Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study

Side-Chain Polarity Modulates the Intrinsic Conformational Landscape of Model Dipeptides

The intrinsic conformational preferences of small peptides may provide additional insight into the thermodynamics and kinetics of protein folding. In this study, we explore the underlying energy landscapes of two model peptides, namely, Ac-Ala-NH₂ and Ac-Ser-NH₂, using geometry-optimization-based tools developed within the context of energy landscape theory. We analyze not only how side-chain polarity influences the structural preferences of the dipeptides, but also other emergent properties of the landscape, including heat capacity profiles, and kinetics of conformational rearrangements. The contrasting topographies of the free energy landscape agree with recent results from Fourier transform microwave spectroscopy experiments, where Ac-Ala-NH₂ was found to exist as a mixture of two conformers, while Ac-Ser-NH₂ remained structurally locked, despite exhibiting an apparently rich conformational landscape.

Reweighting non-equilibrium steady-state dynamics along collective variables

Computer simulations generate microscopic trajectories of complex systems at a single thermodynamic state point. We recently introduced a Maximum Caliber (MaxCal) approach for dynamical reweighting. Our approach mapped these trajectories to a Markovian description on the configurational coordinates and reweighted path probabilities as a function of external forces. Trajectory probabilities can be dynamically reweighted both from and to equilibrium or non-equilibrium steady states. As the system's dimensionality increases, an exhaustive description of the microtrajectories becomes prohibitive-even with a Markovian assumption. Instead, we reduce the dimensionality of the configurational space to collective variables (CVs). Going from configurational to CV space, we define local entropy productions derived from configurationally averaged mean forces. The entropy production is shown to be a suitable constraint on MaxCal for non-equilibrium steady states expressed as a function of CVs. We test the reweighting procedure on two systems: a particle subject to a two-dimensional potential and a coarse-grained peptide. Our CV-based MaxCal approach expands dynamical reweighting to larger systems, for both static and dynamical properties, and across a large range of driving forces.

Path probability ratios for Langevin dynamics-Exact and approximate

Path reweighting is a principally exact method to estimate dynamic properties from biased simulations-provided that the path probability ratio matches the stochastic integrator used in the simulation. Previously reported path probability ratios match the Euler-Maruyama scheme for overdamped Langevin dynamics. Since molecular dynamics simulations use Langevin dynamics rather than overdamped Langevin dynamics, this severely impedes the application of path reweighting methods. Here, we derive the path probability ratio M_L for Langevin dynamics propagated by a variant of the Langevin Leapfrog integrator. This new path probability ratio allows for exact reweighting of Langevin dynamics propagated by this integrator. We also show that a previously derived approximate path probability ratio M_approx differs from the exact M_L only by O(ξ⁴Δt⁴) and thus yields highly accurate dynamic reweighting results. (Δt is the integration time step, and ξ is the collision rate.) The results are tested, and the efficiency of path reweighting is explored using butane as an example.

Dynamic Properties of the Photosensory Domain of Deinococcus radiodurans Bacteriophytochrome

Phytochromes are biological photoreceptors found in all kingdoms of life. Numerous physicochemical and spectroscopic studies of phytochromes have been carried out for many decades, both experimentally and computationally, with the main focus on the photoconversion mechanism involving a tetrapyrrole chromophore. In this computational work, we concentrate on the long-scale dynamic motion of the photosensory domain of Deinococcus radiodurans by means of classical all-atom molecular dynamics (MD) simulations. Conventional and accelerated MD methods in combination with two different force fields, CHARMM27 and AMBER ff14SB, are tested in long atomistic simulations to confront the dynamics of monomer and dimer forms. These calculations highlight dissimilar equilibrium conformations in aqueous solutions and, in turn, different large-scale dynamic behaviors of the monomer form vs the dimer form. While the phytochrome in a monomer form tends to close the cavity entailed between the GAF and PHY domains, the opposite trend is predicted for the phytochrome dimer, which opens up as a consequence of the formation of strong salt bridges between the PHY domains of two molecules in water.

Dynamical reweighting methods for Markov models

Conformational dynamics is essential to biomolecular processes. Markov State Models (MSMs) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations is still at an early stage of development. Several dynamical reweighing approaches have been proposed, which can be classified as approaches based on (i) Kramers rate theory, (ii) rescaling of the probability density flux, (iii) reweighting by formulating a likelihood function, (iv) path reweighting. We present the state-of-the-art and discuss the methodological differences of these methods, their limitations and recent applications.

