All-atom Folding Research Articles

On the role of native contact cooperativity in protein folding

The consistency of energy landscape theory predictions with available experimental data, as well as direct evidence from molecular simulations, have shown that protein folding mechanisms are largely determined by the contacts present in the native structure. As expected, native contacts are generally energetically favorable. However, there are usually at least as many energetically favorable nonnative pairs owing to the greater number of possible nonnative interactions. This apparent frustration must therefore be reduced by the greater cooperativity of native interactions. In this work, we analyze the statistics of contacts in the unbiased all-atom folding trajectories obtained by Shaw and coworkers, focusing on the unfolded state. By computing mutual cooperativities between contacts formed in the unfolded state, we show that native contacts form the most cooperative pairs, while cooperativities among nonnative or between native and nonnative contacts are typically much less favorable or even anticooperative. Furthermore, we show that the largest network of cooperative interactions observed in the unfolded state consists mainly of native contacts, suggesting that this set of mutually reinforcing interactions has evolved to stabilize the native state.

OPUS-Fold3: a gradient-based protein all-atom folding and docking framework on TensorFlow.

For refining and designing protein structures, it is essential to have an efficient protein folding and docking framework that generates a protein 3D structure based on given constraints. In this study, we introduce OPUS-Fold3 as a gradient-based, all-atom protein folding and docking framework, which accurately generates 3D protein structures in compliance with specified constraints, such as a potential function as long as it can be expressed as a function of positions of heavy atoms. Our tests show that, for example, OPUS-Fold3 achieves performance comparable to pyRosetta in backbone folding and significantly better in side-chain modeling. Developed using Python and TensorFlow 2.4, OPUS-Fold3 is user-friendly for any source-code level modifications and can be seamlessly combined with other deep learning models, thus facilitating collaboration between the biology and AI communities. The source code of OPUS-Fold3 can be downloaded from http://github.com/OPUS-MaLab/opus_fold3. It is freely available for academic usage.

De novo design of beta hairpin peptides with custom installed halogen-bonding groups.

Much of the success of computational protein design relies on the huge number of experimental crystal structures available for training and testing. Such information is simply not available for designing solution-stable hairpin peptides, much less ones that incorporate non-canonical amino acids. We tackle this problem using a two-step physics-based approach. First, we use a simple statistical mechanical model, trained on a number of designed hairpin sequences known to be stable in solution, to rank a number of potential designs with desired properties. Then, we perform all-atom folding simulations of the highest-ranked sequences using large-scale distributed computing. To validate our predictions, a selection of designed sequences predicted to have sensitive halogen bond donor-acceptor pairs are synthesized and experimentally characterized using solution-state NMR spectroscopy. Our results show the utility of simple statistical mechanical models, coupled with massively parallel simulations for de novo molecular design of non-natural foldamers. Such designed sequences will help develop model systems to understand the role of halogen bonding in peptide stability.

On the role of cooperativity in funneled energy landscapes.

The consistency of energy landscape theory predictions with available experimental data, as well as direct evidence from molecular simulations, have shown that protein folding mechanisms are largely determined by the contacts present in the native structure. As expected, native contacts are generally energetically favorable, however there are usually at least as many energetically favorable non-native pairs owing to the greater number of possible non-native interactions. This apparent frustration must therefore be reduced by the greater cooperativity of native interactions. In this work, we analyze the unbiased all-atom folding trajectories obtained by Shaw and co-workers, focusing on the unfolded state. By computing mutual cooperativities between contacts formed in the unfolded state, we are able to show that native contacts are largely more cooperative with each other than non-native contacts. Furthermore, we show that our analysis can determine the cooperative structures in the unfolded state and that native contacts can be more accurately predicted from the unfolded state trajectories than from residue contact frequencies in the unfolded state or from statistical pair potentials.

Interpreting Phi-Values using Protein Folding Transition Paths

It is now possible to watch proteins folding and unfolding spontaneously in molecular dynamics simulations using all-atom force fields. Nonetheless, recent results have shown that several force fields may be able to fold the same protein, but with very different mechanisms. Distinguishing which of these is correct by comparison to experiment is tricky due to the transient nature of folding transitions. Very useful information is furnished by protein folding phi-values, which yield residue-resolved information on the relative effect of mutations on protein folding rates compared to protein stability. Since computing phi-values by brute force is very inaccurate and computationally costly, we have developed a theory for estimating phi-values based on folding transition-paths. Applying the theory to all-atom folding simulations by DE Shaw, we find that in many cases the agreement with experimental data is reasonable. We are able to resolve a long-standing controversy in phi-value interpretation, i.e. do fractional phi-values come from parallel pathways or partially formed contacts? The answer is some of each. We show that the diversity of folding pathways can be probed by varying the strength of the perturbing mutation at a given residue. Lastly, we have compared the results directly with all-atom folding simulations using a Go model in order to assess the importance of non-native interactions in protein folding pathways.

