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Structure prediction is an important means to quickly understand new protein functions. However, the prediction of effects of proteins that have no detectable templates is still to be improved. Molecular dynamics simulation is supposed to be the primary research tool for structure predictions, but it still has limitations of huge computational cost in all-atom (AA) models and rough accuracy in coarse-grained (CG) models. We propose a universal multiscale simulation strategy named AIMS in which simulations can iteratively switch among multiple resolutions in order to adaptively trade off AA accuracy and CG high-efficiency. AIMS follows the idea of CG-guided enhanced sampling so that final results always keep AA accuracy. We successfully achieve four ab initio and four data-assisted protein structure predictions using AIMS. The prediction result is an ensemble rather than a structure and provides special insights on folding metastable states. AIMS is estimated to achieve a computational speed about 40 times faster than that of conventional AA simulations.

Background Traditional approaches to elucidation of protein structures by Nuclear Magnetic Resonance spectroscopy (NMR) rely on distance restraints also known as Nuclear Overhauser effects (NOEs). The use of NOEs as the primary source of structure determination by NMR spectroscopy is time consuming and expensive. Residual Dipolar Couplings (RDCs) have become an alternate approach for structure calculation by NMR spectroscopy. In previous works, the software package REDCRAFT has been presented as a means of harnessing the information containing in RDCs for structure calculation of proteins. However, to meet its full potential, several improvements to REDCRAFT must be made. Results In this work, we present improvements to REDCRAFT that include increased usability, better interoperability, and a more robust core algorithm. We have demonstrated the impact of the improved core algorithm in the successful folding of the protein 1A1Z with as high as ±4 Hz of added error. The REDCRAFT computed structure from the highly corrupted data exhibited less than 1.0 Å with respect to the X-ray structure. We have also demonstrated the interoperability of REDCRAFT in a few instances including with PDBMine to reduce the amount of required data in successful folding of proteins to unprecedented levels. Here we have demonstrated the successful folding of the protein 1D3Z (to within 2.4 Å of the X-ray structure) using only N-H RDCs from one alignment medium. Conclusions The additional GUI features of REDCRAFT combined with the NEF compliance have significantly increased the flexibility and usability of this software package. The improvements of the core algorithm have substantially improved the robustness of REDCRAFT in utilizing less experimental data both in quality and quantity.

The computer-aided investigation of protein folding has greatly benefited from coarse-grained models, that is, simplified representations at a resolution level lower than atomistic, providing access to qualitative and quantitative details of the folding process that would be hardly attainable, via all-atom descriptions, for medium to long molecules. Nonetheless, the effectiveness of low-resolution models is itself hampered by the presence, in a small but significant number of proteins, of nontrivial topological self-entanglements. Features such as native state knots or slipknots introduce conformational bottlenecks, affecting the probability to fold into the correct conformation; this limitation is particularly severe in the context of coarse-grained models. In this work, we tackle the relationship between folding probability, protein folding pathway, and protein topology in a set of proteins with a nontrivial degree of topological complexity. To avoid or mitigate the risk of incurring in kinetic traps, we make use of the elastic folder model, a coarse-grained model based on angular potentials optimized toward successful folding via a genetic procedure. This light-weight representation allows us to estimate in silico folding probabilities, which we find to anti-correlate with a measure of topological complexity as well as to correlate remarkably well with experimental measurements of the folding rate. These results strengthen the hypothesis that the topological complexity of the native state decreases the folding probability and that the force-field optimization mimics the evolutionary process these proteins have undergone to avoid kinetic traps.

Significance Protein-folding kinetics is often described as Markovian (i.e., memoryless) diffusion in a one-dimensional free energy landscape, governed by an instantaneous friction coefficient that is fitted to reproduce experimental or simulated folding times. For the α-helix forming polypeptide alanine9 and a specific reaction coordinate that consists of the summed native hydrogen-bond lengths, we demonstrate that the friction extracted from molecular dynamics simulations exhibits significant memory with a decay time that is in the nanosecond range and thus, of the same order as the folding and unfolding times. Our non-Markovian modeling not only reproduces the molecular dynamics simulations accurately but also demonstrates that memory friction effects lead to anomalous and drastically accelerated protein kinetics., We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide alanine9 for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-based non-Markovian model. In contrast, Markovian models do not accurately describe the peptide kinetics and in particular, cannot reproduce the folding and unfolding kinetics simultaneously, even if a spatially dependent friction profile is used. Analysis of the GLE demonstrates that memory effects in the friction significantly speed up peptide folding and unfolding kinetics, as predicted by the Grote–Hynes theory, and are the cause of anomalous diffusion in configuration space. Our methods are applicable to any reaction coordinate and in principle, also to experimental trajectories from single-molecule experiments. Our results demonstrate that a consistent description of protein-folding dynamics must account for memory friction effects.

Sequence-based contact prediction has shown considerable promise in assisting non-homologous structure modeling, but it often requires many homologous sequences and a sufficient number of correct contacts to achieve correct folds. Here, we developed a method, C-QUARK, that integrates multiple deep-learning and coevolution-based contact-maps to guide the replica-exchange Monte Carlo fragment assembly simulations. The method was tested on 247 non-redundant proteins, where C-QUARK could fold 75% of the cases with TM-scores (template-modeling scores) ≥0.5, which was 2.6 times more than that achieved by QUARK. For the 59 cases that had either low contact accuracy or few homologous sequences, C-QUARK correctly folded 6 times more proteins than other contact-based folding methods. C-QUARK was also tested on 64 free-modeling targets from the 13th CASP (critical assessment of protein structure prediction) experiment and had an average GDT_TS (global distance test) score that was 5% higher than the best CASP predictors. These data demonstrate, in a robust manner, the progress in modeling non-homologous protein structures using low-accuracy and sparse contact-map predictions., Predicting protein structure from sequence is still not possible for all proteins. Here, the authors introduce a method that integrates deep learning and information about protein co-evolution to guide the prediction of non-homologous protein structures with greater accuracy.

Meta contact, which combines different contact maps into one to improve contact prediction accuracy and effectively reduce the noise from a single contact map, is a widely used method. However, protein structure prediction using meta contact cannot fully exploit the information carried by original contact maps. In this work, a multi contact-based folding method under the evolutionary algorithm framework, MultiCFold, is proposed. In MultiCFold, the thorough information of different contact maps is directly used by populations to guide protein structure folding. In addition, noncontact is considered as an effective supplement to contact information and can further assist protein folding. MultiCFold is tested on a set of 120 nonredundant proteins, and the average TM-score and average RMSD reach 0.617 and 5.815 Å, respectively. Compared with the meta contact-based method, MetaCFold, average TM-score and average RMSD have a 6.62 and 8.82% improvement. In particular, the import of noncontact information increases the average TM-score by 6.30%. Furthermore, MultiCFold is compared with four state-of-the-art methods of CASP13 on the 24 FM targets, and results show that MultiCFold is significantly better than other methods after the full-atom relax procedure.