Uncertainty quantification for Markov state models of biomolecules constructed using rare event acceleration techniques

Markov state models (MSMs) of biomolecular systems are often constructed using the molecular dynamics (MD) technique. Despite having very long MD trajectories, some states and pathways can be missing in the MD data, which may make the MSMs incomplete. Consequently, uncertainty quantification for the resulting MSM becomes important. Using deca-alanine as a prototype system, we demonstrate that rare-event acceleration techniques can be employed to greatly lower the MSM uncertainty with a high computational efficiency with the assumption that the rare-event acceleration technique is able to determine most pathways that are relevant to the dynamics. In particular, we explore applications of steered MD to construct MSMs. Upper and lower bounds for uncertainty in the resulting MSM are derived. Safeguards are built into our approach to handle scenarios where the rare-event acceleration technique is unable to discover some important pathways.

Acceleration of biomolecular kinetics in Gaussian accelerated molecular dynamics

Recent studies demonstrated that Gaussian accelerated molecular dynamics (GaMD) is a robust computational technique, which provides simultaneous unconstrained enhanced sampling and free energy calculations of biomolecules. However, the exact acceleration of biomolecular dynamics or speedup of kinetic rates in GaMD simulations and, more broadly, in enhanced sampling methods, remains a challenging task to be determined. Here, the GaMD acceleration is examined using alanine dipeptide in explicit solvent as a biomolecular model system. Relative to long conventional molecular dynamics simulation, GaMD simulations exhibited ∼36-67 times speedup for sampling of the backbone dihedral transitions. The acceleration depended on level of the GaMD boost potential. Furthermore, Kramers' rate theory was applied to estimate GaMD acceleration using simulation-derived diffusion coefficients, curvatures and barriers of free energy profiles. In most cases, the calculations also showed significant speedup of dihedral transitions in GaMD, although the GaMD acceleration factors tended to be underestimated by ∼3-96 fold. Because greater boost potential can be applied in GaMD simulations of systems with increased sizes, which potentially leads to higher acceleration, it is subject to future studies on accelerating the dynamics and recovering kinetic rates of larger biomolecules such as proteins and protein-protein/nucleic acid complexes.

A new class of enhanced kinetic sampling methods for building Markov state models

Markov state models (MSMs) and other related kinetic network models are frequently used to study the long-timescale dynamical behavior of biomolecular and materials systems. MSMs are often constructed bottom-up using brute-force molecular dynamics (MD) simulations when the model contains a large number of states and kinetic pathways that are not known a priori. However, the resulting network generally encompasses only parts of the configurational space, and regardless of any additional MD performed, several states and pathways will still remain missing. This implies that the duration for which the MSM can faithfully capture the true dynamics, which we term as the validity time for the MSM, is always finite and unfortunately much shorter than the MD time invested to construct the model. A general framework that relates the kinetic uncertainty in the model to the validity time, missing states and pathways, network topology, and statistical sampling is presented. Performing additional calculations for frequently-sampled states/pathways may not alter the MSM validity time. A new class of enhanced kinetic sampling techniques is introduced that aims at targeting rare states/pathways that contribute most to the uncertainty so that the validity time is boosted in an effective manner. Examples including straightforward 1D energy landscapes, lattice models, and biomolecular systems are provided to illustrate the application of the method. Developments presented here will be of interest to the kinetic Monte Carlo community as well.

Role of Protein Dimeric Interface in Allosteric Inhibition of N-Acetyl-Aspartate Hydrolysis by Human Aspartoacylase

The results of molecular modeling suggest a mechanism of allosteric inhibition upon hydrolysis of N-acetyl-aspartate (NAA), one of the most abundant amino acid derivatives in brain, by human aspartoacylase (hAsp). Details of this reaction are important to suggest the practical ways to control the enzyme activity. Search for allosteric sites using the Allosite web server and SiteMap analysis allowed us to identify substrate binding pockets located at the interface between the subunits of the hAsp dimer molecule. Molecular docking of NAA to the pointed areas at the dimer interface predicted a specific site, in which the substrate molecule interacts with the Gly237, Arg233, Glu290, and Lys292 residues. Analysis of multiple long-scaled molecular dynamics trajectories (the total simulation time exceeded 1.5 μs) showed that binding of NAA to the identified allosteric site induced significant rigidity to the protein loops with the amino acid side chains forming gates to the enzyme active site. Application of the protein dynamical network algorithms showed that substantial reorganization of the signal propagation pathways of intersubunit communication in the dimer occurred upon allosteric NAA binding to the remote site. The modeling approaches provide an explanation to the observed decrease of the reaction rate of NAA hydrolysis by hAsp at high substrate concentrations.

