Multiscale Enhanced Sampling Research Articles

Multiscale Enhanced Sampling Using Machine Learning.

Multiscale enhanced sampling (MSES) allows for an enhanced sampling of all-atom protein structures by coupling with the accelerated dynamics of the associated coarse-grained (CG) model. In this paper, we propose an MSES extension to replace the CG model with the dynamics on the reduced subspace generated by a machine learning approach, the variational autoencoder (VAE). The molecular dynamic (MD) trajectories of the ribose-binding protein (RBP) in both the closed and open forms were used as the input by extracting the inter-residue distances as the structural features in order to train the VAE model, allowing the encoded latent layer to characterize the difference in the structural dynamics of the closed and open forms. The interpolated data characterizing the RBP structural change in between the closed and open forms were thus efficiently generated in the low-dimensional latent space of the VAE, which was then decoded into the time-series data of the inter-residue distances and was useful for driving the structural sampling at an atomistic resolution via the MSES scheme. The free energy surfaces on the latent space demonstrated the refinement of the generated data that had a single basin into the simulated data containing two closed and open basins, thus illustrating the usefulness of the MD simulation together with the molecular mechanics force field in recovering the correct structural ensemble.

Accelerating atomistic simulations of proteins using multiscale enhanced sampling with independent tempering.

Efficient sampling of the conformational space is essential for quantitative simulations of proteins. The multiscale enhanced sampling (MSES) method accelerates atomistic sampling by coupling it to a coarse-grained (CG) simulation. Bias from coupling to the CG model is removed using Hamiltonian replica exchange, such that one could benefit simultaneously from the high accuracy of atomistic models and fast dynamics of CG ones. Here, we extend MSES to allow independent control of the effective temperatures of atomistic and CG simulations, by directly scaling the atomistic and CG Hamiltonians. The new algorithm, named MSES with independent tempering (MSES-IT), supports more sophisticated Hamiltonian and temperature replica exchange protocols to further improve the sampling efficiency. Using a small but nontrivial β-hairpin, we show that setting the effective temperature of CG model in all conditions to its melting temperature maximizes structural transition rates at the CG level and promotes more efficient replica exchange and diffusion in the condition space. As the result, MSES-IT drive faster reversible transitions at the atomic level and leads to significant improvement in generating converged conformational ensembles compared to the original MSES scheme.

Multiscale enhanced sampling of glucokinase: Regulation of the enzymatic reaction via a large scale domain motion

Enhanced sampling yields a comprehensive structural ensemble or a free energy landscape, which is beyond the capability of a conventional molecular dynamics simulation. Our recently developed multiscale enhanced sampling (MSES) method employs a coarse-grained model coupled with the target physical system for the efficient acceleration of the dynamics. MSES has demonstrated applicability to large protein systems in solution, such as intrinsically disordered proteins and protein-protein and protein-ligand interactions. Here, we applied the MSES simulation to an important drug discovery target, glucokinase (GCK), to elucidate the structural basis of the positive cooperativity of the enzymatic reaction at an atomistic resolution. MSES enabled us to compare two sets of the free energy landscapes of GCK, for the glucose-bound and glucose-unbound forms, and thus demonstrated the drastic change of the free energy surface depending on the glucose concentration. In the glucose-bound form, we found two distinct basins separated by a high energy barrier originating from the domain motion and the folding/unfolding of the α13 helix. By contrast, in the glucose-unbound form, a single flat basin extended to the open and super-open states. These features illustrated the two distinct phases achieving the cooperativity, the fast reaction cycle staying in the closed state at a high glucose concentration and the slow cycle primarily in the open/super-open state at a low concentration. The weighted ensemble simulations revealed the kinetics of the structural changes in GCK with the synergetic use of the MSES results; the rate constant of the transition between the closed state and the open/super-open states, kC/O = 1.1 ms-1, is on the same order as the experimental catalytic rate, kcat = 0.22 ms-1. Finally, we discuss the pharmacological activities of GCK activators (small molecular drugs modulating the GCK activity) in terms of the slight changes in the domain motion, depending on their chemical structures as regulators. The present study demonstrated the capability of the enhanced sampling and the associated kinetic calculations for understanding the atomistic structural dynamics of protein systems in physiological environments.

Free-Energy Landscape of Protein-Ligand Interactions Coupled with Protein Structural Changes.

