Rigid-body dynamics in the isothermal-isobaric ensemble: a test on the accuracy and computational efficiency

We have developed a time-reversible rigid-body (rRB) molecular dynamics algorithm in the isothermal-isobaric (NPT) ensemble. The algorithm is an extension of rigid-body dynamics [Matubayasi and Nakahara, J Chem Phys 1999, 110, 3291] to the NPT ensemble on the basis of non-Hamiltonian statistical mechanics [Martyna, G. J. et al., J Chem Phys 1994, 101, 4177]. A series of MD simulations of water as well as fully hydrated lipid bilayer systems have been undertaken to investigate the accuracy and efficiency of the algorithm. The rRB algorithm was shown to be superior to the state-of-the-art constraint-dynamics algorithm SHAKE/RATTLE/ROLL, with respect to computational efficiency. However, it was revealed that both algorithms produced accurate trajectories of molecules in the NPT as well as NVT ensembles, as long as a reasonably short time step was used. A couple of multiple time-step (MTS) integration schemes were also examined. The advantage of the rRB algorithm for computational efficiency increased when the MD simulation was carried out using MTS on parallel processing computer systems; total computer time for MTS-MD of a lipid bilayer using 64 processors was reduced by about 40% using rRB instead of SHAKE/RATTLE/ROLL.     

Density functional theory of fluids in the isothermal-isobaric ensemble

We present a density functional theory for inhomogeneous fluids at constant external pressure. The theory is formulated for a volume-dependent density, n(r,V), defined as the conjugate variable of a generalized external potential, nu(r,V), that conveys the information on the pressure. An exact expression for the isothermal-isobaric free-energy density functional is obtained in terms of the corresponding canonical ensemble functional. As an application we consider a hard-sphere system in a spherical pore with fluctuating radius. In general we obtain very good agreement with simulation. However, in some situations a peak develops in the center of the cavity and the agreement between theory and simulation becomes worse. This happens for systems where the number of particles is close to the magic numbers N=13, 55, and 147.     

Molecular dynamics in the isothermal-isobaric ensemble: the requirement of a "shell" molecule. II. Simulation results

The results of a series of constant pressure and temperature molecular-dynamics (MD) simulation studies based on the rigorous shell particle formulation of the isothermal-isobaric (NpT) ensemble are presented. These MD simulations validate the newly proposed constant pressure equations of motion in which a "shell" particle is used to define uniquely the volume of the system [M. J. Uline and D. S. Corti, J. Chem. Phys. (to be published), preceding paper]. Ensemble averages obtained with the new MD NpT algorithm match the ensemble averages obtained using the previously derived shell particle Monte Carlo NpT method [D. S. Corti, Mol. Phys. 100, 1887 (2002)]. In addition, we also verify that the Hoover NpT MD algorithm [W. G. Hoover, Phys. Rev. A 31, 1695 (1985); 34, 2499 (1986)] generates the correct ensemble averages, though only when periodic boundary conditions are employed. The extension of the shell particle MD algorithm to multicomponent systems is also discussed, in which we show for equilibrium properties that the identity of the shell particle is completely arbitrary when periodic boundary conditions are applied. Self-diffusion coefficients determined with the shell particle equations of motion are also identical to those obtained in other ensembles. Finally, since the mass of the shell particle is known, the system itself, and not a piston of arbitrary mass, controls the time scales for internal pressure and volume fluctuations. We therefore consider the effects of the shell particle on the dynamics of the system. Overall, the shell particle MD algorithm is an effective simulation method for studying systems exposed to a constant external pressure and may provide an advantage over other existing constant pressure approaches when developing nonequilibrium MD methods.     

Molecular dynamics in the isothermal-isobaric ensemble: the requirement of a "shell" molecule. III. Discontinuous potentials

