, and in parallel offset arrangements for aliphatic residue pairs. We then investigate the extent to which the distinctive features of native packing can be explained using Lennard-Jones and electrostatics models. Finally, we derive orientation-dependent pi-pi, cation-pi and hydrophobic interaction potentials based on the differences between the native and compact decoy distributions and investigate their efficacy for high-resolution protein structure prediction. Surprisingly, the orientation-dependent potential derived from the packing arrangements of aliphatic side-chain pairs distinguishes the native structure from compact decoys better than the orientation-dependent potentials describing pi-pi and cation-pi interactions.     

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.     

Alpha-alpha linking motifs and interhelical orientations

While the geometry and sequence preferences of turns that link two beta-strands have been exhaustively explored, the corresponding preferences for sequences that link helical structures have been less well studied. Here we examine the interhelical geometry of two connected helices as a function of their link's length. The interhelical geometry of a helical pair appears to be significantly influenced by the number of linking residues. Furthermore, for relatively short link lengths, a very limited number of predominant conformations are observed, which can be categorized by their phi/psi angles. No more than two predominant linking backbone conformations are observed for a given link length, and some linking backbone conformations correlate strongly with distinctive interhelical geometric parameters. In this study, sequence and hydrogen-bonding patterns were defined for predominant interhelical link motifs. These results should assist in both protein structure prediction and de novo protein design.     

Automatic protein design with all atom force-fields by exact and heuristic optimization

A fully automatic procedure for predicting the amino acid sequences compatible with a given target structure is described. It is based on the CHARMM package, and uses an all atom force-field and rotamer libraries to describe and evaluate side-chain types and conformations. Sequences are ranked by a quantity akin to the free energy of folding, which incorporates hydration effects. Exact (Branch and Bound) and heuristic optimisation procedures are used to identifying highly scoring sequences from an astronomical number of possibilities. These sequences include the minimum free energy sequence, as well as all amino acid sequences whose free energy lies within a specified window from the minimum. Several applications of our procedure are illustrated. Prediction of side-chain conformations for a set of ten proteins yields results comparable to those of established side-chain placement programs. Applications to sequence optimisation comprise the re-design of the protein cores of c-Crk SH3 domain, the B1 domain of protein G and Ubiquitin, and of surface residues of the SH3 domain. In all calculations, no restrictions are imposed on the amino acid composition and identical parameter settings are used for core and surface residues. The best scoring sequences for the protein cores are virtually identical to wild-type. They feature no more than one to three mutations in a total of 11-16 variable positions. Tests suggest that this is due to the balance between various contributions in the force-field rather than to overwhelming influence from packing constraints. The effectiveness of our force-field is further supported by the sequence predictions for surface residues of the SH3 domain. More mutations are predicted than in the core, seemingly in order to optimise the network of complementary interactions between polar and charged groups. This appears to be an important energetic requirement in absence of the partner molecules with which the SH3 domain interacts, which were not included in the calculations. Finally, a detailed comparison between the sequences generated by the heuristic and exact optimisation algorithms, commends a note of caution concerning the efficiency of heuristic procedures in exploring sequence space.     

Effect of site-directed point mutations on protein misfolding: A simulation study

A Monte Carlo simulation based sequence design method is proposed to investigate the role of site-directed point mutations in protein misfolding. Site-directed point mutations are incorporated in the designed sequences of selected proteins. While most mutated sequences correctly fold to their native conformation, some of them stabilize in other nonnative conformations and thus misfold/unfold. The results suggest that a critical number of hydrophobic amino acid residues must be present in the core of the correctly folded proteins, whereas proteins misfold/unfold if this number of hydrophobic residues falls below the critical limit. A protein can accommodate only a particular number of hydrophobic residues at the surface, provided a large number of hydrophilic residues are present at the surface and critical hydrophobicity of the core is preserved. Some surface sites are observed to be equally sensitive toward site-directed point mutations as the core sites. Point mutations with highly polar and charged amino acids increases the misfold/unfold propensity of proteins. Substitution of natural amino acids at sites with different number of nonbonded contacts suggests that both amino acid identity and its respective site-specificity determine the stability of a protein. A clash-match method is developed to calculate the number of matching and clashing interactions in the mutated protein sequences. While misfolded/unfolded sequences have a higher number of clashing and a lower number of matching interactions, the correctly folded sequences have a lower number of clashing and a higher number of matching interactions. These results are valid for different SCOP classes of proteins.     

Repacking of hydrophobic residues in a stable mutant of apocytochrome b562 selected by phage-display and proteolysis

To test a hydrophobic core-directed protein design approach, we previously have used phage-display and proteolysis to select stably folded proteins from a library of mutants of apocytochrome b562. The consensus sequence of the selected mutants has hydrophilic residues at two of the three positions that are designed to form a hydrophobic core. To understand this unexpected result, we determined the high-resolution structure of one of the selected mutants using multi-dimensional nuclear magnetic resonance (NMR). The structure shows that the two hydrophilic residues in the consensus sequence were on the surface of the structure. Instead, two of their neighboring hydrophobic residues reorganized their side-chain conformations and formed the hydrophobic core. This result suggests that the hydrophobic core-directed protein design by phage-display and proteolysis is a valid method in general but alternative hydrophobic packing needs to be considered in the initial design. The unexpected repacking of the hydrophobic residues also highlights the plastic nature of protein structures.     

