A simplified amino acid potential for use in structure predictions of proteins

Solvent effects on kinetic mechanisms of self-assembly by peptide amphiphiles via molecular dynamics simulations

Peptide amphiphiles are known to form a variety of distinctive self-assembled nanostructures (including cylindrical nanofibers in hydrogels) dependent upon the solvent conditions. Using a novel coarse-grained model, large-scale molecular dynamics simulations are performed on a system of 800 peptide amphiphiles (sequence, palmitoyl-Val3Ala3Glu3) to elucidate kinetic mechanisms of molecular assembly as a function of the solvent conditions. The assembly process is found to occur via a multistep process with transient intermediates that ultimately leads to the stabilized nanostructures including open networks of β-sheets, cylindrical nanofibers, and elongated micelles. Different kinetic mechanisms are compared in terms of peptide secondary structures, solvent-accessible surface area, radius of gyration, relative shape anisotropy, intra/intermolecular interactions, and aggregate size dynamics to provide insightful information for the design of functional biomaterials.

Mechanism of the pH-Controlled Self-Assembly of Nanofibers from Peptide Amphiphiles

Stimuli-responsive, self-assembling nanomaterials hold a great promise to revolutionize medicine and technology. However, current discovery is slow and often serendipitous. Here we report a multiscale modeling study to elucidate the pH-controlled self-assembly of nanofibers from the peptide amphiphiles, palmitoyl-I-A₃E₄-NH₂. The coarse-grained simulations revealed the formation of random-coil based spherical micelles at strong electrostatic repulsion. However, at weak or no electrostatic repulsion, the micelles merge into a nanofiber driven by the β-sheet formation between the peptide segments. The all-atom constant pH molecular dynamics revealed a cooperative transition between random coil and β-sheet in the pH range 6-7, matching the CD data. Interestingly, although the bulk pK_a is more than one unit below the transition pH, consistent with the titration data, the highest pK_a's coincide with the transition pH, suggesting that the latter may be tuned by modulating the pK_a's of a few solvent-buried Glu side chains. Together, these data offer, to our best knowledge, the first multiresolution and quantitative view of the pH-dependent self-assembly of nanofibers. The novel protocols and insights gained are expected to advance the computer-aided design and discovery of pH-responsive nanomaterials.

Role of hydrophobicity on self-assembly by peptide amphiphiles via molecular dynamics simulations

Using a novel coarse-grained model, large-scale molecular dynamics simulations were performed to examine self-assembly of 800 peptide amphiphiles (sequence palmitoyl-V3A3E3). Under suitable physiological conditions, these molecules readily assemble into nanofibers leading to hydrogel construction as observed in experiments. Our simulations capture this spontaneous self-assembly process, including formation of secondary structure, to identify morphological transitions of distinctive nanostructures. As the hydrophobic interaction is increased, progression from open networks of secondary structures toward closed cylindrical nanostructures containing either β-sheets or random coils are observed. Moreover, temperature effects are also determined to play an important role in regulating formation of secondary structures within those nanostructures. These understandings of the molecular interactions involved and the role of environmental factors on hydrogel formation provide useful insight for development of innovative smart biomaterials for biomedical applications.

Coarse-grained models of the proteins backbone conformational dynamics

Coarse-grained models are more and more frequently used in the studies of the proteins structural and dynamic properties, since the reduced number of degrees of freedom allows to enhance the conformational space exploration. This chapter attempts to provide an overview of the various coarse-grained models that were applied to study the functional conformational changes of the polypeptides main chain around their native state. It will more specifically discuss the methods used to represent the protein backbone flexibility and to account for the physico-chemical interactions that stabilize the secondary structure elements.

The role of electrostatics and temperature on morphological transitions of hydrogel nanostructures self-assembled by peptide amphiphiles via molecular dynamics simulations

