Going beyond clustering in MD trajectory analysis: an application to villin headpiece folding

Toward a Benchmark for Markov State Models: The Folding of HP35

Adopting a 300 μs long MD trajectory of the folding of villin headpiece (HP35) by D. E. Shaw Research, we recently constructed a Markov state model (MSM) based on inter-residue contacts. The model reproduces the folding time and predicts that the native basin and unfolded region consist of metastable substates that are structurally well-characterized. Recognizing the need to establish well-defined benchmark problems, we study to what extent and in what sense this MSM can be employed as a reference model. Hence, we test the robustness of the MSM by comparing it to models that use alternative combinations of features, dimensionality reduction methods, and clustering schemes. The study suggests some main characteristics of the folding of HP35 that should be reproduced by other competitive models. Moreover, the discussion reveals which parts of the MSM workflow matter most for the considered problem and illustrates the promises and pitfalls of state-based models for the interpretation of biomolecular simulations.

Selecting Features for Markov Modeling: A Case Study on HP35

Markov state models represent a popular means to interpret molecular dynamics trajectories in terms of memoryless transitions between metastable conformational states. To provide a mechanistic understanding of the considered biomolecular process, these states should reflect structurally distinct conformations and ensure a time scale separation between fast intrastate and slow interstate dynamics. Adopting the folding of villin headpiece (HP35) as a well-established model problem, here we discuss the selection of suitable input coordinates or "features", such as backbone dihedral angles and interresidue distances. We show that dihedral angles account accurately for the structure of the native energy basin of HP35, while the unfolded region of the free energy landscape and the folding process are best described by tertiary contacts of the protein. To construct a contact-based model, we consider various ways to define and select contact distances and introduce a low-pass filtering of the feature trajectory as well as a correlation-based characterization of states. Relying on input data that faithfully account for the mechanistic origin of the studied process, the states of the resulting Markov model are clearly discriminated by the features, describe consistently the hierarchical structure of the free energy landscape, and─as a consequence─correctly reproduce the slow time scales of the process.

Iterative Landmark-Based Umbrella Sampling (ILBUS) Protocol for Sampling of Conformational Space of Biomolecules

Computer simulations of biomolecules such as molecular dynamics often suffer from insufficient sampling. Due to limited computational resources, insufficient sampling prevents obtaining proper equilibrium distributions of observed properties. To deal with this problem, we proposed a simulation protocol for efficient resampling of collected off-equilibrium trajectories. These trajectories are utilized for the initial mapping of the conformational space, which is later properly resampled by the introduced Iterative Landmark-Based Umbrella Sampling (ILBUS) method. Reconstruction of static equilibrium properties is achieved by the multistate Bennett acceptance ratio (MBAR) method, which enables efficient use of simulated data. The ILBUS protocol is geometry-based and does not demand any additional collective variable or a dimensional-reduction technique. The only requirement is a set of suitably spaced reference conformations, which serve as landmarks in the mapped conformational space. Additionally, the ILBUS protocol encompasses an iterative process that optimizes the force constant used in the umbrella sampling simulation. Such tuning is an inherent feature of the protocol and does not need to be performed by the user in advance. Furthermore, even the simulations with suboptimal force constants can be used in estimates by MBAR. We demonstrate the feasibility and the performance of this approach in the study of the conformational landscape of the alanine dipeptide, met-enkephalin, and adenylate kinase.

Data-Driven Molecular Dynamics: A Multifaceted Challenge

The big data concept is currently revolutionizing several fields of science including drug discovery and development. While opening up new perspectives for better drug design and related strategies, big data analysis strongly challenges our current ability to manage and exploit an extraordinarily large and possibly diverse amount of information. The recent renewal of machine learning (ML)-based algorithms is key in providing the proper framework for addressing this issue. In this respect, the impact on the exploitation of molecular dynamics (MD) simulations, which have recently reached mainstream status in computational drug discovery, can be remarkable. Here, we review the recent progress in the use of ML methods coupled to biomolecular simulations with potentially relevant implications for drug design. Specifically, we show how different ML-based strategies can be applied to the outcome of MD simulations for gaining knowledge and enhancing sampling. Finally, we discuss how intrinsic limitations of MD in accurately modeling biomolecular systems can be alleviated by including information coming from experimental data.