Gaussian Accelerated Molecular Dynamics in NAMD

Gaussian accelerated molecular dynamics (GaMD) is a recently developed enhanced sampling technique that provides efficient free energy calculations of biomolecules. Like the previous accelerated molecular dynamics (aMD), GaMD allows for “unconstrained” enhanced sampling without the need to set predefined collective variables and so is useful for studying complex biomolecular conformational changes such as protein folding and ligand binding. Furthermore, because the boost potential is constructed using a harmonic function that follows Gaussian distribution in GaMD, cumulant expansion to the second order can be applied to recover the original free energy profiles of proteins and other large biomolecules, which solves a long-standing energetic reweighting problem of the previous aMD method. Taken together, GaMD offers major advantages for both unconstrained enhanced sampling and free energy calculations of large biomolecules. Here, we have implemented GaMD in the NAMD package on top of the existing aMD feature and validated it on three model systems: alanine dipeptide, the chignolin fast-folding protein, and the M₃ muscarinic G protein-coupled receptor (GPCR). For alanine dipeptide, while conventional molecular dynamics (cMD) simulations performed for 30 ns are poorly converged, GaMD simulations of the same length yield free energy profiles that agree quantitatively with those of 1000 ns cMD simulation. Further GaMD simulations have captured folding of the chignolin and binding of the acetylcholine (ACh) endogenous agonist to the M₃ muscarinic receptor. The reweighted free energy profiles are used to characterize the protein folding and ligand binding pathways quantitatively. GaMD implemented in the scalable NAMD is widely applicable to enhanced sampling and free energy calculations of large biomolecules.

Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.

Investigating rare events with nonequilibrium work measurements. II. Transition and reaction rates

We present a formalism for investigating transition pathways and transition probabilities for rare events in biomolecular systems. The formalism is based on combining Transition Path Theory with the results of nonequilibrium work relations, and shows that the equilibrium and nonequilibrium transition rates are in fact related. Aside from its fundamental importance, this allows for the calculation of relative equilibrium reaction rates with driven nonequilibrium simulations such as Steered Molecular Dynamics. The workings of the formalism are illustrated with a few typical numerical examples.

Functional loop dynamics of the streptavidin-biotin complex

Accelerated molecular dynamics (aMD) simulation is employed to study the functional dynamics of the flexible loop(3-4) in the strong-binding streptavidin-biotin complex system. Conventional molecular (cMD) simulation is also performed for comparison. The present study reveals the following important properties of the loop dynamics: (1) The transition of loop(3-4) from open to closed state is observed in 200 ns aMD simulation. (2) In the absence of biotin binding, the open-state streptavidin is more stable, which is consistent with experimental evidences. The free energy (ΔG) difference is about 5 kcal/mol between two states. But with biotin binding, the closed state is more stable due to electrostatic and hydrophobic interactions between the loop(3-4) and biotin. (3) The closure of loop(3-4) is concerted to the stable binding of biotin to streptavidin. When the loop(3-4) is in its open-state, biotin moves out of the binding pocket, indicating that the interactions between the loop(3-4) and biotin are essential in trapping biotin in the binding pocket. (4) In the tetrameric streptavidin system, the conformational change of the loop(3-4) in each monomer is independent of each other. That is, there is no cooperative binding for biotin bound to the four subunits of the tetramer.

Practical hyperdynamics method for systems with large changes in potential energy

A practical hyperdynamics method is proposed to accelerate systems with highly endothermic and exothermic reactions such as hydrocarbon pyrolysis and oxidation reactions. In this method, referred to as the "adaptive hyperdynamics (AHD) method," the bias potential parameters are adaptively updated according to the change in potential energy. The approach is intensively examined for JP-10 (exo-tetrahydrodicyclopentadiene) pyrolysis simulations using the ReaxFF reactive force field. Valid boost parameter ranges are clarified as a result. It is shown that AHD can be used to model pyrolysis at temperatures as low as 1000 K while achieving a boost factor of around 10(5).

