Population Shuffling of Protein Conformations

Motions play a vital role in the functions of many proteins. Discrete conformational transitions to excited states, happening on timescales of hundreds of microseconds, have been extensively characterized. On the other hand, the dynamics of the ground state are widely unexplored. Newly developed high‐power relaxation dispersion experiments allow the detection of motions up to a one‐digit microsecond timescale. These experiments showed that side chains in the hydrophobic core as well as at protein–protein interaction surfaces of both ubiquitin and the third immunoglobulin binding domain of protein G move on the microsecond timescale. Both proteins exhibit plasticity to this microsecond motion through redistribution of the populations of their side‐chain rotamers, which interconvert on the picosecond to nanosecond timescale, making it likely that this “population shuffling” process is a general mechanism.     

Localized and Collective Motions in HET‐s(218‐289) Fibrils from Combined NMR Relaxation and MD Simulation

Nuclear magnetic resonance (NMR) relaxation data and molecular dynamics (MD) simulations are combined to characterize the dynamics of the fungal prion HET‐s(218‐289) in its amyloid form. NMR data is analyzed with the dynamics detector method, which yields timescale‐specific information. An analogous analysis is performed on MD trajectories. Because specific MD predictions can be verified as agreeing with the NMR data, MD was used for further interpretation of NMR results: for the different timescales, cross‐correlation coefficients were derived to quantify the correlation of the motion between different residues. Short timescales are the result of very local motions, while longer timescales are found for longer‐range correlated motion. Similar trends on ns‐ and μs‐timescales suggest that μs motion in fibrils is the result of motion correlated over many fibril layers.     

Hierarchical analysis of conformational dynamics in biomolecules: transition networks of metastable states

Molecular dynamics simulation generates large quantities of data that must be interpreted using physically meaningful analysis. A common approach is to describe the system dynamics in terms of transitions between coarse partitions of conformational space. In contrast to previous work that partitions the space according to geometric proximity, the authors examine here clustering based on kinetics, merging configurational microstates together so as to identify long-lived, i.e., dynamically metastable, states. As test systems microsecond molecular dynamics simulations of the polyalanines Ala(8) and Ala(12) are analyzed. Both systems clearly exhibit metastability, with some kinetically distinct metastable states being geometrically very similar. Using the backbone torsion rotamer pattern to define the microstates, a definition is obtained of metastable states whose lifetimes considerably exceed the memory associated with interstate dynamics, thus allowing the kinetics to be described by a Markov model. This model is shown to be valid by comparison of its predictions with the kinetics obtained directly from the molecular dynamics simulations. In contrast, clustering based on the hydrogen-bonding pattern fails to identify long-lived metastable states or a reliable Markov model. Finally, an approach is proposed to generate a hierarchical model of networks, each having a different number of metastable states. The model hierarchy yields a qualitative understanding of the multiple time and length scales in the dynamics of biomolecules.     

Accelerated molecular dynamics simulations of protein folding

Folding of four fast‐folding proteins, including chignolin, Trp‐cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred‐of‐microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2–2.1 Å of the native NMR or X‐ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second‐order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein‐folding studies. © 2015 Wiley Periodicals, Inc.     

Coarse-grained force field for the nucleosome from self-consistent multiscaling

A coarse-grained simulation model for the nucleosome is developed, using a methodology modified from previous work on the ribosome. Protein residues and DNA nucleotides are represented as beads, interacting through harmonic (for neighboring) or Morse (for nonbonded) potentials. Force-field parameters were estimated by Boltzmann inversion of the corresponding radial distribution functions obtained from a 5-ns all-atom molecular dynamics (MD) simulation, and were refined to produce agreement with the all-atom MD simulation. This self-consistent multiscale approach yields a coarse-grained model that is capable of reproducing equilibrium structural properties calculated from a 50-ns all-atom MD simulation. This coarse-grained model speeds up nucleosome simulations by a factor of 10(3) and is expected to be useful in examining biologically relevant dynamical nucleosome phenomena on the microsecond timescale and beyond.     

Microsecond timescale MD simulations at the transition state of PmHMGR predict remote allosteric residues

Understanding the mechanisms of enzymatic catalysis requires a detailed understanding of the complex interplay of structure and dynamics of large systems that is a challenge for both experimental and computational approaches. More importantly, the computational demands of QM/MM simulations mean that the dynamics of the reaction can only be considered on a timescale of nanoseconds even though the conformational changes needed to reach the catalytically active state happen on a much slower timescale. Here we demonstrate an alternative approach that uses transition state force fields (TSFFs) derived by the quantum-guided molecular mechanics (Q2MM) method that provides a consistent treatment of the entire system at the classical molecular mechanics level and allows simulations at the microsecond timescale. Application of this approach to the second hydride transfer transition state of HMG-CoA reductase from Pseudomonas mevalonii (PmHMGR) identified three remote residues, R396, E399 and L407, (15–27 Å away from the active site) that have a remote dynamic effect on enzyme activity. The predictions were subsequently validated experimentally via site-directed mutagenesis. These results show that microsecond timescale MD simulations of transition states are possible and can predict rather than just rationalize remote allosteric residues.