Smart biomaterials that are self-assembled from peptide amphiphiles (PA) are known to undergo morphological transitions in response to specific physiological stimuli. The design of such customizable hydrogels is of significant interest due to their potential applications in tissue engineering, biomedical imaging, and drug delivery. Using a novel coarse-grained peptide/polymer model, which has been validated by comparison of equilibrium conformations from atomistic simulations, large-scale molecular dynamics simulations are performed to examine the spontaneous self-assembly process. Starting from initial random configurations, these simulations result in the formation of nanostructures of various sizes and shapes as a function of the electrostatics and temperature. At optimal conditions, the self-assembly mechanism for the formation of cylindrical nanofibers is deciphered involving a series of steps: (1) PA molecules quickly undergo micellization whose driving force is the hydrophobic interactions between alkyl tails; (2) neighboring peptide residues within a micelle engage in a slow ordering process that leads to the formation of β-sheets exposing the hydrophobic core; (3) spherical micelles merge together through an end-to-end mechanism to form cylindrical nanofibers that exhibit high structural fidelity to the proposed structure based on experimental data. As the temperature and electrostatics vary, PA molecules undergo alternative kinetic mechanisms, resulting in the formation of a wide spectrum of nanostructures. A phase diagram in the electrostatics-temperature plane is constructed delineating regions of morphological transitions in response to external stimuli.

Construction of an intermediate-resolution lattice model and re-examination of the helix-coil transition: a dynamic Monte Carlo simulation

In protein modeling, spatial resolution and computational efficiency are always incompatible. As a compromise, an intermediate-resolution lattice model has been constructed in the present work. Each residue is decomposed into four basic units, i.e. the α-carbon group, the carboxyl group, the imino group, and the side-chain group, and each basic coarse-grained unit is represented by a minimum cubic box with eight lattice sites. The spacing of the lattice is about 0.56 Å, holding the highest spatial resolution for the present lattice protein models. As the first report of this new model, the helix-coil transition of a polyalanine chain was examined via dynamic Monte Carlo simulation. The period of formed α-helix was about 3.68 residues, close to that of a natural α-helix. The resultant backbone motion was found to be in the realistic regions of the conformational space in the Ramachandran plot. Helix propagation constant and nucleation constant were further determined through the dynamic hydrogen bonding process and torsional angle variation, and the results were used to make comparison between classical Zimm-Bragg theory and Lifson-Roig theory based on the Qian-Schellman relationship. The simulation results confirmed that our lattice model can reproduce the helix-coil transition of polypeptide and construct a moderately fine α-helix conformation without significantly weakening the priority in efficiency for a lattice model.

Coarse grained molecular dynamics simulations of transmembrane protein-lipid systems

Many biological cellular processes occur at the micro- or millisecond time scale. With traditional all-atom molecular modeling techniques it is difficult to investigate the dynamics of long time scales or large systems, such as protein aggregation or activation. Coarse graining (CG) can be used to reduce the number of degrees of freedom in such a system, and reduce the computational complexity. In this paper the first version of a coarse grained model for transmembrane proteins is presented. This model differs from other coarse grained protein models due to the introduction of a novel angle potential as well as a hydrogen bonding potential. These new potentials are used to stabilize the backbone. The model has been validated by investigating the adaptation of the hydrophobic mismatch induced by the insertion of WALP-peptides into a lipid membrane, showing that the first step in the adaptation is an increase in the membrane thickness, followed by a tilting of the peptide.

A coarse-grained protein force field for folding and structure prediction

We have revisited the protein coarse-grained optimized potential for efficient structure prediction (OPEP). The training and validation sets consist of 13 and 16 protein targets. Because optimization depends on details of how the ensemble of decoys is sampled, trial conformations are generated by molecular dynamics, threading, greedy, and Monte Carlo simulations, or taken from publicly available databases. The OPEP parameters are varied by a genetic algorithm using a scoring function which requires that the native structure has the lowest energy, and the native-like structures have energy higher than the native structure but lower than the remote conformations. Overall, we find that OPEP correctly identifies 24 native or native-like states for 29 targets and has very similar capability to the all-atom discrete optimized protein energy model (DOPE), found recently to outperform five currently used energy models.

A Coarse-Grained Protein−Protein Potential Derived from an All-Atom Force Field

In order to study protein-protein nonbonded interactions, we present the development of a new reduced protein model that represents each amino acid residue with one to three coarse grains, whose physical properties are derived in a consistent bottom-up procedure from the higher-resolution all-atom AMBER force field. The resulting potential energy function is pairwise additive and includes distinct van-der-Waals and Coulombic terms. The van-der-Waals effective interactions are deduced from preliminary molecular dynamics simulations of all possible amino acid homodimers. They are best represented by a soft 1/r6 repulsion and a Gaussian attraction, with parameters obeying Lorentz-Berthelot mixing rules. For the Coulombic interaction, coarse grain charges are optimized for each separate protein in order to best represent the all-atom electrostatic potential outside the protein core. This approach leaves the possibility of using any implicit solvent model to describe solvation effects and electrostatic screening. The coarse-grained force field is tested carefully for a small homodimeric complex, the magainin. It is shown to reproduce satisfactorily the specificity of the all-atom underlying potential, in particular within a PB/SA solvation model. The coarse-grained potential is applied to the redocking prediction of three different protein-protein complexes: the magainin dimer, the barnase-barstar, and the trypsin-BPTI complexes. It is shown to provide per se an efficient and discriminating scoring energy function for the protein-protein docking problem that remains pertinent at both the global and refinement stage.