Protein-ligand interactions are frequently coupled with protein structural changes. Focusing on the coupling, we present the free-energy surface (FES) of the ligand-binding process for glutamine-binding protein (GlnBP) and its ligand, glutamine, in which glutamine binding accompanies large-scale domain closure. All-atom simulations were performed in explicit solvents by multiscale enhanced sampling (MSES), which adopts a multicopy and multiscale scheme to achieve enhanced sampling of systems with a large number of degrees of freedom. The structural ensemble derived from the MSES simulation yielded the FES of the coupling, described in terms of both the ligand's and protein's degrees of freedom at atomic resolution, and revealed the tight coupling between the two degrees of freedom. The derived FES led to the determination of definite structural states, which suggested the dominant pathways of glutamine binding to GlnBP: first, glutamine migrates via diffusion to form a dominant encounter complex with Arg75 on the large domain of GlnBP, through strong polar interactions. Subsequently, the closing motion of GlnBP occurs to form ligand interactions with the small domain, finally completing the native-specific complex structure. The formation of hydrogen bonds between glutamine and the small domain is considered to be a rate-limiting step, inducing desolvation of the protein-ligand interface to form the specific native complex. The key interactions to attain high specificity for glutamine, the "door keeper" existing between the two domains (Asp10-Lys115) and the "hydrophobic sandwich" formed between the ligand glutamine and Phe13/Phe50, have been successfully mapped on the pathway derived from the FES.

HyRes: a coarse-grained model for multi-scale enhanced sampling of disordered protein conformations.

Efficient coarse-grained (CG) models can be coupled with atomistic force fields to accelerate the sampling of atomistic energy landscapes in the multi-scale enhanced sampling (MSES) framework. This approach may be particularly suitable for generating atomistic conformational ensembles of intrinsically disordered proteins (IDPs). While MSES is relatively robust to inherent CG artifacts, achieving optimal sampling efficiency requires CG modeling to generate the local and long-range fluctuations that are largely consistent with those at the atomistic level. Here, we describe a new hybrid resolution CG model (HyRes) for MSES simulations of disordered protein states, which is specifically designed to provide semi-quantitative secondary structure propensities together with a qualitative description of long-range nonspecific interactions. The HyRes model contains an atomistic description of the backbone with intermediate resolution side chains. The secondary structure propensities are tuned by adjusting the backbone hydrogen-bonding strength and the ϕ/ψ torsion profile. The sizes and covalent geometries of the side chains are parameterized to reproduce distributions derived from atomistic simulations. Lennard-Jones parameters for sidechain beads are assigned to reproduce statistical potentials derived from the protein structural database, and then globally parameterized with nonspecific electrostatic interactions to reproduce the free energy profiles of pair wise interactions and the key conformational properties of model peptides. Application of HyRes to MSES simulations of small IDPs suggests that it is capable of driving faster structural transitions at the atomistic level and increasing the convergence rate compared to the Cα-only Gō-like models previously utilized. With further optimization, we believe that the new CG model could greatly improve the efficiency of MSES simulations of the larger and more complex IDPs frequently involved in cellular signalling and regulation.

Multiscale enhanced sampling for protein systems: An extension via adiabatic separation

Multiscale enhanced sampling (MSES) calculates the configurational ensemble of all-atom (MM) protein systems with the help of coupling to a coarse-grained (CG) model. Here, for further improvement of the sampling efficiency, the approximation of adiabatic separation was introduced to the original MSES, by adopting a high CG temperature limit. An application to the folding of chignolin in explicit solvent demonstrated that the MSES formula based on adiabatic separation correctly sampled the canonical ensemble with excellent efficiency and robustness against the parameter selection, and thus MSES successfully achieved the scalability for applications to large protein systems.

Extended Phase-Space Methods for Enhanced Sampling in Molecular Simulations: A Review.

Molecular Dynamics simulations are a powerful approach to study biomolecular conformational changes or protein–ligand, protein–protein, and protein–DNA/RNA interactions. Straightforward applications, however, are often hampered by incomplete sampling, since in a typical simulated trajectory the system will spend most of its time trapped by high energy barriers in restricted regions of the configuration space. Over the years, several techniques have been designed to overcome this problem and enhance space sampling. Here, we review a class of methods that rely on the idea of extending the set of dynamical variables of the system by adding extra ones associated to functions describing the process under study. In particular, we illustrate the Temperature Accelerated Molecular Dynamics (TAMD), Logarithmic Mean Force Dynamics (LogMFD), and Multiscale Enhanced Sampling (MSES) algorithms. We also discuss combinations with techniques for searching reaction paths. We show the advantages presented by this approach and how it allows to quickly sample important regions of the free-energy landscape via automatic exploration.