While the field of computational protein design has witnessed amazing progression in recent years, folding properties still constitute a significant barrier towards designing new and larger proteins. In order to assess and improve folding properties of designed proteins, we have developed a genetics-based folding assay and selection system based on the essential enzyme, orotate phosphoribosyl transferase from Escherichia coli. This system allows for both screening of candidate designs with good folding properties and genetic selection of improved designs. Thus, we identified single amino acid substitutions in two failed designs that rescued poorly folding and unstable proteins. Furthermore, when these substitutions were transferred into a well-structured design featuring a complex folding profile, the resulting protein exhibited native-like cooperative folding with significantly improved stability. In protein design, a single amino acid can make the difference between folding and misfolding, and this approach provides a useful new platform to identify and improve candidate designs.

Significance Almost all proteins fold to their lowest free energy state, which is determined by their amino acid sequence. Computational protein design has primarily focused on finding sequences that have very low energy in the target designed structure. However, what is most relevant during folding is not the absolute energy of the folded state but the energy difference between the folded state and the lowest-lying alternative states. We describe a deep learning approach that captures aspects of the folding landscape, in particular the presence of structures in alternative energy minima, and show that it can enhance current protein design methods., The protein design problem is to identify an amino acid sequence that folds to a desired structure. Given Anfinsen’s thermodynamic hypothesis of folding, this can be recast as finding an amino acid sequence for which the desired structure is the lowest energy state. As this calculation involves not only all possible amino acid sequences but also, all possible structures, most current approaches focus instead on the more tractable problem of finding the lowest-energy amino acid sequence for the desired structure, often checking by protein structure prediction in a second step that the desired structure is indeed the lowest-energy conformation for the designed sequence, and typically discarding a large fraction of designed sequences for which this is not the case. Here, we show that by backpropagating gradients through the transform-restrained Rosetta (trRosetta) structure prediction network from the desired structure to the input amino acid sequence, we can directly optimize over all possible amino acid sequences and all possible structures in a single calculation. We find that trRosetta calculations, which consider the full conformational landscape, can be more effective than Rosetta single-point energy estimations in predicting folding and stability of de novo designed proteins. We compare sequence design by conformational landscape optimization with the standard energy-based sequence design methodology in Rosetta and show that the former can result in energy landscapes with fewer alternative energy minima. We show further that more funneled energy landscapes can be designed by combining the strengths of the two approaches: the low-resolution trRosetta model serves to disfavor alternative states, and the high-resolution Rosetta model serves to create a deep energy minimum at the design target structure.

Natural proteins are characterised by a complex folding pathway defined uniquely for each fold. Designed coiled-coil protein origami (CCPO) cages are distinct from natural compact proteins, since their fold is prescribed by discrete long-range interactions between orthogonal pairwise-interacting coiled-coil (CC) modules within a single polypeptide chain. Here, we demonstrate that CCPO proteins fold in a stepwise sequential pathway. Molecular dynamics simulations and stopped-flow Förster resonance energy transfer (FRET) measurements reveal that CCPO folding is dominated by the effective intra-chain distance between CC modules in the primary sequence and subsequent folding intermediates, allowing identical CC modules to be employed for multiple cage edges and thus relaxing CCPO cage design requirements. The number of orthogonal modules required for constructing a CCPO tetrahedron can be reduced from six to as little as three different CC modules. The stepwise modular nature of the folding pathway offers insights into the folding of tandem repeat proteins and can be exploited for the design of modular protein structures based on a given set of orthogonal modules., Coiled-coil protein origami (CCPO) is a strategy for the design of polyhedral cage-shaped protein folds based on coiled-coil (CC) dimer-forming peptides. Here, the authors show that CCPO proteins fold in a multistep process governed by the spatial distance between CC modules in the primary sequence and subsequent folding intermediates, which enables the use of identical CC modules for the CCPO tetrahedron design.

The topology of protein folds can be specified by the inter-residue contact-maps and accurate contact-map prediction can help ab initio structure folding. We developed TripletRes to deduce protein contact-maps from discretized distance profiles by end-to-end training of deep residual neural-networks. Compared to previous approaches, the major advantage of TripletRes is in its ability to learn and directly fuse a triplet of coevolutionary matrices extracted from the whole-genome and metagenome databases and therefore minimize the information loss during the course of contact model training. TripletRes was tested on a large set of 245 non-homologous proteins from CASP 11&12 and CAMEO experiments and outperformed other top methods from CASP12 by at least 58.4% for the CASP 11&12 targets and 44.4% for the CAMEO targets in the top-L long-range contact precision. On the 31 FM targets from the latest CASP13 challenge, TripletRes achieved the highest precision (71.6%) for the top-L/5 long-range contact predictions. It was also shown that a simple re-training of the TripletRes model with more proteins can lead to further improvement with precisions comparable to state-of-the-art methods developed after CASP13. These results demonstrate a novel efficient approach to extend the power of deep convolutional networks for high-accuracy medium- and long-range protein contact-map predictions starting from primary sequences, which are critical for constructing 3D structure of proteins that lack homologous templates in the PDB library., Author summary Ab initio protein folding has been a major unsolved problem in computational biology for more than half a century. Recent community-wide Critical Assessment of Structure Prediction (CASP) experiments have witnessed exciting progress on ab initio structure prediction, which was mainly powered by the boosting of contact-map prediction as the latter can be used as constraints to guide ab initio folding simulations. In this work, we proposed a new open-source deep-learning architecture, TripletRes, built on the residual convolutional neural networks for high-accuracy contact prediction. The large-scale benchmark and blind test results demonstrate competitive performance of the proposed methods to other top approaches in predicting medium- and long-range contact-maps that are critical for guiding protein folding simulations. Detailed data analyses showed that the major advantage of TripletRes lies in the unique protocol to fuse multiple evolutionary feature matrices which are directly extracted from whole-genome and metagenome databases and therefore minimize the information loss during the contact model training.

