In silico folding of a three helix protein and characterization of its free-energy landscape in an all-atom force field

Random coil to globular thermal response of a protein (H3.1) with three knowledge-based coarse-grained potentials

The effect of temperature on the conformation of a histone (H3.1) is studied by a coarse-grained Monte Carlo simulation based on three knowledge-based contact potentials (MJ, BT, BFKV). Despite unique energy and mobility profiles of its residues, the histone H3.1 undergoes a systematic (possibly continuous) structural transition from a random coil to a globular conformation on reducing the temperature. The range over which such a systematic response in variation of the radius of gyration (R(g)) with the temperature (T) occurs, however, depends on the potential, i.e. ΔT(MJ) ≈ 0.013-0.020, ΔT(BT) ≈ 0.018-0.026, and ΔT(BFKV) ≈ 0.006-0.013 (in reduced unit). Unlike MJ and BT potentials, results from the BFKV potential show an anomaly where the magnitude of R(g) decreases on raising the temperature in a range ΔT(A) ≈ 0.015-0.018 before reaching its steady-state random coil configuration. Scaling of the structure factor, S(q) ∝ q(-1/ν), with the wave vector, q=2π/λ, and the wavelength, λ, reveals a systematic change in the effective dimension (D(e)∼1/ν) of the histone with all potentials (MJ, BT, BFKV): D(e)∼3 in the globular structure with D(e)∼2 for the random coil. Reproducibility of the general yet unique (monotonic) structural transition of the protein H3.1 with the temperature (in contrast to non-monotonic structural response of a similar but different protein H2AX) with three interaction sets shows that the knowledge-based contact potential is viable tool to investigate structural response of proteins. Caution should be exercise with the quantitative comparisons due to differences in transition regimes with these interactions.

Performance assessment of different constraining potentials in computational structure prediction for disulfide-bridged proteins

The presence of disulfide bonds in proteins has very important implications on the three-dimensional structure and folding of proteins. An adequate treatment of disulfide bonds in de-novo protein simulations is therefore very important. Here we present a computational study of a set of small disulfide-bridged proteins using an all-atom stochastic search approach and including various constraining potentials to describe the disulfide bonds. The proposed potentials can easily be implemented in any code based on all-atom force fields and employed in simulations to achieve an improved prediction of protein structure. Exploring different potential parameters and comparing the structures to those from unconstrained simulations and to experimental structures by means of a scoring function we demonstrate that the inclusion of constraining potentials improves the quality of final structures significantly. For some proteins (1KVG and 1PG1) the native conformation is visited only in simulations in presence of constraints. Overall, we found that the Morse potential has optimal performance, in particular for the β-sheet proteins.

Modelling proteins: conformational sampling and reconstruction of folding kinetics

In the last decades biomolecular simulation has made tremendous inroads to help elucidate biomolecular processes in-silico. Despite enormous advances in molecular dynamics techniques and the available computational power, many problems involve long time scales and large-scale molecular rearrangements that are still difficult to sample adequately. In this review we therefore summarise recent efforts to fundamentally improve this situation by decoupling the sampling of the energy landscape from the description of the kinetics of the process. Recent years have seen the emergence of many advanced sampling techniques, which permit efficient characterisation of the relevant family of molecular conformations by dispensing with the details of the short-term kinetics of the process. Because these methods generate thermodynamic information at best, they must be complemented by techniques to reconstruct the kinetics of the process using the ensemble of relevant conformations. Here we review recent advances for both types of methods and discuss their perspectives to permit efficient and accurate modelling of large-scale conformational changes in biomolecules. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

Globular structure of a human immunodeficiency virus-1 protease (1DIFA dimer) in an effective solvent medium by a Monte Carlo simulation

A coarse-grained model is used to study the structure and dynamics of a human immunodeficiency virus-1 protease (1DIFA dimer) consisting of 198 residues in an effective solvent medium on a cubic lattice by Monte Carlo simulations for a range of interaction strengths. Energy and mobility profiles of residues are found to depend on the interaction strength and exhibit remarkable segmental symmetries in two monomers. Lowest energy residues such as Arg(41) and Arg(140) (most electrostatic and polar) are not the least mobile; despite the higher energy, the hydrophobic residues (Ile, Leu, and Val) are least mobile and form the core by pinning down the local segments for the globular structure. Variations in the gyration radius (R(g)) and energy (E(c)) of the protein show nonmonotonic dependence on the interaction strength with the smallest R(g) around the largest value of E(c). Pinning of the conformations by the hydrophobic residues at high interaction strength seems to provide seed for the protein chain to collapse.

