Hierarchy of folding and unfolding events of protein G,CI2, and ACBP from explicit-solvent simulations

Sampling a Rare Protein Transition Using Quantum Annealing

Simulating spontaneous structural rearrangements in macromolecules with classical molecular dynamics is an outstanding challenge. Conventional supercomputers can access time intervals of up to tens of μs, while many key events occur on exponentially longer time scales. Path sampling techniques have the advantage of focusing the computational power on barrier-crossing trajectories, but generating uncorrelated transition paths that explore diverse conformational regions remains a problem. We employ a hybrid path-sampling paradigm that addresses this issue by generating trial transition paths using a quantum annealing (QA) machine. We first employ a classical computer to perform an uncharted exploration of the conformational space. The data set generated in this exploration is then postprocessed using a path integral-based method to yield a coarse-grained network representation of the reactive kinetics. By resorting to a quantum annealer, quantum superposition can be exploited to encode all of the transition pathways in the initial quantum state, thus potentially solving the path exploration problem. Furthermore, each QA cycle yields a completely uncorrelated trial trajectory. We previously validated this scheme on a prototypically simple transition, which could be extensively characterized on a desktop computer. Here, we scale up in complexity and perform an all-atom simulation of a protein conformational transition that occurs on the millisecond time scale, obtaining results that match those of the Anton special-purpose supercomputer. Despite limitations due to the available quantum annealers, our study highlights how realistic biomolecular simulations provide potentially impactful new ground for applying, testing, and advancing quantum technologies.

Structure of the space of folding protein sequences defined by large language models

Proteins populate a manifold in the high-dimensional sequence space whose geometrical structure guides their natural evolution. Leveraging recently-developed structure prediction tools based on transformer models, we first examine the protein sequence landscape as defined by an effective energy that is a proxy of sequence foldability. This landscape shares characteristics with optimization challenges encountered in machine learning and constraint satisfaction problems. Our analysis reveals that natural proteins predominantly reside in wide, flat minima within this energy landscape. To investigate further, we employ statistical mechanics algorithms specifically designed to explore regions with high local entropy in relatively flat landscapes. Our findings indicate that these specialized algorithms can identify valleys with higher entropy compared to those found using traditional methods such as Monte Carlo Markov Chains. In a proof-of-concept case, we find that these highly entropic minima exhibit significant similarities to natural sequences, especially in critical key sites and local entropy. Additionally, evaluations through Molecular Dynamics suggests that the stability of these sequences closely resembles that of natural proteins. Our tool combines advancements in machine learning and statistical physics, providing new insights into the exploration of sequence landscapes where wide, flat minima coexist alongside a majority of narrower minima.

Multi-eGO: Model Improvements toward the Study of Complex Self-Assembly Processes

Structure-based models have been instrumental in simulating protein folding and suggesting hypotheses about the mechanisms involved. Nowadays, at least for fast-folding proteins, folding can be simulated in explicit solvent using classical molecular dynamics. However, other self-assembly processes, such as protein aggregation, are still far from being accessible. Recently, we proposed that a hybrid multistate structure-based model, multi-eGO, could help to bridge the gap toward the simulation of out-of-equilibrium, concentration-dependent self-assembly processes. Here, we further improve the model and show how multi-eGO can effectively and accurately learn the conformational ensemble of the amyloid β42 intrinsically disordered peptide, reproduce the well-established folding mechanism of the B1 immunoglobulin-binding domain of streptococcal protein G, and reproduce the aggregation as a function of the concentration of the transthyretin 105-115 amyloidogenic peptide. We envision that by learning from the dynamics of a few minima, multi-eGO can become a platform for simulating processes inaccessible to other simulation techniques.

Computer-aided comprehensive explorations of RNA structural polymorphism through complementary simulation methods

While RNA folding was originally seen as a simple problem to solve, it has been shown that the promiscuous interactions of the nucleobases result in structural polymorphism, with several competing structures generally observed for non-coding RNA. This inherent complexity limits our understanding of these molecules from experiments alone, and computational methods are commonly used to study RNA. Here, we discuss three advanced sampling schemes, namely Hamiltonian-replica exchange molecular dynamics (MD), ratchet-and-pawl MD and discrete path sampling, as well as the HiRE-RNA coarse-graining scheme, and highlight how these approaches are complementary with reference to recent case studies. While all computational methods have their shortcomings, the plurality of simulation methods leads to a better understanding of experimental findings and can inform and guide experimental work on RNA polymorphism.

