Dissipative particle dynamics of non-spherical particles using a Gaussian density model

The Gaussian density molecular model has been adapted for dissipative particle dynamics. The model, when combined with a soft potential, is shown to be a very flexible mesoscale model exhibiting a wide range of phase behaviour. The soft potential allows relatively large time steps to be used and hence a more rapid equilibration. In addition, the model can be used to study both uniaxial and biaxial systems. We have undertaken a number of pilot studies and have demonstrated that the Gaussian model is able to identify nematic–isotropic phase transitions in liquid crystals and the formation of ordered discotic phases.     

Molecular properties of a bent-core nematic liquid crystal A131 by multi-level theory simulations

ABSTRACT

Multi-level theory simulations have been performed to model a number of important molecular properties of a bent-core nematic liquid crystal (LC) A131. These important properties include molecular conformations, molecular Raman spectra, differential polarisability ratios, molecular crystals packing, atomic LC structures, order parameters, and Raman depolarisation spectra. The simulations contain four theory levels, involving molecular quantum chemistry, molecular crystal packing, super cell density functional based tight binding optimisation, and super cell molecular dynamics calculations. To heat initial optimised super cell structures, molecular dynamics simulations reveal phase transitions to uniaxial and biaxial nematic phases from molecular crystals. LC atomic structures result in direct calculations on order parameters, which can be further applied to computations on Raman depolarisation spectra with differential polarisability ratios, obtained in the molecular quantum chemistry theory level. The good agreement of simulated Raman depolarisation spectra with the experiment provides a detailed analysis on the unusually low values of experimental uniaxial order parameters.     

Grand Molecular Dynamics: A Method for Open Systems

We present a new molecular dynamics method for studying the dynamics of open systems. The method couples a classical system to a chemical potential reservior. In the formulation, following the extended system dynamics approach, we introduce a variable, v to represent the coupling to the chemical potential reservoir. The new variable governs the dynamics of the variation of number of particles in the system. The number of particles is determined by taking the integer part of v. The fractional part of the new variable is used to scale the potential energy and the kinetic energy of an additional particle: i.e., we introduce a fractional particle. We give the ansatz Lagrangians and equations of motion for both the isothermal and the adiabatic forms of grand molecular dynamics. The averages calculated over the trajectories generated by these equations of motion represent the classical grand canonical ensemble (μVT) and the constant chemical potential adiabatic ensemble (μVL) averages, respectively. The microcanonical phase space densities of the adiabatic and isothermal forms the molecular dynamics method are shown to be equivalent to adiabatic constant chemical potential ensemble, and grand canonical ensemble partition functions. We also discuss the extension to multi-component systems, molecular fluids, ionic solutions and the problems and solutions associated with the implementation of the method. The statistical expressions for thermodynamic functions such as specific heat; adiabatic bulk modulus, Grüneissen parameter and number fluctuations are derived. These expressions are used to analyse trajectories of constant chemical potential systems.     

Protocol for MM/PBSA molecular dynamics simulations of proteins

Continuum solvent models have been employed in past years for understanding processes such as protein folding or biomolecular association. In the last decade, several attempts have been made to merge atomic detail molecular dynamics simulations with solvent continuum models. Among continuum models, the Poisson-Boltzmann solvent accessible surface area model is one of the oldest and most fundamental. Notwithstanding its wide usage for simulation of biomolecular electrostatic potential, the Poisson-Boltzmann equation has been very seldom used to obtain solvation forces for molecular dynamics simulation. We propose here a fast and reliable methodology to implement continuum forces in standard molecular mechanics and dynamics algorithms. Results for a totally unrestrained 1 ns molecular dynamics simulation of a small protein are quantitatively similar to results obtained by explicit solvent molecular dynamics simulations.     

Constant electric field simulations of the membrane potential illustrated with simple systems

Advances in modern computational methods and technology make it possible to carry out extensive molecular dynamics simulations of complex membrane proteins based on detailed atomic models. The ultimate goal of such detailed simulations is to produce trajectories in which the behavior of the system is as realistic as possible. A critical aspect that requires consideration in the case of biological membrane systems is the existence of a net electric potential difference across the membrane. For meaningful computations, it is important to have well validated methodologies for incorporating the latter in molecular dynamics simulations. A widely used treatment of the membrane potential in molecular dynamics consists of applying an external uniform electric field E perpendicular to the membrane. The field acts on all charged particles throughout the simulated system, and the resulting applied membrane potential V is equal to the applied electric field times the length of the periodic cell in the direction perpendicular to the membrane. A series of test simulations based on simple membrane-slab models are carried out to clarify the consequences of the applied field. These illustrative tests demonstrate that the constant-field method is a simple and valid approach for accounting for the membrane potential in molecular dynamics studies of biomolecular systems. This article is part of a Special Issue entitled: Membrane protein structure and function.     