Geometry and topology are the main factors that determine the functional properties of proteins. In this work, we show how to use the Gauss linking integral (GLN) in the form of a matrix diagram - for a pair of a loop and a tail - to study both the geometry and topology of proteins with closed loops e.g. lassos. We show that the GLN method is a significantly faster technique to detect entanglement in lasso proteins in comparison with other methods. Based on the GLN technique, we conduct comprehensive analysis of all proteins deposited in the PDB and compare it to the statistical properties of the polymers. We found that there are significantly more lassos with negative crossings than those with positive ones in proteins, the average value of maxGLN (maximal GLN between loop and pieces of tail) depends logarithmically on the length of a tail similarly as in the polymers. Next, we show the how high and low GLN values correlate with the internal exibility of proteins, and how the GLN in the form of a matrix diagram can be used to study folding and unfolding routes. Finally, we discuss how the GLN method can be applied to study entanglement between two structures none of which are closed loops. Since this approach is much faster than other linking invariants, the next step will be evaluation of lassos in much longer molecules such as RNA or loops in a single chromosome., 25 pages, 8 figures, submitted to the journal and waiting for reviews, having Supplementary Material

Atomistic simulations can provide valuable, experimentally-verifiable insights into protein folding mechanisms, but existing ab initio simulation methods are restricted to only the smallest proteins due to severe computational speed limits. The folding of larger proteins has been studied using native-centric potential functions, but such models omit the potentially crucial role of non-native interactions. Here, we present an algorithm, entitled DBFOLD, which can predict folding pathways for a wide range of proteins while accounting for the effects of non-native contacts. In addition, DBFOLD can predict the relative rates of different transitions within a protein’s folding pathway. To accomplish this, rather than directly simulating folding, our method combines equilibrium Monte-Carlo simulations, which deploy enhanced sampling, with unfolding simulations at high temperatures. We show that under certain conditions, trajectories from these two types of simulations can be jointly analyzed to compute unknown folding rates from detailed balance. This requires inferring free energies from the equilibrium simulations, and extrapolating transition rates from the unfolding simulations to lower, physiologically-reasonable temperatures at which the native state is marginally stable. As a proof of principle, we show that our method can accurately predict folding pathways and Monte-Carlo rates for the well-characterized Streptococcal protein G. We then show that our method significantly reduces the amount of computation time required to compute the folding pathways of large, misfolding-prone proteins that lie beyond the reach of existing direct simulation. Our algorithm, which is available online, can generate detailed atomistic models of protein folding mechanisms while shedding light on the role of non-native intermediates which may crucially affect organismal fitness and are frequently implicated in disease., Author summary Many proteins must adopt a specific structure in order to function. Computational simulations have been used to shed light on the mechanisms of protein folding, but unfortunately, realistic simulations can typically only be run for small proteins, due to severe limits in computational speed. Here, we present a method to solve this problem, whereby instead of directly simulating folding from an unfolded state, we run simulations that allow for computation of equilibrium folding free energies, alongside high temperature simulations to compute unfolding rates. From these quantities, folding rates can be computed using detailed balance. Importantly, our method can account for the effects of nonnative contacts which transiently form during folding and must be broken prior to adoption of the native state. Such contacts, which are often excluded from simple models of folding, may crucially affect real protein folding pathways and are often observed in folding intermediates implicated in disease.

The understanding of protein structure is vital to determine biological function. We presented an enhanced simulated annealing (ESA) algorithm to investigate protein three-dimensional (3D) structure on a coarse-grained model. Inside the algorithm, we adjusted exploration equations to achieve good search intensity. To that end, our algorithm used (i) a multivariable disturbance operator for diversification of solution, (ii) a sign function to improve randomness of solution, and (iii) taking remainder operation performed on floating-point number to tackle out-of-range solution. By monitoring energy value throughout the simulation, the energy-optimal state can be found. The ESA algorithm was tested on artificial and real protein sequences with different lengths. The results show that our algorithm outperforms conventional simulated annealing algorithm and can compete with the reported algorithms before. Especially, our algorithm can obtain folding conformations with specific structural features. Further analysis shows that simulating trajectory of seeking the lowest energy can exhibit thermodynamic behavior of protein folding. Graphical Abstract.

Traditional molecular dynamics (MD) simulations have difficulties in tracking the slow molecular motions, at least partially due to the waste of sampling in already sampled regions. Here, we proposed a new enhanced sampling method, frontier expansion sampling (FEXS), to improve the sampling efficiency of molecular simulations by iteratively selecting seed structures diversely distributed at the "frontier" of an already sampled region to initiate new simulations. Different from other enhanced sampling methods, FEXS identifies the "frontier" seeds by integrating the Gaussian mixture model and the convex hull algorithm, which effectively improves the structural variation among the selected seeds and thus the descendant simulations. Validation in three protein systems, including the folding of chignolin, open-to-closed transition of maltodextrin binding protein, and internal conformational change of bovine pancreatic trypsin inhibitor, confirmed the effectiveness of this novel method in enhancing the sampling of conventional MD simulations to observe the large-scale protein conformational changes. When compared with other enhanced sampling methods like the structural dissimilarity sampling (SDS), FEXS reached at least the same level of sampling efficiency but was capable of providing complementary information in the three tested protein systems.

Isolating the properties of proteins that allow them to convert sequence into the structure is a long-lasting biophysical problem. In particular, studies focused extensively on the effect of a reduced alphabet size on the folding properties. However, the natural alphabet is a compromise between versatility and optimisation of the available resources. Here, for the first time, we include the impact of the relative availability of the amino acids to extract from the 20 letters the core necessary for protein stability. We present a computational protein design scheme that involves the competition for resources between a protein and a potential interaction partner that, additionally, gives us the chance to investigate the effect of the reduced alphabet on protein-protein interactions. We devise a scheme that automatically identifies the optimal reduced set of letters for the design of the protein, and we observe that even alphabets reduced down to 4 letters allow for single protein folding. However, it is only with 6 letters that we achieve optimal folding, thus recovering experimental observations. Additionally, we notice that the binding between the protein and a potential interaction partner could not be avoided with the investigated reduced alphabets. Therefore, we suggest that aggregation could have been a driving force in the evolution of the large protein alphabet.

“How do proteins fold?” Researchers have been studying different aspects of this question for more than 50 years. The most conceptual aspect of the problem is how protein can find the global free energy minimum in a biologically reasonable time, without exhaustive enumeration of all possible conformations, the so-called “Levinthal’s paradox.” Less conceptual but still critical are aspects about factors defining folding times of particular proteins and about perspectives of machine learning for their prediction. We will discuss in this review the key ideas and discoveries leading to the current understanding of folding kinetics, including the solution of Levinthal’s paradox, as well as the current state of the art in the prediction of protein folding times.

