We report atomically detailed molecular dynamics simulations of the permeation of the lethal factor (LF) N-terminal segment through the anthrax channel. The N-terminal chain is unstructured and leads the permeation process for the LF protein. The simulations were conducted in explicit solvent with milestoning theory, making it possible to extract kinetic information from nanosecond to millisecond time scales. We illustrate that the initial event is strongly influenced by the protonation states of the permeating amino acids. While the N-terminal segment passes easily at high protonation state through the anthrax channel (and the ϕ clamp), the initial permeation represents a critical step, which can be irreversible and establishes a hook in the channel mouth.

Enzymatic reactions usually occur in several steps: a step of substrate binding to the surface of the protein, a step of protein reorganization around the substrate and conduction of a chemical reaction, and a step of product release. The release of inorganic phosphate—PPi—from the matrix of the protein HIV reverse transcriptase is investigated computationally. Atomically detailed simulations with explicit solvent are analyzed to obtain the free energy profile, mean first passage time, and detailed molecular mechanisms of PPi escape. A challenge for the computations is of time scales. The experimental time scale of the process of interest is in milliseconds, and straightforward molecular dynamics simulations are in sub-microseconds. To overcome the time scale gap, we use the algorithm of Milestoning along a reaction coordinate to compute the overall free energy profile and rate. The methods of locally enhanced sampling and steered molecular dynamics determine plausible reaction coordinates. The observed molecular mechanism couples the transfer of the PPi to positively charged lysine side chains that are found on the exit pathway and to an exiting magnesium ion. In accord with experimental findings, the release rate is comparable to the chemical step, allowing for variations in substrate (DNA or RNA template) in which the release becomes rate determining.

We exploit atomically detailed simulations and the milestoning theory to extract coarse grained models of membrane kinetics and thermodynamics. Non-Markovian and Markovian theories for the phosphate group displacements are used to coarsely represent membrane motions. The construction of the two models makes it possible to examine their consistency and accuracy. The equilibrium and fluctuations of the phosphate groups along the normal to the membrane plane are estimated, and milestoning equations are constructed and solved. An optimal Markovian model is constructed that reproduces exactly the equilibrium and mean first passage time (MFPT) of the non-Markovian model. The equilibrium solution of both models is favorably compared to distributions obtained from straightforward molecular dynamics simulations. The picture for the kinetics is complex. Multiple local relaxation times of the mass density are illustrated emphasizing the non-Markovian characteristics of the process. In Markovian modeling, only a single relaxation time is assumed for a state. Mapping of particle dynamics to the dynamics of a field density offers a new way of coarse graining complex systems as membranes that may bridge between atomically detailed models and phenomenological descriptions of macroscopic membranes.

Ketoreductases (KRs) from modular polyketide synthases (PKSs) can perform stereospecific catalysis, selecting a polyketide with a d- or l-α-methyl substituent for NADPH-mediated reduction. In this report, molecular dynamics (MD) simulations were performed to investigate the interactions that control stereospecificity. We studied the A1-type KR from the second module of the amphotericin PKS (A1), which is known to be stereospecific for a d-α-methyl-substituted diketide substrate (dkD). MD simulations of two ternary complexes comprised of the enzyme, NADPH, and either the correct substrate, dkD, or its enantiomer (dkL) were performed. The coordinates for the A1/NADPH binary complex were obtained from a crystal structure (PDB entry 3MJS), and substrates were modeled in the binding pocket in conformations appropriate for reduction. Simulations were intended to reproduce the initial weak binding of the polyketide substrate to the enzyme. Long (tens of nanoseconds) MD simulations show that the correct substrate is retained in a conformation closer to the reactive configuration. Many short (up to a nanosecond) MD runs starting from the initial structures display evidence that Q364, three residues N-terminal to the catalytic tyrosine, forms a hydrogen bond to the incorrect dkL substrate to yield an unreactive conformation that is more favorable than the reactive configuration. This interaction is not as strong for dkD, as the d-α-methyl substituent is positioned between the glutamine and the reactive site. This result correlates with experimental findings [Zheng, J., et al. (2010) Structure 18, 913–922] in which a Q364H mutant was observed to lose stereospecificity.