Flexible fitting of atomic structures into electron microscopy maps using molecular dynamics

A novel method to flexibly fit atomic structures into electron microscopy (EM) maps using molecular dynamics simulations is presented. The simulations incorporate the EM data as an external potential added to the molecular dynamics force field, allowing all internal features present in the EM map to be used in the fitting process, while the model remains fully flexible and stereochemically correct. The molecular dynamics flexible fitting (MDFF) method is validated for available crystal structures of protein and RNA in different conformations; measures to assess and monitor the fitting process are introduced. The MDFF method is then used to obtain high-resolution structures of the E. coli ribosome in different functional states imaged by cryo-EM.     

Folding Lennard-Jones proteins by a contact potential

We studied the possibility to approximate a Lennard-Jones interaction by a pairwise contact potential. First we used a Lennard-Jones potential to design off-lattice, protein-like heteropolymer sequences, whose lowest energy (native) conformations were then identified by molecular dynamics. Then we turned to investigate whether one can find a pairwise contact potential, whose ground states are the contact maps associated with these native conformations. We show that such a requirement cannot be satisfied exactly, i.e., no such contact parameters exist. Nevertheless, we found that one can find contact energy parameters for which an energy minimization procedure, acting in the space of contact maps, yields maps whose corresponding structures are close to the native ones. Finally, we show that when these structures are used as the initial point of a molecular dynamics energy minimization process, the correct native folds are recovered with high probability.     

Molecular Dynamics as a Mathematical Mapping. II. Partial Derivatives in the Microcanonical Ensemble

Abstract

Performing molecular dynamics in a fully continuous and differentiable framework can be viewed as a deterministic mathematical mapping between, on one side, the force field parameters that describe the potential energy interactions and input macroscopic conditions, and, on the other, the calculated corresponding macroscopic properties of the bulk molecular system.

Within this framework, it is possible to apply standard methods of variational calculus for the computation of the partial derivatives of the molecular dynamics mapping based on the integration of either the adjoint equations or the sensitivity equations of the classical Newtonian equations of motion. We present procedures for these computations in the standard microcanonical (N, V, E) ensemble, and compare the computational efficiency of the two approaches. The general formulations developed are applied to the specific example of bulk ethane fluid.

With these procedures in place, it is now possible to compute the partial derivatives of any property determined by molecular dynamics with respect to any input property and any potential parameter. Moreover, these derivatives are computed to essentially the same level of numerical accuracy as the output properties themselves.     

Modeling the binding of three toxins to the voltage-gated potassium channel (Kv1.3)

The conduction properties of the voltage-gated potassium channel Kv1.3 and its modes of interaction with several polypeptide venoms are examined using Brownian dynamics simulations and molecular dynamics calculations. Employing an open-state homology model of Kv1.3, we first determine current-voltage and current-concentration curves and ascertain that simulated results accord with experimental measurements. We then investigate, using a molecular docking method and molecular dynamics simulations, the complexes formed between the Kv1.3 channel and several Kv-specific polypeptide toxins that are known to interfere with the conducting mechanisms of several classes of voltage-gated K⁺ channels. The depths of potential of mean force encountered by charybdotoxin, α-KTx3.7 (also known as OSK1) and ShK are, respectively, −19, −27, and −25 kT. The dissociation constants calculated from the profiles of potential of mean force correspond closely to the experimentally determined values. We pinpoint the residues in the toxins and the channel that are critical for the formation of the stable venom-channel complexes.     

Protein structure determination using a database of interatomic distance probabilities

The accelerated pace of genomic sequencing has increased the demand for structural models of gene products. Improved quantitative methods are needed to study the many systems (e.g., macromolecular assemblies) for which data are scarce. Here, we describe a new molecular dynamics method for protein structure determination and molecular modeling. An energy function, or database potential, is derived from distributions of interatomic distances obtained from a database of known structures. X-ray crystal structures are refined by molecular dynamics with the new energy function replacing the Van der Waals potential. Compared to standard methods, this method improved the atomic positions, interatomic distances, and side-chain dihedral angles of structures randomized to mimic the early stages of refinement. The greatest enhancement in side-chain placement was observed for groups that are characteristically buried. More accurate calculated model phases will follow from improved interatomic distances. Details usually seen only in high-resolution refinements were improved, as is shown by an R-factor analysis. The improvements were greatest when refinements were carried out using X-ray data truncated at 3.5 A. The database potential should therefore be a valuable tool for determining X-ray structures, especially when only low-resolution data are available.     