Made available in DSpace on 2020-12-10T19:41:27Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-11-01 Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) NSF CAREER award Center for Theoretical Biological Physics - NSF Protein folding occurs in a high dimensional phase space, and the representation of the associated energy landscape is nontrivial. A widely applied approach to studying folding landscapes is to describe the dynamics along a small number of reaction coordinates. However, other strategies involve more elaborate analysis of the complex phase space. There have been many attempts to obtain a more detailed representation of all available conformations for a given system. In this work, we address this problem using a metric based on internal distances between amino acids to describe the differences between any two conformations. Using an effective projection method, we are able to go beyond the typical one-dimensional representation and provide intuitive two dimensional visualizations of the landscape. We refer to this method as the energy landscape visualization method (ELViM). We have applied this methodology using a C-alpha structure-based model to study the folding of two well-known proteins: SH3 domain and protein-A. Our visualization method yields a detailed description of the folding process, making possible the identification of transition state regions, and establishing the paths that lead to the native state. For SH3, we have analyzed structural differences in the distribution of folding routes. The competition between the native and mirror structures in protein A is also discussed. Finally, the method is applied to study conformational changes in the protein elongation factor thermally unstable. Distinct features of ELViM are that it does not require or assume a reaction coordinate, and it does not require analysis of kinetic aspects of the system. Univ Estadual Paulista, Inst Biociencias Letras & Ciencias Exatas, Dept Fis, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil Northeastern Univ, Dept Phys, Boston, MA 02115 USA Rice Univ, Ctr Theoret Biol Phys, Houston, TX 77005 USA Univ Estadual Paulista, Inst Biociencias Letras & Ciencias Exatas, Dept Fis, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil FAPESP: 2018/18668-1 FAPESP: 2016/19766-1 FAPESP: 2014/50739-5 NSF CAREER award: MCB-1350312 Center for Theoretical Biological Physics - NSF: PHY-1427654

Coarse-grained models are an attractive tool for studying the long time scale dynamics of large macromolecules at a level that cannot be studied directly by experiment and is still out of reach for atomistic simulation. However, coarse models involve approximations that may affect their predictive power. We propose a modeling framework that allows us to design simplified models to accurately reproduce experimental observables. We demonstrate the approach on the folding mechanism of a WW domain. We show that when the correct coarsening resolution is used not only do the optimized models match the Reference model simulated experimental data accurately but additional observables not directly targeted during the optimization procedure are also reproduced. Additionally, the analysis of the results shows that localized frustration plays an important role in the folding mechanism of this protein and suggests that nontrivial aspects of the protein dynamics are evolutionary conserved.

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic-hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H-H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H's at even positions and the other side ignores H's at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H-H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.

The design of protein conformational switches—or proteins that change conformations in response to a signal such as ligand binding—has great potential for developing novel biosensors, diagnostic tools, and therapeutic agents. Among the defining properties of such switches, the response time has been the most challenging to optimize. Here we apply a computational design strategy in synergistic combination with biophysical experiments to rationally improve the response time of an engineered protein-based Ca2+-sensor in which the switching process occurs via mutually exclusive folding of two alternate frames. Notably, our strategy identifies mutations that increase switching rates by as much as 32-fold, achieving response times on the order of fast physiological Ca2+ fluctuations. Our computational design strategy is general and may aid in optimizing the kinetics of other protein conformational switches., The rational optimization of response times of protein conformational switches is a major challenge for biomolecular switch design. Here the authors present a generally applicable computational design strategy that in combination with biophysical experiments can improve response times using a Ca2+-sensor as an example.

In this paper, we present a fast and adaptive correlation guided enhanced sampling method (CORE-MD II). The CORE-MD II technique relies, in part, on partitioning of the entire pathway into short trajectories that we refer to as instances. The sampling within each instance is accelerated by adaptive path-dependent metadynamics simulations. The second part of this approach involves kinetic Monte Carlo (kMC) sampling between the different states that have been accessed during each instance. Through the combination of the partition of the total simulation into short non-equilibrium simulations and the kMC sampling, the CORE-MD II method is capable of sampling protein folding without any a priori definitions of reaction pathways and additional parameters. In the validation simulations, we applied the CORE-MD II on the dialanine peptide and the folding of two peptides: TrpCage and TrpZip2. In a comparison with long time equilibrium Molecular Dynamics (MD), 1 µs replica exchange MD (REMD), and CORE-MD I simulations, we find that the level of convergence of the CORE-MD II method is improved by a factor of 8.8, while the CORE-MD II method reaches acceleration factors of ∼120. In the CORE-MD II simulation of TrpZip2, we observe the formation of the native state in contrast to the REMD and the CORE-MD I simulations. The method is broadly applicable for MD simulations and is not restricted to simulations of protein folding or even biomolecules but also applicable to simulations of protein aggregation, protein signaling, or even materials science simulations.

Exploring structure space to understand stability Understanding the determinants of protein stability is challenging because native proteins have conformations that are optimized for function. Proteins designed without functional bias could give insight into how structure determines stability, but this requires a large sample size. Rocklin et al. report a high-throughput protein design and characterization method that allows them to measure thousands of miniproteins (see the Perspective by Woolfson et al. ). Iterative rounds of design and characterization increased the design success rate from 6 to 47%, which provides insight into the balance of forces that determine protein stability. Science , this issue p. 168 ; see also p. 133

Replica exchange molecular dynamics (REMD) and integrated-tempering-sampling (ITS) are two representative enhanced sampling methods which utilize parallel and integrated tempering approaches, respectively. In this work, a partitioned integrated-tempering-sampling (P-ITS) method is proposed which takes advantage of the benefits of both parallel and integrated tempering approaches. Using P-ITS, the folding pathways of a series of proteins with diverse native structures are explored on multidimensional free-energy landscapes, and the associated thermodynamics are evaluated. In comparison to the original form of ITS, P-ITS improves the sampling efficiency and measures the folding/unfolding thermodynamic quantities more consistently with experimental data. In comparison to REMD, P-ITS significantly reduces the requirement of computational resources and meanwhile achieves similar simulation results. The observed structural characterizations of transition and intermediate states of the proteins under study are in good agreement with previous experimental and simulation studies on the same proteins and homologues. Therefore, the P-ITS method has great potential in simulating the structural dynamics of complex biomolecular systems.