Slow Escape from a Helical Misfolded State of the Pore-Forming Toxin Cytolysin A

The pore-forming toxin cytolysin A (ClyA) is expressed as a large α-helical monomer that, upon interaction with membranes, undergoes a major conformational rearrangement into the protomer conformation, which then assembles into a cytolytic pore. Here, we investigate the folding kinetics of the ClyA monomer with single-molecule Förster resonance energy transfer spectroscopy in combination with microfluidic mixing, stopped-flow circular dichroism experiments, and molecular simulations. The complex folding process occurs over a broad range of time scales, from hundreds of nanoseconds to minutes. The very slow formation of the native state occurs from a rapidly formed and highly collapsed intermediate with large helical content and nonnative topology. Molecular dynamics simulations suggest pronounced non-native interactions as the origin of the slow escape from this deep trap in the free-energy surface, and a variational enhanced path-sampling approach enables a glimpse of the folding process that is supported by the experimental data.

Fast and flexible coarse-grained prediction of protein folding routes using ensemble modeling and evolutionary sequence variation

MOTIVATION

Protein folding is a dynamic process through which polypeptide chains reach their native 3D structures. Although the importance of this mechanism is widely acknowledged, very few high-throughput computational methods have been developed to study it.

RESULTS

In this paper, we report a computational platform named P3Fold that combines statistical and evolutionary information for predicting and analyzing protein folding routes. P3Fold uses coarse-grained modeling and efficient combinatorial schemes to predict residue contacts and evaluate the folding routes of a protein sequence within minutes or hours. To facilitate access to this technology, we devise graphical representations and implement an interactive web interface that allows end-users to leverage P3Fold predictions. Finally, we use P3Fold to conduct large and short scale experiments on the human proteome that reveal the broad conservation and variations of structural intermediates within protein families.

AVAILABILITY AND IMPLEMENTATION

A Web server of P3Fold is freely available at http://csb.cs.mcgill.ca/P3Fold.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Successes and challenges in simulating the folding of large proteins

Computational simulations of protein folding can be used to interpret experimental folding results, to design new folding experiments, and to test the effects of mutations and small molecules on folding. However, whereas major experimental and computational progress has been made in understanding how small proteins fold, research on larger, multidomain proteins, which comprise the majority of proteins, is less advanced. Specifically, large proteins often fold via long-lived partially folded intermediates, whose structures, potentially toxic oligomerization, and interactions with cellular chaperones remain poorly understood. Molecular dynamics based folding simulations that rely on knowledge of the native structure can provide critical, detailed information on folding free energy landscapes, intermediates, and pathways. Further, increases in computational power and methodological advances have made folding simulations of large proteins practical and valuable. Here, using serpins that inhibit proteases as an example, we review native-centric methods for simulating the folding of large proteins. These synergistic approaches range from Gō and related structure-based models that can predict the effects of the native structure on folding to all-atom-based methods that include side-chain chemistry and can predict how disease-associated mutations may impact folding. The application of these computational approaches to serpins and other large proteins highlights the successes and limitations of current computational methods and underscores how computational results can be used to inform experiments. These powerful simulation approaches in combination with experiments can provide unique insights into how large proteins fold and misfold, expanding our ability to predict and manipulate protein folding.

All-Atom Simulations Reveal How Single-Point Mutations Promote Serpin Misfolding

Protein misfolding is implicated in many diseases, including serpinopathies. For the canonical inhibitory serpin α₁-antitrypsin, mutations can result in protein deficiencies leading to lung disease, and misfolded mutants can accumulate in hepatocytes, leading to liver disease. Using all-atom simulations based on the recently developed bias functional algorithm, we elucidate how wild-type α₁-antitrypsin folds and how the disease-associated S (Glu264Val) and Z (Glu342Lys) mutations lead to misfolding. The deleterious Z mutation disrupts folding at an early stage, whereas the relatively benign S mutant shows late-stage minor misfolding. A number of suppressor mutations ameliorate the effects of the Z mutation, and simulations on these mutants help to elucidate the relative roles of steric clashes and electrostatic interactions in Z misfolding. These results demonstrate a striking correlation between atomistic events and disease severity and shine light on the mechanisms driving chains away from their correct folding routes.