Machine learning approach for accurate backmapping of coarse-grained models to all-atom models

Four different machine learning (ML) regression models: artificial neural network, k-nearest neighbors, Gaussian process regression and random forest were built to backmap coarse-grained models to all-atom models.

PCAViz: An Open-Source Python/JavaScript Toolkit for Visualizing Molecular Dynamics Simulations in the Web Browser

Molecular dynamics (MD) simulations reveal molecular motions at atomic resolution. Recent advances in high-performance computing now enable microsecond-long simulations capable of sampling a wide range of biologically relevant events. But the disk space required to store an MD trajectory increases with simulation length and system size, complicating collaborative sharing and visualization. To overcome these limitations, we created PCAViz, an open-source toolkit for sharing and visualizing MD trajectories via the web browser. PCAViz includes two components: the PCAViz Compressor, which compresses and saves simulation data; and the PCAViz Interpreter, which decompresses the data in users’ browsers and feeds it to any of several browser-based molecular-visualization libraries (e.g., 3Dmol.js, NGL Viewer, etc.). An easy-to-install WordPress plugin enables “plug-and-play” trajectory visualization. PCAViz will appeal to a broad audience of researchers and educators. The source code is available at http://durrantlab.com/pcaviz/, and the WordPress plugin is available via the official WordPress Plugin Directory.

Unrolr: Structural analysis of protein conformations using stochastic proximity embedding

Molecular dynamics (MD) simulations are widely used to explore the conformational space of biological macromolecules. Advances in hardware, as well as in methods, make the generation of large and complex MD datasets much more common. Although different clustering and dimensionality reduction methods have been applied to MD simulations, there remains a need for improved strategies that handle nonlinear data and/or can be applied to very large datasets. We present an original implementation of the pivot-based version of the stochastic proximity embedding method aimed at large MD datasets using the dihedral distance as a metric. The advantages of the algorithm in terms of data storage and computational efficiency are presented, as well as the implementation realized. Application and testing through the analysis of a 200 ns accelerated MD simulation of a 35-residue villin headpiece is discussed. Analysis of the simulation shows the promise of this method to organize large conformational ensembles. © 2018 Wiley Periodicals, Inc.

Machine-Learning Enabled New Insights into the Coil-to-Globule Transition of Thermosensitive Polymers Using a Coarse-Grained Model

We present a computational framework that integrates coarse-grained (CG) molecular dynamics (MD) simulations and a data-driven machine-learning (ML) method to gain insights into the conformations of polymers in solutions. We employ this framework to study conformational transition of a model thermosensitive polymer, poly( N-isopropylacrylamide) (PNIPAM). Here, we have developed the first of its kind, a temperature-independent CG model of PNIPAM that can accurately predict its experimental lower critical solution temperature (LCST) while retaining the tacticity in the presence of an explicit water model. The CG model was extensively validated by performing CG MD simulations with different initial conformations, varying the radius of gyration of chain, the chain length, and the angle between the adjacent monomers of the initial configuration of PNIPAM (total simulation time = 90 μs). Moreover, for the first time, we utilize the nonmetric multidimensional scaling (NMDS) method, a data-driven ML approach, to gain further insights into the mechanisms and pathways of this coil-to-globule transition by analyzing CG MD simulation trajectories. NMDS analysis provides entirely new insights and shows multiple metastable states of PNIPAM during its coil-to-globule transition above the LCST.