Atomically detailed simulations of HIV RT are performed to investigate the contributions of the conformational transition to the overall rate and specificity of enzyme catalysis. A number of different scenarios are considered within Milestoning theory to provide a more complete picture of the process of opening and closing the enzyme. We consider the open to closed transition in the absence of and with the correct and incorrect substrates. We also consider the free energy profile and the kinetics of the conformational change after the chemistry step in which a new base was added to the DNA, but the DNA was not yet displaced. We partition the free energy along the reaction coordinate and analyze the importance of different protein domains. Strikingly, significant influence on the free energy profile is detected for amino acids far from the active site. The overall long-range impact is about 50 percent of the total. We also illustrate that the overall rate is not necessarily determined by the highest free energy barrier along the reaction path (with respect to the free enzyme and substrate) and that the specificity is not necessarily determined by the same reaction step that determines the rate.

Protein switches are made of highly similar sequences that fold to dramatically different structures. A structural switching system with 31 sequence variants for α and α+β folds has been illustrated experimentally by He et al., Structure, 2012, 20, 283 and is investigated computationally in the present study. Methods to assign a sequence to one of the two folds are reported and analyzed. A fast and accurate protocol to identify the correct fold of the 31 sequences is based on enriching modeled structures using short molecular dynamics (MD) trajectories and scoring these structures with coarse-grained energy functions. We examine five coarse-grained energy functions and illustrate that the Hinds–Levitt potential works the best for this task. We show that enrichment by MD significantly enhances prediction accuracy. Finally, we find that melting temperature correlates well with the energy difference between the two folds (correlation coefficient ∼−0.7). The correlation reduces dramatically (∼0.4) if the absolute energy of the correct fold is considered. Moreover, prediction of melting temperature is sensitive to the structural templates. We emphasize in our analyses the use of native structures as templates since these folds are more readily available from structural biology experiments.

An algorithm and software to refine parameters of empirical energy functions according to condensed phase experimental measurements are discussed. The algorithm is based on sensitivity analysis and local minimization of the differences between experiment and simulation as a function of potential parameters. It is illustrated for a toy problem of alanine dipeptide and is applied to folding of the peptide WAAAH. The helix fraction is highly sensitive to the potential parameters, while the slope of the melting curve is not. The sensitivity variations make it difficult to satisfy both observations simultaneously. We conjecture that there is no set of parameters that reproduces experimental melting curves of short peptides that are modeled with the usual functional form of a force field.

The efficiency and accuracy of thermodynamic cycle calculations are considered. It is rigorously shown that the energy of the mutated part (MP) need not be scaled in a thermodynamic cycle computed with dual topology. Hence, there is no need to scale to zero any of the self-interactions (i.e., the interactions involving only particles of the same MP) regardless of whether the MP is bound or not to the main system. This observation carries a promise to lower computational resources and increase accuracy. A numerical test of a complete thermodynamic cycle illustrates cost and accuracy considerations.

We report graphics processing unit (GPU) and Open-MP parallel implementations of water-specific force calculations and of bond constraints for use in molecular dynamics simulations. We focus on a typical laboratory computing environment in which a CPU with a few cores is attached to a GPU. We discuss in detail the design of the code, and we illustrate performance comparable to highly optimized codes such as GROMACS. Besides speed, our code shows excellent energy conservation. Utilization of water-specific lists allows the efficient calculations of nonbonded interactions that include water molecules and results in a speed-up factor of more than 40 on the GPU compared to code optimized on a single CPU core for systems larger than 20 000 atoms. This is up 4-fold from a factor of 10 reported in our initial GPU implementation that did not include a water-specific code. Another optimization is the implementation of constrained dynamics entirely on the GPU. The routine, which enforces constraints of all bonds, runs in parallel on multiple Open-MP cores or entirely on the GPU. It is based on the conjugate gradient solution of the Lagrange multipliers (CG SHAKE). The GPU implementation is partially in double precision and requires no communication with the CPU during the execution of the SHAKE algorithm. The (parallel) implementation of SHAKE allows an increase of the time step to 2.0 fs while maintaining excellent energy conservation. Interestingly, CG SHAKE is faster than the usual bond relaxation algorithm even on a single core if high accuracy is expected. The significant speedup of the optimized components transfers the computational bottleneck of the MD calculation to the reciprocal part of particle mesh Ewald (PME).