Based on the approach of Gruhn and Monson [Phys. Rev. E 63, 061106 (2001)], we present a new method for deriving the collisions dynamics for particles that interact via discontinuous potentials. By invoking the conservation of the extended Hamiltonian, we generate molecular dynamics (MD) algorithms for simulating the hard-sphere and square-well fluids within the isothermal-isobaric (NpT) ensemble. Consistent with the recent rigorous reformulation of the NpT ensemble partition function, the equations of motion impose a constant external pressure via the introduction of a shell particle of known mass [M. J. Uline and D. S. Corti, J. Chem. Phys. 123, 164101 (2005); 123, 164102 (2005)], which serves to define uniquely the volume of the system. The particles are also connected to a temperature reservoir through the use of a chain of Nose-Hoover thermostats, the properties of which are not affected by a hard-sphere or square-well collision. By using the Liouville operator formalism and the Trotter expansion theorem to integrate the equations of motion, the update of the thermostat variables can be decoupled from the update of the positions of the particles and the momentum changes upon a collision. Hence, once the appropriate collision dynamics for the isobaric-isenthalpic (NpH) equations of motion is known, the adaptation of the algorithm to the NpT ensemble is straightforward. Results of MD simulations for the pure component square-well fluid are presented and serve to validate our algorithm. Finally, since the mass of the shell particle is known, the system itself, and not a piston of arbitrary mass, controls the time scales for internal pressure and volume fluctuations. We therefore consider the influence of the shell particle algorithm on the dynamics of the square-well fluid.     

Molecular simulation of dendrimers and their mixtures under shear: comparison of isothermal-isobaric (NpT) and isothermal-isochoric (NVT) ensemble systems

Flow properties of dendrimers are studied with the aid of nonequilibrium molecular dynamics techniques. Simulations are performed in the NpT ensemble using the NpT-SLLOD algorithm [P. J. Davis and D. J. Evans, J. Chem. Phys. 100, 541 (1994)] and are compared to the results from simulations performed in the NVT ensemble reported earlier [J. T. Bosko, B. D. Todd, and R. J. Sadus, Chem. Phys. 121, 12050 (2004)]. Shear thickening observed at high strain rates vanishes in systems kept under constant pressure. Also the exponents in the power-law dependencies of the viscosity and the normal stress coefficients change. The variations are significant only at high strain rates and do not affect largely microscopic properties such as shape, alignment, or rotation of molecules. The NpT-SLLOD algorithm has been applied to study various systems including dendrimers in solution and their blends with linear chain molecules of the same molecular mass, and some results for these systems are presented.     

Molecular dynamics in the isothermal-isobaric ensemble: the requirement of a "shell" molecule. I. Theory and phase-space analysis

Current constant pressure molecular-dynamics (MD) algorithms are not consistent with the recent reformulation of the isothermal-isobaric (NpT) ensemble. The NpT ensemble partition function requires the use of a "shell" molecule to identify uniquely the volume of the system, thereby avoiding the redundant counting of configurations [e.g., G. J. M. Koper and H. Reiss, J. Phys. Chem. 100, 422 (1996); D. S. Corti, Phys. Rev. E, 64, 016128 (2001)]. So far, only the NpT Monte Carlo method has been updated to allow the system volume to be defined by a shell particle [D. S. Corti, Mol. Phys. 100, 1887 (2002)]. A shell particle has yet to be incorporated into MD simulations. The proper modification of the NpT MD algorithm is therefore the subject of this paper. Unlike Andersen's method [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)] where a piston of unknown mass serves to control the response time of volume fluctuations, the newly proposed equations of motion impose a constant external pressure via the introduction of a shell particle of known mass. Hence, the system itself sets the time scales for pressure and volume fluctuations. The new algorithm is subject to a number of fundamentally rigorous tests to ensure that the equations of motion sample phase space correctly. We also show that the Hoover NpT algorithm [W. G. Hoover, Phys. Rev. A. 31, 1695 (1985); 34, 2499 (1986)] does sample phase correctly, but only when periodic boundary conditions are employed.     

Hamilton-Jacobi equation for the least-action/least-time dynamical path based on fast marching method

Classical dynamics can be described with Newton's equation of motion or, totally equivalently, using the Hamilton-Jacobi equation. Here, the possibility of using the Hamilton-Jacobi equation to describe chemical reaction dynamics is explored. This requires an efficient computational approach for constructing the physically and chemically relevant solutions to the Hamilton-Jacobi equation; here we solve Hamilton-Jacobi equations on a Cartesian grid using Sethian's fast marching method. Using this method, we can--starting from an arbitrary initial conformation--find reaction paths that minimize the action or the time. The method is demonstrated by computing the mechanism for two different systems: a model system with four different stationary configurations and the H+H(2)-->H(2)+H reaction. Least-time paths (termed brachistochrones in classical mechanics) seem to be a suitable chioce for the reaction coordinate, allowing one to determine the key intermediates and final product of a chemical reaction. For conservative systems the Hamilton-Jacobi equation does not depend on the time, so this approach may be useful for simulating systems where important motions occur on a variety of different time scales.     