Multiscale enhanced sampling of intrinsically disordered protein conformations.

In a recently developed multiscale enhanced sampling (MSES) technique, topology-based coarse-grained (CG) models are coupled to atomistic force fields to enhance the sampling of atomistic protein conformations. Here, the MSES protocol is refined by designing more sophisticated Hamiltonian/temperature replica exchange schemes that involve additional parameters in the MSES coupling restraint potential, to more carefully control how conformations are coupled between the atomistic and CG models. A specific focus is to derive an optimal MSES protocol for simulating conformational ensembles of intrinsically disordered proteins (IDPs). The efficacy of the refined protocols, referred to as MSES-soft asymptote (SA), was evaluated using two model peptides with various levels of residual helicities. The results show that MSES-SA generates more reversible helix-coil transitions and leads to improved convergence on various ensemble conformational properties. This study further suggests that more detailed CG models are likely necessary for more effective sampling of local conformational transition of IDPs. © 2015 Wiley Periodicals, Inc.

Refining Multi-Scale Enhanced Sampling for Simulating Disordered Protein Conformations

In the recently developed multiscale enhanced sampling (MSES) technique, topology-based coarse-grained (CG) models are coupled to atomistic protein force field to enhance the sampling of atomistic conformational space (Zhang and Chen, J. Chem Theory Comput, 2014). Here, we further refine the MSES protocol by designing more sophisticated Hamiltonian/temperature replica exchange schemes to more carefully control how the conformations are coupled between the atomistic and CG models, with a specific focus on optimizing the protocol for simulating disordered protein conformations. Preliminary results show that the new MSES protocols are effective in achieving better convergence in simulation of so-called intrinsically disordered proteins.

Energy landscape of all-atom protein-protein interactions revealed by multiscale enhanced sampling.

Protein-protein interactions are regulated by a subtle balance of complicated atomic interactions and solvation at the interface. To understand such an elusive phenomenon, it is necessary to thoroughly survey the large configurational space from the stable complex structure to the dissociated states using the all-atom model in explicit solvent and to delineate the energy landscape of protein-protein interactions. In this study, we carried out a multiscale enhanced sampling (MSES) simulation of the formation of a barnase-barstar complex, which is a protein complex characterized by an extraordinary tight and fast binding, to determine the energy landscape of atomistic protein-protein interactions. The MSES adopts a multicopy and multiscale scheme to enable for the enhanced sampling of the all-atom model of large proteins including explicit solvent. During the 100-ns MSES simulation of the barnase-barstar system, we observed the association-dissociation processes of the atomistic protein complex in solution several times, which contained not only the native complex structure but also fully non-native configurations. The sampled distributions suggest that a large variety of non-native states went downhill to the stable complex structure, like a fast folding on a funnel-like potential. This funnel landscape is attributed to dominant configurations in the early stage of the association process characterized by near-native orientations, which will accelerate the native inter-molecular interactions. These configurations are guided mostly by the shape complementarity between barnase and barstar, and lead to the fast formation of the final complex structure along the downhill energy landscape.

Multiscale enhanced sampling driven by multiple coarse-grained models

Enhanced sampling has increased its importance in simulations of large-scale functional dynamics of proteins. “Multiscale enhanced sampling (MSES)” is an enhanced sampling method applicable to large protein systems, in which all-atom (MM) sampling is extended through a coupling with the accelerated dynamics of a coarse-grained (CG) model. Here, we show that the sampling efficiency of MSES can be further improved by using multiple CG copies instead of a single CG model and by introducing repulsive forces between the CG copies. An application to chignolin folding in explicit solvent has demonstrated a significant improvement in sampling efficiency due to the extension.

Accelerate Sampling in Atomistic Energy Landscapes Using Topology-Based Coarse-Grained Models

We describe a multiscale enhanced sampling (MSES) method where efficient topology-based coarse-grained models are coupled with all-atom ones to enhance the sampling of atomistic protein energy landscape. The bias from the coupling is removed by Hamiltonian replica exchange, thus allowing one to benefit simultaneously from faster transitions of coarse-grained modeling and accuracy of atomistic force fields. The method is demonstrated by calculating the conformational equilibria of several small but nontrivial β-hairpins with varied stabilities.

