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International audience; The development of ultrafast kinetic methods is one of the factors that allowed the research on protein folding to flourish over the last twenty years. The introduction of new optical triggering techniques enabled to experimentally investigate the protein dynamics at the nanosecond to millisecond timescale, allowing researchers to test theoretical predictions and providing experimental benchmarks for computer simulations. In this work the details of how to perform kinetic experiments by the laserinduced temperature jump technique, using the two most commonly used probing techniques (namely infrared absorption and fluorescence spectroscopy) are given, with a strong emphasis on the practical details.

Strategies for investigating and optimizing the expression and folding of proteins for biotechnological and pharmaceutical purposes are in high demand. Here, we describe a dual-reporter biosensor system that simultaneously assesses in vivo protein translation and protein folding, thereby enabling rapid screening of mutant libraries. We have validated the dual-reporter system on five different proteins and find an excellent correlation between reporter signals and the levels of protein expression and solubility of the proteins. We further demonstrate the applicability of the dual-reporter system as a screening assay for deep mutational scanning experiments. The system enables high throughput selection of protein variants with high expression levels and altered protein stability. Next generation sequencing analysis of the resulting libraries of protein variants show a good correlation between computationally predicted and experimentally determined protein stabilities. We furthermore show that the mutational experimental data obtained using this system may be useful for protein structure calculations., Heterologous expression of recombinant proteins often results in misfolding, aggregation and degradation. Here, we show an in vivo dual-biosensor system that simultaneously assesses protein translation and protein folding, thereby enabling rapid screening of expression strains as well as mutant libraries.

Motivation The development of an open-source platform to predict protein 1D features and 3D structure is an important task. In this paper, we report an open-source toolkit for protein 3D structure modeling, named OPUS-X. It contains three modules: OPUS-TASS2, which predicts protein torsion angles, secondary structure and solvent accessibility; OPUS-Contact, which measures the distance and orientation information between different residue pairs; and OPUS-Fold2, which uses the constraints derived from the first two modules to guide folding. Results OPUS-TASS2 is an upgraded version of our previous method OPUS-TASS. OPUS-TASS2 integrates protein global structure information and significantly outperforms OPUS-TASS. OPUS-Contact combines multiple raw co-evolutionary features with protein 1D features predicted by OPUS-TASS2, and delivers better results than the open-source state-of-the-art method trRosetta. OPUS-Fold2 is a complementary version of our previous method OPUS-Fold. OPUS-Fold2 is a gradient-based protein folding framework based on the differentiable energy terms in opposed to OPUS-Fold that is a sampling-based method used to deal with the non-differentiable terms. OPUS-Fold2 exhibits comparable performance to the Rosetta folding protocol in trRosetta when using identical inputs. OPUS-Fold2 is written in Python and TensorFlow2.4, which is user-friendly to any source-code-level modification. Availabilityand implementation The code and pre-trained models of OPUS-X can be downloaded from https://github.com/OPUS-MaLab/opus_x. Supplementary information Supplementary data are available at Bioinformatics online.

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.

The snake cube puzzle made of a linear array of 27 cubes and its modified and extended versions are used as theoretical models to study the mechanism of folding of proteins into their sequence-specific native three-dimensional structures. Each of the three versions is characterized by the respective set of characteristics attributed to each of its constituent cubes and an array is characterized by its specific sequence of the cube characteristics. The aim of the puzzles is to fold the cube array into a compact 3×3×3 cubic structure. In all three versions, out of all possible sequences, only a limited fraction of sequences are found foldable into the compact cube. Even among foldable sequences, the structures folded into the compact 3×3×3 cube are found often not uniquely determined from the sequence. By comparing the results obtained for the three versions of models, we conclude that the power of the hydrophobic interactions to make the folded structure unique to the sequence is much weaker than the geometrical varieties of constituent cubes as modelled in the original snake cube puzzle. However, when this weak cube attribute is compounded to that of the original snake cube puzzle, the power is enhanced very effectively. This is a strong manifestation of the consistency principle: The sequence-specific native structure of protein is realized as a result of consistency of various types of interactions working in protein.

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.

