Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Water polarization induced by thermal gradients: the extended simple point charge model (SPC/E)

We investigate the non-equilibrium response of extended simple point charge (SPC/E) water to thermal gradients. Using non-equilibrium molecular dynamics simulations, we show that SPC/E water features the thermo-polarization orientation effect, namely, water becomes polarized as a response to a thermal gradient. The polarization field increases linearly with the thermal gradient, in agreement with predictions of non-equilibrium thermodynamics theory. This observation confirms the generality of the thermo-polarization effect, first reported using the Modified Central Force Model (MCFM), and shows this physical effect is present irrespective of the water model details, in particular, dipole moment magnitude and model flexibility. The magnitude of the effect is the same for both models, although the sign of the electrostatic field is reversed in going from the MCFM to the SPC/E model. We further analyze the impact that the molecular geometry and mass distribution has on the magnitude of the polarization. Our results indicate that the thermo-polarization effect should be observed in a wide range of polar fluids, including fluids where hydrogen bonding is not present. Using various molecular models, we show that the polarization of these fluids under appropriate thermodynamic conditions can be of the same order or stronger than in water.

Free energy calculations for molecular solids using GROMACS

In this work, we describe a procedure to evaluate the free energy of molecular solids with the GROMACS molecular dynamics package. The free energy is calculated using the Einstein molecule method that can be regarded as a small modification of the Einstein crystal method. Here, the position and orientation of the molecules is fixed by using an Einstein field that binds with harmonic springs at least three non-collinear atoms (or points of the molecule) to their reference positions. The validity of the Einstein field is tested by performing free-energy calculations of methanol, water (ice), and patchy colloids molecular solids. The free energies calculated with GROMACS show a very good agreement with those obtained using Monte Carlo and with previously published results.

Polarizable six-point water models from computational and empirical optimization

Tröster et al. (J. Phys. Chem B 2013, 117, 9486-9500) recently suggested a mixed computational and empirical approach to the optimization of polarizable molecular mechanics (PMM) water models. In the empirical part the parameters of Buckingham potentials are optimized by PMM molecular dynamics (MD) simulations. The computational part applies hybrid calculations, which combine the quantum mechanical description of a H2O molecule by density functional theory (DFT) with a PMM model of its liquid phase environment generated by MD. While the static dipole moments and polarizabilities of the PMM water models are fixed at the experimental gas phase values, the DFT/PMM calculations are employed to optimize the remaining electrostatic properties. These properties cover the width of a Gaussian inducible dipole positioned at the oxygen and the locations of massless negative charge points within the molecule (the positive charges are attached to the hydrogens). The authors considered the cases of one and two negative charges rendering the PMM four- and five-point models TL4P and TL5P. Here we extend their approach to three negative charges, thus suggesting the PMM six-point model TL6P. As compared to the predecessors and to other PMM models, which also exhibit partial charges at fixed positions, TL6P turned out to predict all studied properties of liquid water at p0 = 1 bar and T0 = 300 K with a remarkable accuracy. These properties cover, for instance, the diffusion constant, viscosity, isobaric heat capacity, isothermal compressibility, dielectric constant, density, and the isobaric thermal expansion coefficient. This success concurrently provides a microscopic physical explanation of corresponding shortcomings of previous models. It uniquely assigns the failures of previous models to substantial inaccuracies in the description of the higher electrostatic multipole moments of liquid phase water molecules. Resulting favorable properties concerning the transferability to other temperatures and conditions like the melting of ice are also discussed.

A systematic development of a polarizable potential of water

Based on extensive studies of existing potentials we propose a new molecular model for water. The new model is rigid and contains three Gaussian charges. Contrary to other models, all charges take part in the polarization of the molecule. They are connected by harmonic springs to their gas-phase positions: the negative charge to a prescribed point on the main axis of the molecule; the positive charges to the hydrogens. The mechanical equilibrium between the electrostatic forces and the spring forces determines the polarization of the molecule which is established by iteration at every timestep. The model gives excellent estimates for ambient liquid properties and reasonably good results from high-pressure solids to gas-phase clusters. We present a detailed description of the development of this model and a large number of calculated properties compared to the estimates of the nonpolarizable TIP4P∕2005 [J. L. F. Abascal and C. Vega, J. Chem. Phys. 123, 234505 (2005)], the polarizable GCPM [P. Paricaud, M. Predota, A. A. Chialvo, and P. T. Cummings, J. Chem. Phys. 122, 244511 (2005)], and our earlier BKd3 model [P. T. Kiss and A. Baranyai, J. Chem. Phys. 137, 084506 (2012)]. The best overall performance is shown by the new model.

Is there a third order phase transition for supercritical fluids?