Transition path theory from biased simulations

Transition Path Theory (TPT) provides a rigorous framework to investigate the dynamics of rare thermally activated transitions. In this theory, a central role is played by the forward committor function q⁺(x), which provides the ideal reaction coordinate. Furthermore, the reactive dynamics and kinetics are fully characterized in terms of two time-independent scalar and vector distributions. In this work, we develop a scheme which enables all these ingredients of TPT to be efficiently computed using the short non-equilibrium trajectories generated by means of a specific combination of enhanced path sampling techniques. In particular, first we further extend the recently introduced self-consistent path sampling algorithm in order to compute the committor q⁺(x). Next, we show how this result can be exploited in order to define efficient algorithms which enable us to directly sample the transition path ensemble.

Emergent Properties of Antiagglomerant Films Control Methane Transport: Implications for Hydrate Management

The relationship between collective properties and performance of antiagglomerants (AAs) used in hydrate management is handled using molecular dynamics simulations and enhanced sampling techniques. A thin film of AAs adsorbed at the interface between one flat sII methane hydrate substrate and a fluid hydrocarbon mixture containing methane and n-dodecane is studied. The AA considered is a surface-active compound with a complex hydrophilic head that contains both amide and tertiary ammonium cation groups and hydrophobic tails. At a sufficiently high AA density, the interplay between the surfactant layer and the liquid hydrocarbon excludes methane from the interfacial region. In this scenario, we combine metadynamics and umbrella sampling frameworks to study accurately the free-energy landscape and the equilibrium rates associated with the transport of one methane molecule across the AA film. We observe that the local configurational changes of the liquid hydrocarbon packed within the AA film are associated with high free-energy barriers for methane transport. The time scales estimated for the transport of methane across the AA film can be, in some cases, comparable to those reported in the literature for the growth of hydrates, suggesting that one possible mechanism by which AAs delay the formation of hydrate plugs could be providing a barrier to methane transport. Considering the interplay between the structural design and collective properties of AAs might be of relevance to improve their performance in flow assurance.

Self-consistent calculation of protein folding pathways

We introduce an iterative algorithm to efficiently simulate protein folding and other conformational transitions, using state-of-the-art all-atom force fields. Starting from the Langevin equation, we obtain a self-consistent stochastic equation of motion, which directly yields the reaction pathways. From the solution of this set of equations we derive a stochastic estimate of the reaction coordinate. We validate this approach against the results of plain MD simulations of the folding of a small protein, which were performed on the Anton supercomputer. In order to explore the computational efficiency of this algorithm, we apply it to generate a folding pathway of a protein that consists of 130 amino acids and has a folding rate of the order of s^-1.

On-the-Fly Specifications of Reaction Coordinates in Parallel Cascade Selection Molecular Dynamics Accelerate Conformational Transitions of Proteins

Parallel Cascade Selection Molecular Dynamics (PaCS-MD) is an efficient conformational sampling method for generating a set of reactive trajectories that connect a given reactant and a product. In PaCS-MD, initial structures relevant to conformational transitions are reasonably selected by referring to a set of reaction coordinates (RCs), and short-time molecular dynamics (MD) simulations are independently launched from them. To efficiently perform PaCS-MD, specifications of RCs are essential, but specifying reasonable RCs is generally nontrivial. In the present study, we propose on-the-fly specifications of RCs as an extended PaCS-MD. In the present method, n types of RCs are provided as candidates a priori as follows: RC = (X₁, X₂, ..., X _n), and one of the RCs is specified in a cycle-dependent manner, i.e. the reasonable RC is searched at every cycle by evaluating gradients of the RCs, i.e. RC with the steepest gradient for cycle is regarded as the reasonable RC, and conformational resampling proceeds along it, promoting conformational transition of a given protein. For a demonstration, the extended PaCS-MD was applied to reproduce the open-closed conformational transition of T4 lysozyme (T4L). As candidates of possible RCs, (1) root-mean square distance, (2) principal coordinates, (3) accessible surface area, (4) radius of gyration, and (5) end-to-end distance were adopted in the cycle-dependent specifications of RCs. Through the demonstration, the extended PaCS-MD successfully reproduced the conformational transition from the open to closed states of T4L. As a more complicated practice, a dimerization process of diubiquitin was efficiently reproduced with the extended PaCS-MD, showing the high conformational sampling efficiency of the present algorithm. In contrast, the conventional PaCS-MD with a fixed RC sometimes failed to generate a set of reactive trajectories when an unreasonable RC was specified, i.e. the conformational sampling efficiency of PaCS-MD might more or less depend on the specified RCs. Judging from the present demonstrations, on-the-fly specifications of RCs might be effective in reproducing/predicting essential transitions of a given protein.