INTRODUCCIÓN: Las proteínas son una de las moléculas orgánicas que cumplen funciones vitales en la mantención de la vida y reproducción celular, su fabricación es un proceso complejo gobernado por una secuencia de plegamientos aún desconocida. En el contexto del Covid19, la iniciativa Folding@home llevó a cabo un proyecto de computación distribuida que permite la simulación del proceso de plegamiento de la proteína Spike del Covid19, cuya función es acoplarse al receptor ACE2 de las células animales y así penetrar a la célula y utilizar su maquinaria para reproducirse. OBJETIVO: Probar que el tiempo computacional ocioso disponible en los laboratorios de informática educacionales, puede ser usado para la simulación del plegamiento de proteínas. MÉTODO: Esta fue una investigación descriptiva donde se instaló un software cliente en computadores de gama baja que continuamente enviaron unidades de trabajo de plegamiento proteico a un servidor central. RESULTADOS: Tras 90 días de trabajo, un clúster de 27 PCs finalizaron 1993 unidades de trabajo de simulación de la proteína Spike. DISCUSIÓN Y CONCLUSIONES: A pesar de que el piloteo fue un éxito, se advierte que el software cliente debe ser optimizado para sacar el máximo de provecho a los diferentes procesadores y sistemas operativos con los cuales es compatible el software de computación distribuida proveído por Folding@home.

The analysis of protein folding reactions by monitoring the kinetic effects of specifically designed single-point mutations, the so-termed phi-value analysis, has been a favorite technique to experimentally probe the mechanisms of protein folding. The idea behind phi-value analysis is that the effects that mutations have on the folding and unfolding rate constants report on the energetic/structural features of the folding transition state ensemble (TSE), which is the highest point in the free energy surface connecting the native and unfolded states, and thus the rate limiting step that ultimately defines the folding mechanism. For single-domain, two-state folding proteins, the general procedure to perform the phi-value analysis of protein folding is relatively simple to implement in the lab. Once the mutations have been produced and purified, the researcher needs to follow a few specific guidelines to perform the experiments and to analyze the data so produced. In this chapter, a step-by-step description of how to measure and interpret the effects induced by site-directed mutations on the folding and unfolding rate constants of a protein of interest is provided. Some possible solutions to the most typical problems that arise when performing phi-value analysis in the lab are also provided.

Computational coarse-grained models play a fundamental role as a research tool in protein folding, and they are important in bridging theory and experiments. Folding mechanisms are generally discussed using the energy landscape framework, which is well mapped within a class of simplified structure-based models. In this chapter, simplified computer models are discussed with special focus on structure-based ones.

Datasets representing the conformational landscapes of protein structures are high dimensional and hence present computational challenges. Efficient and effective dimensionality reduction of these datasets is therefore paramount to our ability to analyze the conformational landscapes of proteins and extract important information regarding protein folding, conformational changes and binding. Representing the structures with fewer attributes that capture the most variance of the data, makes for quicker and precise analysis of these structures. In this work we make use of dimensionality reduction methods for reducing the number of instances and for feature reduction. The reduced dataset that is obtained is then subjected to topological and quantitative analysis. In this step we perform hierarchical clustering to obtain different sets of conformation clusters that may correspond to intermediate structures. The structures represented by these conformations are then analyzed by studying their high dimension topological properties to identify truly distinct conformations and holes in the conformational space that may represent high energy barriers. Our results show that the clusters closely follow known experimental results about intermediate structures, as well as binding and folding events.

Approximating protein unfolding by an all-or-none cooperative event is a convenient assumption that can provide precious global information on protein stability. It is however quickly emerging that the scenario is far more complex and that global denaturation curves often hide a rich heterogeneity of states that are largely probe dependent. In this review, we revisit the importance of gaining site-specific information on the unfolding process. We focus on nuclear magnetic resonance, as this is the main technique able to provide site-specific information. We review historical and most modern approaches that have allowed an appreciable advancement of the field of protein folding. We also demonstrate how unfolding is a reporter dependent event, suggesting the outmost importance of selecting the reporter carefully.

Cryo-electron microscopy (EM) requires molecular modeling to refine structural details from data. Ensemble models arrive at low free-energy molecular structures, but are computationally expensive and limited to resolving only small proteins that cannot be resolved by cryo-EM. Here, we introduce CryoFold - a pipeline of molecular dynamics simulations that determines ensembles of protein structures directly from sequence by integrating density data of varying sparsity at 3-5 Å resolution with coarse-grained topological knowledge of the protein folds. We present six examples showing its broad applicability for folding proteins between 72 to 2000 residues, including large membrane and multi-domain systems, and results from two EMDB competitions. Driven by data from a single state, CryoFold discovers ensembles of common low-energy models together with rare low-probability structures that capture the equilibrium distribution of proteins constrained by the density maps. Many of these conformations, unseen by traditional methods, are experimentally validated and functionally relevant. We arrive at a set of best practices for data-guided protein folding that are controlled using a Python GUI.

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.

Protein structure prediction has long been considered a gateway problem for understanding protein folding. Recent advances in deep learning have achieved unprecedented success at predicting a protein’s crystal structure, but whether this achievement relates to a better modelling of the folding process remains an open question. In this work, we compare the pathways generated by state-of-the-art protein structure prediction methods to experimental folding data. The methods considered were AlphaFold 2, RoseTTAFold, trRosetta, RaptorX, DMPfold, EVfold, SAINT2 and Rosetta. We find evidence that their simulated dynamics capture some information about the folding pathwhay, but their predictive ability is worse than a trivial classifier using sequence-agnostic features like chain length. The folding trajectories produced are also uncorrelated with parameters such as intermediate structures and the folding rate constant. These results suggest that recent advances in protein structure prediction do not yet provide an enhanced understanding of the principles underpinning protein folding.

Conformational sampling of biomolecules using molecular dynamics simulations often produces large amount of high dimensional data that makes it difficult to interpret using conventional analysis techniques. Dimensionality reduction methods are thus required to extract useful and relevant information. Here we devise a machine learning method, Gaussian mixture variational autoencoder (GMVAE) that can simultaneously perform dimensionality reduction and clustering of biomolecular conformations in an unsupervised way. We show that GMVAE can learn a reduced representation of the free energy landscape of protein folding with highly separated clusters that correspond to the metastable states during folding. Since GMVAE uses a mixture of Gaussians as the prior, it can directly acknowledge the multi-basin nature of protein folding free-energy landscape. To make the model end-to-end differentialble, we use a Gumbel-softmax distribution. We test the model on three long-timescale protein folding trajectories and show that GMVAE embedding resembles the folding funnel with folded states down the funnel and unfolded states outer in the funnel path. Additionally, we show that the latent space of GMVAE can be used for kinetic analysis and Markov state models built on this embedding produce folding and unfolding timescales that are in close agreement with other rigorous dynamical embeddings such as time independent component analysis (TICA).

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.

Graphical abstract, Protein folding and function are closely connected, but the exact mechanisms by which proteins fold remain elusive. Early folding residues (EFRs) are amino acids within a particular protein that induce the very first stages of the folding process. High-resolution EFR data are only available for few proteins, which has previously enabled the training of a protein sequence-based machine learning 'black box' predictor (EFoldMine). Such a black box approach does not allow a direct extraction of the 'early folding rules' embedded in the protein sequence, whilst such interpretation is essential to improve our understanding of how the folding process works. We here apply and investigate a novel 'grey box' approach to the prediction of EFRs from protein sequence to gain mechanistic residue-level insights into the sequence determinants of EFRs in proteins. We interpret the rule set for three datasets, a default set comprised of natural proteins, a scrambled set comprised of the scrambled default set sequences, and a set of de novo designed proteins. Finally, we relate these data to the secondary structure adopted in the folded protein and provide all information online via http://xefoldmine.bio2byte.be/, as a resource to help understand and steer early protein folding.

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.

RNA molecules participate in many important biological processes, and they need to fold into well-defined secondary and tertiary structures to realize their functions. Like the well-known protein folding problem, there is also an RNA folding problem. The folding problem includes two aspects: structure prediction and folding mechanism. Although the former has been widely studied, the latter is still not well understood. Here we present a deep reinforcement learning algorithms 2dRNA-Fold to study the fastest folding paths of RNA secondary structure. 2dRNA-Fold uses a neural network combined with Monte Carlo tree search to select residue pairing step by step according to a given RNA sequence until the final secondary structure is formed. We apply 2dRNA-Fold to several short RNA molecules and one longer RNA 1Y26 and find that their fastest folding paths show some interesting features. 2dRNA-Fold is further trained using a set of RNA molecules from the dataset bpRNA and is used to predict RNA secondary structure. Since in 2dRNA-Fold the scoring to determine next step is based on possible base pairings, the learned or predicted fastest folding path may not agree with the actual folding paths determined by free energy according to physical laws.

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.

Proteins are translated from the N- to the C-terminus, raising the basic question of how this innate directionality affects their evolution. To explore this question, we analyze 16,200 structures from the protein data bank (PDB). We find remarkable enrichment of α-helices at the C terminus and β-strands at the N terminus. Furthermore, this α-β asymmetry correlates with sequence length and contact order, both determinants of folding rate, hinting at possible links to co-translational folding (CTF). Hence, we propose the 'slowest-first' scheme, whereby protein sequences evolved structural asymmetry to accelerate CTF: the slowest of the cooperatively-folding segments are positioned near the N terminus so they have more time to fold during translation. A phenomenological model predicts that CTF can be accelerated by asymmetry in folding rate, up to double the rate, when folding time is commensurate with translation time; analysis of the PDB predicts that structural asymmetry is indeed maximal in this regime. This correspondence is greater in prokaryotes, which generally require faster protein production. Altogether, this indicates that accelerating CTF is a substantial evolutionary force whose interplay with stability and functionality is encoded in secondary structure asymmetry. SIGNIFICANCE Proteins are inherently asymmetric, as they are translated sequentially from the N- to the C-terminal. To see how this affects protein evolution we analyse protein structures, finding corresponding asymmetries in secondary structure: α-helices are enriched at the C-terminal and β-sheets at the N-terminal. To explain this significant asymmetry, we propose the 'slowest-first' scheme: slow-folding structures are located at the N-terminal so they are translated first and thus have more time to fold during translation. The asymmetry peaks when folding time and translation time are similar, where our model predicts that proteins can benefit most from α-β asymmetry. Altogether, this work provides evidence for the evolution of structural asymmetry in proteins to accelerate co-translational folding, and proposes further experimental tests.

Stunning advances have been achieved in addressing the protein folding problem, providing deeper understanding of the mechanisms by which proteins navigate energy landscapes to reach their native states and enabling powerful algorithms to connect sequence to structure. However, the realities of the in vivo protein folding problem remain a challenge to reckon with. Here, we discuss the concept of the "proteome folding problem"-the problem of how organisms build and maintain a functional proteome-by admitting that folding energy landscapes are characterized by many misfolded states and that cells must deploy a network of chaperones and degradation enzymes to minimize deleterious impacts of these off-pathway species. The resulting proteostasis network is an inextricable part of in vivo protein folding and must be understood in detail if we are to solve the proteome folding problem. We discuss how the development of computational models for the proteostasis network's actions and the relationship to the biophysical properties of the proteome has begun to offer new insights and capabilities.

Cotranslational folding depends on the folding speed and stability of the nascent protein. It remains difficult, however, to predict which proteins cotranslationally fold. Here, we simulate evolution of model proteins to investigate how native structure influences evolution of cotranslational folding. We developed a model that connects protein folding during and after translation to cellular fitness. Model proteins evolved improved folding speed and stability, with proteins adopting one of two strategies for folding quickly. Low contact order proteins evolve to fold cotranslationally. Such proteins adopt native conformations early on during the translation process, with each subsequently translated residue establishing additional native contacts. On the other hand, high contact order proteins tend not to be stable in their native conformations until the full chain is nearly extruded. We also simulated evolution of slowly translating codons, finding that slower translation speeds at certain positions enhances cotranslational folding. Finally, we investigated real protein structures using a previously published data set that identified evolutionarily conserved rare codons in Escherichia coli genes and associated such codons with cotranslational folding intermediates. We found that protein substructures preceding conserved rare codons tend to have lower contact orders, in line with our finding that lower contact order proteins are more likely to fold cotranslationally. Our work shows how evolutionary selection pressure can cause proteins with local contact topologies to evolve cotranslational folding.