Transition state force fields enable MD simulations at the transition state of HMGCoA reductase that sample the transition state ensemble on the μs timescale to identify remote residues that affect the reaction rate.     

Reaching multi‐nanosecond timescales in combined QM/MM molecular dynamics simulations through parallel horsetail sampling

We report an enhanced sampling technique that allows to reach the multi‐nanosecond timescale in quantum mechanics/molecular mechanics molecular dynamics simulations. The proposed technique, called horsetail sampling, is a specific type of multiple molecular dynamics approach exhibiting high parallel efficiency. It couples a main simulation with a large number of shorter trajectories launched on independent processors at periodic time intervals. The technique is applied to study hydrogen peroxide at the water liquid–vapor interface, a system of considerable atmospheric relevance. A total simulation time of a little more than 6 ns has been attained for a total CPU time of 5.1 years representing only about 20 days of wall‐clock time. The discussion of the results highlights the strong influence of the solvation effects at the interface on the structure and the electronic properties of the solute. © 2017 Wiley Periodicals, Inc.     

Structural dissimilarity sampling with dynamically self‐guiding selection

Structural dissimilarity sampling (SDS) has been proposed as an enhanced conformational sampling method for reproducing the structural transitions of a given protein. SDS consists of cycles of two steps: (1) Selections of initial structures with structural dissimilarities by referring to a measure. (2) Conformational resampling by restarting short‐time molecular dynamics (MD) simulations from the initial structures. In the present study, an efficient measure is proposed as a dynamically self‐guiding selection to accelerate the structural transitions from a reactant state to a product state as an extension to the original SDS. In the extended SDS, the inner product (IP ) between the reactant and the snapshots generated by short‐time MD simulations are evaluated and ranked according to the IP s at every cycle. Then, the snapshots with low IP s are selected as initial structures for the short‐time MD simulations. This scheme enables one to choose dissimilar and distant initial structures from the reactant, and thus the initial structures dynamically head towards the product, promoting structural transitions from the reactant. To confirm the conformational sampling efficiency, the extended SDS was applied to maltodextrin binding protein (MBP), and we successfully reproduced the structural transition from the open to closed states with submicrosecond‐order simulation times. However, a conventional long‐time MD simulation failed to reproduce the same structural transition. We also compared the performance with that obtained by the ordinary SDS and other sampling techniques that have been developed by us to characterize the possible utility of the extended SDS for actual applications. © 2017 Wiley Periodicals, Inc.     

Advances in Enhanced Sampling Molecular Dynamics Simulations for Biomolecules

Molecular dynamics simulation has emerged as a powerful computational tool for studying biomolecules as it can provide atomic insights into the conformational transitions involved in biological functions. However, when applied to complex biological macromolecules, the conformational sampling ability of conventional molecular dynamics is limited by the rugged free energy landscapes, leading to inherent timescale gaps between molecular dynamics simulations and real biological processes. To address this issue, several advanced enhanced sampling methods have been proposed to improve the sampling efficiency in molecular dynamics. In this review, the theoretical basis, practical applications, and recent improvements of both constraint and unconstrained enhanced sampling methods are summarized. Furthermore, the combined utilizations of different enhanced sampling methods that take advantage of both approaches are also briefly discussed.     

Contrasting photodynamics between C60-dithiapyrene and C60-pyrene dyads

The photodynamics of a C60-dithiapyrene donor-acceptor conjugate were compared with the corresponding C60-pyrene conjugate. The photoinduced charge separation and subsequent charge recombination processes were examined by time-resolved fluorescence measurements on the picosecond timescale and transient absorption measurements on the picosecond and microsecond timescales with detection in the visible and near-infrared regions. We have observed quite long lifetimes (i.e., up to 1.01 ns) for the photogenerated charge-separated state in a C60-dithiapyrene dyad without the need for i) a long spacer between the two moieties, or ii) a gain in aromaticity in the radical ion pair.     

On the orientation of a designed transmembrane peptide: toward the right tilt angle?