Many proteins contain regions of intrinsic disorder, not folding into unique, stable conformations. Numerous experimental methods have been developed to measure the disorder of all or select residues. In the absence of experimental data, computational methods are often utilized to identify these disordered regions and thus gain a better understanding of both structure and function. Many freely available computational methods have been developed to predict regions of intrinsic disorder from the primary sequence of a protein, including our recently developed Rosetta ResidueDisorder. While these methods are very useful, they are only designed to predict intrinsic disorder from the sequence. However, it would be useful to have a method that could also measure intrinsic disorder directly from structure. Such a method might also be used to identify changes in the structure of systems that can transition from folded to unfolded or vice versa, even systems that are not intrinsically disordered. Here we extended the capabilities of Rosetta ResidueDisorder to measure the intrinsic disorder from the coordinates of a single conformation of a protein. As a proof of principle, we show that ResidueDisorder can measure the intrinsic disorder from the coordinates with a higher accuracy (69.2%) than when predicted from sequence (65.4%) using a benchmark set of 229 proteins, showing that intrinsic disorder can be measured accurately from single structures over a large range of intrinsic disorder (0-100%). Additionally, we used ResidueDisorder to analyze unfolding trajectories of 12 fast-folding, nonintrinsically disordered proteins generated using molecular dynamics (MD), specifically steered MD (SMD), high-temperature MD, and accelerated MD (aMD) as well as long-time scale folding/unfolding trajectories. Using ResidueDisorder, a clear correlation between RMSD with respect to the native structure and measured fraction of denatured residues was observed. Finally, we introduced methods to predict folding/unfolding transitions as well as a native-like structure in the absence of a crystal structure from folding/unfolding MD trajectories. Rosetta ResidueDisorder is available as an application in the Rosetta software suite with the addition of new capabilities for directly identifying denatured regions and predicting events.

Despite the development of massively parallel computing hardware including inexpensive graphics processing units (GPUs), it has remained infeasible to simulate the folding of atomistic proteins at room temperature using conventional molecular dynamics (MD) beyond the μs scale. Here we report the folding of atomistic, implicitly solvated protein systems with folding times τ(f) ranging from ~10 μs to ~100 ms using the weighted ensemble (WE) strategy in combination with GPU computing. Starting from an initial structure or set of structures, WE organizes an ensemble of GPU-accelerated MD trajectory segments via intermittent pruning and replication events to generate statistically unbiased estimates of rate constants for rare events such as folding; no biasing forces are used. Although the variance among atomistic WE folding runs is significant, multiple independent runs are used to reduce and quantify statistical uncertainty. Folding times are estimated directly from WE probability flux and from history-augmented Markov analysis of the WE data. Three systems were examined: NTL9 at low solvent viscosity (yielding τ(f) = 0.8 − μs), NTL9 at water-like viscosity (τ(f) = 0.2 − 2 ms), and Protein G at low viscosity (τ(f) = 3 − 200 ms). In all cases the folding time, uncertainty, and ensemble properties could be estimated from WE simulation; for Protein G, this characterization required significantly less overall computing than would be required to observe a single folding event with conventional MD simulations. Our results suggest that the use and calibration of force fields and solvent models for precise estimation of kinetic quantities is becoming feasible.

Adaptive sampling methods, often used in combination with Markov state models, are becoming increasingly popular for speeding up rare events in simulation such as molecular dynamics (MD) without biasing the system dynamics. Several adaptive sampling strategies have been proposed, but it is not clear which methods perform better for different physical systems. In this work, we present a systematic evaluation of selected adaptive sampling strategies on a wide selection of fast folding proteins. The adaptive sampling strategies were emulated using models constructed on already existing MD trajectories. We provide theoretical limits for the sampling speed-up and compare the performance of different strategies with and without using some a priori knowledge of the system. The results show that for different goals, different adaptive sampling strategies are optimal. In order to sample slow dynamical processes such as protein folding without a priori knowledge of the system, a strategy based on the identification of a set of metastable regions is consistently the most efficient, while a strategy based on the identification of microstates performs better if the goal is to explore newer regions of the conformational space. Interestingly, the maximum speed-up achievable for the adaptive sampling of slow processes increases for proteins with longer folding times, encouraging the application of these methods for the characterization of slower processes, beyond the fast-folding proteins considered here.

Protein folding and structure prediction are two sides of the same coin. Contact maps and the related techniques of constraint-based structure reconstruction can be considered as unifying aspects of both processes. We present the Structural Relevance (SR) score which quantifies the information content of individual contacts and residues in the context of the whole native structure. The physical process of protein folding is commonly characterized with spatial and temporal resolution: some residues are Early Folding while others are Highly Stable with respect to unfolding events. We employ the proposed SR score to demonstrate that folding initiation and structure stabilization are subprocesses realized by distinct sets of residues. The example of cytochrome c is used to demonstrate how StructureDistiller identifies the most important contacts needed for correct protein folding. This shows that entries of a contact map are not equally relevant for structural integrity. The proposed StructureDistiller algorithm identifies contacts with the highest information content; these entries convey unique constraints not captured by other contacts. Identification of the most informative contacts effectively doubles resilience toward contacts which are not observed in the native contact map. Furthermore, this knowledge increases reconstruction fidelity on sparse contact maps significantly by 0.4 Å.

Display Omitted Prediction performance of protein structural class has been improved.A high-quality feature extraction technique has been designed.A recursive feature selection has been used to reduce feature abundance. Structural class characterizes the overall folding type of a protein or its domain. Many methods have been proposed to improve the prediction accuracy of protein structural class in recent years, but it is still a challenge for the low-similarity sequences. In this study, we introduce a feature extraction technique based on auto cross covariance (ACC) transformation of position-specific score matrix (PSSM) to represent a protein sequence. Then support vector machine-recursive feature elimination (SVM-RFE) is adopted to select top K features according to their importance and these features are input to a support vector machine (SVM) to conduct the prediction. Performance evaluation of the proposed method is performed using the jackknife test on three low-similarity datasets, i.e., D640, 1189 and 25PDB. By means of this method, the overall accuracies of 97.2%, 96.2%, and 93.3% are achieved on these three datasets, which are higher than those of most existing methods. This suggests that the proposed method could serve as a very cost-effective tool for predicting protein structural class especially for low-similarity datasets.