In this paper, we report an open-source toolkit for protein 3D structure modeling, named OPUS-X. It contains three modules: OPUS-TASS2, which predicts protein torsion angles, secondary structure and solvent accessibility; OPUS-Contact, which measures the distance and orientations information between different residue pairs; and OPUS-Fold2, which uses the constraints derived from the first two modules to guide folding. OPUS-TASS2 is an upgraded version of our previous method OPUSS-TASS (Bioinformatics2020,36(20), 5021-5026). OPUS-TASS2 integrates protein global structure information and significantly outperforms OPUS-TASS. OPUS-Contact combines multiple raw co-evolutionary features with protein 1D features predicted by OPUS-TASS2, and delivers better results than the open-source state-of-the-art method trRosetta. OPUS-Fold2 is a complementary version of our previous method OPUS-Fold (J. Chem. Theory Comput.2020,16(6), 3970-3976). OPUS-Fold2 is a gradient-based protein folding framework based on the differentiable energy terms in opposed to OPUS-Fold that is a sampling-based method used to deal with the non-differentiable terms. OPUS-Fold2 exhibits comparable performance to the Rosetta folding protocol in trRosetta when using identical inputs. OPUS-Fold2 is written in Python and TensorFlow2.4, which is user-friendly to any source-code level modification. The code and pre-trained models of OPUS-X can be downloaded fromhttps://github.com/OPUS-MaLab/opus_x.

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.

Earlier experiments suggest that the evolutionary information (conservation and coevolution) encoded in protein sequences is necessary and sufficient to specify the fold of a protein family. However, there is no computational work to quantify the effect of such evolutionary information on the folding process. Here we explore the role of early folding steps for sequences designed using coevolution and conservation through a combination of computational and experimental methods. We simulated a repertoire of native and designed WW domain sequences to analyze early local contact formation and found that the N-terminal β-hairpin turn would not form correctly due to strong non-native local contacts in unfoldable sequences. Through a maximum likelihood approach, we identified five local contacts that play a critical role in folding, suggesting that a small subset of amino acid pairs can be used to solve the "needle in the haystack" problem to design foldable sequences. Thus, using the contact probability of those five local contacts that form during the early stage of folding, we built a classification model that predicts the foldability of a WW sequence with 81% accuracy. This classification model was used to redesign WW domain sequences that could not fold due to frustration and make them foldable by introducing a few mutations that led to the stabilization of these critical local contacts. The experimental analysis shows that a redesigned sequence folds and binds to polyproline peptides with a similar affinity as those observed for native WW domains. Overall, our analysis shows that evolutionary-designed sequences should not only satisfy the folding stability but also ensure a minimally frustrated folding landscape.

Motivation The mathematically optimal solution in computational protein folding simulations does not always correspond to the native structure, due to the imperfection of the energy force fields. There is therefore a need to search for more diverse suboptimal solutions in order to identify the states close to the native. We propose a novel multimodal optimization protocol to improve the conformation sampling efficiency and modeling accuracy of de novo protein structure folding simulations. Results A distance-assisted multimodal optimization sampling algorithm, MMpred, is proposed for de novo protein structure prediction. The protocol consists of three stages: The first is a modal exploration stage, in which a structural similarity evaluation model DMscore is designed to control the diversity of conformations, generating a population of diverse structures in different low-energy basins. The second is a modal maintaining stage, where an adaptive clustering algorithm MNDcluster is proposed to divide the populations and merge the modal by adjusting the annealing temperature to locate the promising basins. In the last stage of modal exploitation, a greedy search strategy is used to accelerate the convergence of the modal. Distance constraint information is used to construct the conformation scoring model to guide sampling. MMpred is tested on a large set of 320 non-redundant proteins, where MMpred obtains models with TM-score≥0.5 on 291 cases, which is 28% higher than that of Rosetta guided with the same set of distance constraints. In addition, on 320 benchmark proteins, the enhanced version of MMpred (E-MMpred) has 167 targets better than trRosetta when the best of five models are evaluated. The average TM-score of the best model of E-MMpred is 0.732, which is comparable to trRosetta (0.730). Availability and implementation The source code and executable are freely available at https://github.com/iobio-zjut/MMpred. Supplementary information Supplementary data are available at Bioinformatics online.