The orientation of the transmembrane peptide WALP23 under small hydrophobic mismatch has been assessed through long-time-scale molecular dynamics simulations of hundreds of nanoseconds. Each simulation gives systematically large tilt angles (>30 degrees). In addition, the peptide visits various azimuthal rotations that mostly depend on the initial conditions and converge very slowly. In contrast, small tilt angles as well as a well-defined azimuthal rotation were suggested by recent solid-state 2H NMR studies on the same system. To optimally compare our simulations with NMR data, we concatenated the different trajectories in order to increase the sampling. The agreement with 2H NMR quadrupolar splittings is spectacularly better when these latter are back-calculated from the concatenated trajectory than from any individual simulation. From these ensembled-average quadrupolar splittings, we then applied the GALA method as described by Strandberg et al. (Biophys J. 2004, 86, 3709-3721), which basically derives the peptide orientation (tilt and azimuth) from the splittings. We find small tilt angles (6.5 degrees), whereas the real observed tilt in the concatenated trajectory presents a higher value (33.5 degrees). We thus propose that the small tilt angles estimated by the GALA method are the result of averaging effects, provided that the peptide visits many states of different azimuthal rotations. We discuss how to improve the method and suggest some other experiments to confirm this hypothesis. This work also highlights the need to run several and rather long trajectories in order to predict the peptide orientation from computer simulations.     

On the structural convergence of biomolecular simulations by determination of the effective sample size

Although atomistic simulations of proteins and other biological systems are approaching microsecond timescales, the quality of simulation trajectories has remained difficult to assess. Such assessment is critical not only for establishing the relevance of any individual simulation but also in the extremely active field of developing computational methods. Here we map the trajectory assessment problem onto a simple statistical calculation of the "effective sample size", that is, the number of statistically independent configurations. The mapping is achieved by asking the question, "How much time must elapse between snapshots included in a sample for that sample to exhibit the statistical properties expected for independent and identically distributed configurations?" Our method is more general than autocorrelation methods in that it directly probes the configuration-space distribution without requiring a priori definition of configurational substates and without any fitting parameters. We show that the method is equally and directly applicable to toy models, peptides, and a 72-residue protein model. Variants of our approach can readily be applied to a wide range of physical and chemical systems.     

Molecular latent space simulators

Small integration time steps limit molecular dynamics (MD) simulations to millisecond time scales. Markov state models (MSMs) and equation-free approaches learn low-dimensional kinetic models from MD simulation data by performing configurational or dynamical coarse-graining of the state space. The learned kinetic models enable the efficient generation of dynamical trajectories over vastly longer time scales than are accessible by MD, but the discretization of configurational space and/or absence of a means to reconstruct molecular configurations precludes the generation of continuous atomistic molecular trajectories. We propose latent space simulators (LSS) to learn kinetic models for continuous atomistic simulation trajectories by training three deep learning networks to (i) learn the slow collective variables of the molecular system, (ii) propagate the system dynamics within this slow latent space, and (iii) generatively reconstruct molecular configurations. We demonstrate the approach in an application to Trp-cage miniprotein to produce novel ultra-long synthetic folding trajectories that accurately reproduce atomistic molecular structure, thermodynamics, and kinetics at six orders of magnitude lower cost than MD. The dramatically lower cost of trajectory generation enables greatly improved sampling and greatly reduced statistical uncertainties in estimated thermodynamic averages and kinetic rates.

Latent space simulators learn kinetic models for atomistic simulations and generate novel trajectories at six orders of magnitude lower cost.     

Picosecond Switchable Azo Dyes

Azo dyes that combine electron-withdrawing thiazole/benzothiazole heterocycles and electron-donating amino groups within the very same covalent skeleton exhibit relaxation times for their thermal isomerization kinetics within milli- and microsecond timescales at room temperature. Notably, the thermal back reaction of the corresponding benzothiazolium and thiazolium salts occurred much faster, within the picosecond temporal domain. In fact, these new light-sensitive platforms are the first molecular azo derivatives capable of reversible switching between their trans and cis isomers in a subnanosecond timescale under ambient conditions. In addition, theoretical calculations revealed very low activation energies for the isomerization process, in accordance with the fast subnanosecond kinetics that were observed experimentally.     

Choice of Force Fields and Water Models for Sampling Solution Conformations of Bacteriophage T4 Lysozyme

A protein may exist as an ensemble of different conformations in solution, which cannot be represented by a single static structure. Molecular dynamics (MD) simulation has become a useful tool for sampling protein conformations in solution, but force fields and water models are important issues. This work presents a case study of the bacteriophage T4 lysozyme (T4L). We have found that MD simulations using a classic AMBER99SB force field and TIP4P water model cannot well describe hinge-bending domain motion of the wild-type T4L at the timescale of one microsecond. Other combinations, such as a residue-specific force field called RSFF2+ and a dispersion-corrected water model TIP4P-D, are able to sample reasonable solution conformations of T4L, which are in good agreement with experimental data. This primary study may provide candidates of force fields and water models for further investigating conformational transition of T4L.     

