Multiscale molecular dynamics/hydrodynamics implementation of two dimensional “Mercedes Benz” water model

A multiscale Molecular Dynamics/Hydrodynamics implementation of the 2D Mercedes Benz (MB or BN2D) [1] water model is developed and investigated. The concept and the governing equations of multiscale coupling together with the results of the two-way coupling implementation are reported. The sensitivity of the multiscale model for obtaining macroscopic and microscopic parameters of the system, such as macroscopic density and velocity fluctuations, radial distribution and velocity autocorrelation functions of MB particles, is evaluated. Critical issues for extending the current model to large systems are discussed

How Water's Properties Are Encoded in Its Molecular Structure and Energies.

How are water's material properties encoded within the structure of the water molecule? This is pertinent to understanding Earth's living systems, its materials, its geochemistry and geophysics, and a broad spectrum of its industrial chemistry. Water has distinctive liquid and solid properties: It is highly cohesive. It has volumetric anomalies-water's solid (ice) floats on its liquid; pressure can melt the solid rather than freezing the liquid; heating can shrink the liquid. It has more solid phases than other materials. Its supercooled liquid has divergent thermodynamic response functions. Its glassy state is neither fragile nor strong. Its component ions-hydroxide and protons-diffuse much faster than other ions. Aqueous solvation of ions or oils entails large entropies and heat capacities. We review how these properties are encoded within water's molecular structure and energies, as understood from theories, simulations, and experiments. Like simpler liquids, water molecules are nearly spherical and interact with each other through van der Waals forces. Unlike simpler liquids, water's orientation-dependent hydrogen bonding leads to open tetrahedral cage-like structuring that contributes to its remarkable volumetric and thermal properties

Molecular Dynamics implementation of BN2D or 'Mercedes Benz' water model

Two-dimensional 'Mercedes Benz' (MB) or BN2D water model (Naim, 1971) is implemented in Molecular Dynamics. It is known that the MB model can capture abnormal properties of real water (high heat capacity, minima of pressure and isothermal compressibility, negative thermal expansion coefficient) (Silverstein et al., 1998). In this work formulas for calculating the thermodynamic, structural and dynamic properties in microcanonical (NVE) and isothermal-isobaric (NPT) ensembles for the model from Molecular Dynamics simulation are derived and verified against known Monte Carlo results. The convergence of the thermodynamic properties and the system's numerical stability are investigated. The results qualitatively reproduce the peculiarities of real water making the model a visually convenient tool that also requires less computational resources, thus allowing simulations of large (hydrodynamic scale) molecular systems. We provide the open source code written in C/C++ for the BN2D water model implementation using Molecular Dynamics

Bridging large and small scales of water models using hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework

This thesis presents a two-dimensional water model investigation and development of a multiscale method for the modelling of large systems, such as virus in water or peptide immersed in the solvent. We have implemented a two-dimensional ‘Mercedes Benz’ (MB) or BN2D water model using Molecular Dynamics. We have studied its dynamical and structural properties dependence on the model’s parameters. For the first time we derived formulas to calculate thermodynamic properties of the MB model in the microcanonical (NVE) ensemble. We also derived equations of motion in the isothermal–isobaric (NPT) ensemble. We have analysed the rotational degree of freedom of the model in both ensembles. We have developed and implemented a self-consistent multiscale method, which is able to communicate micro- and macro- scales. This multiscale method assumes, that matter consists of the two phases. One phase is related to micro- and the other to macroscale. We simulate the macro scale using Landau Lifshitz-Fluctuating Hydrodynamics, while we describe the microscale using Molecular Dynamics. We have demonstrated that the communication between the disparate scales is possible without introduction of fictitious interface or approximations which reduce the accuracy of the information exchange between the scales. We have investigated control parameters, which were introduced to control the contribution of each phases to the matter behaviour. We have shown, that microscales inherit dynamical properties of the macroscales and vice versa, depending on the concentration of each phase. We have shown, that Radial Distribution Function is not altered and velocity autocorrelation functions are gradually transformed, from Molecular Dynamics to Fluctuating Hydrodynamics description, when phase balance is changed. In this work we test our multiscale method for the liquid argon, BN2D and SPC/E water models. For the SPC/E water model we investigate microscale fluctuations which are computed using advanced mapping technique of the small scales to the large scales, which was developed by Voulgarakisand et. al