Using Spectral Representation to Classify Proteins' Conformational States

Numerous proteins are molecular targets for drug action and hence are important in drug discovery. Structure-based computational drug discovery relies on detailed information regarding protein conformations for subsequent drug screening in silico. There are two key issues in analyzing protein conformations in virtual screening. The first considers the protein’s conformational change in response to physical and chemical conditions. The second is the protein’s atomic resolution reconstruction from X-ray crystallography or nuclear magnetic resonance (NMR) data. In this latter problem, information is needed regarding the sample’s position relative to the source of X-rays. Here, we introduce a new measure for classifying protein conformational states using spectral representation and Wigner’s D-functions. Predictions based on the new measure are in good agreement with conformational states of proteins. These results could also be applied to improve conformational alignment of the snapshots given by protein crystallography.

Towards the SMART workflow system for computational spectroscopy

Is it possible to convert highly specialized research in the field of computational spectroscopy into robust and user-friendly aids to experiments and industrial applications?

Predicting protein backbone chemical shifts from Cα coordinates: extracting high resolution experimental observables from low resolution models

Given the demonstrated utility of coarse-grained modeling and simulations approaches in studying protein structure and dynamics, developing methods that allow experimental observables to be directly recovered from coarse-grained models is of great importance. In this work, we develop one such method that enables protein backbone chemical shifts (¹HN, ¹Hα, ¹³Cα, ¹³C, ¹³Cβ, and ¹⁵N) to be predicted from Cα coordinates. We show that our Cα-based method, LARMOR^Cα, predicts backbone chemical shifts with comparable accuracy to some all-atom approaches. More importantly, we demonstrate that LARMOR^Cα predicted chemical shifts are able to resolve native structure from decoy pools that contain both native and non-native models, and so it is sensitive to protein structure. As an application, we use LARMOR^Cα to characterize the transient state of the fast-folding protein gpW using recently published NMR relaxation dispersion derived backbone chemical shifts. The model we obtain is consistent with the previously proposed model based on independent analysis of the chemical shift dispersion pattern of the transient state. We anticipate that LARMOR^Cα will find utility as a tool that enables important protein conformational substates to be identified by “parsing” trajectories and ensembles generated using coarse-grained modeling and simulations.

Computational Design of Biomimetic Phosphate Scavengers

Phosphorus has long been the target of much research, but in recent years the focus has shifted from being limited only to reducing its detrimental environmental impact, to also looking at how it is linked to the global food security. Therefore, the interest in finding novel techniques for phosphorus recovery, as well as improving existing techniques, has increased. In this study we apply a hybrid simulation approach of molecular dynamics and quantum mechanics to investigate the binding modes of phosphate anions by a small intrinsically disordered peptide. Our results confirm that the conformational ensemble of the peptide is significantly changed, or stabilized, by the binding of phosphate anions and that binding does not take place purely as a result of a stable P-loop binding nest, but rather that multiple binding modes may be involved. Such small synthetic peptides capable of binding phosphate could be the starting point of new novel technological approaches toward phosphorus recovery, and they represent an excellent model system for investigating the nature and dynamics of functional de novo designed intrinsically disordered proteins.

Fast recovery of free energy landscapes via diffusion-map-directed molecular dynamics

The reaction pathways characterizing macromolecular systems of biological interest are associated with high free energy barriers. Resorting to the standard all-atom molecular dynamics (MD) to explore such critical regions may be inappropriate as the time needed to observe the relevant transitions can be remarkably long. In this paper, we present a new method called Extended Diffusion-Map-directed Molecular Dynamics (extended DM-d-MD) used to enhance the sampling of MD trajectories in such a way as to rapidly cover all important regions of the free energy landscape including deep metastable states and critical transition paths. Moreover, extended DM-d-MD was combined with a reweighting scheme enabling to save on-the-fly information about the Boltzmann distribution. Our algorithm was successfully applied to two systems, alanine dipeptide and alanine-12. Due to the enhanced sampling, the Boltzmann distribution is recovered much faster than in plain MD simulations. For alanine dipeptide, we report a speedup of one order of magnitude with respect to plain MD simulations. For alanine-12, our algorithm allows us to highlight all important unfolded basins in several days of computation when one single misfolded event is barely observable within the same amount of computational time by plain MD simulations. Our method is reaction coordinate free, shows little dependence on the a priori knowledge of the system, and can be implemented in such a way that the biased steps are not computationally expensive with respect to MD simulations thus making our approach well adapted for larger complex systems from which little information is known.

Structural cluster analysis of chemical reactions in solution

We introduce a simple and general approach to the problem of clustering structures from atomic trajectories of chemical reactions in solution. By considering distance metrics which are invariant under permutation of identical atoms or molecules, we demonstrate that it is possible to automatically resolve as distinct structural clusters the configurations corresponding to reactants, products, and transition states, even in presence of atom-exchanges and of hundreds of solvent molecules. Our approach strongly simplifies the analysis of large trajectories and it opens the way to the construction of kinetic network models of activated processes in solution employing the available efficient schemes developed for proteins conformational ensembles.

Electronic polarization stabilizes tertiary structure prediction of HP-36

Molecular dynamic (MD) simulations with both implicit and explicit solvent models have been carried out to study the folding dynamics of HP-36 protein. Starting from the extended conformation, the secondary structure of all three helices in HP-36 was formed in about 50 ns and remained stable in the remaining simulation. However, the formation of the tertiary structure was difficult. Although some intermediates were close to the native structure, the overall conformation was not stable. Further analysis revealed that the large structure fluctuation of loop and hydrophobic core regions was devoted mostly to the instability of the structure during MD simulation. The backbone root-mean-square deviation (RMSD) of the loop and hydrophobic core regions showed strong correlation with the backbone RMSD of the whole protein. The free energy landscape indicated that the distribution of main chain torsions in loop and turn regions was far away from the native state. Starting from an intermediate structure extracted from the initial AMBER simulation, HP-36 was found to generally fold to the native state under the dynamically adjusted polarized protein-specific charge (DPPC) simulation, while the peptide did not fold into the native structure when AMBER force filed was used. The two best folded structures were extracted and taken into further simulations in water employing AMBER03 charge and DPPC for 25 ns. Result showed that introducing polarization effect into interacting potential could stabilize the near-native protein structure.

Collecting and assessing human lactate dehydrogenase-A conformations for structure-based virtual screening

Human lactate dehydrogenase-A (LDHA) is emerging as a promising anticancer target. Up to now, structure-based investigations for identifying inhibitors of this enzyme have not explicitly accounted for active site flexibility. In the present study, by combining replica exchange molecular dynamics with network and cluster analyses, we identified reliable LDHA conformations for structure-based ligand design. The selected conformations were challenged and validated by retrospective virtual screening simulations.

MOLECULAR DYNAMICS SIMULATIONS OF HELIX BUNDLE PROTEINS USING UNRES FORCE FIELD AND ALL-ATOM FORCE FIELD

We have investigated the folding of two helix-bundle proteins, 36-residue Villin headpiece and 56-residue E-domain of Staphylococcal protein A, by combining molecular dynamics (MD) simulations with Coarse-Grained United-Residue (UNRES) Force Field and all-atom force field. Starting from extended structures, each of the proteins was folded to a stable structure within a short time frame using the UNRES model. However, the secondary structures of helices were not well formed. Further refinement using MD simulations with the all-atom force field was able to fold the protein structure into the native-like state with the smallest main-chain root-mean-square deviation of around 3 Å. Detailed analysis of the folding trajectories was presented and the performance of GPU-based MD simulations was also discussed.

Thermal unfolding pathway of PHD2 catalytic domain in three different PHD2 species: computational approaches

Prolyl hydroxylase domain 2 containing protein (PHD2) is a key protein in regulation of angiogenesis and metastasis. In normoxic condition, PHD2 triggers the degradation of hypoxia-inducible factor 1 (HIF-1α) that induces the expression of hypoxia response genes. Therefore the correct function of PHD2 would inhibit angiogenesis and consequent metastasis of tumor cells in normoxic condition. PHD2 mutations were reported in some common cancers. However, high levels of HIF-1α protein were observed even in normoxic metastatic tumors with normal expression of wild type PHD2. PHD2 malfunctions due to protein misfolding may be the underlying reason of metastasis and invasion in such cases. In this study, we scrutinize the unfolding pathways of the PHD2 catalytic domain’s possible species and demonstrate the properties of their unfolding states by computational approaches. Our study introduces the possibility of aggregation disaster for the prominent species of PHD2 during its partial unfolding. This may justify PHD2 inability to regulate HIF-1α level in some normoxic tumor types.