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 ability to construct novel enzymes is a major aim in de novo protein design. A popular enzyme fold for design attempts is the TIM barrel. This fold is a common topology for enzymes and can harbor many diverse reactions. The recent de novo design of a four‐fold symmetric TIM barrel provides a well understood minimal scaffold for potential enzyme designs. Here we explore opportunities to extend and diversify this scaffold by adding a short de novo helix on top of the barrel. Due to the size of the protein, we developed a design pipeline based on computational ab initio folding that solves a less complex sub‐problem focused around the helix and its vicinity and adapt it to the entire protein. We provide biochemical characterization and a high‐resolution X‐ray structure for one variant and compare it to our design model. The successful extension of this robust TIM‐barrel scaffold opens opportunities to diversify it towards more pocket like arrangements and as such can be considered a building block for future design of binding or catalytic sites., PDB Code(s): 7A8S

Assessment of protein stability and function is key to the understanding of biological systems and plays an important role in the development of protein-based drugs. In this work, we introduce an integrated approach based on Taylor dispersion analysis (TDA), flow induced dispersion analysis (FIDA), and in-line intrinsic fluorescence which enables rapid and detailed assessment of protein stability and unfolding. We demonstrate that the new platform is able to efficiently characterize chemically induced protein unfolding of human serum albumin (HSA) in great detail. The combined platform enables local structural changes to be probed by monitoring changes in intrinsic fluorescence and loss of binding of a low-molecular weight ligand. Simultaneously, the size of the unfolding HSA is obtained by TDA on the same samples. The integration of the methodologies enables a fully automated characterization of HSA using only a few hundred nanoliters of sample. We envision that the presented methodology will find applications in fundamental biophysics and biology as well as in stability screens of protein-based drug candidates.

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.

To achieve a good understanding of the characteristics of a protein, it is important to study its stability and folding kinetics. Investigations of protein stability have been recently applied to drug-target identification, drug screening, and proteomic studies. The efficiency of the experiments performed to study protein stability and folding kinetics is now a crucial factor that needs to be optimized for these potential applications. However, the standard procedures used to carry out these experiments are usually complicated and time consuming. Large number of measurements is the bottleneck that limits the application of protein folding to large-scale experiments. To overcome this limitation, we developed a method denoted as "one-pot analysis" which is based on taking a single measurement from a mixture of samples rather than from every sample. We combined one-pot analysis with pulse proteolysis to determine the effects of the binding of maltose to maltose-binding protein on the protein folding properties. After carrying out a simple optimization, we demonstrated that protein stability or unfolding kinetics could be measured accurately with just one detection measurement. We then further applied the optimized conditions to cellular thermal shift assay (CETSA). Combining one-pot analysis with CETSA led to a successful determination of the effects of the binding of methotrexate to dihydrofolate reductase in HCT116 cancer cells. Our results demonstrated the applicability of one-pot analysis to energetics-based methods for studying protein folding. We expect the combination of one-pot analysis and energetics-based methods to significantly benefit studies such as drug-target identification, proteomic investigations, and drug screening.

In the cell, protein folding begins during protein synthesis/translation and thus is a co-translational process. Co-translational protein folding is tightly linked to translation elongation, which is not a uniform process. While there are many reasons for translation non-uniformity, it is generally believed that non-uniform synonymous codon usage is one of the key factors modulating translation elongation rates. Frequent/optimal codons as a rule are translated more rapidly than infrequently used ones and vice versa. Over 30 years ago, it was hypothesized that changes in synonymous codon usage affecting translation elongation rates could impinge on co-translation protein folding and that many synonymous codons are strategically placed within mRNA to ensure a particular translation kinetics facilitating productive step-by-step co-translational folding of proteins. It was suggested that this particular translation kinetics (and, specifically, translation pause sites) may define the window of opportunity for the protein parts to fold locally, particularly at the critical points where folding is far from equilibrium. It was thus hypothesized that synonymous codons may provide a secondary code for protein folding in the cell. Although, mostly accepted now, this hypothesis appeared to be difficult to prove and many convincing results were obtained only relatively recently. Here, I review the progress in the field and explain, why this simple idea appeared to be so challenging to prove.