Three-dimensional "Mercedes-Benz" model for water

Peer reviewe

Computational Studies of 2D Diffusion and Water Nucleation

Molecular simulations for nearly any molecule can currently be conducted, but often these calculations are costly and can only be accomplished using multiple nodes on a super computer. These topics of research use the new and novel approach of approximating water using "Rose Equations" to create an accurate 2D model of water molecules. This research was published in a special edition of the Journal of Molecular Liquids dedicated to Vokjko Vlachy, whose work with an analogous 2D model known as the "Mercedes Benz Model" inspired this project. While the previous "Mercedes Benz" model of water approximated many properties of real water due to the constraints of Monte-Carlo sampling certain properties, such as coefficients of diffusion, could not be calculated. This new 2D model was created by modifying simple trigonometric (Rose) functions to give an approximation of real water that consists of one central atom and three surrounding Hydrogen bonding arms. Because all of the simulations were done in 2D different properties could be quickly probed at varying temperatures using multiple starting configurations to give proper statistical accuracy. This model was then expanded to give visual insights into the properties of particles when confined to nanotubes. This visual representation was created using free software known as Pov-Ray. Pov-Ray was then used to help elucidate nucleation events within 3D water environments. This newly created software has the ability to represent every ring within a simulation of particles as determined by simple geometric means.Chemistr

Lattice Boltzmann modeling of water-like fluids

We review recent advances on the mesoscopic modeling of water-like fluids,based on the lattice Boltzmann (LB) methodology.The main idea is to enrich the basic LB (hydro)-dynamics with angular degrees of freedom responding to suitable directional potentials between water-like molecules.The model is shown to reproduce some microscopic features of liquid water, such as an average number of hydrogen bonds per molecules (HBs) between $3$ and $4$, as well as a qualitatively correctstatistics of the hydrogen bond angle as a function of the temperature.Future developments, based on the coupling the present water-like LB model with the dynamics of suspended bodies,such as biopolymers, may open new angles of attack to the simulation of complex biofluidic problems, such as protein folding and aggregation, and the motion of large biomolecules in complex cellular environments

Bayesian selection for coarse-grained models of liquid water

The necessity for accurate and computationally efficient representations of water in atomistic simulations that can span biologically relevant timescales has born the necessity of coarse-grained (CG) modeling. Despite numerous advances, CG water models rely mostly on a-priori specified assumptions. How these assumptions affect the model accuracy, efficiency, and in particular transferability, has not been systematically investigated. Here we propose a data driven, comparison and selection for CG water models through a Hierarchical Bayesian framework. We examine CG water models that differ in their level of coarse-graining, structure, and number of interaction sites. We find that the importance of electrostatic interactions for the physical system under consideration is a dominant criterion for the model selection. Multi-site models are favored, unless the effects of water in electrostatic screening are not relevant, in which case the single site model is preferred due to its computational savings. The charge distribution is found to play an important role in the multi-site model's accuracy while the flexibility of the bonds/angles may only slightly improve the models. Furthermore, we find significant variations in the computational cost of these models. We present a data informed rationale for the selection of CG water models and provide guidance for future water model designs

Is it the shape of the cavity, or the shape of the water in the cavity?

Historical interpretations of the thermodynamics characterizing biomolecular recognition have marginalized the role of water. An important (even, perhaps, dominant) contribution to molecular recognition in water comes from the “hydrophobic effect,” in which non-polar portions of a ligand interact preferentially with non-polar regions of a protein. Water surrounds the ligand, and water fills the binding pocket of the protein: when the protein-ligand complex forms, and hydrophobic surfaces of the binding pocket and the ligand approach one another, the molecules (and hydrogen-bonded networks of molecules) of water associated with both surfaces rearrange and, in part, entirely escape into the bulk solution. It is now clear that neither of the two most commonly cited rationalizations for the hydrophobic effect—an entropy-dominated hydrophobic effect, in which ordered waters at the surface of the ligand, and water at the surface of the protein, are released to the bulk upon binding, and a “lock-and-key” model, in which the surface of a ligand interacts directly with a surface of a protein having a complementary shape–can account for water-mediated interactions between the ligand and the protein, and neither is sufficient to account for the experimental observation of both entropy- andenthalpy-dominated hydrophobic effects. What is now clear is that there is no single hydrophobic effect, with a universally applicable, common, thermodynamic description: different processes (i.e., partitioning between phases of different hydrophobicity, aggregation in water, and binding) with different thermodynamics, depend on the molecular-level details of the structures of the molecules involved, and of the aggregates that form. A “water-centric” description of the hydrophobic effect in biomolecular recognition focuses on the structures of water surrounding the ligand, and of water filling the binding pocket of the protein, both before and after binding. This view attributes the hydrophobic effect to changes in the free energy of the networks of hydrogen bonds that are formed, broken, or re-arranged when two hydrophobic surfaces approach (but do not necessarily contact) one another. The details of the molecular topography (and the polar character) of the mole- cular surfaces play an important role in determining the structure of these networks of hydrogen-bonded waters, and in the thermodynamic description of the hydrophobic effect(s). Theorists have led the formulation of this “water-centric view”, although experiments are now supplying support for it. It poses complex problems for would-be “designers” of protein-ligand interactions, and for so-called “rational drug design”.Chemistry and Chemical Biolog

A hybrid molecular dynamics/fluctuating hydrodynamics method for modelling liquids at multiple scales in space and time

A new 3D implementation of a hybrid model based on the analogy with two-phase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the Landau-Lifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single "zoom-in" user-defined function s that has the meaning of a partial concentration in the two-phase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported