Standard Molecular Dynamics Simulations Research Articles

Holo-like and Druggable Protein Conformations from Enhanced Sampling of Binding Pocket Volume and Shape.

Understanding molecular recognition of small molecules by proteins in atomistic detail is key for drug design. Molecular docking is a widely used computational method to mimic ligand-protein association in silico. However, predicting conformational changes occurring in proteins upon ligand binding is still a major challenge. Ensemble docking approaches address this issue by considering a set of different conformations of the protein obtained either experimentally or from computer simulations, e.g., molecular dynamics. However, holo structures prone to host (the correct) ligands are generally poorly sampled by standard molecular dynamics simulations of the apo protein. In order to address this limitation, we introduce a computational approach based on metadynamics simulations called ensemble docking with enhanced sampling of pocket shape (EDES) that allows holo-like conformations of proteins to be generated by exploiting only their apo structures. This is achieved by defining a set of collective variables that effectively sample different shapes of the binding site, ultimately mimicking the steric effect due to the ligand. We assessed the method on three challenging proteins undergoing different extents of conformational changes upon ligand binding. In all cases our protocol generates a significant fraction of structures featuring a low RMSD from the experimental holo geometry. Moreover, ensemble docking calculations using those conformations yielded in all cases native-like poses among the top-ranked ones.

Long-Ranged Protein-Glycan Interactions Stabilize Von Willebrand Factor A2 Domain from Mechanical Unfolding

von Willebrand Factor (vWF) is a large multimeric protein that binds to platelets and collagen in blood clotting. vWF A2 domain hosts a proteolytic site for ADAMTS13 (A Disintegrin and Metalloprotease with a ThromboSpondin type 1 motif, member 13) to regulate the size of vWF multimers. This regulation process is highly sensitive to force conditions and protein-glycan interactions as the process occurs in flowing blood. There are two sites on A2 domain (N1515 and N1574) bearing various N-linked glycan structures. In this study, we used molecular dynamics (MD) simulation to study the force-induced unfolding of A2 domain with or without a single N-linked glycan type on each site. The sequential pullout of β-strands was used to represent a characteristic unfolding sequence of A2. This unfolding sequence varied due to protein-glycan interactions. The force-extension and total energy-extension profiles also show differences in magnitude but similar characteristic shapes between the systems with or without glycans. Systems with N-linked glycans encountered higher energy barriers for full unfolding and even for unfolding up to the point of ADAMTS13 cleavage site exposure. Interestingly, there is not much difference observed for A2 domain structure itself with or without glycans from standard MD simulations, suggesting roles of N-glycans in A2 unfolding through long-ranged protein-glycan interactions.

A Suite of Tutorials for the WESTPA Rare-Events Sampling Software [Article v1.0

The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present five tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. Users are expected to already have significant experience with running standard molecular dynamics simulations using the underlying dynamics engine of interest (e.g. Amber, Gromacs, OpenMM). The tutorials range from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding.

Targeted Molecular Dynamics Calculations of Free Energy Profiles Using a Nonequilibrium Friction Correction.

As standard unbiased molecular dynamics (MD) simulations become impractical for sampling rare events, "targeted MD" employs a moving distance constraint to enforce rare transitions along some reaction coordinate x. To calculate free energy profiles from these nonequilibrium simulations via Δ G( x) = W( x) - Wdiss( x), apart from the (readily obtained) work W( x) performed on the system, the dissipated work Wdiss( x) is also required. By employing a second-order cumulant expansion of Jarzynski's equality combined with an analysis within Langevin theory, the dissipated work can be expressed via a nonequilibrium friction coefficient ΓNEQ( x) that may be calculated on-the-fly from constraint force fluctuations. Adopting the ion dissociation of NaCl in water as a test system, this friction correction is shown to result in accurate free energy profiles, even for a modest number of simulations and at high constraint velocities. As a bonus, the analysis of ΓNEQ( x) may yield valuable insight into the microscopic mechanism of friction.

Long-ranged Protein-glycan Interactions Stabilize von Willebrand Factor A2 Domain from Mechanical Unfolding

von Willebrand Factor (vWF) is a large multimeric protein that binds to platelets and collagen in blood clotting. vWF A2 domain hosts a proteolytic site for ADAMTS13 (A Disintegrin and Metalloprotease with a ThromboSpondin type 1 motif, member 13) to regulate the size of vWF multimers. This regulation process is highly sensitive to force conditions and protein-glycan interactions as the process occurs in flowing blood. There are two sites on A2 domain (N1515 and N1574) bearing various N-linked glycan structures. In this study, we used molecular dynamics (MD) simulation to study the force-induced unfolding of A2 domain with and without a single N-linked glycan type on each site. The sequential pullout of β-strands was used to represent a characteristic unfolding sequence of A2. This unfolding sequence varied due to protein-glycan interactions. The force-extension and total energy-extension profiles also show differences in magnitude but similar characteristic shapes between the systems with and without glycans. Systems with N-linked glycans encountered higher energy barriers for full unfolding and even for unfolding up to the point of ADAMTS13 cleavage site exposure. Interestingly, there is not much difference observed for A2 domain structure itself with and without glycans from standard MD simulations, suggesting roles of N-glycans in A2 unfolding through long-ranged protein-glycan interactions.

Molecular Insights into the Unusual Structure of an Antifreeze Protein with a Hydrated Core.

The primary driving force for protein folding is the formation of a well-packed, anhydrous core. However, recently, the crystal structure of an antifreeze protein, maxi, has been resolved where the core of the protein is filled with water, which apparently contradicts the existing notion of protein folding. Here, we have performed standard molecular dynamics (MD) simulation, replica exchange MD (REMD) simulation, and umbrella sampling using TIP4P water at various temperatures (300, 260, and 240 K) to explore the origin of this unusual structural feature. It is evident from standard MD and REMD simulations that the protein is found to be stable at 240 K in its unusual state. The core of protein has two layers of semi-clathrate water separating the methyl groups of alanine residues from different helical strands. However, with increasing temperature (260 and 300 K), the stability decreases as the core becomes dehydrated, and methyl groups of alanine are tightly packed driven by hydrophobic interactions. Calculation of the potential of mean force by an umbrella sampling technique between a pair of model hydrophobes resembling maxi protein at 240 K shows the stabilization of second solvent-separated minima (SSM), which provides a thermodynamic rationale of the unusual structural feature in terms of weakening of the hydrophobic interaction. Because the stabilization of SSMs is implicated for cold denaturation, it suggests that the maxi protein is so designed by nature where the cold denatured-like state becomes the biologically active form as it works near or below the freezing point of water.

Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration.

Macromolecular and biomolecular folding landscapes typically contain high free energy barriers that impede efficient sampling of configurational space by standard molecular dynamics simulation. Biased sampling can artificially drive the simulation along prespecified collective variables (CVs), but success depends critically on the availability of good CVs associated with the important collective dynamical motions. Nonlinear machine learning techniques can identify such CVs but typically do not furnish an explicit relationship with the atomic coordinates necessary to perform biased sampling. In this work, we employ auto-associative artificial neural networks ("autoencoders") to learn nonlinear CVs that are explicit and differentiable functions of the atomic coordinates. Our approach offers substantial speedups in exploration of configurational space, and is distinguished from existing approaches by its capacity to simultaneously discover and directly accelerate along data-driven CVs. We demonstrate the approach in simulations of alanine dipeptide and Trp-cage, and have developed an open-source and freely available implementation within OpenMM. © 2018 Wiley Periodicals, Inc.

Activation Dynamics of the Neurotensin G Protein-Coupled Receptor 1

A replica-exchange protocol remarkably enhances the sampling of the activation dynamics of the neurotensin receptor type 1, a G protein-coupled receptor (GPCR) and important drug target. Our work highlights the dynamic communication between conformational changes of the agonist and the G protein-binding site, via contraction-oscillation of the orthosteric pocket. It also gives insights into the mechanism by which certain mutations diminish or stimulate activation. The replica-exchange protocol effectively enhances barrier crossing where standard brute-force molecular dynamics simulations fail. It is readily applicable to other GPCRs and represents a promising approach for virtual ligand screening, using the typical features of receptor activation as a benchmark.

Role of Inosine⁻Uracil Base Pairs in the Canonical RNA Duplexes.

Adenosine to inosine (A–I) editing is the most common modification of double-stranded RNA (dsRNA). This change is mediated by adenosine deaminases acting on RNA (ADARs) enzymes with a preference of U>A>C>G for 5′ neighbor and G>C=A>U or G>C>U=A for 3′ neighbor. A–I editing occurs most frequently in the non-coding regions containing repetitive elements such as ALUs. It leads to disruption of RNA duplex structure, which prevents induction of innate immune response. We employed standard and biased molecular dynamics (MD) simulations to analyze the behavior of RNA duplexes with single and tandem inosine–uracil (I–U) base pairs in different sequence context. Our analysis showed that the I–U pairs induce changes in base pair and base pair step parameters and have different dynamics when compared with standard canonical base pairs. In particular, the first I–U pair from tandem I–U/I–U systems exhibited increased dynamics depending on its neighboring 5′ base. We discovered that UII sequence, which is frequently edited, has lower flexibility compared with other sequences (AII, GII, CII), hence it only modestly disrupts dsRNA. This might indicate that the UAA motifs in ALUs do not have to be sufficiently effective in preventing immune signaling.

Simulations of submonolayer Xe on Pt(111): The case for a chaotic low temperature phase.

Molecular dynamics simulations are reported for the structural and thermodynamic properties of submonolayer xenon adsorbed on the (111) surface of platinum for temperatures up to the (apparently incipient) triple point and beyond. While the motion of the atoms in the surface plane is treated with a standard two-dimensional molecular dynamics simulation, the model takes into consideration the thermal excitation of quantum states associated with surface-normal dynamics in an attempt to describe the apparent smoothing of the corrugation with increasing temperature. We examine the importance of this thermal smoothing to the relative stability of several observed and proposed low-temperature structures. Structure factor calculations are compared to experimental results in an attempt to determine the low temperature structure of this system. These calculations provide strong evidence that, at very low temperatures, the domain wall structure of a xenon monolayer adsorbed on a Pt(111) substrate possesses a chaotic-like nature, exhibiting long-lived meta-stable states with pinned domain walls, these walls having narrow widths and irregular shapes. This result is contrary to the standard wisdom regarding this system, namely, that the very low temperature phase of this system is a striped incommensurate phase. We present the case for further experimental investigation of this and similar systems as possible examples of chaotic low temperature phases in two dimensions.

Calcium ions in aqueous solutions: Accurate force field description aided by ab initio molecular dynamics and neutron scattering.

We present a combination of force field and ab initio molecular dynamics simulations together with neutron scattering experiments with isotopic substitution that aim at characterizing ion hydration and pairing in aqueous calcium chloride and formate/acetate solutions. Benchmarking against neutron scattering data on concentrated solutions together with ion pairing free energy profiles from ab initio molecular dynamics allows us to develop an accurate calcium force field which accounts in a mean-field way for electronic polarization effects via charge rescaling. This refined calcium parameterization is directly usable for standard molecular dynamics simulations of processes involving this key biological signaling ion.

Identification of GPCR Transition Pathways using Go Models

One caveat of standard all-atom molecular dynamics (MD) simulations is that they are resource-intensive, particularly when inspecting state transition pathways. To date, the timescales involved in processes such as G protein-coupled receptor (GPCR) activation make it largely impossible to study them using standard all-atom MD under equilibrium conditions. Indeed, the nature of their activation/deactivation pathway(s) is not yet fully characterized. To overcome this issue, our group previously showed that simpler structure-based (Go-like) potentials could be used to study GPCR state transitions, yielding results in qualitative agreement with those obtained from standard all-atom simulations but with negligible computational cost. These potentials are energetically smooth by design with few non-native traps and a single global energy minimum corresponding to the end-point of the transition of interest. In the case of rhodopsin, a prototypical GPCR, two distinct but reproducible pathways were observed to be populated during activation and deactivation. While it is possible that a separation of pathways is mechanistically required for function, it could also be the result of simulating state transitions occurring in two separate energy surfaces out of equilibrium (one for activation and one for deactivation). To address this potential source of error, we implemented a strategy for modeling Go-like energy landscapes with multiple energy minima at all-heavy atom resolution. This approach allows the study of state interconversion in equilibrium and extensive sampling, still at a low computational cost. Moreover, it can also be used for quick hypothesis testing, to characterize the effects of different ligands, model point mutations, study substate fluctuations and guide all-atom simulations by quickly generating reasonable reaction coordinates. As long as the end states are known, this strategy can be extrapolated to almost any biomolecular system in a straight forward manner, complementing current standard all-atom MD approaches.