Spontaneous fibril formation by polyalanines; discontinuous molecular dynamics simulations

Fibrillary protein aggregates rich in beta-sheet structure have been implicated in the pathology of several neurodegenerative diseases. In this work, we investigate the formation of fibrils by performing discontinuous molecular dynamics simulations on systems containing 12 to 96 model Ac-KA(14)K-NH(2) peptides using our newly developed off-lattice, implicit-solvent, intermediate-resolution model, PRIME. We find that, at a low concentration, random-coil peptides assemble into alpha-helices at low temperatures. At intermediate concentrations, random-coil peptides assemble into alpha-helices at low temperatures and large beta-sheet structures at high temperatures. At high concentrations, the system forms beta-sheets over a wide range of temperatures. These assemble into fibrils above a critical temperature which decreases with concentration and exceeds the isolated peptide's folding temperature. At very high temperatures and all concentrations, the system is in a random-coil state. All of these results are in good qualitative agreement with those by Blondelle and co-workers on Ac-KA(14)K-NH(2) peptides. The fibrils observed in our simulations mimic the structural characteristics observed in experiments in terms of the number of sheets formed, the values of the intra- and intersheet separations, and the parallel peptide arrangement within each beta-sheet. Finally, we find that when the strength of the hydrophobic interaction between nonpolar side chains is high compared to the strength of hydrogen bonding, amorphous aggregates, rather than fibrillar aggregates, are formed.

Evaluation of the protein solvent-accessible surface using reduced representations in terms of critical points of the electron density

The aim of our study is the development of a method for calculating the interface of dimerization of protein-protein complexes based on simplified medium-resolution structures. In particular, we wished to evaluate if the existing concepts for the computation of the Solvent-Accessible Surface Area (SASA) of macromolecules could be applied to medium-resolution models. Therefore, we selected a set of 140 protein chains and computed their reduced representations by topological analysis of their electron density maps at 2.85 A crystallographic resolution. This procedure leads to a limited number of critical points (CPs) that can be identified and associated to backbone and side-chain parts. To evaluate the SASA and interfaces of dimerization of the reduced representations, we chose and modified two existing programs that calculate the SASA of atomic representations, and tested (1) several radii tables of amino acids, (2) the influence of the backbone and side-chain points, and (3) the radius of the solvent molecule, which rolls over the surface. The results are shown in terms of relative error compared to the values calculated on the corresponding atomic representations of the proteins.

A simple procedure to weight empirical potentials in a fitness function so as to optimize its performance in ab initio protein-folding problem

In an approach to the protein folding problem by a Genetic Algorithm, the fitness function plays a critical role. Empirical potentials are generally used to build the fitness function, and they must be weighted to obtain a valuable one. The weights are generally found by the comparison with a set of misfolded structures (decoys), but a dependence of the obtained fitness generally arises on the used decoys. Here we describe a general procedure to find out, from a given set of potentials, their better linear combination that could either identify the wild structure or prove their powerlessness. We use topological considerations over the hyperspace of the potentials, and a multiple linear inequalities solver. The iterated method flows through the following steps: it determines a direction in the hyperspace of the potentials, which identifies the native structure as a vertex among a set of misfolded decoys. A multiple linear inequalities solver obtains the direction. A Genetic Algorithm, tailored to the specific problem, uses the fitness function defined by this direction and generally reaches a new structure better than the experimental one, which is added to the ensemble. The decoys so generated are not dependent on a deterministic criterion. This iterative procedure can be stopped either by identifying an effective fitness function or by proving the impossibility of its achievement. In order to test the method under the hardest conditions, we choose numerous and heterogeneous quantities as components of the fitness function. This method could be a useful tool for the scientific community in order to test any fitness proposed and to recognize the most important components on which it is built.