All-atom calculation of protein free-energy profiles

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

Efficient Sampling of Knotting-Unknotting Pathways for Semiflexible Gaussian Chains

We propose a stochastic method to generate exactly the overdamped Langevin dynamics of semi-flexible Gaussian chains, conditioned to evolve between given initial and final conformations in a preassigned time. The initial and final conformations have no restrictions, and hence can be in any knotted state. Our method allows the generation of statistically independent paths in a computationally efficient manner. We show that these conditioned paths can be exactly generated by a set of local stochastic differential equations. The method is used to analyze the transition routes between various knots in crossable filamentous structures, thus mimicking topological reconnections occurring in soft matter systems or those introduced in DNA by topoisomerase enzymes. We find that the average number of crossings, writhe and unknotting number are not necessarily monotonic in time and that more complex topologies than the initial and final ones can be visited along the route.

Folding Mechanism of Proteins Im7 and Im9: Insight from All-Atom Simulations in Implicit and Explicit Solvent

Im7 and Im9 are evolutionary related proteins with almost identical native structures. In spite of their structural similarity, experiments show that Im7 folds through a long-lived on-pathway intermediate, while Im9 folds according to two-state kinetics. In this work, we use a recently developed enhanced path sampling method to generate many folding trajectories for these proteins, using realistic atomistic force fields, in both implicit and explicit solvent. Overall, our results are in good agreement with the experimental ϕ values and with the result of ϕ-value-restrained molecular dynamics (MD) simulations. However, our implicit solvent simulations fail to predict a qualitative difference in the folding pathways of Im7 and Im9. In contrast, our simulations in explicit solvent correctly reproduce the fact that only protein Im7 folds through a on-pathway intermediate. By analyzing our atomistic trajectories, we provide a physical picture which explains the observed difference in the folding kinetics of these chains.

Numerical analysis of Pickering emulsion stability: insights from ABMD simulations

The issue of the stability of Pickering emulsions is tackled at a mesoscopic level using dissipative particle dynamics simulations within the Adiabatic Biased Molecular Dynamics framework. We consider the early stage of the coalescence process between two spherical water droplets in a decane solvent. The droplets are stabilized by Janus nanoparticles of different shapes (spherical and ellipsoidal) with different three-phase contact angles. Given a sufficiently dense layer of particles on the droplets, we show that the stabilization mechanism strongly depends on the collision speed. This is consistent with a coalescence mechanism governed by the rheology of the interfacial region. When the system is forced to coalesce sufficiently slowly, we investigate at a mesoscopic level how the ability of the nanoparticles to stabilize Pickering emulsions is discriminated by nanoparticle mobility and the associated caging effect. These properties are both related to the interparticle interaction and the hydrodynamic resistance in the liquid film between the approaching interfaces.

Computing Reaction Pathways of Rare Biomolecular Transitions using Atomistic Force-Fields

The Dominant Reaction Pathway (DRP) method is an approximate variational scheme which can be used to compute reaction pathways in conformational transitions undergone by large biomolecules (up to ~10(3) amino-acids) using realistic all-atom force fields. We first review the status of development of this method. Next, we discuss its validation against the results of plain MD protein folding simulations performed by the DE-Shaw group using the Anton supercomputer. Finally, we review a few representative applications of the DRP approach to study reactions which are far too complex and rare to be investigated by plain MD, even on the Anton machine.