Template-free protein structure prediction and quality assessment with an all-atom free-energy model

Biophysical forcefields have contributed less than originally anticipated to recent progress in protein structure prediction. Here, we have investigated the selectivity of a recently developed all-atom free-energy forcefield for protein structure prediction and quality assessment (QA). Using a heuristic method, but excluding homology, we generated decoy-sets for all targets of the CASP7 protein structure prediction assessment with <150 amino acids. The decoys in each set were then ranked by energy in short relaxation simulations and the best low-energy cluster was submitted as a prediction. For four of nine template-free targets, this approach generated high-ranking predictions within the top 10 models submitted in CASP7 for the respective targets. For these targets, our de-novo predictions had an average GDT_S score of 42.81, significantly above the average of all groups. The refinement protocol has difficulty for oligomeric targets and when no near-native decoys are generated in the decoy library. For targets with high-quality decoy sets the refinement approach was highly selective. Motivated by this observation, we rescored all server submissions up to 200 amino acids using a similar refinement protocol, but using no clustering, in a QA exercise. We found an excellent correlation between the best server models and those with the lowest energy in the forcefield. The free-energy refinement protocol may thus be an efficient tool for relative QA and protein structure prediction.

Free-energy-driven folding and thermodynamics of the 67-residue protein GS-alpha3W--a large-scale Monte Carlo study

Utilizing the computational power of a few thousand processors on a BlueGene/P, we have explored the folding mechanism of the 67-residue protein GS-alpha(3)W. Results from our large-scale simulation indicate a diffusion-collision mechanism for folding. However, the lower-than-expected frequency of native-like configurations at physiological temperatures indicates shortcomings of our energy function. Our results suggest that computational studies of large proteins call for redevelopment and reparametrization of force fields that in turn require extensive simulations only possible with the newly available supercomputers with computing powers reaching the petaflop range.

A free-energy approach for all-atom protein simulation

All-atom free-energy methods offer a promising alternative to kinetic molecular mechanics simulations of protein folding and association. Here we report an accurate, transferable all-atom biophysical force field (PFF02) that stabilizes the native conformation of a wide range of proteins as the global optimum of the free-energy landscape. For 32 proteins of the ROSETTA decoy set and six proteins that we have previously folded with PFF01, we find near-native conformations with an average backbone RMSD of 2.14 A to the native conformation and an average Z-score of -3.46 to the corresponding decoy set. We used nonequilibrium sampling techniques starting from completely extended conformations to exhaustively sample the energy surface of three nonhomologous hairpin-peptides, a three-stranded beta-sheet, the all-helical 40 amino-acid HIV accessory protein, and a zinc-finger beta beta alpha motif, and find near-native conformations for the minimal energy for each protein. Using a massively parallel evolutionary algorithm, we also obtain a near-native low-energy conformation for the 54 amino-acid engrailed homeodomain. Our force field thus stabilized near-native conformations for a total of 20 proteins of all structure classes with an average RMSD of only 3.06 A to their respective experimental conformations.

Residue energy and mobility in sequence to global structure and dynamics of a HIV-1 protease (1DIFA) by a coarse-grained Monte Carlo simulation

Energy, mobility, and structural profiles of residues in a specific sequence of human immunodeficiency virus (HIV)-1 protease chain and its global conformation and dynamics are studied by a coarse-grained computer simulation model on a cubic lattice. HIV-1 protease is described by a chain of 99 residues (nodes) in a specific sequence (1DIFA) with N- and C-terminals on the lattice, where empty lattice sites represent an effective solvent medium. Internal structures of the residues are ignored but their specificities are captured via an interaction (epsilon(ij)) matrix (residue-residue, residue-solvent) of the coefficient (fepsilon(ij)) of the Lennard-Jones potential. Simulations are performed for a range of interaction strength (f) with the solvent-residue interaction describing the quality of the solvent. Snapshots of the protein show considerable changes in the conformation of the protein on varying the interaction. From the mobility and energy profiles of the residues, it is possible to identify the active (and not so active) segments of the protein and consequently their role in proteolysis. Contrary to interaction thermodynamics, the hydrophobic residues possess higher configurational energy and lower mobility while the electrostatic and polar residues are more mobile despite their lower interaction energy. Segments of hydrophobic core residues, crucial for the structural evolution of the protein are identified-some of which are consistent with recent molecular dynamics simulation in context to possible clinical observations. Global energy and radius of gyration of the protein exhibit nonmonotonic dependence on the interaction strength (f) with opposite trends, e.g., rapid transition into globular structure with higher energy. Variations of the rms displacement of the protein and that of a tracer residue, Gly(49), with the time steps show how they slow down on increasing the interaction strength.

An effective all-atom potential for proteins

We describe and test an implicit solvent all-atom potential for simulations of protein folding and aggregation. The potential is developed through studies of structural and thermodynamic properties of 17 peptides with diverse secondary structure. Results obtained using the final form of the potential are presented for all these peptides. The same model, with unchanged parameters, is furthermore applied to a heterodimeric coiled-coil system, a mixed α/β protein and a three-helix-bundle protein, with very good results. The computational efficiency of the potential makes it possible to investigate the free-energy landscape of these 49–67-residue systems with high statistical accuracy, using only modest computational resources by today's standards.