Protein-protein docking with a reduced protein model accounting for side-chain flexibility

A protein-protein docking approach has been developed based on a reduced protein representation with up to three pseudo atoms per amino acid residue. Docking is performed by energy minimization in rotational and translational degrees of freedom. The reduced protein representation allows an efficient search for docking minima on the protein surfaces within. During docking, an effective energy function between pseudo atoms has been used based on amino acid size and physico-chemical character. Energy minimization of protein test complexes in the reduced representation results in geometries close to experiment with backbone root mean square deviations (RMSDs) of approximately 1 to 3 A for the mobile protein partner from the experimental geometry. For most test cases, the energy-minimized experimental structure scores among the top five energy minima in systematic docking studies when using both partners in their bound conformations. To account for side-chain conformational changes in case of using unbound protein conformations, a multicopy approach has been used to select the most favorable side-chain conformation during the docking process. The multicopy approach significantly improves the docking performance, using unbound (apo) binding partners without a significant increase in computer time. For most docking test systems using unbound partners, and without accounting for any information about the known binding geometry, a solution within approximately 2 to 3.5 A RMSD of the full mobile partner from the experimental geometry was found among the 40 top-scoring complexes. The approach could be extended to include protein loop flexibility, and might also be useful for docking of modeled protein structures.

Protein refolding versus aggregation: computer simulations on an intermediate-resolution protein model

Computer simulations are performed on a system of eight model peptide chains to study how the competition between protein refolding and aggregation affects the optimal conditions for refolding of four-helix bundles. The discontinuous molecular dynamics algorithm is utilized along with an intermediate-resolution protein model that we developed for this work. Physically, the model is much more detailed than any model used to date for simulations of protein aggregation. Each model residue consists of a detailed, three-bead backbone and a simplified, single-bead side-chain. Excluded volume, hydrogen bond, and hydrophobic interactions are modeled with discontinuous (i.e. hard-sphere and square-well) potentials. Simulations efficiently sample conformational space, and complete folding trajectories from random initial configurations to two four-helix bundles are possible within two days on a single processor workstation. Folding of the bundles follows two main pathways, one through a trimeric intermediate and the other through an intermediate with two dimers. The proportion of trajectories that follow each route is significantly different for the eight-peptide system in this work than in a previously studied four-peptide system, which yields one four-helix bundle, suggesting, as our previous simulations have, that protein folding properties are strongly influenced by the presence of other proteins. Folding of the bundles is optimal within a fixed temperature range, with the high-temperature boundary a function of the complexity of the protein (or oligomer) to be folded and the low-temperature boundary a function of the complexity of the protein's environment. Above the optimal temperature range for folding, the model chains tend to unfold; below the optimal range, the model chains tend to aggregate. As has been seen previously, aggregates have substantial levels of native secondary structure, suggesting that aggregates are composed largely of partially folded intermediates, not denatured chains.

alpha-helix formation: discontinuous molecular dynamics on an intermediate-resolution protein model

An intermediate-resolution model of small, homogeneous peptides is introduced, and discontinuous molecular dynamics simulation is applied to study secondary structure formation. Physically, each model residue consists of a detailed three-bead backbone and a simplified single-bead side-chain. Excluded volume and hydrogen bond interactions are constructed with discontinuous (i.e., hard-sphere and square-well) potentials. Simulation results show that the backbone motion of the model is limited to realistic regions of Phi-Psi conformational space. Model polyalanine chains undergo a locally cooperative transition to form alpha-helices that are stabilized by backbone hydrogen bonding, while model polyglycine chains tend to adopt nonhelical structures. When side-chain size is increased beyond a critical diameter, steric interactions prevent formation of long alpha-helices. These trends in helicity as a function of residue type have been well documented by experimental, theoretical, and simulation studies and demonstrate the ability of the intermediate-resolution model developed in this work to accurately mimic realistic peptide behavior. The efficient algorithm used permits observation of the complete helix-coil transition within 15 min on a single-processor workstation, suggesting that simulations of very long times are possible with this model.