Improving Internal Peptide Dynamics in the Coarse-Grained MARTINI Model: Toward Large-Scale Simulations of Amyloid- and Elastin-like Peptides

We present an extension of the coarse-grained MARTINI model for proteins and apply this extension to amyloid- and elastin-like peptides. Atomistic simulations of tetrapeptides, octapeptides, and longer peptides in solution are used as a reference to parametrize a set of pseudodihedral potentials that describe the internal flexibility of MARTINI peptides. We assess the performance of the resulting model in reproducing various structural properties computed from atomistic trajectories of peptides in water. The addition of new dihedral angle potentials improves agreement with the contact maps computed from atomistic simulations significantly. We also address the question of which parameters derived from atomistic trajectories are transferable between different lengths of peptides. The modified coarse-grained model shows reasonable transferability of parameters for the amyloid- and elastin-like peptides. In addition, the improved coarse-grained model is also applied to investigate the self-assembly of β-sheet forming peptides on the microsecond time scale. The octapeptides SNNFGAIL and (GV)(4) are used to examine peptide aggregation in different environments, in water, and at the water-octane interface. At the interface, peptide adsorption occurs rapidly, and peptides spontaneously aggregate in favor of stretched conformers resembling β-strands.     

Microsecond molecular dynamics simulations of the kinetic pathways of gas hydrate formation from solid surfaces

In this paper, we report microsecond molecular dynamics simulations of the kinetic pathway of CO(2) hydrate formation triggered by hydroxylated silica surfaces. Our simulation results show that the nucleation of the CO(2) hydrate is a three-stage process. First, an icelike layer is formed closest to the substrates on the nanosecond scale. Then, on the submicrosecond timescale, a thin layer with intermediate structure is induced to compensate for the structure mismatch between the icelike layer and the final stable CO(2) hydrate. Finally, on the microsecond timescale, the nucleation of the first CO(2) hydrate motif layer is generated from the intermediate structure that acts as nucleation seeds. We also address the effects of the distance between two surfaces.     

Direct simulation of early-stage sec-facilitated protein translocation

Direct simulations reveal key mechanistic features of early-stage protein translocation and membrane integration via the Sec-translocon channel. We present a novel computational protocol that combines non-equilibrium growth of the nascent protein with microsecond timescale molecular dynamics trajectories. Analysis of multiple, long timescale simulations elucidates molecular features of protein insertion into the translocon, including signal-peptide docking at the translocon lateral gate (LG), large lengthscale conformational rearrangement of the translocon LG helices, and partial membrane integration of hydrophobic nascent-protein sequences. Furthermore, the simulations demonstrate the role of specific molecular interactions in the regulation of protein secretion, membrane integration, and integral membrane protein topology. Salt-bridge contacts between the nascent-protein N-terminus, cytosolic translocon residues, and phospholipid head groups are shown to favor conformations of the nascent protein upon early-stage insertion that are consistent with the Type II (N(cyt)/C(exo)) integral membrane protein topology, and extended hydrophobic contacts between the nascent protein and the membrane lipid bilayer are shown to stabilize configurations that are consistent with the Type III (N(exo)/C(cyt)) topology. These results provide a detailed, mechanistic basis for understanding experimentally observed correlations between integral membrane protein topology, translocon mutagenesis, and nascent-protein sequence.     

Optimal use of data in parallel tempering simulations for the construction of discrete-state Markov models of biomolecular dynamics

Parallel tempering (PT) molecular dynamics simulations have been extensively investigated as a means of efficient sampling of the configurations of biomolecular systems. Recent work has demonstrated how the short physical trajectories generated in PT simulations of biomolecules can be used to construct the Markov models describing biomolecular dynamics at each simulated temperature. While this approach describes the temperature-dependent kinetics, it does not make optimal use of all available PT data, instead estimating the rates at a given temperature using only data from that temperature. This can be problematic, as some relevant transitions or states may not be sufficiently sampled at the temperature of interest, but might be readily sampled at nearby temperatures. Further, the comparison of temperature-dependent properties can suffer from the false assumption that data collected from different temperatures are uncorrelated. We propose here a strategy in which, by a simple modification of the PT protocol, the harvested trajectories can be reweighted, permitting data from all temperatures to contribute to the estimated kinetic model. The method reduces the statistical uncertainty in the kinetic model relative to the single temperature approach and provides estimates of transition probabilities even for transitions not observed at the temperature of interest. Further, the method allows the kinetics to be estimated at temperatures other than those at which simulations were run. We illustrate this method by applying it to the generation of a Markov model of the conformational dynamics of the solvated terminally blocked alanine peptide.