Native state conformational heterogeneity of HP35 revealed by time-resolved FRET

The villin headpiece subdomain (HP35) has become one of the most widely used model systems in protein folding studies, due to its small size and ultrafast folding kinetics. Here, we use HP35 as a test bed to show that the fluorescence decay kinetics of an unnatural amino acid, p-cyanophenylalanine (Phe(CN)), which are modulated by a nearby quencher (e.g., tryptophan or 7-azatryptophan) through the mechanism of fluorescence resonance energy transfer (FRET), can be used to detect protein conformational heterogeneity. This method is based on the notion that protein conformations having different donor-acceptor distances and interconverting slowly compared to the fluorescence lifetime of the donor (Phe(CN)) would exhibit different donor fluorescence lifetimes. Our results provide strong evidence suggesting that the native free energy basin of HP35 is populated with conformations that differ mostly in the position and mean helicity of the C-terminal helix. This finding is consistent with several previous experimental and computational studies. Moreover, this result holds strong implications for computational investigation of the folding mechanism of HP35.

Structural Characterization of λ-Repressor Folding from All-Atom Molecular Dynamics Simulations

The five-helix bundle λ-repressor fragment is a fast-folding protein. A length of 80 amino acid residues puts it on the large end among all known microsecond folders and its size poses a computational challenge for molecular dynamics (MD) studies. We simulated the folding of a novel λ-repressor fast-folding mutant (λ-HG) in explicit solvent using an all-atom description. By means of a recently developed tempering method, we observed reversible folding and unfolding of λ-repressor in a 10-microsecond trajectory. The folding kinetics was also investigated through a set of MD simulations run at different temperatures that together covered more than 125 microseconds. The protein was seen to fold into a native-like topology at intermediate temperature and a slow-folding pathway was identified. The simulations suggest new experimental observables for better monitoring the folding process, and a novel mutation expected to accelerate λ-repressor folding.

Conformational dynamics of human IAPP monomers

We study the conformational dynamics of the human Islet Amyloid Polypeptide (hIAPP) molecule - a 37 residue-long peptide associated to type 2 diabetes - using molecular dynamics (MD) simulations. We identify partially structured conformational states of the hIAPP monomer, categorized by both end-to-end distance and secondary structure, as suggested by previous experimental and computational studies. The MD trajectories of hIAPP are analyzed using data-driven methods, in particular principal component analysis, in order to identify preferred conformational states of the amylin monomer and to discuss their relative stability as compared to corresponding states in the amylin dimer. These potential hIAPP conformational states could be further tested and described experimentally, or in conjunction with modern computational analysis tools such as Markov state-based methods for extracting kinetics and thermodynamics from atomistic MD trajectories.

Identifying Metastable States of Folding Proteins

Recent molecular dynamics simulations of biopolymers have shown that in many cases the global features of the free energy landscape can be characterized in terms of the metastable conformational states of the system. To identify these states, a conceptionally and computationally simple approach is proposed. It consists of (i) an initial preprocessing via principal component analysis to reduce the dimensionality of the data, followed by k-means clustering to generate up to 10(4) microstates, (ii) the most probable path algorithm to identify the metastable states of the system, and (iii) boundary corrections of these states via the introduction of cluster cores in order to obtain the correct dynamics. By adopting two well-studied model problems, hepta-alanine and the villin headpiece protein, the potential and the performance of the approach are demonstrated.