Accelerate Sampling in Atomistic Energy Landscapes using Topology-Based Coarse-Grained Models

Successful simulations of biomolecules require sufficient sampling of the relevant conformational space. This has remained a major challenge due to large conformational space and significant energy barriers, especially with atomistic force fields. Temperature replica exchange (REX) has emerged as a powerful and popular technique for enhanced sampling. Yet, efficiency of temperature REX can be severely limited by the presence of sharp cooperative conformational transitions as well as due to large entropic barriers frequently associated with folding transitions. A coarse-grained representation is often necessary to significantly reduce the conformational space and allows faster sampling of reversible conformational transitions, albeit at the expense of reduced detail and accuracy. Here, we describe a multi-scale enhanced sampling (MSES) method that directly couples topology-based coarse-grained protein models with atomistic ones to accelerate the sampling of complex and rough atomistic energy landscapes. The bias from the coupling potential is completely removed by performing Hamiltonian/temperature REX, allowing one to benefit simultaneously from faster transitions of the coarse-grained model and the accuracy of the atomistic force field. The method has been applied to implicit solvent simulations of several peptides and small proteins including protein GB1, protein A and villin headpiece. The results demonstrate that MSES dramatically increases the number of folding/unfolding transitions sampled and improve the convergence of various thermodynamic properties of interest in all cases. Importantly, this method is simple and fully scalable to larger and more complex systems.

Multiscale enhanced path sampling based on the Onsager-Machlup action: Application to a model polymer

We propose a novel path sampling method based on the Onsager-Machlup (OM) action by generalizing the multiscale enhanced sampling technique suggested by Moritsugu and co-workers [J. Chem. Phys. 133, 224105 (2010)]. The basic idea of this method is that the system we want to study (for example, some molecular system described by molecular mechanics) is coupled to a coarse-grained (CG) system, which can move more quickly and can be computed more efficiently than the original system. We simulate this combined system (original + CG system) using Langevin dynamics where different heat baths are coupled to the two systems. When the coupling is strong enough, the original system is guided by the CG system, and is able to sample the configuration and path space with more efficiency. We need to correct the bias caused by the coupling, however, by employing the Hamiltonian replica exchange, where we prepare many path replicas with different coupling strengths. As a result, an unbiased path ensemble for the original system can be found in the weakest coupling path ensemble. This strategy is easily implemented because a weight for a path calculated by the OM action is formally the same as the Boltzmann weight if we properly define the path "Hamiltonian." We apply this method to a model polymer with Asakura-Oosawa interaction, and compare the results with the conventional transition path sampling method.

Disorder-to-Order Transition of an Intrinsically Disordered Region of Sortase Revealed by Multiscale Enhanced Sampling

Molecular functions of intrinsically disordered proteins (IDPs) or intrinsically disordered regions (IDRs), such as molecular recognition and cellular signaling, are ascribed to dynamic changes in the conformational space in response to binding of target molecules. Sortase, a transpeptitase in Gram-positive bacteria, has an IDR in a loop which undergoes a disordered-to-ordered transition (called "disordered loop"), accompanying a tilt of another loop ("dynamic loop"), upon binding of a signal peptide and a calcium ion. In this study, all-atom conformational ensembles of sortase were calculated for the four different binding states (with/without the peptide and with/without a calcium ion) by the multiscale enhanced sampling (MSES) simulation to examine how the binding of the peptide and/or calcium influences the conformational ensemble. The MSES is a multiscale and multicopy simulation method that allows an enhanced sampling of the all-atom model of large proteins including explicit solvent. A 100 ns MSES simulation of the ligand-free sortase using 20 replicas (in total 2 μs) demonstrated large flexibility in both the disordered and dynamic loops; however, their distributions were not random but had a clear preference which populates the N-terminal part of the disordered loop near the bound form. The MSES simulations of the three binding states clarified the allosteric mechanism of sortase: the N- and C-terminal parts of the disordered loop undergo a disorder-to-order transition independently of each other upon binding of the peptide and a calcium ion, respectively; however, upon binding of both ligands, the two parts work cooperatively to stabilize the bound peptide.