Cross dimerization of amyloid-β and αsynuclein proteins in aqueous environment: a molecular dynamics simulations study

Self-assembly of the intrinsically unstructured proteins, amyloid beta (Aβ) and alpha synclein (αSyn), are associated with Alzheimer's Disease, and Parkinson's and Lewy Body Diseases, respectively. Importantly, pathological overlaps between these neurodegenerative diseases, and the possibilities of interactions between Aβ and αSyn in biological milieu emerge from several recent clinical reports and in vitro studies. Nevertheless, there are very few molecular level studies that have probed the nature of spontaneous interactions between these two sequentially dissimilar proteins and key characteristics of the resulting cross complexes. In this study, we have used atomistic molecular dynamics simulations to probe the possibility of cross dimerization between αSyn1-95 and Aβ1-42, and thereby gain insights into their plausible early assembly pathways in aqueous environment. Our analyses indicate a strong probability of association between the two sequences, with inter-protein attractive electrostatic interactions playing dominant roles. Principal component analysis revealed significant heterogeneity in the strength and nature of the associations in the key interaction modes. In most, the interactions of repeating Lys residues, mainly in the imperfect repeats 'KTKEGV' present in αSyn1-95 were found to be essential for cross interactions and formation of inter-protein salt bridges. Additionally, a hydrophobicity driven interaction mode devoid of salt bridges, where the non-amyloid component (NAC) region of αSyn1-95 came in contact with the hydrophobic core of Aβ1-42 was observed. The existence of such hetero complexes, and therefore hetero assembly pathways may lead to polymorphic aggregates with variations in pathological attributes. Our results provide a perspective on development of therapeutic strategies for preventing pathogenic interactions between these proteins.

Trypsinogen activation as observed in accelerated molecular dynamics simulations

Serine proteases are involved in many fundamental physiological processes, and control of their activity mainly results from the fact that they are synthetized in an inactive form that becomes active upon cleavage. Three decades ago Martin Karplus's group performed the first molecular dynamics simulations of trypsin, the most studied member of the serine protease family, to address the transition from the zymogen to its active form. Based on the computational power available at the time, only high frequency fluctuations, but not the transition steps, could be observed. By performing accelerated molecular dynamics (aMD) simulations, an interesting approach that increases the configurational sampling of atomistic simulations, we were able to observe the N-terminal tail insertion, a crucial step of the transition mechanism. Our results also support the hypothesis that the hydrophobic effect is the main force guiding the insertion step, although substantial enthalpic contributions are important in the activation mechanism. As the N-terminal tail insertion is a conserved step in the activation of serine proteases, these results afford new perspective on the underlying thermodynamics of the transition from the zymogen to the active enzyme.

Adaptive accelerated ReaxFF reactive dynamics with validation from simulating hydrogen combustion

We develop here the methodology for dramatically accelerating the ReaxFF reactive force field based reactive molecular dynamics (RMD) simulations through use of the bond boost concept (BB), which we validate here for describing hydrogen combustion. The bond order, undercoordination, and overcoordination concepts of ReaxFF ensure that the BB correctly adapts to the instantaneous configurations in the reactive system to automatically identify the reactions appropriate to receive the bond boost. We refer to this as adaptive Accelerated ReaxFF Reactive Dynamics or aARRDyn. To validate the aARRDyn methodology, we determined the detailed sequence of reactions for hydrogen combustion with and without the BB. We validate that the kinetics and reaction mechanisms (that is the detailed sequences of reactive intermediates and their subsequent transformation to others) for H2 oxidation obtained from aARRDyn agrees well with the brute force reactive molecular dynamics (BF-RMD) at 2498 K. Using aARRDyn, we then extend our simulations to the whole range of combustion temperatures from ignition (798 K) to flame temperature (2998K), and demonstrate that, over this full temperature range, the reaction rates predicted by aARRDyn agree well with the BF-RMD values, extrapolated to lower temperatures. For the aARRDyn simulation at 798 K we find that the time period for half the H2 to form H2O product is ∼538 s, whereas the computational cost was just 1289 ps, a speed increase of ∼0.42 trillion (10(12)) over BF-RMD. In carrying out these RMD simulations we found that the ReaxFF-COH2008 version of the ReaxFF force field was not accurate for such intermediates as H3O. Consequently we reoptimized the fit to a quantum mechanics (QM) level, leading to the ReaxFF-OH2014 force field that was used in the simulations.