We investigate the kinetics and thermodynamics of a helical turn formation in the peptide Ac-WAAAH-NH2. NMR measurements indicate that this peptide has significant tendency to form a structure of a helical turn, while temperature dependent CD establishes the helix fraction at different temperatures. Molecular dynamics and milestoning simulations agree with experimental observables and suggest an atomically detailed picture for the turn formation. Using a network representation, two alternative mechanisms of folding are identified: (i) a direct co-operative mechanism from the unfolded to the folded state without intermediate formation of hydrogen bonds and (ii) an indirect mechanism with structural intermediates with two residues in a helical conformation. This picture is consistent with kinetic measurements that reveal two experimental time scales of sub-nanosecond and several nanoseconds.

Initial events of helix breakage as a function of load are considered using molecular dynamics simulations and milestoning analysis. A helix length of ∼100 amino acids is considered as a model for typical helices found in molecular machines and as a model that minimizes end effects for early events of unfolding. Transitions of individual amino acids (averaged over the helix’s interior residues) are examined and its surrounding hydrogen bonds are considered. Dense kinetic networks are constructed that, with milestoning analysis, provide the overall kinetics of early breakage events. Network analysis and selection of MaxFlux pathways illustrate that load impacts unfolding mechanisms in addition to time scales. At relatively high (100 pN) load levels, the principal intermediate is the 310-helix, while at relatively low (10 pN) levels the π-helix is significantly populated, albeit not as an unfolding intermediate. Coarse variables are examined at different levels of resolution; the rate of unfolding illustrates remarkable stability under changes in the coarsening. Consistent prediction of about ∼5 ns for the time of a single amino-acid unfolding event are obtained. Hydrogen bonds are much faster coarse variables (by about 2 orders of magnitude) compared to backbone torsional transition, which gates unfolding and thereby provides the appropriate coarse variable for the initiation of unfolding. Results provide an atomic description of “catch–bond” behavior, based on alternative pathways, in which unfolding of a simple protein structural element occurs over longer timescales for intermediate (10 pN) loads than for zero (0 pN) or large (100 pN) loads.

We report an optimized version of the molecular dynamics program MOIL that runs on a shared memory system with OpenMP and exploits the power of a graphics processing unit (GPU). The model is of a heterogeneous computing system on a single node with several cores sharing the same memory and a GPU. This is a typical laboratory tool, which provides excellent performance at minimal cost. Besides performance, emphasis is on the accuracy and stability of the algorithm probed by energy conservation for explicit-solvent atomically detailed models. Especially for long simulations, energy conservation is critical due to the phenomenon known as “energy drift” in which energy errors accumulate linearly as a function of simulation time. To achieve long-time dynamics with acceptable accuracy, the drift must be particularly small. We identify several means of controlling long-time numerical accuracy while maintaining excellent speedup. To maintain a high level of energy conservation, SHAKE and the Ewald reciprocal summation are run in double precision. Double precision summation of real-space nonbonded interactions improves energy conservation. In our best option, the energy drift using 1 fs for a time step while constraining the distances of all bonds is undetectable in a 10 ns simulation of solvated DHFR (dihydrofolate reductase). Faster options, SHAKing only bonds with hydrogen atoms, are also very well behaved and have drifts of less than 1 kcal/mol per nanosecond of the same system. CPU/GPU implementations require changes in programming models. We consider the use of a list of neighbors and quadratic versus linear interpolation in lookup tables of different sizes. Quadratic interpolation with a smaller number of grid points is faster than linear lookup tables (with finer representation) without a loss of accuracy. Atomic neighbor lists were found most efficient. Typical speedups are about a factor of 10 compared to a single-core single-precision code.

The method of Directional Milestoning is revisited. We start from an exact and more general expression and state the conditions and validity of the memory-loss approximation. An algorithm to compute a reaction coordinate from Directional Milestoning data is presented. The reaction coordinate is calculated as a set of discrete jumps between Milestones that maximizes the flux between two stable states. As an application we consider a conformational transition in solvated adenosine. We compare a long molecular dynamic trajectory with Directional Milestoning and discuss the differences between the maximum flux path and minimum energy coordinates.