PACS Codes: 87.14.E-, 87.15.A-, 87.15.Cc

Folding proteins by first-passage-times-optimized replica exchange

Replica exchange simulations have become the method of choice in computational protein science, but they still often do not allow an efficient sampling of low-energy protein configurations. Here, we reconstruct replica flow in the temperature ladder from first passage times and use it for temperature optimization, thereby maximizing sampling. The method is applied in simulations of folding thermodynamics for a number of proteins starting from the pentapeptide Met-enkephalin, through the 36-residue HP-36, up to the 67-residue protein GS-alpha3W.

Conformational landscape of the HIV-V3 hairpin loop from all-atom free-energy simulations

Small beta hairpins have many distinct biological functions, including their involvement in chemokine and viral receptor recognition. The relevance of structural similarities between different hairpin loops with near homologous sequences is not yet understood, calling for the development of methods for de novo hairpin structure prediction and simulation. De novo folding of beta strands is more difficult than that of helical proteins because of nonlocal hydrogen bonding patterns that connect amino acids that are distant in the amino acid sequence and there is a large variety of possible hydrogen bond patterns. Here we use a greedy version of the basin hopping technique with our free-energy forcefield PFF02 to reproducibly and predictively fold the hairpin structure of a HIV-V3 loop. We performed 20 independent basin hopping runs for 500 cycles corresponding to 7.4 x 10(7) energy evaluations each. The lowest energy structure found in the simulation has a backbone root mean square deviation (bRMSD) of only 2.04 A to the native conformation. The lowest 9 out of the 20 simulations converged to conformations deviating less than 2.5 A bRMSD from native.

Conformation of a coarse-grained protein chain (an aspartic acid protease) model in effective solvent by a bond-fluctuating Monte Carlo simulation

In a coarse-grained description of a protein chain, all of the 20 amino acid residues can be broadly divided into three groups: Hydrophobic (H) , polar (P) , and electrostatic (E) . A protein can be described by nodes tethered in a chain with a node representing an amino acid group. Aspartic acid protease consists of 99 residues in a well-defined sequence of H , P , and E nodes tethered together by fluctuating bonds. The protein chain is placed on a cubic lattice where empty lattice sites constitute an effective solvent medium. The amino groups (nodes) interact with the solvent (S) sites with appropriate attractive (PS) and repulsive (HS) interactions with the solvent and execute their stochastic movement with the Metropolis algorithm. Variations of the root mean square displacements of the center of mass and that of its center node of the protease chain and its gyration radius with the time steps are examined for different solvent strength. The structure of the protease swells on increasing the solvent interaction strength which tends to enhance the relaxation time to reach the diffusive behavior of the chain. Equilibrium radius of gyration increases linearly on increasing the solvent strength: A slow rate of increase in weak solvent regime is followed by a faster swelling in stronger solvent. Variation of the gyration radius with the time steps suggests that the protein chain moves via contraction and expansion in a somewhat quasiperiodic pattern particularly in strong solvent.

Folding pathway of the b1 domain of protein G explored by multiscale modeling

The understanding of the folding mechanisms of single-domain proteins is an essential step in the understanding of protein folding in general. Recently, we developed a mesoscopic CA-CB side-chain protein model, which was successfully applied in protein structure prediction, studies of protein thermodynamics, and modeling of protein complexes. In this research, this model is employed in a detailed characterization of the folding process of a simple globular protein, the B1 domain of IgG-binding protein G (GB1). There is a vast body of experimental facts and theoretical findings for this protein. Performing unbiased, ab initio simulations, we demonstrated that the GB1 folding proceeds via the formation of an extended folding nucleus, followed by slow structure fine-tuning. Remarkably, a subset of native interactions drives the folding from the very beginning. The emerging comprehensive picture of GB1 folding perfectly matches and extends the previous experimental and theoretical studies.

A water-explicit lattice model of heat-, cold-, and pressure-induced protein unfolding

We investigate the effect of temperature and pressure on polypeptide conformational stability using a two-dimensional square lattice model in which water is represented explicitly. The model captures many aspects of water thermodynamics, including the existence of density anomalies, and we consider here the simplest representation of a protein: a hydrophobic homopolymer. We show that an explicit treatment of hydrophobic hydration is sufficient to produce cold, pressure, and thermal denaturation. We investigate the effects of the enthalpic and entropic components of the water-protein interactions on the overall folding phase diagram, and show that even a schematic model such as the one we consider yields reasonable values for the temperature and pressure ranges within which highly compact homopolymer configurations are thermodynamically stable.