Insights into Ligand-Protein Binding from Local Mechanical Response

Computational studies of ligand–protein binding are crucial for properly designing novel compounds of potential pharmacological interest. In this respect, researchers are increasingly interested in steered molecular dynamics for ligand–protein binding and unbinding studies. In particular, it has been suggested that analyzing the work profiles along the ligand–protein undocking paths could be fruitful. Here, we propose that small portions of work profiles, termed “local mechanical responses” of the system to a steering force, could serve as a universal measure for capturing relevant information about the system under investigation. Specifically, we first collected a high number of steering trajectories using two biological systems of increasing complexity (i.e., alanine dipeptide and (R)-roscovitine/CDK5 complex). Then, we devised a novel postprocessing tool to be applied to the local mechanical responses, to extract structural information related to the biological processes under investigation. Despite the out-of-equilibrium character of the trajectories, the analysis carried out on the work profiles provided pivotal information about the investigated biological processes. This could eventually be applied to drug design.

Bridging the Gap between Folding Simulations and Experiments: The Case of the Villin Headpiece

The increasing accuracy of molecular dynamics force fields parameters and the increasing resolution of experimental results allow one to carefully compare and complement in silico data with experimental observations. Here, we study the human villin headpiece C-terminal helical subdomain (HP35) with the recent highly optimized Amber99SB*-ILDN force field and compare the results with recent high resolution triplet-triplet energy transfer (TTET) experiments. The correct reproduction of the main structural features reveals a good agreement between experimental data and simulations.

The protein folding network indicates that the ultrafast folding mutant of villin headpiece subdomain has a deeper folding funnel

Protein folding is a dynamic process with continuous transitions among different conformations. In this work, the dynamics in the protein folding network of villin headpiece subdomain (HP35) has been investigated based on multiple reversible folding trajectories of HP35 and its ultrafast folding mutant where sub-angstrom folding was achieved. The four folding states were clearly separated on the network, validating the classification of the states. Examination of the eight conformers with different formation of the individual helices revealed high plasticity of the three helices in all the four states. A consistent feature between the wild type and mutant protein is the dominant conformer 111 (all three helices formed) in the folded state and conformers 111 and 011 (helices II and III formed) in the major intermediate state, indicating the critical role of helices II and III in the folding mechanism. When compared to the wild type, the folding landscape of the ultrafast folding mutant exhibited a deeper folding funnel towards the folded state. The very beginning of the folding (0-10 ns) was very similar for both protein variants but it soon diverged and displayed different folding pathways. Although going through the major intermediate state is the dominant pathway for both, it was also observed that some folding went through the minor intermediate state for the mutant. The intriguing difference resulting from the mutation at two residues in helix III has been carefully analyzed and discussed in details.

Quantum clustering and network analysis of MD simulation trajectories to probe the conformational ensembles of protein-ligand interactions

In this article, we present a novel application of a quantum clustering (QC) technique to objectively cluster the conformations, sampled by molecular dynamics simulations performed on different ligand bound structures of the protein. We further portray each conformational population in terms of dynamically stable network parameters which beautifully capture the ligand induced variations in the ensemble in atomistic detail. The conformational populations thus identified by the QC method and verified by network parameters are evaluated for different ligand bound states of the protein pyrrolysyl-tRNA synthetase (DhPylRS) from D. hafniense. The ligand/environment induced re-distribution of protein conformational ensembles forms the basis for understanding several important biological phenomena such as allostery and enzyme catalysis. The atomistic level characterization of each population in the conformational ensemble in terms of the re-orchestrated networks of amino acids is a challenging problem, especially when the changes are minimal at the backbone level. Here we demonstrate that the QC method is sensitive to such subtle changes and is able to cluster MD snapshots which are similar at the side-chain interaction level. Although we have applied these methods on simulation trajectories of a modest time scale (20 ns each), we emphasize that our methodology provides a general approach towards an objective clustering of large-scale MD simulation data and may be applied to probe multistate equilibria at higher time scales, and to problems related to protein folding for any protein or protein-protein/RNA/DNA complex of interest with a known structure.