Complex pathways in folding of protein G explored by simulation and experiment

The B1 domain of protein G has been a classic model system of folding for decades, the subject of numerous experimental and computational studies. Most of the experimental work has focused on whether the protein folds via an intermediate, but the evidence is mostly limited to relatively slow kinetic observations with a few structural probes. In this work we observe folding on the submillisecond timescale with microfluidic mixers using a variety of probes including tryptophan fluorescence, circular dichroism, and photochemical oxidation. We find that each probe yields different kinetics and compare these observations with a Markov State Model constructed from large-scale molecular dynamics simulations and find a complex network of states that yield different kinetics for different observables. We conclude that there are many folding pathways before the final folding step and that these paths do not have large free energy barriers.

Variational scheme to compute protein reaction pathways using atomistic force fields with explicit solvent

We introduce a variational approximation to the microscopic dynamics of rare conformational transitions of macromolecules. Within this framework it is possible to simulate on a small computer cluster reactions as complex as protein folding, using state of the art all-atom force fields in explicit solvent. We test this method against MD simulations of the folding of an α and a β protein performed with the same all-atom force field on the Anton supercomputer. We find that our approach yields results consistent with those of MD simulations, at a computational cost orders of magnitude smaller.

Serpin latency transition at atomic resolution

Protease inhibition by serpins requires a large conformational transition from an active, metastable state to an inactive, stable state. Similar reactions can also occur in the absence of proteases, and these latency transitions take hours, making their time scales many orders of magnitude larger than are currently accessible using conventional molecular dynamics simulations. Using a variational path sampling algorithm, we simulated the entire serpin active-to-latent transition in all-atom detail with a physically realistic force field using a standard computing cluster. These simulations provide a unifying picture explaining existing experimental data for the latency transition of the serpin plasminogen activator inhibitor-1 (PAI-1). They predict a long-lived intermediate that resembles a previously proposed, partially loop-inserted, prelatent state; correctly predict the effects of PAI-1 mutations on the kinetics; and provide a potential means to identify ligands able to accelerate the latency transition. Interestingly, although all of the simulated PAI-1 variants readily access the prelatent intermediate, this conformation is not populated in the active-to-latent transition of another serpin, α1-antitrypsin, which does not readily go latent. Thus, these simulations also help elucidate why some inhibitory serpin families are more conformationally labile than others.

Tracking conformational dynamics of polypeptides by nonlinear electronic spectroscopy of aromatic residues: a first-principles simulation study

The ability of nonlinear electronic spectroscopy to track folding/unfolding processes of proteins in solution by monitoring aromatic interactions is investigated by first-principles simulations of two-dimensional (2D) electronic spectra of a model peptide. A dominant reaction pathway approach is employed to determine the unfolding pathway of a tetrapeptide, which connects the initial folded configuration with stacked aromatic side chains and the final unfolded state with distant noninteracting aromatic residues. The π-stacking and excitonic coupling effects are included through ab initio simulations based on multiconfigurational methods within a hybrid quantum mechanics/molecular mechanics scheme. It is shown that linear absorption spectroscopy in the ultraviolet (UV) region is unable to resolve the unstacking dynamics characterized by the three-step process: T-shaped→twisted offset stacking→unstacking. Conversely, pump-probe spectroscopy can be used to resolve aromatic interactions by probing in the visible region, the excited-state absorptions (ESAs) that involve charge-transfer states. 2D UV spectroscopy offers the highest sensitivity to the unfolding process, by providing the disentanglement of ESA signals belonging to different aromatic chromophores and high correlation between the conformational dynamics and the quartic splitting.