Protein structure prediction by all-atom free-energy refinement

Background

The reliable prediction of protein tertiary structure from the amino acid sequence remains challenging even for small proteins. We have developed an all-atom free-energy protein forcefield (PFF01) that we could use to fold several small proteins from completely extended conformations. Because the computational cost of de-novo folding studies rises steeply with system size, this approach is unsuitable for structure prediction purposes. We therefore investigate here a low-cost free-energy relaxation protocol for protein structure prediction that combines heuristic methods for model generation with all-atom free-energy relaxation in PFF01.

Results

We use PFF01 to rank and cluster the conformations for 32 proteins generated by ROSETTA. For 22/10 high-quality/low quality decoy sets we select near-native conformations with an average C_α root mean square deviation of 3.03 Å/6.04 Å. The protocol incorporates an inherent reliability indicator that succeeds for 78% of the decoy sets. In over 90% of these cases near-native conformations are selected from the decoy set. This success rate is rationalized by the quality of the decoys and the selectivity of the PFF01 forcefield, which ranks near-native conformations an average 3.06 standard deviations below that of the relaxed decoys (Z-score).

Conclusion

All-atom free-energy relaxation with PFF01 emerges as a powerful low-cost approach toward generic de-novo protein structure prediction. The approach can be applied to large all-atom decoy sets of any origin and requires no preexisting structural information to identify the native conformation. The study provides evidence that a large class of proteins may be foldable by PFF01.

Comparison of stochastic optimization methods for all-atom folding of the Trp-Cage protein

The performances of three different stochastic optimization methods for all-atom protein structure prediction are investigated and compared. We use the recently developed all-atom free-energy force field (PFF01), which was demonstrated to correctly predict the native conformation of several proteins as the global optimum of the free energy surface. The trp-cage protein (PDB-code 1L2Y) is folded with the stochastic tunneling method, a modified parallel tempering method, and the basin-hopping technique. All the methods correctly identify the native conformation, and their relative efficiency is discussed.

All-atomde novo protein folding with a scalable evolutionary algorithm

The search for efficient and predictive methods to describe the protein folding process at the all-atom level remains an important grand-computational challenge. The development of multi-teraflop architectures, such as the IBM BlueGene used in this study, has been motivated in part by the large computational requirements of such studies. Here we report the predictive all-atom folding of the forty-amino acid HIV accessory protein using an evolutionary stochastic optimization technique. We implemented the optimization method as a master-client model on an IBM BlueGene, where the algorithm scales near perfectly from 64 to 4096 processors in virtual processor mode. Starting from a completely extended conformation, we optimize a population of 64 conformations of the protein in our all-atom free-energy model PFF01. Using 2048 processors the algorithm predictively folds the protein to a near-native conformation with an RMS deviation of 3.43 A in < 24 h.

An evolutionary strategy for all-atom folding of the 60-amino-acid bacterial ribosomal protein l20

We have investigated an evolutionary algorithm for de novo all-atom folding of the bacterial ribosomal protein L20. We report results of two simulations that converge to near-native conformations of this 60-amino-acid, four-helix protein. We observe a steady increase of "native content" in both simulated ensembles and a large number of near-native conformations in their final populations. We argue that these structures represent a significant fraction of the low-energy metastable conformations, which characterize the folding funnel of this protein. These data validate our all-atom free-energy force field PFF01 for tertiary structure prediction of a previously inaccessible structural family of proteins. We also compare folding simulations of the evolutionary algorithm with the basin-hopping technique for the Trp-cage protein. We find that the evolutionary algorithm generates a dynamic memory in the simulated population, which leads to faster overall convergence.

Basin hopping simulations for all-atom protein folding

We investigate different protocols of the basin hopping technique for de novo protein folding. Using the protein free-energy force field PFF01 we report the reproducible all-atom folding of the 20-amino-acid tryptophan-cage protein [Protein Data Bank (PDB) code: 112y] and of the recently discovered 26-amino-acid potassium channel blocker (PDB code: 1wqc), which exhibits an unusual fold. We find that simulations with increasing cycle length and random starting temperatures perform best in comparison with other parametrizations. The basin hopping technique emerges as a simple but very efficient and robust workhorse for all-atom protein folding.

Free-energy landscape of the villin headpiece in an all-atom force field

We investigate the landscape of the internal free-energy of the 36 amino acid villin headpiece with a modified basin hopping method in the all-atom force field PFF01, which was previously used to predictively fold several helical proteins with atomic resolution. We identify near native conformations of the protein as the global optimum of the force field. More than half of the twenty best simulations started from random initial conditions converge to the folding funnel of the native conformation, but several competing low-energy metastable conformations were observed. From 76,000 independently generated conformations we derived a decoy tree which illustrates the topological structure of the entire low-energy part of the free-energy landscape and characterizes the ensemble of metastable conformations. These emerge as similar in secondary content, but differ in tertiary arrangement.