Experimental strategy for characterization of essential dynamical variables in oscillatory systems: effect of double-layer capacitance on the stability of electrochemical oscillators

An experimentally accessible algorithm for changing the time scale associated with a dynamical variable is proposed. In general, a differential controller can be applied to (a) identify the essential species in oscillatory systems and (b) explore their role in the feedback loops. Here, we report on classifying electrochemical oscillators by changing the time scale over which the electrode potential varies; the type of different electrochemical oscillators is identified based on whether the controlled modification of pseudo-capacitance induces or suppresses current oscillations.     

A quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution based on the framework of mixed quantum-classical molecular dynamics

We present a quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution in the framework of mixed quantum-classical molecular dynamics, where the reactant and product states are explicitly defined by dividing the double-well potential into the reactant and product wells. The equation can describe quantum reaction processes such as tunneling and thermal excitation and relaxation assisted by the solvent. Fluctuations of the zero-point energy level, the height of the barrier, and the curvature of the well are all included in the equation. Here, the equation was combined with the surface hopping technique in order to describe the motion of the classical solvent. Applying the present method to model systems, we show two numerical examples in order to demonstrate the potential power of the present method. The first example is a proton transfer by tunneling where the high-energy product state was stabilized very rapidly by solvation. The second example shows a thermal activation mechanism, i.e., the initial vibrational excitation in the reactant well followed by the reacting transition above the barrier and the final vibrational relaxation in the product well.     

Ensemble pharmacophore meets ensemble docking: a novel screening strategy for the identification of RIPK1 inhibitors

Programmed cell death has been a fascinating area of research since it throws new challenges and questions in spite of the tremendous ongoing research in this field. Recently, necroptosis, a programmed form of necrotic cell death, has been implicated in many diseases including neurological disorders. Receptor interacting serine/threonine protein kinase 1 (RIPK1) is an important regulatory protein involved in the necroptosis and inhibition of this protein is essential to stop necroptotic process and eventually cell death. Current structure-based virtual screening methods involve a wide range of strategies and recently, considering the multiple protein structures for pharmacophore extraction has been emphasized as a way to improve the outcome. However, using the pharmacophoric information completely during docking is very important. Further, in such methods, using the appropriate protein structures for docking is desirable. If not, potential compound hits, obtained through pharmacophore-based screening, may not have correct ranks and scores after docking. Therefore, a comprehensive integration of different ensemble methods is essential, which may provide better virtual screening results. In this study, dual ensemble screening, a novel computational strategy was used to identify diverse and potent inhibitors against RIPK1. All the pharmacophore features present in the binding site were captured using both the apo and holo protein structures and an ensemble pharmacophore was built by combining these features. This ensemble pharmacophore was employed in pharmacophore-based screening of ZINC database. The compound hits, thus obtained, were subjected to ensemble docking. The leads acquired through docking were further validated through feature evaluation and molecular dynamics simulation.     

Bioorthogonal chemistry: a covalent strategy for the study of biological systems

The development of genetically encoded, wavelength-tunable fluorescent proteins has provided a powerful imaging tool to the study of protein dynamics and functions in cellular and organismal biology. However, many biological functions are not directly encoded in the protein primary sequence, e.g., dynamic regulation afforded by protein posttranslational modifications such as phosphorylation. To meet this challenge, an emerging field of bioorthogonal chemistry has promised to offer a versatile strategy to selectively label a biomolecule of interest and track their dynamic regulations in its native habitat. This strategy has been successfully applied to the studies of all classes of biomolecules in living systems, including proteins, nucleic acids, carbohydrates, and lipids. Whereas the incorporation of a bioorthogonal reporter site-selectively into a biomolecule through either genetic or metabolic approaches has been well established, the development of bioorthogonal reactions that allow fast ligation of exogenous chemical probes with the bioorthogonal reporter in living systems remains in its early stage. Here, we review the recent development of bioorthogonal reactions and their applications in various biological systems, with a detailed discussion about our own work—the development of the tetrazole based, photoinducible 1,3-dipolar cycloaddition reaction.     