Free energy landscape of G-protein coupled receptors, explored by accelerated molecular dynamics

G-protein coupled receptors (GPCRs) mediate cellular responses to various hormones and neurotransmitters and are important targets for treating a wide spectrum of diseases. They are known to adopt multiple conformational states (e.g., inactive, intermediate and active) during their modulation of various cell signaling pathways. Here, the free energy landscape of GPCRs is explored using accelerated molecular dynamics (aMD) simulations as demonstrated on the M2 muscarinic receptor, a key GPCR that regulates human heart rate and contractile forces of cardiomyocytes. Free energy profiles of important structural motifs that undergo conformational transitions upon GPCR activation and allosteric signaling are analyzed in detail, including the Arg(3.50)-Glu(6.30) ionic lock, the Trp(6.48) toggle switch and the hydrogen interactions between Tyr(5.58)-Tyr(7.53).

Substrate-dependent dynamics of UDP-galactopyranose mutase: Implications for drug design

Trypanosoma cruzi is the causative agent of Chagas disease, a neglected tropical disease that represents one of the major health challenges of the Latin American countries. Successful efforts were made during the last few decades to control the transmission of this disease, but there is still no treatment for the 10 million adults in the chronic phase of the disease. In T. cruzi, as well as in other pathogens, the flavoenzyme UDP-galactopyranose mutase (UGM) catalyzes the conversion of UDP-galactopyranose to UDP-galactofuranose, a precursor of the cell surface β-galactofuranose that is involved in the virulence of the pathogen. The fact that UGM is not present in humans makes inhibition of this enzyme a good approach in the design of new Chagas therapeutics. By performing a series of computer simulations of T. cruzi UGM in the presence or absence of an active site ligand, we address the molecular details of the mechanism that controls the uptake and retention of the substrate. The simulations suggest a modular mechanism in which each moiety of the substrate controls the flexibility of a different protein loop. Furthermore, the calculations indicate that interactions with the substrate diphosphate moiety are especially important for stabilizing the closed active site. This hypothesis is supported with kinetics measurements of site-directed mutants of T. cruzi UGM. Our results extend our knowledge of UGM dynamics and offer new alternatives for the prospective design of drugs.

w-REXAMD: A Hamiltonian Replica Exchange Approach to Improve Free Energy Calculations for Systems with Kinetically Trapped Conformations

Free energy governs the equilibrium extent of many biological processes. High barriers separating free energy minima often limit the sampling in molecular dynamics (MD) simulations, leading to inaccurate free energies. Here, we demonstrate enhanced sampling and improved free energy calculations, relative to conventional MD, using windowed accelerated MD within a Hamiltonian replica exchange framework (w-REXAMD). We show that for a case in which multiple conformations are separated by large free energy barriers, w-REXAMD is a useful enhanced sampling technique, without any necessary reweighting.

Improved Statistical Sampling and Accuracy with Accelerated Molecular Dynamics on Rotatable Torsions

In enhanced sampling techniques, the precision of the reweighted ensemble properties is often decreased due to large variation in statistical weights and reduction in the effective sampling size. To abate this reweighting problem, here, we propose a general accelerated molecular dynamics (aMD) approach in which only the rotatable dihedrals are subjected to aMD (RaMD), unlike the typical implementation wherein all dihedrals are boosted (all-aMD). Nonrotatable and improper dihedrals are marginally important to conformational changes or the different rotameric states. Not accelerating them avoids the sharp increases in the potential energies due to small deviations from their minimum energy conformations and leads to improvement in the precision of RaMD. We present benchmark studies on two model dipeptides, Ace-Ala-Nme and Ace-Trp-Nme, simulated with normal MD, all-aMD, and RaMD. We carry out a systematic comparison between the performances of both forms of aMD using a theory that allows quantitative estimation of the effective number of sampled points and the associated uncertainty. Our results indicate that, for the same level of acceleration and simulation length, as used in all-aMD, RaMD results in significantly less loss in the effective sample size and, hence, increased accuracy in the sampling of φ-ψ space. RaMD yields an accuracy comparable to that of all-aMD, from simulation lengths 5 to 1000 times shorter, depending on the peptide and the acceleration level. Such improvement in speed and accuracy over all-aMD is highly remarkable, suggesting RaMD as a promising method for sampling larger biomolecules.