Reduction of All-Atom Protein Folding Dynamics to One-Dimensional Diffusion.

Theoretical models have often modeled protein folding dynamics as diffusion on a low-dimensional free energy surface, a remarkable simplification. However, the accuracy of such an approximation and the number of dimensions required were not clear. For all-atom folding simulations of ten small proteins in explicit solvent we show that the folding dynamics can indeed be accurately described as diffusion on just a single coordinate, the fraction of native contacts (Q). The diffusion models reproduce both folding rates, and finer details such as transition-path durations and diffusive propagators. The Q-averaged diffusion coefficients decrease with chain length, as anticipated from energy landscape theory. Although the Q-diffusion model does not capture transition-path durations for the protein NuG2, we show that this can be accomplished by designing an improved coordinate Qopt. Overall, one-dimensional diffusion on a suitable coordinate turns out to be a remarkably faithful model for the dynamics of the proteins considered.

Even with nonnative interactions, the updated folding transition states of the homologs Proteins G & L are extensive and similar

Experimental and computational folding studies of Proteins L & G and NuG2 typically find that sequence differences determine which of the two hairpins is formed in the transition state ensemble (TSE). However, our recent work on Protein L finds that its TSE contains both hairpins, compelling a reassessment of the influence of sequence on the folding behavior of the other two homologs. We characterize the TSEs for Protein G and NuG2b, a triple mutant of NuG2, using ψ analysis, a method for identifying contacts in the TSE. All three homologs are found to share a common and near-native TSE topology with interactions between all four strands. However, the helical content varies in the TSE, being largely absent in Proteins G & L but partially present in NuG2b. The variability likely arises from competing propensities for the formation of nonnative β turns in the naturally occurring proteins, as observed in our TerItFix folding algorithm. All-atom folding simulations of NuG2b recapitulate the observed TSEs with four strands for 5 of 27 transition paths [Lindorff-Larsen K, Piana S, Dror RO, Shaw DE (2011) Science 334(6055):517-520]. Our data support the view that homologous proteins have similar folding mechanisms, even when nonnative interactions are present in the transition state. These findings emphasize the ongoing challenge of accurately characterizing and predicting TSEs, even for relatively simple proteins.

Parallel continuous simulated tempering and its applications in large-scale molecular simulations

In this paper, we introduce a parallel continuous simulated tempering (PCST) method for enhanced sampling in studying large complex systems. It mainly inherits the continuous simulated tempering (CST) method in our previous studies [C. Zhang and J. Ma, J. Chem. Phys. 130, 194112 (2009); C. Zhang and J. Ma, J. Chem. Phys. 132, 244101 (2010)], while adopts the spirit of parallel tempering (PT), or replica exchange method, by employing multiple copies with different temperature distributions. Differing from conventional PT methods, despite the large stride of total temperature range, the PCST method requires very few copies of simulations, typically 2-3 copies, yet it is still capable of maintaining a high rate of exchange between neighboring copies. Furthermore, in PCST method, the size of the system does not dramatically affect the number of copy needed because the exchange rate is independent of total potential energy, thus providing an enormous advantage over conventional PT methods in studying very large systems. The sampling efficiency of PCST was tested in two-dimensional Ising model, Lennard-Jones liquid and all-atom folding simulation of a small globular protein trp-cage in explicit solvent. The results demonstrate that the PCST method significantly improves sampling efficiency compared with other methods and it is particularly effective in simulating systems with long relaxation time or correlation time. We expect the PCST method to be a good alternative to parallel tempering methods in simulating large systems such as phase transition and dynamics of macromolecules in explicit solvent.

Thermodynamic Characterization of Protein Folding using Monte Carlo Methods

The study of protein folding has been a difficult challenge in molecular biology and simulation science.Recent publications showed the reproducible folding of small protein using molecular dynamics simulations. This large conformational changes can be only achieved by using specialized supercomputers [1]. In contrast to molecular dynamics simulations, Monte Carlo based simulations are not constrained solving Newton's equation of motion and therefore may be used conventional computer architectures to sample the protein folding process. Here we show fast reproducible all-atom folding transitions of the villin headpiece (Figure 1) simulated using SIMONA[2], a Monte Carlo based simulation package for nanoscale simulations including a variant of the Amber99SB∗-ILDN[3]. The results demonstrate the applicability of Monte Carlo simulation techniques to the investigation of large-scale conformational changes of proteins on conventional computer architectures. The computing time for observing folding/refolding events can be significantly reduced in comparison with molecular dynamics simulations. The thermodynamic characterization of simulated proteins can be compared with the experimental results.[1] Shaw, D. E. et al. Science 330, 341-346 (2010).[2] Wolf, M., Strunk, T. et al. J Comput Chem (2012).[3] Lindorff-Larsen et al. Science 334, 517-520 (2011).View Large Image | View Hi-Res Image | Download PowerPoint Slide

A Minima Hopping Study of All-Atom Protein Folding and Structure Prediction

The minima hopping algorithm (MHOP) to find global minima on potential energy surfaces is used for protein structure prediction. The energy surface of the protein is represented with an all-atom OPLS force field and an implicit free energy solvation term. The system we studied here is the small 10-residue beta-hairpin mini-protein, chignolin. Starting from a completely extended structure, we found minima with <0.5 A rms coordinate deviation from the geometry-optimized native experimental conformation. A few lowest-energy conformations were used for the calculation of NMR-restraint violations and chemical shifts, and the local minima found during each run leading to the global minimum were connected to trace out a search pathway of the folding process.