Finite-size effects of Kirkwood–Buff integrals from molecular simulations

The modelling of thermodynamic properties of liquids from local density fluctuations is relevant to many chemical and biological processes. The Kirkwood–Buff (KB) theory connects the microscopic structure of isotropic liquids with macroscopic properties such as partial derivatives of activity coefficients, partial molar volumes and compressibilities. Originally, KB integrals were formulated for open and infinite systems which are difficult to access with standard Molecular Dynamics (MD) simulations. Recently, KB integrals for finite and open systems were formulated (J Phys Chem Lett. 2013;4:235). From the scaling of KB integrals for finite subvolumes, embedded in larger reservoirs, with the inverse of the size of these subvolumes, estimates for KB integrals in the thermodynamic limit are obtained. Two system size effects are observed in MD simulations: (1) effects due to the size of the simulation box and the size of the finite subvolume embedded in the simulation box, and (2) effects due to computing radial distribution functions (RDF) from a closed and finite system. In this study, we investigate the two effects in detail by computing KB integrals using the following methods: (1) Monte Carlo simulations of finite subvolumes of a liquid with an analytic RDF and (2) MD simulations of a WCA mixture for various simulation box sizes, but at the same thermodynamic state. We investigate the effect of the size of the simulation box and quantify the differences compared to KB integrals computed in the thermodynamic limit. We demonstrate that calculations of KB integrals should not be extended beyond half the size of the simulation box. For finite-size effects related to the RDF, we find that the Van der Vegt correction (J Chem Theory Comput. 2013;9:1347) yields the most accurate results.

An efficient method for computing excess free energy of liquid

We present a new theoretical method for efficient calculation of free energy of liquid. This interaction entropy method allows one to compute entropy and free energy of liquid from standard single step MD (molecular dynamics) simulation directly in liquid state without the need to perform MD simulations at many intermediate states as required in thermodynamic integration or free energy perturbation methods. In this new approach, one only needs to evaluate the interaction energy of a single (fixed) liquid molecule with the rest of liquid molecules as a function of time from a standard MD simulation of liquid and the fluctuation of distribution of this interaction energy is then used to calculate the interaction entropy of the liquid. Explicit theoretical derivation of this interaction entropy approach is provided and numerical calculations for the benchmark liquid water system were carried out using three different water models. Numerical analysis of the result was performed and comparison of the computational result with experimental data and other theoretical results were provided. Excellent agreement of calculated free energies with the experimental data using TIP4P model is obtained for liquid water.

Classical Molecular Dynamics with Mobile Protons.

An important limitation of standard classical molecular dynamics simulations is the inability to make or break chemical bonds. This restricts severely our ability to study processes that involve even the simplest of chemical reactions, the transfer of a proton. Existing approaches for allowing proton transfer in the context of classical mechanics are rather cumbersome and have not achieved widespread use and routine status. Here we reconsider the combination of molecular dynamics with periodic stochastic proton hops. To ensure computational efficiency, we propose a non-Boltzmann acceptance criterion that is heuristically adjusted to maintain the correct or desirable thermodynamic equilibria between different protonation states and proton transfer rates. Parameters are proposed for hydronium, Asp, Glu, and His. The algorithm is implemented in the program CHARMM and tested on proton diffusion in bulk water and carbon nanotubes and on proton conductance in the gramicidin A channel. Using hopping parameters determined from proton diffusion in bulk water, the model reproduces the enhanced proton diffusivity in carbon nanotubes and gives a reasonable estimate of the proton conductance in gramicidin A.

What Can Human-Guided Simulations Bring to RNA Folding?

Inspired by the recent success of scientific-discovery games for predicting protein tertiary and RNA secondary structures, we have developed an open software for coarse-grained RNA folding simulations, guided by human intuition. To determine the extent to which interactive simulations can accurately predict 3D RNA structures of increasing complexity and lengths (four RNAs with 22–47 nucleotides), an interactive experiment was conducted with 141 participants who had very little knowledge of nucleic acids systems and computer simulations, and had received only a brief description of the important forces stabilizing RNA structures. Their structures and full trajectories have been analyzed statistically and compared to standard replica exchange molecular dynamics simulations. Our analyses show that participants gain easily chemical intelligence to fold simple and nontrivial topologies, with little computer time, and this result opens the door for the use of human-guided simulations to RNA folding. Our experiment shows that interactive simulations have better chances of success when the user widely explores the conformational space. Interestingly, providing on-the-fly feedback of the root mean square deviation with respect to the experimental structure did not improve the quality of the proposed models.

Application of advanced sampling and analysis methods to predict the structure of adsorbed protein on a material surface.