Over the past two decades, one of the standard models of protein folding has been the "two-state" model, in which a protein only resides in the folded or fully unfolded states with a single pathway between them. Recent advances in spatial and temporal resolution of biophysical measurements have revealed "beyond-two-state" complexity in protein folding, even for small, single-domain proteins. In this work, we used high-resolution optical tweezers to investigate the folding/unfolding kinetics of the B1 domain of immunoglobulin-binding protein G (GB1), a well-studied model system. Experiments were performed for GB1 both in and out of equilibrium using force spectroscopy. When the force was gradually ramped, simple single-peak folding force distributions were observed, while multiple rupture peaks were seen in the unfolding force distributions, consistent with multiple force-dependent parallel unfolding pathways. Force-dependent folding and unfolding rate constants were directly determined by both force-jump and fixed-trap measurements. Monte Carlo modeling using these rate constants was in good agreement with the force ramp data. The unfolding rate constants exhibited two different behaviors at low vs high force. At high force, the unfolding rate constant increased with increasing force, as previously reported by high force, high pulling speed force ramp measurements. However, at low force, the situation reversed and the unfolding rate constant decreased with increasing force. Taken together, these data indicate that this small protein has multiple distinct pathways to the native state on the free energy landscape.

The topology of protein folds can be specified by the inter-residue contact-maps and accurate contact-map prediction can helpab initiostructure 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 and CAMEO experiments, and outperformed other state-of-the-art methods by at least 58.4% for the CASP 11&12 and 44.4% for the CAMEO targets in the top-Llong-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. 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.AvailabilityThe training and testing data, standalone package, and the online server for TripletRes are available athttps://zhanglab.ccmb.med.umich.edu/TripletRes/.Author SummaryAb initioprotein 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 onab initiostructure prediction, which was mainly powered by the boosting of contact-map prediction as the latter can be used as constraints to guideab initiofolding 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 significant advancement of the proposed methods over other 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.

Protein structure prediction and design can be regarded as two inverse processes governed by the same folding principle. Although progress remained stagnant over the past two decades, the recent application of deep neural networks to spatial constraint prediction and end-to-end model training has significantly improved the accuracy of protein structure prediction, largely solving the problem at the fold level for single-domain proteins. The field of protein design has also witnessed dramatic improvement, where noticeable examples have shown that information stored in neural-network models can be used to advance functional protein design. Thus, incorporation of deep learning techniques into different steps of protein folding and design approaches represents an exciting future direction and should continue to have a transformative impact on both fields.

International audience; The predictive capabilities of deep neural networks (DNNs) continue to evolve to increasingly impressive levels. However, it is still unclear how training procedures for DNNs succeed in finding parameters that produce good results for such high-dimensional and nonconvex loss functions. In particular, we wish to understand why simple optimization schemes, such as stochastic gradient descent, do not end up trapped in local minima with high loss values that would not yield useful predictions. We explain the optimizability of DNNs by characterizing the local minima and transition states of the loss-function landscape (LFL) along with their connectivity. We show that the LFL of a DNN in the shallow network or data-abundant limit is funneled, and thus easy to optimize. Crucially, in the opposite low-data/deep limit, although the number of minima increases, the landscape is characterized by many minima with similar loss values separated by low barriers. This organization is different from the hierarchical landscapes of structural glass formers and explains why minimization procedures commonly employed by the machine-learning community can navigate the LFL successfully and reach low-lying solutions.

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.

Atomistic simulations can provide valuable, experimentally-verifiable insights into protein folding mechanisms, but existingab initiosimulation 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, withunfoldingsimulations 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 methods. 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 summaryMany 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.

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.