The role of non-native interactions in the folding of knotted proteins: insights from molecular dynamics simulations

For several decades, the presence of knots in naturally-occurring proteins was largely ruled out a priori for its supposed incompatibility with the efficiency and robustness of folding processes. For this very same reason, the later discovery of several unrelated families of knotted proteins motivated researchers to look into the physico-chemical mechanisms governing the concerted sequence of folding steps leading to the consistent formation of the same knot type in the same protein location. Besides experiments, computational studies are providing considerable insight into these mechanisms. Here, we revisit a number of such recent investigations within a common conceptual and methodological framework. By considering studies employing protein models with different structural resolution (coarse-grained or atomistic) and various force fields (from pure native-centric to realistic atomistic ones), we focus on the role of native and non-native interactions. For various unrelated instances of knotted proteins, non-native interactions are shown to be very important for favoring the emergence of conformations primed for successful self-knotting events.

Characterization of the free-energy landscapes of proteins by NMR-guided metadynamics

The use of free-energy landscapes rationalizes a wide range of aspects of protein behavior by providing a clear illustration of the different states accessible to these molecules, as well as of their populations and pathways of interconversion. The determination of the free-energy landscapes of proteins by computational methods is, however, very challenging as it requires an extensive sampling of their conformational spaces. We describe here a technique to achieve this goal with relatively limited computational resources by incorporating nuclear magnetic resonance (NMR) chemical shifts as collective variables in metadynamics simulations. As in this approach the chemical shifts are not used as structural restraints, the resulting free-energy landscapes correspond to the force fields used in the simulations. We illustrate this approach in the case of the third Ig-binding domain of protein G from streptococcal bacteria (GB3). Our calculations reveal the existence of a folding intermediate of GB3 with nonnative structural elements. Furthermore, the availability of the free-energy landscape enables the folding mechanism of GB3 to be elucidated by analyzing the conformational ensembles corresponding to the native, intermediate, and unfolded states, as well as the transition states between them. Taken together, these results show that, by incorporating experimental data as collective variables in metadynamics simulations, it is possible to enhance the sampling efficiency by two or more orders of magnitude with respect to standard molecular dynamics simulations, and thus to estimate free-energy differences among the different states of a protein with a k(B)T accuracy by generating trajectories of just a few microseconds.

Folding pathways of a knotted protein with a realistic atomistic force field

We report on atomistic simulation of the folding of a natively-knotted protein, MJ0366, based on a realistic force field. To the best of our knowledge this is the first reported effort where a realistic force field is used to investigate the folding pathways of a protein with complex native topology. By using the dominant-reaction pathway scheme we collected about 30 successful folding trajectories for the 82-amino acid long trefoil-knotted protein. Despite the dissimilarity of their initial unfolded configuration, these trajectories reach the natively-knotted state through a remarkably similar succession of steps. In particular it is found that knotting occurs essentially through a threading mechanism, involving the passage of the C-terminal through an open region created by the formation of the native -sheet at an earlier stage. The dominance of the knotting by threading mechanism is not observed in MJ0366 folding simulations using simplified, native-centric models. This points to a previously underappreciated role of concerted amino acid interactions, including non-native ones, in aiding the appropriate order of contact formation to achieve knotting.

It has been recently observed that the native structure of proteins can contain knots. These are formed during the folding process and are tightened in a specific (i.e. native) location, along the poly-peptide chain. The existence of knots hence implies a high degree coordination of local and global conformational changes, during the folding reaction. In this work we investigate how the knot is formed and what are the dynamical mechanisms which drive the self-entanglement process. To this end, we report on the first atomistically detailed numerical simulation of the folding of a knotted protein, based on a realistic description of the inter-atomic forces. These simulations show that the knot is formed by following a specific sequence of contacts. The comparison of the findings with those based on simplified folding models suggest that the productive succession of contacts is aided by a concerted interplay of amino acid interactions, arguably including non-native ones.

Microscopically computing free-energy profiles and transition path time of rare macromolecular transitions

We introduce a rigorous method to microscopically compute the observables which characterize the thermodynamics and kinetics of rare macromolecular transitions for which it is possible to identify a priori a slow reaction coordinate. In order to sample the ensemble of statistically significant reaction pathways, we define a biased molecular dynamics (MD) in which barrier-crossing transitions are accelerated without introducing any unphysical external force. In contrast to other biased MD methods, in the present approach the systematic errors which are generated in order to accelerate the transition can be analytically calculated and therefore can be corrected for. This allows for a computationally efficient reconstruction of the free-energy profile as a function of the reaction coordinate and for the calculation of the corresponding diffusion coefficient. The transition path time can then be readily evaluated within the dominant reaction pathways approach. We illustrate and test this method by characterizing a thermally activated transition on a two-dimensional energy surface and the folding of a small protein fragment within a coarse-grained model.