Bioorthogonal chemistry:a covalent strategy for the study of biological systems

The development of genetically encoded,wavelength-tunable fluorescent proteins has provided a powerful imaging tool to the study of protein dynamics and functions in cellular and organismal biology.However,many biological functions are not directly encoded in the protein primary sequence,e.g.,dynamic regulation afforded by protein posttranslational modifications such as phosphorylation.To meet this challenge,an emerging field of bioorthogonal chemistry has promised to offer a versatile strategy to selective...     

Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach

A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schon and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Buttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.     

A comparative study of molecular dynamics in Cartesian and in internal coordinates: dynamical instability in the latter caused by nonlinearity of the equations of motion

The stability of a general molecular dynamics (MD) integration scheme is examined for simulations in generalized (internal plus external) coordinates (GCs). An analytic expression is derived for the local error in energy during each integration time step. This shows that the explicit dependence of the mass-matrix on GCs, which makes the system's Lagrange equations of motion nonlinear, causes MD simulations in GCs to be less stable than those in Cartesian coordinates (CCs). In terms of CCs, the corresponding mass-matrix depends only on atomic masses and thus atomistic motion is subject to the linear Newton equations, which makes the system more stable. Also investigated are two MD methods in GCs that utilize nonzero elements of the vibrational spectroscopic B-matrices. One updates positions and velocities in GCs that are iteratively adjusted so as to conform to the velocity Verlet equivalent in GCs. The other updates positions in GCs and velocities in CCs that are adjusted to satisfy the internal constraints of the new constrained WIGGLE MD scheme. The proposed methods are applied to an isolated n-octane molecule and their performances are compared with those of several CCMD schemes. The simulation results are found to be consistent with the analytic stability analysis. Finally, a method is presented for computing nonzero elements of B-matrices for external rotations without imposing the Casimir-Eckart conditions.     

Analyses of the electronic collective motions by means of a nonlinear dynamical equation

A nonlinear dynamical equation for the electronic collective motion is presented by employing the traditional time-dependent procedure. The equation is applied to the model π-electron system of ethylene, and the effects of nonlinear interactions are investigated using its several states as reference states. It is shown that the nonlinear correlation plays an important role in describing the change of the lower excited states.     

Chemical equilibria of multiple-reaction systems from reaction ensemble Monte Carlo simulation and a predictive equation of state: Combined hydrogenation of ethylene and propylene

Successful application of the reaction ensemble Monte Carlo (REMC) method to compute multiple-reaction chemical equilibria requires a reasonably high acceptance probability for all forward and backward reaction moves during the production stage of a simulation run. To achieve this for a system that involves almost irreversible multiple reactions, it is necessary to choose a thermodynamically-equivalent alternative set of linearly independent reactions, such that the occurrence of very large chemical equilibrium constants is avoided for as many reactions in the set as possible. In this work, the need for such a strategy is justified and applied to the combined hydrogenation of ethylene and propylene, which involves six components and requires a set of four linearly independent reactions. Already validated effective pair potential models were used: one-center Lennard–Jones (1CLJ) models for hydrogen and methane, two-center LJ plus point quadrupole (2CLJQ) models for ethylene, ethane and propylene, and a three-center LJ (3CLJ) model for propane. No binary adjustable parameters were needed to compute the unlike-pair LJ interactions. Simulation results were obtained for the effect of temperature and pressure on the conversions of ethylene and propylene, yield of methane, and density of the system at equilibrium. These results were found to be in very good agreement with calculations using the PSRK group contribution equation of state.     

Hierarchical equations of motion in the Libra software package

We report the implementation of a hierarchical equations of motion (HEOM) module within the open-source Libra software. It includes the standard and scaled HEOM algorithms for computing the dynamics of open quantum systems interacting with a harmonic bath. The module allows the computing of the evolution of the reduced density matrix, as well as spectral lineshapes. The truncation, filtering, and “update list” schemes, as well as OpenMP parallelization, allow for further computational saving. The package is written in a mix of C++ and Python languages, delivering the best compromise between user friendliness and efficiency. The Python layer of the package takes advantage of standard Python libraries, such as h5py, which allows efficient storage and retrieval of the generated results. The package can be seamlessly used within Jupyter notebooks; its careful design shall provide the maximal convenience and intuitiveness to its users.