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.     

A simple physical model for the prediction and design of protein-DNA interactions

Protein-DNA interactions are crucial for many biological processes. Attempts to model these interactions have generally taken the form of amino acid-base recognition codes or purely sequence-based profile methods, which depend on the availability of extensive sequence and structural information for specific structural families, neglect side-chain conformational variability, and lack generality beyond the structural family used to train the model. Here, we take advantage of recent advances in rotamer-based protein design and the large number of structurally characterized protein-DNA complexes to develop and parameterize a simple physical model for protein-DNA interactions. The model shows considerable promise for redesigning amino acids at protein-DNA interfaces, as design calculations recover the amino acid residue identities and conformations at these interfaces with accuracies comparable to sequence recovery in globular proteins. The model shows promise also for predicting DNA-binding specificity for fixed protein sequences: native DNA sequences are selected correctly from pools of competing DNA substrates; however, incorporation of backbone movement will likely be required to improve performance in homology modeling applications. Interestingly, optimization of zinc finger protein amino acid sequences for high-affinity binding to specific DNA sequences results in proteins with little or no predicted specificity, suggesting that naturally occurring DNA-binding proteins are optimized for specificity rather than affinity. When combined with algorithms that optimize specificity directly, the simple computational model developed here should be useful for the engineering of proteins with novel DNA-binding specificities.     

Coupling backbone flexibility and amino acid sequence selection in protein design.

Using a protein design algorithm that considers side-chain packing quantitatively, the effect of explicit backbone motion on the selection of amino acids in protein design was assessed in the core of the streptococcal protein G beta 1 domain (G beta 1). Concerted backbone motion was introduced by varying G beta 1's supersecondary structure parameter values. The stability and structural flexibility of seven of the redesigned proteins were determined experimentally and showed that core variants containing as many as 6 of 10 possible mutations retain native-like properties. This result demonstrates that backbone flexibility can be combined explicitly with amino acid side-chain selection and that the selection algorithm is sufficiently robust to tolerate perturbations as large as 15% of G beta 1's native supersecondary structure parameter values.     

The dominant role of side-chain backbone interactions in structural realization of amino acid code. ChiRotor: a side-chain prediction algorithm based on side-chain backbone interactions

The basic differences between the 20 natural amino acid residues are due to differences in their side-chain structures. This characteristic design of protein building blocks implies that side-chain-side-chain interactions play an important, even dominant role in 3D-structural realization of amino acid codes. Here we present the results of a comparative analysis of the contributions of side-chain-side-chain (s-s) and side-chain-backbone (s-b) interactions to the stabilization of folded protein structures within the framework of the CHARMm molecular data model. Contrary to intuition, our results suggest that side-chain-backbone interactions play the major role in side-chain packing, in stabilizing the folded structures, and in differentiating the folded structures from the unfolded or misfolded structures, while the interactions between side chains have a secondary effect. An additional analysis of electrostatic energies suggests that combinatorial dominance of the interactions between opposite charges makes the electrostatic interactions act as an unspecific folding force that stabilizes not only native structure, but also compact random conformations. This observation is in agreement with experimental findings that, in the denatured state, the charge-charge interactions stabilize more compact conformations. Taking advantage of the dominant role of side-chain-backbone interactions in side-chain packing to reduce the combinatorial problem, we developed a new algorithm, ChiRotor, for rapid prediction of side-chain conformations. We present the results of a validation study of the method based on a set of high resolution X-ray structures.     

Identification of amino acids involved in protein structural uniqueness: implication for de novo protein design

Structural uniqueness is characteristic of native proteins and is essential to express their biological functions. The major factors that bring about the uniqueness are specific interactions between hydrophobic residues and their unique packing in the protein core. To find the origin of the uniqueness in their amino acid sequences, we analyzed the distribution of the side chain rotational isomers (rotamers) of hydrophobic amino acids in protein tertiary structures and derived deltaS(contact), the conformational-entropy changes of side chains by residue-residue contacts in each secondary structure. The deltaS(contact) values indicate distinct tendencies of the residue pairs to restrict side chain conformation by inter-residue contacts. Of the hydrophobic residues in alpha-helices, aliphatic residues (Leu, Val, Ile) strongly restrict the side chain conformations of each other. In beta-sheets, Met is most strongly restricted by contact with Ile, whereas Leu, Val and Ile are less affected by other residues in contact than those in alpha-helices. In designed and native protein variants, deltaS(contact) was found to correlate with the folding-unfolding cooperativity. Thus, it can be used as a specificity parameter for designing artificial proteins with a unique structure.     