Accelerated molecular dynamics in computational drug design

The method of accelerated molecular dynamics (aMD) has been shown to increase the rate of phase-space sampling in biomolecular simulations. In this chapter, we discuss the theory behind aMD and describe the implementation of two versions: dual-boost and selective aMD. Each method has its practical advantages: dual-boost aMD is useful for increasing sampling of global conformational motions while selective aMD can improve the rate of convergence of free energy calculations. Special emphasis is placed on the use of these methods in computer-aided drug design, and the example of oseltamivir binding to neuraminidase is highlighted for both cases.

Guide to virtual screening: application to the Akt phosphatase PHLPP

We present an example-based description of virtual screening (VS) techniques used to identify new regulators of the Akt phosphatase PHLPP (PH domain Leucine repeat Protein Phosphatase). This enzyme opposes the effects of two kinases, Akt and PKC, which play a major role in cell growth and survival. Therefore, PHLPP is a potential therapeutic target in pathophysiologies where these pathways are either repressed, such as in diabetes and cardiovascular diseases, or over-activated as in cancer. To the best of our knowledge, no PHLPP inhibitors have been reported so far in the literature. In this study, we used a combination of chemical and virtual screening techniques that led to the identification of a number of inhibiting compounds with diverse scaffolds. These compounds bind PHLPP and inhibit cell death when tested in cellular assays. We employed GLIDE docking software to screen a library of more than 40,000 compounds selected from the NCI open depository (250,000 compounds) by similarity searches. We compare the efficiency at which we determined binding compounds from the chemical screen, and compare enrichment factors of the virtually discovered compounds over chemical screening.

Protecting High Energy Barriers: A New Equation to Regulate Boost Energy in Accelerated Molecular Dynamics Simulations

Molecular dynamics (MD) is one of the most common tools in computational chemistry. Recently, our group has employed accelerated molecular dynamics (aMD) to improve the conformational sampling over conventional molecular dynamics techniques. In the original aMD implementation, sampling is greatly improved by raising energy wells below a predefined energy level. Recently, our group presented an alternative aMD implementation where simulations are accelerated by lowering energy barriers of the potential energy surface. When coupled with thermodynamic integration simulations, this implementation showed very promising results. However, when applied to large systems, such as proteins, the simulation tends to be biased to high energy regions of the potential landscape. The reason for this behavior lies in the boost equation used since the highest energy barriers are dramatically more affected than the lower ones. To address this issue, in this work, we present a new boost equation that prevents oversampling of unfavorable high energy conformational states. The new boost potential provides not only better recovery of statistics throughout the simulation but also enhanced sampling of statistically relevant regions in explicit solvent MD simulations.

Large-scale conformational changes of Trypanosoma cruzi proline racemase predicted by accelerated molecular dynamics simulation

Chagas' disease, caused by the protozoan parasite Trypanosoma cruzi (T. cruzi), is a life-threatening illness affecting 11-18 million people. Currently available treatments are limited, with unacceptable efficacy and safety profiles. Recent studies have revealed an essential T. cruzi proline racemase enzyme (TcPR) as an attractive candidate for improved chemotherapeutic intervention. Conformational changes associated with substrate binding to TcPR are believed to expose critical residues that elicit a host mitogenic B-cell response, a process contributing to parasite persistence and immune system evasion. Characterization of the conformational states of TcPR requires access to long-time-scale motions that are currently inaccessible by standard molecular dynamics simulations. Here we describe advanced accelerated molecular dynamics that extend the effective simulation time and capture large-scale motions of functional relevance. Conservation and fragment mapping analyses identified potential conformational epitopes located in the vicinity of newly identified transient binding pockets. The newly identified open TcPR conformations revealed by this study along with knowledge of the closed to open interconversion mechanism advances our understanding of TcPR function. The results and the strategy adopted in this work constitute an important step toward the rationalization of the molecular basis behind the mitogenic B-cell response of TcPR and provide new insights for future structure-based drug discovery.