Two-state protein folding kinetics through all-atom molecular dynamics based sampling

This review focuses on advanced computational techniques that employ all atom molecular dynamics to study the folding of small two state proteins. As protein folding is a rare event process, special sampling techniques are required to overcome high folding free energy barriers. Several biased sampling methods enable computation of the free energy landscape. Trajectory based sampling methods can assess the kinetics and the dynamical folding mechanisms. Proper sampling is only the first step, and further analysis is required to obtain the folding mechanisms reaction coordinate. Only a combination of several simulation techniques can solve the sampling problems connected with all-atom protein folding, and allow computation of experimental observables that can validate the force fields and simulation techniques. Several of the involved issues are illustrated with folding of small protein (fragments) such as beta hairpins and the Trp-cage mini protein.

All-atom folding studies of a DNA binding protein in a free-energy force field

We have recently extended our free-energy force field for the better treatment of beta-sheetstructured proteins. The new force field, PFF02, nevertheless stabilizes helical proteins.Here we investigate the folding of the experimentally resolvable fragment of a DNA bindinghelical protein with a modified evolutionary algorithm. Our simulations converge to ahelical ensemble. The energetically best conformation is within 4.4 Å of the experimentalconformation, missing a single break in the second helix, which may result from flexibletails at the end of the molecule.

Predictive and reproducible de novo all-atom folding of aβ-hairpin loop in an improved free-energy forcefield

We have recently improved our free-energy forcefield for all-atom de novo protein folding toaddress the folding of proteins with beta-sheet secondary structure. The folding of betastrands is nevertheless more difficult than that of helical proteins, because of non-localinteractions between regions of the protein chain that are not consecutive in the amino acidsequence. Here we use a greedy version of the basin-hopping technique with ourfree-energy forcefield PFF02 to reproducibly and predictively fold the structure of aβ-hairpin loop. The lowest energy structure found in the simulation has a backbone rootmean square deviation of only 2.62 Å to the native conformation. The side-chain alignment isalso correctly predicted, as are four of the five backbone hydrogen bonds found in thenative structure.

All‐atom de 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.

De Novo Folding of the DNA‐Binding ATF‐2 Zinc Finger Motif in an All‐Atom Free‐Energy Forcefield

Finger formation: Predictive all-atom folding of a DNA-binding αββ-zinc-finger motif in a free-energy forcefield has been demonstrated. The three models (shown in different shades of blue in the picture) show the lowest energy structures found in the simulation. The low-energy region of the free-energy surface and important steps of the folding pathway have been analyzed to help elucidate zinc-finger formation and function.

Hydrophobic Aided Replica Exchange: an Efficient Algorithm for Protein Folding in Explicit Solvent

A hydrophobic aided replica exchange method (HAREM) is introduced to accelerate the simulation of all-atom protein folding in explicit solvent. This method is based on exaggerating the hydrophobic effect of various protein amino acids in water by attenuating the protein-water attractive interactions (mimicking the Chaperon effect) while leaving other interactions among protein atoms and water molecules unchanged. The method is applied to a small representative protein, the alpha-helix 3K(I), and it is found that the HAREM method successfully folds the protein within 4 ns, while the regular replica exchange method does not fold the same protein within 5 ns, even with many more replicas.

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.

Biomolecular Structure Prediction Stochastic Optimization Methods

Biomolecular structure prediction remains an important challenge to biophysical chemistry. We recently developed an all-atom free energy force field (PFF01) for protein structure prediction with stochastic optimization methods. We review recent studies, which demonstrated all-atom folding of several proteins and summarize recent progress for in-silico high-throughput screening strategies for rational drug design, which are also based on the use of stochastic optimization methods to determine the conformation of the receptor-ligand complex.

Accelerating all-atom protein folding simulations through reduced dihedral barriers

Protein folding requires extensive changes of backbone and sidechain dihedral angles, whose energy barriers constitute obstacles for the folding kinetics. Folding of small proteins is furthermore thought to be path-independent. Here, we propose that time-consuming all-atom protein folding simulations may be accelerated through a reduction of the dihedral barriers of the force field. In order to investigate this hypothesis, we performed various folding simulations of two small proteins. We report an acceleration towards smaller root-mean-square deviations from the native protein structure using our proposed method.