Hydrophobic Core Formation and Dehydration in Protein Folding Studied by Generalized-Ensemble Simulations

Despite its small size, chicken villin headpiece subdomain HP36 folds into the native structure with a stable hydrophobic core within several microseconds. How such a small protein keeps up its conformational stability and fast folding in solution is an important issue for understanding molecular mechanisms of protein folding. In this study, we performed multicanonical replica-exchange simulations of HP36 in explicit water, starting from a fully extended conformation. We observed at least five events of HP36 folding into nativelike conformations. The smallest backbone root mean-square deviation from the crystal structure was 1.1 Å. In the nativelike conformations, the stably formed hydrophobic core was fully dehydrated. Statistical analyses of the simulation trajectories show the following sequential events in folding of HP36: 1), Helix 3 is formed at the earliest stage; 2), the backbone and the side chains near the loop between Helices 2 and 3 take nativelike conformations; and 3), the side-chain packing at the hydrophobic core and the dehydration of the core side chains take place simultaneously at the later stage of folding. This sequence suggests that the initial folding nucleus is not necessarily the same as the hydrophobic core, consistent with a recent experimental ϕ-value analysis.     

Fragment-based local statistical potentials derived by combining an alphabet of protein local structures with secondary structures and solvent accessibilities

General and transferable statistical potentials to quantify the compatibility between local structures and local sequences of peptide fragments in proteins were derived. In the derivation, structure clusters of fragments are obtained by clustering five-residue fragments in native proteins based on their conformations represented by a local structure alphabet (de Brevern et al., Proteins 2000;41:271-287), secondary structure states, and solvent accessibilities. On the basis of the native sequences of the structurally clustered fragments, the probabilities of different amino acid sequences were estimated for each structure cluster. From the sequence probabilities, statistical energies as a function of sequence for a given structure were directly derived. The same sequence probabilities were employed in a database-matching approach to derive statistical energies as a function of local structure for a given sequence. Compared with prior models of local statistical potentials, we provided an integrated approach in which local conformations and local environments are treated jointly, structures are treated in units of fragments instead of individual residues so that coupling between the conformations of adjacent residues is included, and strong interdependences between the conformations of overlapping or neighboring fragment units are also considered. In tests including fragment threading, pseudosequence design, and local structure predictions, the potentials performed at least comparably and, in most cases, better than a number of existing models applicable to the same contexts indicating the advantages of such an integrated approach for deriving local potentials and suggesting applicability of the statistical potentials derived here in sequence designs and structure predictions.     

Characterization of the backbone geometry of protein native state structures

We present a simple method for analyzing the geometry of noncovalent residue-residue interactions stabilizing the protein structure, which takes into account the constraints on the local backbone geometry. We find that the principal geometrical constraints are amino acid aspecific and are associated with hydrogen bond formation in helices and sheets. In contrast, amino acid residues in nonhelical and nonextended conformations, which make noncovalent interactions stabilizing the protein tertiary structure, display greater flexibility. We apply the method to an analysis of the packing of helices in helical bundle proteins requiring an efficient packing of amino acid side-chains of the interacting helices.     

Using a Hydrophobic Contact Potential to Evaluate Native and Near-native Folds Generated by Molecular Dynamics Simulations

There are several knowledge-based energy functions that can distinguish the native fold from a pool of grossly misfolded decoys for a given sequence of amino acids. These decoys, which are typically generated by mounting, or “threading”, the sequence onto the backbones of unrelated protein structures, tend to be non-compact and quite different from the native structure: the root-mean-squared (RMS) deviations from the native are commonly in the range of 15 to 20 Å. Effective energy functions should also demonstrate a similar recognition capability when presented with compact decoys that depart only slightly in conformation from the correct structure (i.e. those with RMS deviations of ∼5 Å or less). Recently, we developed a simple yet powerful method for native fold recognition based on the tendency for native folds to form hydrophobic cores. Our energy measure, which we call the hydrophobic fitness score, is challenged to recognize the native fold from 2000 near-native structures generated for each of five small monomeric proteins. First, 1000 conformations for each protein were generated by molecular dynamics simulation at room temperature. The average RMS deviation of this set of 5000 was 1.5 Å. A total of 323 decoys had energies lower than native; however, none of these had RMS deviations greater than 2 Å. Another 1000 structures were generated for each at high temperature, in which a greater range of conformational space was explored (4.3 Å average RMS deviation). Out of this set, only seven decoys were misrecognized. The hydrophobic fitness energy of a conformation is strongly dependent upon the RMS deviation. On average our potential yields energy values which are lowest for the population of structures generated at room temperature, intermediate for those produced at high temperature and highest for those constructed by threading methods. In general, the lowest energy decoy conformations have backbones very close to native structure. The possible utility of our method for screening backbone candidates for the purpose of modelling by side-chain packing optimization is discussed.