We prove that according to Molecular Dynamics (MD) simulations of liquid mixtures of Lennard-Jones (L-J) particles, there is no third order phase transition in the supercritical regime beyond Andrew's critical point. This result is in open contrast with recent theoretical studies and experiments which instead suggest not only its existence but also its universality regarding the chemical nature of the fluid. We argue that our results are solid enough to go beyond the limitations of MD and the generic character of L-J models, thus suggesting a rather smooth liquid-vapor thermodynamic behavior of fluids in supercritical regime.

A continuous mixture of two different dimers in liquid water

Liquid water is formed by a continuous mixture of two different dimers (cis and trans) with distinct energies related to different relative water molecule orientations.

A study of the ice–water interface using the TIP4P/2005 water model

The structure and fluctuations of the ice–water interface are studied by means of computer simulations using the TIP4P/2005 model.

Advanced potential energy surfaces for condensed phase simulation

Computational modeling at the atomistic and mesoscopic levels has undergone dramatic development in the past 10 years to meet the challenge of adequately accounting for the many-body nature of intermolecular interactions. At the heart of this challenge is the ability to identify the strengths and specific limitations of pairwise-additive interactions, to improve classical models to explicitly account for many-body effects, and consequently to enhance their ability to describe a wider range of reference data and build confidence in their predictive capacity. However, the corresponding computational cost of these advanced classical models increases significantly enough that statistical convergence of condensed phase observables becomes more difficult to achieve. Here we review a hierarchy of potential energy surface models used in molecular simulations for systems with many degrees of freedom that best meet the trade-off between accuracy and computational speed in order to define a sweet spot for a given scientific problem of interest.

Systematic improvement of a classical molecular model of water

We report the iAMOEBA ("inexpensive AMOEBA") classical polarizable water model. The iAMOEBA model uses a direct approximation to describe electronic polarizability, in which the induced dipoles are determined directly from the permanent multipole electric fields and do not interact with one another. The direct approximation reduces the computational cost relative to a fully self-consistent polarizable model such as AMOEBA. The model is parameterized using ForceBalance, a systematic optimization method that simultaneously utilizes training data from experimental measurements and high-level ab initio calculations. We show that iAMOEBA is a highly accurate model for water in the solid, liquid, and gas phases, with the ability to fully capture the effects of electronic polarization and predict a comprehensive set of water properties beyond the training data set including the phase diagram. The increased accuracy of iAMOEBA over the fully polarizable AMOEBA model demonstrates ForceBalance as a method that allows the researcher to systematically improve empirical models by efficiently utilizing the available data.

Polarizable water models from mixed computational and empirical optimization

Here we suggest a mixed computational and empirical approach serving to optimize the parameters of complex and polarizable molecular mechanics (PMM) models for complicated liquids. The computational part of the parameter optimization relies on hybrid calculations combining density functional theory (DFT) for a solute molecule with a PMM treatment of its solvent environment at well-defined thermodynamic conditions. As an application we have developed PMM models for water featuring ν = 3, 4, and 5 points of force action, a Gaussian inducible dipole and a Buckingham potential at the oxygen, the experimental liquid phase geometry, the experimental gas phase polarizability α(exp)(g) = 1.47 ų, and, for ν = 4 and 5, the gas phase value μ(exp)(g) = 1.855 D for the static dipole moment. The widths of the Gaussian dipoles and, for ν = 4 and 5, also the electrostatic geometries of these so-called TLνP models are derived from self-consistent DFT/PMM calculations, and the parameters of the Buckingham potentials (and the static TL3P dipole moment) are estimated from molecular dynamics (MD) simulations. The high quality of the resulting models is demonstrated for the observables targeted during optimization (potential energy per molecule, pressure, radial distribution functions) and a series of predicted properties (quadrupole moments, density at constant pressure, dielectric constant, diffusivity, viscosity, compressibility, heat capacity) at certain standard conditions. Remaining deficiencies and possible ways for their removal are discussed.

Water and water-like liquids: relationships between structure, entropy and mobility

Liquids with very diverse underlying interactions share the thermodynamic and transport anomalies of water, including metalloids, ionic melts and mesoscopic fluids. The generic feature that characterises such water-like liquids is a density-driven shift in the nature of local order in the condensed phases. The key semiquantitative relationships between structural order, thermodynamics and transport that are necessary in order to map out the consequences of this common qualitative feature for liquid-state properties and phase transformations of such systems are reviewed here. The application of these ideas to understand and model tetrahedral liquids, especially water, is discussed and possible extensions to other complex fluids are considered.