Enhanced Lipid Diffusion and Mixing in Accelerated Molecular Dynamics

Accelerated molecular dynamics (aMD) is an enhanced sampling technique that expedites conformational space sampling by reducing the barriers separating various low-energy states of a system. Here, we present the first application of the aMD method on lipid membranes. Altogether, ∼1.5 μs simulations were performed on three systems: a pure POPC bilayer, a pure DMPC bilayer, and a mixed POPC:DMPC bilayer. Overall, the aMD simulations are found to produce significant speedup in trans–gauche isomerization and lipid lateral diffusion versus those in conventional MD (cMD) simulations. Further comparison of a 70-ns aMD run and a 300-ns cMD run of the mixed POPC:DMPC bilayer shows that the two simulations yield similar lipid mixing behaviors, with aMD generating a 2–3-fold speedup compared to cMD. Our results demonstrate that the aMD method is an efficient approach for the study of bilayer structural and dynamic properties. On the basis of simulations of the three bilayer systems, we also discuss the impact of aMD parameters on various lipid properties, which can be used as a guideline for future aMD simulations of membrane systems.

Integrating diffusion maps with umbrella sampling: application to alanine dipeptide

Nonlinear dimensionality reduction techniques can be applied to molecular simulation trajectories to systematically extract a small number of variables with which to parametrize the important dynamical motions of the system. For molecular systems exhibiting free energy barriers exceeding a few k(B)T, inadequate sampling of the barrier regions between stable or metastable basins can lead to a poor global characterization of the free energy landscape. We present an adaptation of a nonlinear dimensionality reduction technique known as the diffusion map that extends its applicability to biased umbrella sampling simulation trajectories in which restraining potentials are employed to drive the system into high free energy regions and improve sampling of phase space. We then propose a bootstrapped approach to iteratively discover good low-dimensional parametrizations by interleaving successive rounds of umbrella sampling and diffusion mapping, and we illustrate the technique through a study of alanine dipeptide in explicit solvent.

Implementation of Accelerated Molecular Dynamics in NAMD

Accelerated molecular dynamics (aMD) is an enhanced-sampling method that improves the conformational space sampling by reducing energy barriers separating different states of a system. Here we present the implementation of aMD in the parallel simulation program NAMD. We show that aMD simulations performed with NAMD have only a small overhead compared with classical MD simulations. Through example applications to the alanine dipeptide, we discuss the choice of acceleration parameters, the interpretation of aMD results, as well as the advantages and limitations of the aMD method.

Coupling Constant pH Molecular Dynamics with Accelerated Molecular Dynamics

An extension of the constant pH method originally implemented by Mongan et al. (J. Comput. Chem.2004, 25, 2038−2048) is proposed in this study. This adapted version of the method couples the constant pH methodology with the enhanced sampling technique of accelerated molecular dynamics, in an attempt to overcome the sampling issues encountered with current standard constant pH molecular dynamics methods. Although good results were reported by Mongan et al. on application of the standard method to the hen egg-white lysozyme (HEWL) system, residues which possess strong interactions with neighboring groups tend to converge slowly, resulting in the reported inconsistencies for predicted pK_a values, as highlighted by the authors. The application of the coupled method described in this study to the HEWL system displays improvements over the standard version of the method, with the improved sampling leading to faster convergence and producing pK_a values in closer agreement to those obtained experimentally for the more slowly converging residues.

Introducing sampling entropy in repository based adaptive umbrella sampling

Determining free energy surfaces along chosen reaction coordinates is a common and important task in simulating complex systems. Due to the complexity of energy landscapes and the existence of high barriers, one widely pursued objective to develop efficient simulation methods is to achieve uniform sampling among thermodynamic states of interest. In this work, we have demonstrated sampling entropy (SE) as an excellent indicator for uniform sampling as well as for the convergence of free energy simulations. By introducing SE and the concentration theorem into the biasing-potential-updating scheme, we have further improved the adaptivity, robustness, and applicability of our recently developed repository based adaptive umbrella sampling (RBAUS) approach [H. Zheng and Y. Zhang, J. Chem. Phys. 128, 204106 (2008)]. Besides simulations of one dimensional free energy profiles for various systems, the generality and efficiency of this new RBAUS-SE approach have been further demonstrated by determining two dimensional free energy surfaces for the alanine dipeptide in gas phase as well as in water.