Assembly of a tetrameric alpha-helical bundle: computer simulations on an intermediate-resolution protein model

Discontinuous molecular dynamics (DMD) simulation on an intermediate-resolution protein model is used to study the folding of an isolated, small model peptide to an amphipathic alpha-helix and the assembly of four of these model peptides into a four-helix bundle. A total of 129 simulations were performed on the isolated peptide, and 50 simulations were performed on the four-peptide system. Simulations efficiently sample conformational space allowing complete folding trajectories from random initial configurations to be observed within 15 min for the one-peptide system and within 15 h for the four-peptide system on a 500-MHz workstation. The native structures of both the alpha-helix and the four-helix bundle are consistent with experimental characterization studies and with results from previous simulations on these model peptides. In both the one- and four-peptide systems, the native state is achieved during simulations within an optimal temperature range, a phenomenon also observed experimentally. The ease with which our simulations yield reasonable estimates of folded structures demonstrates the power of the intermediate-resolution model developed for this work and the DMD algorithm and suggests that simulations of very long times and of multiprotein systems may be possible with this model.

Ab initio protein structure prediction using physicochemical potentials and a simplified off-lattice model

This study describes a computational method for ab inito protein structure prediction. Protein conformation has been modeled by using six optimized backbone torsion angles and fixed side chains approximating rotationally averaged real side chains. The approximations aim to keep complexity of the structure description to a minimum without seriously compromising the accuracy of the structural representation. An evolutionary Monte Carlo algorithm has been developed to search through this restricted conformational space to locate low-energy protein structures. A simple physicochemical force field has been developed to assess the energies of different conformations within this structural description. The corresponding residue interaction energies are based on hydrophobic, hydrophilic, steric, and hydrogen-bonding potentials. The search procedure has been used to locate native energy minima from primary sequence alone. The 3-D structures of polypeptides up to 38 residues with both beta and alpha secondary structural elements have been accurately predicted. The search procedure has been found to be highly efficient and follows an energetically and structurally plausible pathway to locate native populations. The simple force field described in the study has been compared with a more complex all-atom model and been found to be similarly effective in predicting the structures of proposed independent folding units. Proteins 2001;43:186-202.

Predicting the structures of 18 peptides using Geocore

We describe an extensive test of Geocore, an ab initio peptide folding algorithm. We studied 18 short molecules for which there are structures in the Protein Data Bank; chains are up to 31 monomers long. Except for the very shortest peptides, an extremely simple energy function is sufficient to discriminate the true native state from more than 10(8) lowest energy conformations that are searched explicitly for each peptide. A high incidence of native-like structures is found within the best few hundred conformations generated by Geocore for each amino acid sequence. Predictions improve when the number of discrete phi/psi choices is increased.

Reduced protein models and their application to the protein folding problem

One of the most important unsolved problems of computational biology is prediction of the three-dimensional structure of a protein from its amino acid sequence. In practice, the solution to the protein folding problem demands that two interrelated problems be simultaneously addressed. Potentials that recognize the native state from the myriad of misfolded conformations are required, and the multiple minima conformational search problem must be solved. A means of partly surmounting both problems is to use reduced protein models and knowledge-based potentials. Such models have been employed to elucidate a number of general features of protein folding, including the nature of the energy landscape, the factors responsible for the uniqueness of the native state and the origin of the two-state thermodynamic behavior of globular proteins. Reduced models have also been used to predict protein tertiary and quaternary structure. When combined with a limited amount of experimental information about secondary and tertiary structure, molecules of substantial complexity can be assembled. If predicted secondary structure and tertiary restraints are employed, low resolution models of single domain proteins can be successfully predicted. Thus, simplified protein models have played an important role in furthering the understanding of the physical properties of proteins.

Fold assembly of small proteins using monte carlo simulations driven by restraints derived from multiple sequence alignments

The feasibility of predicting the global fold of small proteins by incorporating predicted secondary and tertiary restraints into ab initio folding simulations has been demonstrated on a test set comprised of 20 non-homologous proteins, of which one was a blind prediction of target 42 in the recent CASP2 contest. These proteins contain from 37 to 100 residues and represent all secondary structural classes and a representative variety of global topologies. Secondary structure restraints are provided by the PHD secondary structure prediction algorithm that incorporates multiple sequence information. Predicted tertiary restraints are derived from multiple sequence alignments via a two-step process. First, seed side-chain contacts are identified from correlated mutation analysis, and then a threading-based algorithm is used to expand the number of these seed contacts. A lattice-based reduced protein model and a folding algorithm designed to incorporate these predicted restraints is described. Depending upon fold complexity, it is possible to assemble native-like topologies whose coordinate root-mean-square deviation from native is between 3.0 A and 6.5 A. The requisite level of accuracy in side-chain contact map prediction can be roughly 25% on average, provided that about 60% of the contact predictions are correct within +/-1 residue and 95% of the predictions are correct within +/-4 residues. Precision in tertiary contact prediction is more critical than absolute accuracy. Furthermore, only a subset of the tertiary contacts, on the order of 25% of the total, is sufficient for successful topology assembly. Overall, this study suggests that the use of restraints derived from multiple sequence alignments combined with a fold assembly algorithm holds considerable promise for the prediction of the global topology of small proteins.