Assessing the ecological significance of molecular diversity data in natural plant populations

Despite extensive research for several decades, there remains a lack of understanding of the processes that determine the dynamics of natural plant communities. In this paper some current concepts in vegetation dynamics are reviewed and an attempt is made to provide a perspective of the way in which data for molecular diversity might be used to help in developing an understanding of population processes. It is proposed that data from assessments of general population diversity, and specific ecophysiological traits can be used to assess the potential for individual species to compete and substitute for each other in a community.Keywords: Natural plant communities, dynamics, molecular diversity, population diversity, ecophysiological traits.      

Dynamics and ordering in mixed model membranes of dimyristoylphosphatidylcholine and dimyristoylphosphatidylserine: a 250-GHz electron spin resonance study using cholestane.

We report here on a 250-GHz electron spin resonance (ESR) study of macroscopically aligned model membranes composed of mixtures of dimyristoylphosphatidylcholine (DMPC) and dimyristoylphosphatidylserine (DMPS), utilizing the nixtroxide-labeled cholesterol analog cholestane (CSL). Two clearly resolved spectral components, distinct in both their ordering and dynamics, are resolved. The major component in membranes composed mostly of DMPC shows typical characteristics, with the long axis of CSL parallel to the bilayer normal with slow (10(6) </= R </= 10(7) s-1) rotational diffusion rates, as expected for cholesterol. The second component grows in as the mole fraction of DMPS increases. A detailed analysis shows that CSL senses a local, strongly biaxial environment. Our results imply that the inefficient packing between cholesterol and DMPS occurs probably because of the strong interactions between the PS headgroups, which provide the local biaxiality. Such a packing of the headgroups has been predicted by molecular dynamics simulations but had not been observed experimentally. The analysis of these spectral components was greatly aided by the excellent orientational resolution provided by the 250-GHz spectra. This enabled the key qualitative features of this interpretation to be "read" off the spectra before the detailed analysis.     

Methods for monitoring signaling molecules in cellular compartments

Cells, irrespective of whether they are from multicellular or single-celled organisms, must communicate with the external environment through dynamic regulation of their internal metabolism, which are critical for their survival. Fluorescent and bioluminescent proteins, and related genetic engineering technologies, have provided new opportunities to investigate the molecular dynamics of cells and their internal compartments, with high spatio-temporal resolution. In this review article, since there is a sufficient number of previous reviews summarizing the history of their development and the techniques behind them, here we will focus on molecular features or technologies that have the potential to further open novel investigations of cellular and subcellular dynamics.     

Langevin dynamics of peptides: the frictional dependence of isomerization rates of N-acetylalanyl-N'-methylamide.

The rate constant for the transition between the equatorial and axial conformations of N-acetylalanyl-N'-methylamide has been determined from Langevin dynamics (LD) simulations with no explicit solvent. The isomerization rate is maximum at collision frequency gamma = 2 ps-1, shows diffusive character for gamma greater than or equal to 10 ps-1, but does not approach zero even at gamma = 0.01 ps-1. This behavior differs from that found for a one-dimensional bistable potential and indicates that both collisional energy transfer with solvent and vibrational energy transfer between internal modes are important in the dynamics of barrier crossing for this system. It is suggested that conformational searches of peptides be carried out using LD with a collision frequency that maximizes the isomerization rate (i.e., gamma approximately 2 ps-1). This method is expected to be more efficient than either molecular dynamics in vacuo (which corresponds to LD with gamma = 0) or molecular dynamics in solvent (where dynamics is largely diffusive).     

Remarks on discrete and continuous large-scale models of DNA dynamics.

We present a comparison of the continuous versus discrete models of large-scale DNA conformation, focusing on issues of relevance to molecular dynamics. Starting from conventional expressions for elastic potential energy, we derive elastic dynamic equations in terms of Cartesian coordinates of the helical axis curve, together with a twist function representing the helical or excess twist. It is noted that the conventional potential energies for the two models are not consistent. In addition, we derive expressions for random Brownian forcing for the nonlinear elastic dynamics and discuss the nature of such forces in a continuous system.