Protein folding/unfolding is a complicated process that defies high-resolution characterization by experimental methods. As an alternative, atomistic molecular dynamics simulations are now routinely employed to elucidate and magnify the accompanying conformational changes and the role of solvent in the folding process. However, the level of detail necessary to map the process at high spatial-temporal resolution provides an overwhelming amount of data. As more and better tools are developed for analysis of these large data sets and validation of the simulations, one is still left with the problem of visualizing the results in ways that provide insight into the folding/unfolding process. While viewing and interrogating static crystal structures has become commonplace, more and different approaches are required for dynamic, interconverting, unfolding, and refolding proteins. Here we review a variety of approaches, ranging from straightforward to complex and unintuitive for multiscale analysis and visualization of protein folding and unfolding.

Background Accelerated molecular dynamics (aMD) has been proven to be a powerful biasing method for enhanced sampling of biomolecular conformations on general-purpose computational platforms. Biologically important long timescale events that are beyond the reach of standard molecular dynamics can be accessed without losing the detailed atomistic description of the system in aMD. Over other biasing methods, aMD offers the advantages of tuning the level of acceleration to access the desired timescale without any advance knowledge of the reaction coordinate. Scope of review Recent advances in the implementation of aMD and its applications to small peptides and biological macromolecules are reviewed here along with a brief account of all the aMD variants introduced in the last decade. Major conclusions In comparison to the original implementation of aMD, the recent variant in which all the rotatable dihedral angles are accelerated (RaMD) exhibits faster convergence rates and significant improvement in statistical accuracy of retrieved thermodynamic properties. RaMD in conjunction with accelerating diffusive degrees of freedom, i.e. dual boosting, has been rigorously tested for the most difficult conformational sampling problem, protein folding. It has been shown that RaMD with dual boosting is capable of efficiently sampling multiple folding and unfolding events in small fast folding proteins. General significance RaMD with the dual boost approach opens exciting possibilities for sampling multiple timescales in biomolecules. While equilibrium properties can be recovered satisfactorily from aMD-based methods, directly obtaining dynamics and kinetic rates for larger systems presents a future challenge. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

The polypeptide chain folding process appears to be a multi-stage phenomenon. The scientific community has recently devoted much attention to early stages of this process, with numerous attempts at simulating them—either experimentally or in silico. This paper presents a comparative analysis of the predicted and observed results of folding simulations. The proposed technique, based on statistical dictionaries, yields a global accuracy of 57 %—a marked improvement over older approaches (with an accuracy of approximately 46 %).

The Outlier FLOODing method (OFLOOD) is proposed as an efficient conformational sampling method to extract biologically rare events such as protein folding. In OFLOOD, sparse distributions (outliers in the conformational space) were regarded as relevant states for the transitions. Then, the transitions were enhanced through conformational resampling from the outliers. This evidence indicates that the conformational resampling of the sparse distributions might increase chances for promoting the transitions from the outliers to other meta-stable states, which resembles a conformational flooding from the outliers to the neighboring clusters. OFLOOD consists of (i) detections of outliers from conformational distributions and (ii) conformational resampling from the outliers by molecular dynamics (MD) simulations. Cycles of (i) and (ii) are simply repeated. As demonstrations, OFLOOD was applied to folding of Chignolin and HP35. In both cases, OFLOOD automatically extracted folding pathways from unfolded structures with ns-order computational costs, although µs-order canonical MD failed to extract them.

Summary Models of symmetric protein evolution typically invoke gene duplication and fusion events, in which repetition of a structural motif generates foldable, stable symmetric protein architecture. Success of such evolutionary processes suggests that the duplicated structural motif must be capable of nucleating protein folding. If correct, symmetric expansion of a folding nucleus sequence derived from an extant symmetric fold may be an elegant and computationally tractable solution to de novo protein design. We report the efficient de novo design of a β-trefoil protein by symmetric expansion of a β-trefoil folding nucleus, previously identified by ɸ-value analysis. The resulting protein, having exact sequence symmetry, exhibits superior folding properties compared to its naturally evolved progenitor—with the potential for redundant folding nuclei. In principle, folding nucleus symmetric expansion can be applied to any given symmetric protein fold (that is, nearly one-third of the known proteome) provided information of the folding nucleus is available.

Computational elucidation of membrane protein (MP) structures is challenging partially due to lack of sufficient solved structures for homology modeling. Here we describe a high-throughput deep transfer learning method that first predicts MP contacts by learning from non-membrane proteins (non-MPs) and then predicting three-dimensional structure models using the predicted contacts as distance restraints. Tested on 510 non-redundant MPs, our method has contact prediction accuracy at least 0.18 better than existing methods, predicts correct folds for 218 MPs (TMscore at least 0.6), and generates three-dimensional models with RMSD less than 4 Angstrom and 5 Angstrom for 57 and 108 MPs, respectively. A rigorous blind test in the continuous automated model evaluation (CAMEO) project shows that our method predicted high-resolution three-dimensional models for two recent test MPs of 210 residues with RMSD close to 2 Angstrom. We estimated that our method could predict correct folds for between 1,345 and 1,871 reviewed human multi-pass MPs including a few hundred new folds, which shall facilitate the discovery of drugs targeting at membrane proteins.

Tzul et al. (1) report different unfolding rates and similar folding rates for a number of thioredoxins. The authors interpret this result as evidence of the principle of minimal frustration. Their study includes several resurrected Precambrian thioredoxins that we have previously prepared and characterized (2⇓⇓–5). We agree that the principle of minimal frustration is essential to understand protein evolution. However, approximate folding-rate invariance is easily explained without invoking this principle. Thioredoxin kinetic stability relies on a transition state that is substantially unstructured (5, 6). Therefore, mutations that changed unfolding rates to tune kinetic stability during evolution likely had much less effect on folding rates, as implied by the well-known principles of ϕ-value analysis (7). Moreover, our experimental results are not consistent with folding-rate invariance being a general feature of thioredoxins. Fig. 1 shows folding–unfolding rates for the modern Escherichia coli thioredoxin and a resurrected Precambrian thioredoxin. The unfolding of the ancestral protein is ∼three orders-of-magnitude slower than the unfolding of the modern protein, indicating enhanced kinetic stability. However, in clear … [↵][1]2To whom correspondence should be addressed. Email: sanchezr{at}ugr.es. [1]: #xref-corresp-1-1

The hydrophobic-polar (HP) model is commonly used for predicting protein folding structures and hydrophobic interactions. This study developed a particle swarm optimization (PSO)-based algorithm combined with local search algorithms; specifically, the high exploration PSO (HEPSO) algorithm (which can execute global search processes) was combined with three local search algorithms (hill-climbing algorithm, greedy algorithm, and Tabu table), yielding the proposed HE-L-PSO algorithm. By using 20 known protein structures, we evaluated the performance of the HE-L-PSO algorithm in predicting protein folding in the HP model. The proposed HE-L-PSO algorithm exhibited favorable performance in predicting both short and long amino acid sequences with high reproducibility and stability, compared with seven reported algorithms. The HE-L-PSO algorithm yielded optimal solutions for all predicted protein folding structures. All HE-L-PSO-predicted protein folding structures possessed a hydrophobic core that is similar to normal protein folding.