Discrete Haar transform and protein structure

The discrete Haar transform of the sequence of the backbone dihedral angles (phi and psi) was performed over a set of X-ray protein structures of high resolution from the Brookhaven Protein Data Bank. Afterwards, the new dihedral angles were calculated by the inverse transform, using a growing number of Haar functions, from the lower to the higher degree. New structures were obtained using these dihedral angles, with standard values for bond lengths and angles, and with omega = 0 degree. The reconstructed structures were compared with the experimental ones, and analyzed by visual inspection and statistical analysis. When half of the Haar coefficients were used, all the reconstructed structures were not yet collapsed to a tertiary folding, but they showed yet realized most of the secondary motifs. These results indicate a substantial separation of structural information in the space of Haar transform, with the secondary structural information mainly present in the Haar coefficients of lower degrees, and the tertiary one present in the higher degree coefficients. Because of this separation, the representation of the folded structures in the space of Haar transform seems a promising candidate to encompass the problem of premature convergence in genetic algorithms.

Factors affecting the ability of energy functions to discriminate correct from incorrect folds

Eighteen low and medium resolution empirical energy functions were tested for their ability to distinguish correct from incorrect folds from three test sets of decoy protein conformations. The energy functions included 13 pairwise potentials of mean force, covering a wide range of functional forms and methods of parameterization, four potentials that attempt to detect properly formed hydrophobic cores, and one environment-based potential. the first of the three test sets consists of large ensembles of plausible conformations for eight small proteins, all of which have correct native secondary structure and are reasonably compact. The second is the set of all subconformations in a database of known protein structures applied to the sequences in that database (ungapped threading). The third is a set of ensembles of 1000 conformations each for seven small proteins taken from molecular dynamics simulations at 298 K and 498 K. Our results show that there are functions effective for each challenge set; moreover, success in one test is no guarantee of success in another. We examine the factors that seem to be important for accurate discrimination of correct structures in each of the test sets, and note that extremely simple functions are often as effective as more complex functions.

Inter-residue potentials in globular proteins and the dominance of highly specific hydrophilic interactions at close separation

Residue-specific potentials between pairs of side-chains and pairs of side-chain-backbone interaction sites have been generated by collecting radial distribution data for 302 protein structures. Multiple atomic interactions have been utilized to enhance the specificity and smooth the distance-dependence of the potentials. The potentials are demonstrated to successfully discriminate correct sequences in inverse folding experiments. Many specific effects are observable in the non-bonded potentials; grouping of residue types is inappropriate, since each residue type manifests some unique behavior. Only a weak dependence is seen on protein size and composition. Effective contact potentials operating in three different environments (self, solvent-exposed and residue-exposed) and over any distance range are presented. The effective contact potentials obtained from the integration of radial distributions over the distance interval r < or = 6.4 A are in excellent agreement with published values. The hydrophobic interactions are verified to be dominantly strong in this range. Comparison of these with a newly derived set of effective contact potentials for closer inter-residue separations (r < or = 4.0 A) demonstrates drastic changes in the most favorable interactions. In the closer approach case, where the number of pairs with a given residue is approximately one, the highly specific interactions between charged and polar side-chains predominate. These closer approach values could be utilized to select successively the relative positions and directions of residue side-chains in protein simulations, following a hierarchical algorithm optimizing side-chain-side-chain interactions over the two successively closer distance ranges. The homogeneous contribution to stability is stronger than the specific contribution by about a factor of 5. Overall, the total non-bonded interaction energy calculated for individual proteins follows a dependence on the number of residues of the form of n1.28, indicating an enhanced stability for larger proteins.