Milestoning is a method for calculating kinetics and thermodynamics of long time processes typically not accessible for straightforward Molecular Dynamics (MD) simulation. In the Milestoning approach, the system of interest is partitioned into cells by dividing hypersurfaces (Milestones) and transitions are computed between nearby hypersurfaces. Kinetics and thermodynamics are derived from the statistics of these transitions. The original Milestoning work concentrated on systems in which a one-dimensional reaction coordinate or an order parameter could be identified. In many biomolecular processes, the reaction proceeds via multiple channels or following more than a single-order parameter. A description based on a one-dimensional reaction coordinate may be insufficient. In the present paper, we introduce a variation that overcomes this limitation. Following the ideas of Vanden-Eijnden and Venturoli on Voronoi cells that avoid the use of an order parameter ( J. Chem. Phys. 2009, 130, 194101), we describe another way to “Milestone” systems without a reaction coordinate. We examine the assumptions of the Milestoning calculations of mean first passage times (MFPT) and describe strategies to weaken these assumptions. The method described in this paper, Directional Milestoning, arranges hypersurfaces in higher dimensions that “tag” trajectories such that efficient calculations can be done and at the same time the assumptions required for exact calculations of MFPTs are satisfied approximately. In the original Milestoning papers, trajectories are initiated from an equilibrium set of conformations. Here a more accurate distribution, that mimics the first hitting point distribution, is used. We demonstrate the usage of Directional Milestoning in conformational transitions of alanine dipeptide (in vacuum and in aqueous solution) and compare the correctness, efficiency, and statistical stability of the method with exact MD and with a related method.

Myosin II is a molecular motor that converts chemical to mechanical energy and enables muscle operations. After a power stroke, a recovery transition completes the cycle and returns the molecular motor to its prestroke state. Atomically detailed simulations in the framework of the Milestoning theory are used to calculate kinetics and mechanisms of the recovery stroke. Milestoning divides the process into transitions between hyper-surfaces (Milestones) along a reaction coordinate. Decorrelation of dynamics between sequential Milestones is assumed, which speeds up the atomically detailed simulations by a factor of millions. Two hundred trajectories of myosin with explicit water solvation are used to sample transitions between sequential pairs of Milestones. Collective motions of hundreds of atoms are described at atomic resolution and at the millisecond time scale. The experimentally measured transition time of about a millisecond is in good agreement with the computed time. The simulations support a sequential mechanism. In the first step the P-loop and switch 2 close on the ATP and in the second step the mechanical relaxation is induced via the relay and the SH1 helices. We propose that the entropy of switch 2 helps to drive the power stroke. Secondary structure elements are progressing through a small number of discrete states in a network of activated transitions and are assisted by side chain flips between rotameric states. The few-state sequential mechanism is likely to enhance the efficiency of the relaxation reducing the probability of off-pathway intermediates.

Understanding and linking at the molecular level a disease phenotype to a specific genotype often requires going through a protein structure and function. In this issue of Structure, Gao et al. (2015) perform large scale analysis of available sequences and structural data for more than 6000 mutants representing more than 600 proteins to uncover some interesting structural effects of disease-associated mutations.

Refinement of protein structures from a correct topology to atomically detailed resolution has proven remarkably difficult. Jian et al. (in this issue of Structure) illustrate a significant advance in this task by carefully incorporating into the refinement process many body interactions extracted from fragment statistics.

Nearly every enzyme undergoes a significant change in structure after binding it's substrate. Experimental and theoretical analyses of the role of changes in HIV reverse transcriptase structure in selecting a correct substrate are presented. Atomically detailed simulations using the Milestoning method predict a rate and free energy profile of the conformational change commensurate with experimental data. A large conformational change occurring on a millisecond timescale locks the correct nucleotide at the active site but promotes release of a mismatched nucleotide. The positions along the reaction coordinate that decide the yield of the reaction are not determined by the chemical step. Rather, the initial steps of weak substrate binding and protein conformational transition significantly enrich the yield of a reaction with a correct substrate, whereas the same steps diminish the reaction probability of an incorrect substrate.Highlights► Kinetics and atomic simulations quantitatively explain nucleotide binding to HIV-RT ► Reaction path, free energy, and kinetics of HIV-RT transition are computed ► Simulations show that specificity is based on induced fit ► Specificity is determined by the rate of conformation change not only chemical step