Motivation From evolutionary interference, function annotation to structural prediction, protein sequence comparison has provided crucial biological insights. While many sequence alignment algorithms have been developed, existing approaches often cannot detect hidden structural relationships in the ‘twilight zone’ of low sequence identity. To address this critical problem, we introduce a computational algorithm that performs protein Sequence Alignments from deep-Learning of Structural Alignments (SAdLSA, silent ‘d’). The key idea is to implicitly learn the protein folding code from many thousands of structural alignments using experimentally determined protein structures. Results To demonstrate that the folding code was learned, we first show that SAdLSA trained on pure α-helical proteins successfully recognizes pairs of structurally related pure β-sheet protein domains. Subsequent training and benchmarking on larger, highly challenging datasets show significant improvement over established approaches. For challenging cases, SAdLSA is ∼150% better than HHsearch for generating pairwise alignments and ∼50% better for identifying the proteins with the best alignments in a sequence library. The time complexity of SAdLSA is O(N) thanks to GPU acceleration. Availability and implementation Datasets and source codes of SAdLSA are available free of charge for academic users at http://sites.gatech.edu/cssb/sadlsa/. Supplementary information Supplementary data are available at Bioinformatics online.

Theory, computation and experiment have matched up for the folding of small proteins in vitro, a difficult feat because folding energy landscapes are fairly smooth and free energy differences between states are small. Smoothness means that protein structure and folding are susceptible to the local environment inside living cells. Theory, computation and experiment are now exploring cellular modulation of energy landscapes. Interesting concepts have emerged, such as co-evolution of protein surfaces with their cellular environment to reduce detrimental interactions. Here we look at very recent work beginning to bring together theory, simulations and experiments in the area of protein landscape modulation, to see what problems might be solved in the near future by combining these approaches.

Sampling from the equilibrium distribution has always been a major problem in molecular simulations due to the very high dimensionality of the conformational space. Over several decades, many approaches have been used to overcome the problem. In particular, we focus on unbiased simulation methods such as parallel and adaptive sampling. Here, we recast adaptive sampling schemes on the basis of multi-armed bandits and develop a novel adaptive sampling algorithm under this framework, AdaptiveBandit. We test it on multiple simplified potentials and in a protein folding scenario. We find that this framework performs similarly to or better than previous methods in every type of test potential. Furthermore, it provides a novel framework to develop new sampling algorithms with better asymptotic characteristics.

Protein folding is a central challenge in computational biology, with important applications in molecular biology, drug discovery and catalyst design. As a hard combinatorial optimisation problem, it has been studied as a potential target problem for quantum annealing. Although several experimental implementations have been discussed in the literature, the computational scaling of these approaches has not been elucidated. In this article, we present a numerical study of quantum annealing applied to a large number of small peptide folding problems, aiming to infer useful insights for near-term applications. We present two conclusions: that even naive quantum annealing, when applied to protein lattice folding, has the potential to outperform classical approaches, and that careful engineering of the Hamiltonians and schedules involved can deliver notable relative improvements for this problem. Overall, our results suggest that quantum algorithms may well offer improvements for problems in the protein folding and structure prediction realm., Comment: 45 pages, 18 figures

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.

The correct folding of proteins is of paramount importance for their function, and protein misfolding is believed to be the primary cause of a wide range of diseases. Protein folding has been investigated with time-averaged methods and time-resolved spectroscopy, but observing the structural dynamics of the unfolding process in real-time is challenging. Here, we demonstrate an approach to directly reveal the structural changes in the unfolding reaction. We use nano- to millisecond time-resolved x-ray solution scattering to probe the unfolding of apomyoglobin. The unfolding reaction was triggered using a temperature jump, which was induced by a nanosecond laser pulse. We demonstrate a new strategy to interpret time-resolved x-ray solution scattering data, which evaluates ensembles of structures obtained from molecular dynamics simulations. We find that apomyoglobin passes three states when unfolding, which we characterize as native, molten globule, and unfolded. The molten globule dominates the population under the conditions investigated herein, whereas native and unfolded structures primarily contribute before the laser jump and 30 μs after it, respectively. The molten globule retains much of the native structure but shows a dynamic pattern of inter-residue contacts. Our study demonstrates a new strategy to directly observe structural changes over the cause of the unfolding reaction, providing time- and spatially resolved atomic details of the folding mechanism of globular proteins.