Protein folding: the endgame

The last stage of protein folding, the "endgame," involves the ordering of amino acid side-chains into a well defined and closely packed configuration. We review a number of topics related to this process. We first describe how the observed packing in protein crystal structures is measured. Such measurements show that the protein interior is packed exceptionally tightly, more so than the protein surface or surrounding solvent and even more efficiently than crystals of simple organic molecules. In vitro protein folding experiments also show that the protein is close-packed in solution and that the tight packing and intercalation of side-chains is a final and essential step in the folding pathway. These experimental observations, in turn, suggest that a folded protein structure can be described as a kind of three-dimensional jigsaw puzzle and that predicting side-chain packing is possible in the sense of solving this puzzle. The major difficulty that must be overcome in predicting side-chain packing is a combinatorial "explosion" in the number of possible configurations. There has been much recent progress towards overcoming this problem, and we survey a variety of the approaches. These approaches differ principally in whether they use ab initio (physical) or more knowledge-based methods, how they divide up and search conformational space, and how they evaluate candidate configurations (using scoring functions). The accuracy of side-chain prediction depends crucially on the (assumed) positioning of the main-chain. Methods for predicting main-chain conformation are, in a sense, not as developed as that for side-chains. We conclude by surveying these methods. As with side-chain prediction, there are a great variety of approaches, which differ in how they divide up and search space and in how they score candidate conformations.

A fast conformational search strategy for finding low energy structures of model proteins

We describe a new computer algorithm for finding low-energy conformations of proteins. It is a chain-growth method that uses a heuristic bias function to help assemble a hydrophobic core. We call it the Core-directed chain Growth method (CG). We test the CG method on several well-known literature examples of HP lattice model proteins [in which proteins are modeled as sequences of hydrophobic (H) and polar (P) monomers], ranging from 20-64 monomers in two dimensions, and up to 88-mers in three dimensions. Previous nonexhaustive methods--Monte Carlo, a Genetic Algorithm, Hydrophobic Zippers, and Contact Interactions--have been tried on these same model sequences. CG is substantially better at finding the global optima, and avoiding local optima, and it does so in comparable or shorter times. CG finds the global minimum energy of the longest HP lattice model chain for which the global optimum is known, a 3D 88-mer that has only been reachable before by the CHCC complete search method. CG has the potential advantage that it should have nonexponential scaling with chain length. We believe this is a promising method for conformational searching in protein folding algorithms.

A pseudo-particle approach for studying protein-ligand models truncated to their active sites

A molecular dynamics method has been developed to describe the structural and dynamic properties of protein-ligand complexes that are truncated to their active sites. The active site is comprised of the ligand and discontinuous, positionally unrestrained peptide chains. This truncated active-site complex is surrounded by big unspecific pseudo-particles representing the complete protein and the solvent. Thus, knowledge of the folding of the outer parts of the protein is not required, and the method can be applied to protein models, derived from homology modeling. The method has been tested using ligand complexes of adenylate kinase, retinol binding protein, HIV-1 protease, and human leucocyte antigen. Comparisons with their crystal structures and with results from time-demanding simulations of the whole complexes in explicit water solvent show that the ligand binding properties are conserved. Most of the hydrogen bonds between the ligand and the active-site residues are reproduced and, furthermore, the simulation time is reduced.

Structure-derived potentials and protein simulations

There has recently been an explosion in the number of structure-derived potential functions that are based on the increasing number of high-resolution protein crystal structures. These functions differ principally in their reference states; the usual two classes correspond either to initial solvent exposure or to residue exposure of residues. Reference states are critically important for applications of these potentials functions. Inspection of the potential functions and their derivation can tell us not only about protein interaction strengths themselves, but can also provide suggestions for the design of better folding simulations. An appropriate goal in this field is achieving self-consistency between the details in the derivation of potentials and the applied simulations.

Structure of a cyclic peptide with a catalytic triad, determined by computer simulation and NMR spectroscopy

We report the design of a cyclic, eight-residue peptide that possesses the catalytic triad residues of the serine proteases. A manually built model has been relaxed by 0.3 ns of molecular dynamics simulation at room temperature, during which no major changes occurred in the peptide. The molecule has been synthesised and purified. Two-dimensional NMR spectroscopy provided 35 distance and 7 torsion angle constraints, which were used to determine the three-dimensional structure. The experimental conformation agrees with the predicted one at the beta-turn, but deviates in the arrangement of the disulphide bridge that closes the backbone to a ring. A 1.2 ns simulation at 600 K provided extended sampling of conformation space. The disulphide bridge reoriented into the experimental arrangement, producing a minimum backbone rmsd from the experimental conformation of 0.8 A. At a later stage in the simulation, a transition at Ser3 produced more pronounced high-temperature behaviour. The peptide hydrolyses p-nitrophenyl acetate about nine times faster than free histidine.