The distributions of different cations around A-RNA are computed by Poisson-Boltzmann (PB) equation and replica exchange molecular dynamics (MD). Both the nonlinear PB and size-modified PB theories are considered. The number of ions bound to A-RNA, which can be measured experimentally, is well reproduced in all methods. On the other hand, the radial ion distribution profiles show differences between MD and PB. We showed that PB results are sensitive to ion size and functional form of the solvent dielectric region but not the solvent dielectric boundary definition. Size-modified PB agrees with replica exchange molecular dynamics much better than nonlinear PB when the ion sizes are chosen from atomistic simulations. The distribution of ions 14 Å away from the RNA central axis are reasonably well reproduced by size-modified PB for all ion types with a uniform solvent dielectric model and a sharp dielectric boundary between solvent and RNA. However, this model does not agree with MD for shorter distances from the A-RNA. A distance-dependent solvent dielectric function proposed by another research group improves the agreement for sodium and strontium ions, even for shorter distances from the A-RNA. However, Mg2+ distributions are still at significant variances for shorter distances.

RNA molecules play critical roles in many cellular processes. Traditionally viewed as genetic messengers, RNA molecules were recently discovered to have diverse functions related to gene regulation and expression. RNA also has great potential as a therapeutic and a tool for further investigation of gene regulation. Metal ions are an integral part of RNA structure and should be considered in any experimental or theoretical study of RNA. Here, we report a multidisciplinary approach that combines anomalous small-angle x-ray scattering and molecular-dynamics (MD) simulations with explicit solvent and ions around RNA. From experiment and simulation results, we find excellent agreement in the number and distribution of excess monovalent and divalent ions around a short RNA duplex. Although similar agreement can be obtained from a continuum description of the solvent and mobile ions (by solving the Poisson-Boltzmann equation and accounting for finite ion size), the use of MD is easily extended to flexible RNA systems with thermal fluctuations. Therefore, we also model a short RNA pseudoknot and find good agreement between the MD results and the experimentally derived solution structures. Surprisingly, both deviate from crystal structure predictions. These favorable comparisons of experiment and simulations encourage work on RNA in all-atom dynamic models.

Coiled coils are important structural motifs formed by two or more amphipathic α-helices that twist into a supercoil. These motifs are found in a wide range of proteins, including motor proteins and structural proteins, that are known to transmit mechanical loads. We analyze atomically detailed simulations of coiled-coil cracking under load with Milestoning. Milestoning is an approach that captures the main features of the process in a network, quantifying kinetics and thermodynamics. A 112-residue segment of the β-myosin S2 domain was subjected to constant-magnitude (0–200 pN) and constant-direction tensile forces in molecular dynamics simulations. Twenty 20 ns straightforward simulations at several load levels revealed that initial single-residue cracking events (Ψ > 90°) at loads <100 pN were accompanied by rapid refolding without either intra- or interhelix unfolding propagation. Only initial unfolding events at the highest load (200 pN) regularly propagated along and between helices. Analysis of hydrophobic interactions and of interhelix hydrogen bonds did not show significant variation as a function of load. Unfolding events were overwhelmingly located in the vicinity of E929, a charged residue in a hydrophobic position of the heptad repeat. Milestoning network analysis of E929 cracking determined that the mean first-passage time ranges from 20 ns (200 pN) to 80 ns (50 pN), which is ∼20 times the mean first-passage time of an isolated helix with the same sequence.

Recent computational studies (Cecchini et al., 2010; Tehver and Thirumalai, 2010) have brought us closer to watching a molecular machine, myosin, in action. This significant achievement, obtained by sensible physical approximations, opens a highway to improve the integration of computational methods and experimental results.

Protein switches are made of highly similar sequences that fold to dramatically different structures. A structural switching system with 31 sequence variants for α and α+β folds has been illustrated experimentally by He et al., Structure, 2012, 20, 283 and is investigated computationally in the present study. Methods to assign a sequence to one of the two folds are reported and analyzed. A fast and accurate protocol to identify the correct fold of the 31 sequences is based on enriching modeled structures using short molecular dynamics (MD) trajectories and scoring these structures with coarse-grained energy functions. We examine five coarse-grained energy functions and illustrate that the Hinds–Levitt potential works the best for this task. We show that enrichment by MD significantly enhances prediction accuracy. Finally, we find that melting temperature correlates well with the energy difference between the two folds (correlation coefficient ∼−0.7). The correlation reduces dramatically (∼0.4) if the absolute energy of the correct fold is considered. Moreover, prediction of melting temperature is sensitive to the structural templates. We emphasize in our analyses the use of native structures as templates since these folds are more readily available from structural biology experiments.