Molecular modelling studies on Arylthioindoles as potent inhibitors of tubulin polymerization

The crucial role played by microtubules in the life of eukaryotic cell makes tubulin an important route for the anticancer therapy. The Arylthioindoles (ATIs) along with the corresponding ketone and methylene compounds are potent tubulin assembly inhibitors. We are here reporting the result of a series of docking and molecular dynamics experiments on this series of compounds. The results obtained from our in silico studies not only provided us with an insight on the nature of the binding of the ATIs to tubulin, but were also at the core of the design of a new series of potent inhibitors of tubulin polymerization.

Folding network of villin headpiece subdomain

Protein folding is a complex multidimensional process that is difficult to illustrate by the traditional analyses based on one- or two-dimensional profiles. Analyses based on transition networks have become an alternative approach that has the potential to reveal detailed features of protein folding dynamics. However, due to the lack of successful reversible folding of proteins from conventional molecular-dynamics simulations, this approach has rarely been utilized. Here, we analyzed the folding network from several 10 μs conventional molecular-dynamics reversible folding trajectories of villin headpiece subdomain (HP35). The folding network revealed more complexity than the traditional two-dimensional map and demonstrated a variety of conformations in the unfolded state, intermediate states, and the native state. Of note, deep enthalpic traps at the unfolded state were observed on the folding landscape. Furthermore, in contrast to the clear separation of the native state and the primary intermediate state shown on the two-dimensional map, the two states were mingled on the folding network, and prevalent interstate transitions were observed between these two states. A more complete picture of the folding mechanism of HP35 emerged when the traditional and network analyses were considered together.

Challenges in protein folding simulations: Timescale, representation, and analysis

Experimental studies of protein folding processes are frequently hampered by the fact that only low resolution structural data can be obtained with sufficient temporal resolution. Molecular dynamics simulations offer a complementary approach, providing extremely high resolution spatial and temporal data on folding processes. The effectiveness of such simulations is currently hampered by continuing questions regarding the ability of molecular dynamics force fields to reproduce the true potential energy surfaces of proteins, and ongoing difficulties with obtaining sufficient sampling to meaningfully comment on folding mechanisms. We review recent progress in the simulation of three common model systems for protein folding, and discuss how recent advances in technology and theory are allowing protein folding simulations to address their current shortcomings.

Dynamics of protein folding: probing the kinetic network of folding-unfolding transitions with experiment and theory

The problem of spontaneous folding of amino acid chains into highly organized, biologically functional three-dimensional protein structures continues to challenge the modern science. Understanding how proteins fold requires characterization of the underlying energy landscapes as well as the dynamics of the polypeptide chains in all stages of the folding process. In recent years, important advances toward these goals have been achieved owing to the rapidly growing interdisciplinary interest and significant progress in both experimental techniques and theoretical methods. Improvements in the experimental time resolution led to determination of the timescales of the important elementary events in folding, such as formation of secondary structure and tertiary contacts. Sensitive single molecule methods made possible probing the distributions of the unfolded and folded states and following the folding reaction of individual protein molecules. Discovery of proteins that fold in microseconds opened the possibility of atomic-level theoretical simulations of folding and their direct comparisons with experimental data, as well as of direct experimental observation of the barrier-less folding transition. The ultra-fast folding also brought new questions, concerning the intrinsic limits of the folding rates and experimental signatures of barrier-less "downhill" folding. These problems will require novel approaches for even more detailed experimental investigations of the folding dynamics as well as for the analysis of the folding kinetic data. For theoretical simulations of folding, a main challenge is how to extract the relevant information from overwhelmingly detailed atomistic trajectories. New theoretical methods have been devised to allow a systematic approach towards a quantitative analysis of the kinetic network of folding-unfolding transitions between various configuration states of a protein, revealing the transition states and the associated folding pathways at multiple levels, from atomistic to coarse-grained representations. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

Modelling proteins: conformational sampling and reconstruction of folding kinetics

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