Slow unfolded-state structuring in Acyl-CoA binding protein folding revealed by simulation and experiment

Protein folding is a fundamental process in biology, key to understanding many human diseases. Experimentally, proteins often appear to fold via simple two- or three-state mechanisms involving mainly native-state interactions, yet recent network models built from atomistic simulations of small proteins suggest the existence of many possible metastable states and folding pathways. We reconcile these two pictures in a combined experimental and simulation study of acyl-coenzyme A binding protein (ACBP), a two-state folder (folding time ~10 ms) exhibiting residual unfolded-state structure, and a putative early folding intermediate. Using single-molecule FRET in conjunction with side-chain mutagenesis, we first demonstrate that the denatured state of ACBP at near-zero denaturant is unusually compact and enriched in long-range structure that can be perturbed by discrete hydrophobic core mutations. We then employ ultrafast laminar-flow mixing experiments to study the folding kinetics of ACBP on the microsecond time scale. These studies, along with Trp-Cys quenching measurements of unfolded-state dynamics, suggest that unfolded-state structure forms on a surprisingly slow (~100 μs) time scale, and that sequence mutations strikingly perturb both time-resolved and equilibrium smFRET measurements in a similar way. A Markov state model (MSM) of the ACBP folding reaction, constructed from over 30 ms of molecular dynamics trajectory data, predicts a complex network of metastable stables, residual unfolded-state structure, and kinetics consistent with experiment but no well-defined intermediate preceding the main folding barrier. Taken together, these experimental and simulation results suggest that the previously characterized fast kinetic phase is not due to formation of a barrier-limited intermediate but rather to a more heterogeneous and slow acquisition of unfolded-state structure.

Dominant folding pathways of a WW domain

We investigate the folding mechanism of the WW domain Fip35 using a realistic atomistic force field by applying the Dominant Reaction Pathways approach. We find evidence for the existence of two folding pathways, which differ by the order of formation of the two hairpins. This result is consistent with the analysis of the experimental data on the folding kinetics of WW domains and with the results obtained from large-scale molecular dynamics simulations of this system. Free-energy calculations performed in two coarse-grained models support the robustness of our results and suggest that the qualitative structure of the dominant paths are mostly shaped by the native interactions. Computing a folding trajectory in atomistic detail only required about one hour on 48 Central Processing Units. The gain in computational efficiency opens the door to a systematic investigation of the folding pathways of a large number of globular proteins.

Exploring the role of topological frustration in actin refolding with molecular simulations

Actin plays crucial roles in the life of the cell while being notorious for its inability to reach a functional conformation without the help of assistant proteins. In eukaryotes, for example, the cytosolic chaperonin containing TCP-1 (CCT) and prefoldin (PFD) are required for actin folding assistance and prevention of protein aggregation in the crowded cellular environment. The folding of non-native actin is known to occur in a number of steps, but the reasons underlying its folding difficulty are unknown. Because a full, atomistic-level, investigation of the kinetics and thermodynamics of folding of such a large molecule is beyond computational reach, we focused our investigation on the role of topological frustration on the folding of actin. Namely, we studied the (re)folding of actin using simulations of a variant self-organized polymer model (SOP-DH) starting from a stretched state, leading to results that correlate well with experimentally driven conclusions and allowing us to make a number of testable predictions. Primarily, our simulations reveal that the successful refolding of the C-terminus end of actin occurs through a zipping process in which the α-helices wind up turn by turn upon formation of their native tertiary contacts. In turn, an early formation of the helical structure in this region of the chain has deleterious effects for actin's refolding fitness. Moreover, the C-terminus refolding is a very rare event in our simulations, in agreement with the large activation barrier predicted on the basis of experimental studies of actin unfolding in EDTA. We also discovered that subdomain 4 has a low refolding probability, which can help explain why many of the non-native actin target binding sites for CCT and PFD are located within this subdomain.