Nonequilibrium drivings applied in molecular dynamics (MD) simulations can efficiently extend the visiting range of protein conformations, but might compel systems to go far away from equilibrium and thus mainly explore irrelevant conformations. Here we propose a general method, called adaptive nonequilibrium simulation (ANES), to automatically adjust the external driving on the fly, based on the feedback of the short-time average response of system. Thus, the ANES approximately keeps the local equilibrium but efficiently accelerates the global motion. We illustrate the capability of the ANES in highly efficiently exploring metastable conformations in the deca-alanine peptide and find that the $0.2\ensuremath{-}\ensuremath{\mu}\mathrm{s}$ ANES approximately captures the important states and folding and unfolding pathways in the HP35 solution by comparing with the result of the recent $398\ensuremath{-}\ensuremath{\mu}\mathrm{s}$ equilibrium MD simulation on Anton [S. Piana et al., Proc. Natl. Acad. Sci. USA 109, 17845 (2012)].

Intracellular protein folding (PF) is performed in a highly inhomogeneous, crowded, and correlated environment. Due to this inherent complexity, the study and understanding of PF phenomena is a fundamental issue in the field of computational systems biology. In particular, it is important to use a modeled medium that accurately reflects PF in natural systems. In the current study, we present a simulation wherein PF is carried out within an inhomogeneous modeled medium. Simulation resources included a two-dimensional hydrophobic-polar (HP) model, evolutionary algorithms, and the dual site-bond model. The dual site-bond model was used to develop an environment where HP beads could be folded. Our modeled medium included correlation lengths and fractal-like behavior, which were selected according to HP sequence lengths to induce folding in a crowded environment. Analysis of three benchmark HP sequences showed that the modeled inhomogeneous space played an important role in deeper energy folding and obtained better performance and convergence compared with homogeneous environments. Our computational approach also demonstrated that our correlated network provided a better space for PF. Thus, our approach represents a major advancement in PF simulations, not only for folding but also for understanding functional chemical structure and physicochemical properties of proteins in crowded molecular systems, which normally occur in nature.

The Bias Functional (BF) approach is a variational method which enables one to efficiently generate ensembles of reactive trajectories for complex biomolecular transitions, using ordinary computer clusters. For example, this scheme was applied to simulate in atomistic detail the folding of proteins consisting of several hundreds of amino acids and with experimental folding time of several minutes. A drawback of the BF approach is that it produces trajectories which do not satisfy microscopic reversibility. Consequently, this method cannot be used to directly compute equilibrium observables, such as free energy landscapes or equilibrium constants. In this work, we develop a statistical analysis which permits us to compute the potential of mean-force (PMF) along an arbitrary collective coordinate, by exploiting the information contained in the reactive trajectories calculated with the BF approach. We assess the accuracy and computational efficiency of this scheme by comparing its results with the PMF obtained for a small protein by means of plain molecular dynamics.

My least favorite opening sentence of a scientific article is: “Recently there has been much interest in….” Unless the sentence goes on to explain why there is so much interest in the topic, it is unlikely to excite the curiosity of the reader.

The ability to design and construct structures with atomic level precision is one of the key goals of nanotechnology. Proteins offer an attractive target for atomic design, as they can be synthesized chemically or biologically, and can self-assemble. However the generalized protein folding and design problem is unsolved. One approach to simplifying the problem is to use a repetitive protein as a scaffold. Repeat proteins are intrinsically modular, and their folding and structures are better understood than large globular domains. Here, we have developed a new class of synthetic repeat protein, based on the pentapeptide repeat family of beta-solenoid proteins. We have constructed length variants of the basic scaffold, and computationally designed de novo loops projecting from the scaffold core. The experimentally solved 3.56 ˚A resolution crystal structure of one designed loop matches closely the designed hairpin structure, showing the computational design of a backbone extension onto a synthetic protein core without the use of backbone fragments from known structures. Two other loop designs were not clearly resolved in the crystal structures and one loop appeared to be in an incorrect conformation. We have also shown that the repeat unit can accommodate whole domain insertions by inserting a domain into one of the designed loops.

Background Simulating protein folding motions is an important problem in computational biology. Motion planning algorithms, such as Probabilistic Roadmap Methods, have been successful in modeling the folding landscape. Probabilistic Roadmap Methods and variants contain several phases (i.e., sampling, connection, and path extraction). Most of the time is spent in the connection phase and selecting which variant to employ is a difficult task. Global machine learning has been applied to the connection phase but is inefficient in situations with varying topology, such as those typical of folding landscapes. Results We develop a local learning algorithm that exploits the past performance of methods within the neighborhood of the current connection attempts as a basis for learning. It is sensitive not only to different types of landscapes but also to differing regions in the landscape itself, removing the need to explicitly partition the landscape. We perform experiments on 23 proteins of varying secondary structure makeup with 52–114 residues. We compare the success rate when using our methods and other methods. We demonstrate a clear need for learning (i.e., only learning methods were able to validate against all available experimental data) and show that local learning is superior to global learning producing, in many cases, significantly higher quality results than the other methods. Conclusions We present an algorithm that uses local learning to select appropriate connection methods in the context of roadmap construction for protein folding. Our method removes the burden of deciding which method to use, leverages the strengths of the individual input methods, and it is extendable to include other future connection methods.

In this paper, we present a coarse replica exchange molecular dynamics (REMD) approach, based on kinetic Monte Carlo (kMC). The new development significantly can reduce the amount of replicas and the computational cost needed to enhance sampling in protein simulations. We introduce 2 different methods which primarily differ in the exchange scheme between the parallel ensembles. We apply this approach on folding of 2 different β-stranded peptides: the C-terminal β-hairpin fragment of GB1 and TrpZip4. Additionally, we use the new simulation technique to study the folding of TrpCage, a small fast folding α-helical peptide. Subsequently, we apply the new methodology on conformation changes in signaling of the light-oxygen voltage (LOV) sensitive domain from Avena sativa (AsLOV2). Our results agree well with data reported in the literature. In simulations of dialanine, we compare the statistical sampling of the 2 techniques with conventional REMD and analyze their performance. The new techniques can reduce the computational cost of REMD significantly and can be used in enhanced sampling simulations of biomolecules.