The use of standard molecular dynamics simulation methods to predict the interactions of a protein with a material surface have the inherent limitations of lacking the ability to determine the most likely conformations and orientations of the adsorbed protein on the surface and to determine the level of convergence attained by the simulation. In addition, standard mixing rules are typically applied to combine the nonbonded force field parameters of the solution and solid phases the system to represent interfacial behavior without validation. As a means to circumvent these problems, the authors demonstrate the application of an efficient advanced sampling method (TIGER2A) for the simulation of the adsorption of hen egg-white lysozyme on a crystalline (110) high-density polyethylene surface plane. Simulations are conducted to generate a Boltzmann-weighted ensemble of sampled states using force field parameters that were validated to represent interfacial behavior for this system. The resulting ensembles of sampled states were then analyzed using an in-house-developed cluster analysis method to predict the most probable orientations and conformations of the protein on the surface based on the amount of sampling performed, from which free energy differences between the adsorbed states were able to be calculated. In addition, by conducting two independent sets of TIGER2A simulations combined with cluster analyses, the authors demonstrate a method to estimate the degree of convergence achieved for a given amount of sampling. The results from these simulations demonstrate that these methods enable the most probable orientations and conformations of an adsorbed protein to be predicted and that the use of our validated interfacial force field parameter set provides closer agreement to available experimental results compared to using standard CHARMM force field parameterization to represent molecular behavior at the interface.

Molecular ‘time‐machines’ to unravel key biological events for drug design

Molecular dynamics (MD) has become a routine tool in structural biology and structure‐based drug design (SBDD). MD offers extraordinary insights into the structures and dynamics of biological systems. With the current capabilities of high‐performance supercomputers, it is now possible to perform MD simulations of systems as large as millions of atoms and for several nanoseconds timescale. Nevertheless, many complicated molecular mechanisms, including ligand binding/unbinding and protein folding, usually take place on timescales of several microseconds to milliseconds, which are beyond the practical limits of standard MD simulations. Such issues with traditional MD approaches can be effectively tackled with new generation MD methods, such as enhanced sampling MD approaches and coarse‐grained MD (CG‐MD) scheme. The former employ a bias to steer the simulations and reveal biological events that are usually very slow, while the latter groups atoms as interaction beads, thereby reducing the system size and facilitating longer MD simulations that can witness large conformational changes in biological systems. In this review, we outline many of such advanced MD methods, and discuss how their applications are providing significant insights into important biological processes, particularly those relevant to drug design and discovery. WIREs Comput Mol Sci 2017, 7:e1306. doi: 10.1002/wcms.1306This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics Molecular and Statistical Mechanics > Free Energy Methods Software > Simulation Methods

Anesthetics mechanism on a DMPC lipid membrane model: Insights from molecular dynamics simulations

To provide insight into the molecular mechanisms of local anesthetic action, we have carried out an extensive investigation of two amide type local anesthetics, lidocaine and articaine in both charged and uncharged forms, interacting with DMPC lipid membrane. We have applied both standard molecular dynamics simulations and metadynamics simulations to provide a detailed description of the free energy landscape of anesthetics embedded in the lipid bilayer. The global minimum of the free energy surface (equilibrium position of anesthetics in the lipid membrane) occurred around 1nm of the bilayer center. The uncharged anesthetics show more affinity to bind to this region compared to the charged drugs. The binding free energy of uncharged lidocaine in the membrane (−30.3kJ/mol) is higher than uncharged articaine (−24.0kJ/mol), which is in good agreement with higher lipid solubility of lidocaine relative to the articaine. The octanol/water partition coefficient of uncharged drugs was also investigated using expanded ensemble simulations. In addition, complementary standard MD simulations were carried out to study the partitioning behavior of multiple anesthetics inside the lipid bilayer. The results obtained here are in line with previously reported simulations and suggest that the different forms of anesthetics induce different structural modifications in the lipid bilayer, which can provide new insights into their complex membrane translocation phenomena.

Microscopic derivation of particle-based coarse-grained dynamics: Exact expression for memory function.

We consider the generalized Langevin equations of motion describing exactly the particle-based coarse-grained dynamics in the classical microscopic ensemble that were derived recently within the Mori-Zwanzig formalism based on new projection operators [S. Izvekov, J. Chem. Phys. 138(13), 134106 (2013)]. The fundamental difference between the new family of projection operators and the standard Zwanzig projection operator used in the past to derive the coarse-grained equations of motion is that the new operators average out the explicit irrelevant trajectories leading to the possibility of solving the projected dynamics exactly. We clarify the definition of the projection operators and revisit the formalism to compute the projected dynamics exactly for the microscopic system in equilibrium. The resulting expression for the projected force is in the form of a "generalized additive fluctuating force" describing the departure of the generalized microscopic force associated with the coarse-grained coordinate from its projection. Starting with this key expression, we formulate a new exact formula for the memory function in terms of microscopic and coarse-grained conservative forces. We conclude by studying two independent limiting cases of practical importance: the Markov limit (vanishing correlations of projected force) and the limit of weak dependence of the memory function on the particle momenta. We present computationally affordable expressions which can be efficiently evaluated from standard molecular dynamics simulations.