Transition path sampling and forward flux sampling. Applications to biological systems

The last decade has seen a rapid growth in the number of simulation methods and applications dealing with the sampling of transition pathways of rare nanoscale events. Such studies are crucial, for example, for understanding the mechanism and kinetics of conformational transitions and enzymatic events associated with the function of biomolecules. In this review, a broad account of transition path sampling approaches is provided, starting from the general concepts, progressing to the specific principles that underlie some of the most important methods, and eventually singling out the so-called forward flux sampling method for a more detailed description. This is done because forward flux sampling, despite its appealing simplicity and potential efficiency, has thus far received limited attention from practitioners. While path sampling methods have a widespread application to many types of rare transitional events, here only recent applications involving biomolecules are reviewed, including isomerization, protein folding, and enzyme catalysis.

A kinetic model of trp-cage folding from multiple biased molecular dynamics simulations

Trp-cage is a designed 20-residue polypeptide that, in spite of its size, shares several features with larger globular proteins.Although the system has been intensively investigated experimentally and theoretically, its folding mechanism is not yet fully understood. Indeed, some experiments suggest a two-state behavior, while others point to the presence of intermediates. In this work we show that the results of a bias-exchange metadynamics simulation can be used for constructing a detailed thermodynamic and kinetic model of the system. The model, although constructed from a biased simulation, has a quality similar to those extracted from the analysis of long unbiased molecular dynamics trajectories. This is demonstrated by a careful benchmark of the approach on a smaller system, the solvated Ace-Ala3-Nme peptide. For theTrp-cage folding, the model predicts that the relaxation time of 3100 ns observed experimentally is due to the presence of a compact molten globule-like conformation. This state has an occupancy of only 3% at 300 K, but acts as a kinetic trap.Instead, non-compact structures relax to the folded state on the sub-microsecond timescale. The model also predicts the presence of a state at Calpha-RMSD of 4.4 A from the NMR structure in which the Trp strongly interacts with Pro12. This state can explain the abnormal temperature dependence of the Pro12-delta3 and Gly11-alpha3 chemical shifts. The structures of the two most stable misfolded intermediates are in agreement with NMR experiments on the unfolded protein. Our work shows that, using biased molecular dynamics trajectories, it is possible to construct a model describing in detail the Trp-cage folding kinetics and thermodynamics in agreement with experimental data.

E9-Im9 colicin DNase-immunity protein biomolecular association in water: a multiple-copy and accelerated molecular dynamics simulation study

Protein-protein transient and dynamic interactions underlie all biological processes. The molecular dynamics (MD) of the E9 colicin DNase protein, its Im9 inhibitor protein, and their E9-Im9 recognition complex are investigated by combining multiple-copy (MC) MD and accelerated MD (aMD) explicit-solvent simulation approaches, after validation with crystalline-phase and solution experiments. Im9 shows higher flexibility than its E9 counterpart. Im9 displays a significant reduction of backbone flexibility and a remarkable increase in motional correlation upon E9 association. Im9 loops 23-31 and 54-64 open with respect to the E9-Im9 X-ray structure and show high conformational diversity. Upon association a large fraction (approximately 20 nm2) of E9 and Im9 protein surfaces become inaccessible to water. Numerous salt bridges transiently occurring throughout our six 50 ns long MC-MD simulations are not present in the X-ray model. Among these Im9 Glu31-E9 Arg96 and Im9 Glu41-Lys89 involve interface interactions. Through the use of 10 ns of Im9 aMD simulation, we reconcile the largest thermodynamic impact measured for Asp51Ala mutation with Im9 structure and dynamics. Lys57 acts as an essential molecular switch to shift Im9 surface loop towards an ideal configuration for E9 inhibition. This is achieved by switching Asp60-Lys57 and Asp62-Lys57 hydrogen bonds to Asp51-Lys57 salt bridge. E9-Im9 recognition involves shifts of conformational distributions, reorganization of intramolecular hydrogen bond patterns, and formation of new inter- and intramolecular interactions. The description of key transient biological interactions can be significantly enriched by the dynamic and atomic-level information provided by computer simulations.