The space accessed by a folding macromolecule is vast, and how to best project computer simulations of protein folding trajectories into an interpretable sequence of discrete states is an open research problem. There are numerous alternative ways of associating individual configurations into collective states, and in deciding on the number of such clustered states there is a trade-off between human interpretability (smaller number of states) and accuracy of representation (larger number of states). Here we introduce a trajectory likelihood measure for assessing alternative discrete state models of protein folding. We find that widely used rmsd-based clustering methods require large numbers of initial states and a second agglomeration step based on kinetic connectivity to produce models with high predictive power; this is the approach taken in elegant recent work with Markov State Models of protein folding. In contrast, we find that grouping of states based on secondary structure pairings or contact maps, when refined with K-means clustering, yields higher likelihood models with many fewer states. Using the most predictive contact map representation to study the folding transitions of the WW domain in very long molecular dynamics simulations, we identify new states and transitions. The methods should be generally useful for investigating the structural transitions in protein folding simulations for larger proteins.

A simple model is presented that describes general features of protein folding, in good agreement with experimental results and detailed all-atom simulations. Starting from microscopic physics, and with no free parameters, this model predicts that protein folding occurs remarkably quickly because native-like states are kinetic hubs. A hub-like network arises naturally out of microscopic physical concerns, specifically the kinetic longevity of native contacts during a search of globular conformations. The model predicts folding times scaling as τ(f) ~ e(ξN) in the number of residues, but because the model shows ξ is small, the folding times are much faster than Levinthal's approximation. Importantly, the folding time scale is found to be small due to the topology and structure of the network. We show explicitly how our model agrees with generic experimental features of the folding process, including the scaling of τ(f) with N, two-state thermodynamics, a sharp peak in C(V), and native-state fluctuations.

A chain tree is a data structure for changing protein conformations. It enables very fast detection of clashes and free energy potential calculations. A modified version of chain trees that adjust themselves to the changing conformations of folding proteins is introduced. This results in much tighter bounding volume hierarchies and therefore fewer intersection checks. Computational results indicate that the efficiency of the adjustable chain trees is significantly improved compared to the traditional chain trees.

The phenomenon of protein folding is a fundamental issue in the field of the computational molecular biology. The protein folding inside the cells is performed in a highly inhomogeneous, tortuous, and correlated environment. Therefore, it is important to include in the theoretical studies the medium where the protein folding is developed. In this work we present the combination of three models to mimic the protein folding inside of an inhomogeneous medium. The models used here are Hydrophobic-Polar (HP) in 2D square arrangement, Evolutionary Algorithms (EA), and the Dual Site Bond Model (DSBM). The DSBM model is used to simulate the environment where the HP beads are folded; in this case the medium is correlated and is fractal-like. The analysis of five benchmark HP sequences shows that the inhomogeneous space provided with a given correlation length and fractal dimension plays an important role for correct folding of these sequences, which does not occur in a homogeneous space.

Translation speed can affect the cotranslational folding of nascent peptide. Experimental observations have indicated that slowing down translation rates of codons can increase the probability of protein cotranslational folding. Recently, a kinetic modeling indicates that fast translation can also increase the probability of cotranslational protein folding by avoiding misfolded intermediates. We show that the villin headpiece subdomain HP35 is an ideal model to demonstrate this phenomenon. We studied cotranslational folding of HP35 with different fast translation speeds by all-atom molecular dynamics simulations and found that HP35 can fold along a well-defined pathway that passes the on-pathway intermediate but avoids the misfolded off-pathway intermediate in certain case. This greatly increases the probability of HP35 cotranslational folding and the approximate mean first passage time of folding into native state is about 1.67μs. Since we also considered the space-confined effect of the ribosomal exit tunnel on the cotranslational folding, our simulation results suggested alternative mechanism for the increasing of cotranslational folding probability by fast translation speed.

Recent work has shown that NMR structures can be determined by integrating sparse NMR data with structure prediction methods such as Rosetta. The experimental data serve to guide the search for the lowest energy state towards the deep minimum at the native state which is frequently missed in Rosetta de novo structure calculations. However, as the protein size increases, sampling again becomes limiting; for example, the standard Rosetta protocol involving Monte Carlo fragment insertion starting from an extended chain fails to converge for proteins over 150 amino acids even with guidance from chemical shifts (CS-Rosetta) and other NMR data. The primary limitation of this protocol--that every folding trajectory is completely independent of every other--was recently overcome with the development of a new approach involving resolution-adapted structural recombination (RASREC). Here we describe the RASREC approach in detail and compare it to standard CS-Rosetta. We show that the improved sampling of RASREC is essential in obtaining accurate structures over a benchmark set of 11 proteins in the 15-25 kDa size range using chemical shifts, backbone RDCs and HN-HN NOE data; in a number of cases the improved sampling methodology makes a larger contribution than incorporation of additional experimental data. Experimental data are invaluable for guiding sampling to the vicinity of the global energy minimum, but for larger proteins, the standard Rosetta fold-from-extended-chain protocol does not converge on the native minimum even with experimental data and the more powerful RASREC approach is necessary to converge to accurate solutions.

Foldit is a multiplayer online game in which players collaborate and compete to create accurate protein structure models. For specific hard problems, Foldit player solutions can in some cases outperform state-of-the-art computational methods. However, very little is known about how collaborative gameplay produces these results and whether Foldit player strategies can be formalized and structured so that they can be used by computers. To determine whether high performing player strategies could be collectively codified, we augmented the Foldit gameplay mechanics with tools for players to encode their folding strategies as “recipes” and to share their recipes with other players, who are able to further modify and redistribute them. Here we describe the rapid social evolution of player-developed folding algorithms that took place in the year following the introduction of these tools. Players developed over 5,400 different recipes, both by creating new algorithms and by modifying and recombining successful recipes developed by other players. The most successful recipes rapidly spread through the Foldit player population, and two of the recipes became particularly dominant. Examination of the algorithms encoded in these two recipes revealed a striking similarity to an unpublished algorithm developed by scientists over the same period. Benchmark calculations show that the new algorithm independently discovered by scientists and by Foldit players outperforms previously published methods. Thus, online scientific game frameworks have the potential not only to solve hard scientific problems, but also to discover and formalize effective new strategies and algorithms.