Alkali halide solutions under thermal gradients: soret coefficients and heat transfer mechanisms

We report an extensive analysis of the non-equilibrium response of alkali halide aqueous solutions (Na(+)/K(+)-Cl(-)) to thermal gradients using state of the art non-equilibrium molecular dynamics simulations and thermal diffusion forced Rayleigh scattering experiments. The coupling between the thermal gradient and the resulting ionic salt mass flux is quantified through the Soret coefficient. We find the Soret coefficient is of the order of 10(-3) K(-1) for a wide range of concentrations. These relatively simple solutions feature a very rich behavior. The Soret coefficient decreases with concentration at high temperatures (higher than T ∼ 315 K), whereas it increases at lower temperatures. In agreement with previous experiments, we find evidence for sign inversion in the Soret coefficient of NaCl and KCl solutions. We use an atomistic non-equilibrium molecular dynamics approach to compute the Soret coefficients in a wide range of conditions and to attain further microscopic insight on the heat transport mechanism and the behavior of the Soret coefficient in aqueous solutions. The models employed in this work reproduce the magnitude of the Soret coefficient, and the general dependence of this coefficient with temperature and salt concentration. We use the computer simulations as a microscopic approach to establish a correlation between the sign and magnitude of the Soret coefficients and ionic solvation and hydrogen bond structure of the solutions. Finally, we report an analysis of heat transport in ionic solution by quantifying the solution thermal conductivity as a function of concentration. The simulations accurately reproduce the decrease of the thermal conductivity with increasing salt concentration that is observed in experiments. An explanation of this behavior is provided.

Dynamics of nanoscale droplets on moving surfaces

We use molecular dynamics (MD) simulations to investigate the dynamic wetting of nanoscale water droplets on moving surfaces. The density and hydrogen bonding profiles along the direction normal to the surface are reported, and the width of the water depletion layer is evaluated first for droplets on three different static surfaces: silicon, graphite, and a fictitious superhydrophobic surface. The advancing and receding contact angles, and contact angle hysteresis, are then measured as a function of capillary number on smooth moving silicon and graphite surfaces. Our results for the silicon surface show that molecular displacements at the contact line are influenced greatly by interactions with the solid surface and partly by viscous dissipation effects induced through the movement of the surface. For the graphite surface, however, both the advancing and receding contact angles values are close to the static contact angle value and are independent of the capillary number; i.e., viscous dissipation effects are negligible. This finding is in contrast with the wetting dynamics of macroscale water droplets, which show significant dependence on the capillary number.

Electronically coarse-grained model for water

We introduce an electronically coarse-grained description of water representing all long range, many-body electronic responses via an embedded quantum oscillator. Leading-order response coefficients and gas phase electrostatic moments are exactly reproduced. Molecular dynamics, using electronic path integral sampling, shows that this framework is sufficient for a realistic liquid to emerge naturally with transferability extending further to nonambient state points and to the free water surface. The model allows the strength of many-body dispersion and polarization to be adjusted independently and these are found to have significant effects on the condensed phase.

A density-functional theory-based neural network potential for water clusters including van der Waals corrections

The fundamental importance of water for many chemical processes has motivated the development of countless efficient but approximate water potentials for large-scale molecular dynamics simulations, from simple empirical force fields to very sophisticated flexible water models. Accurate and generally applicable water potentials should fulfill a number of requirements. They should have a quality close to quantum chemical methods, they should explicitly depend on all degrees of freedom including all relevant many-body interactions, and they should be able to describe molecular dissociation and recombination. In this work, we present a high-dimensional neural network (NN) potential for water clusters based on density-functional theory (DFT) calculations, which is constructed using clusters containing up to 10 monomers and is in principle able to meet all these requirements. We investigate the reliability of specific parametrizations employing two frequently used generalized gradient approximation (GGA) exchange-correlation functionals, PBE and RPBE, as reference methods. We find that the binding energy errors of the NN potentials with respect to DFT are significantly lower than the typical uncertainties of DFT calculations arising from the choice of the exchange-correlation functional. Further, we examine the role of van der Waals interactions, which are not properly described by GGA functionals. Specifically, we incorporate the D3 scheme suggested by Grimme (J. Chem. Phys. 2010, 132, 154104) in our potentials and demonstrate that it can be applied to GGA-based NN potentials in the same way as to DFT calculations without modification. Our results show that the description of small water clusters provided by the RPBE functional is significantly improved if van der Waals interactions are included, while in case of the PBE functional, which is well-known to yield stronger binding than RPBE, van der Waals corrections lead to overestimated binding energies.

A molecular dynamics study of the equation of state and the structure of supercooled aqueous solutions of methanol

We perform molecular dynamics computer simulations in order to study the equation of state and the structure of supercooled aqueous solutions of methanol at methanol mole fractions x(m) = 0.05 and x(m) = 0.10. We model the solvent using the TIP4P/2005 potential and the methanol using the OPLS-AA force field. We find that for x(m) = 0.05 the behavior of the equation of state, studied in the P - T and P - ρ planes, is consistent with the presence of a liquid-liquid phase transition, reminiscent of that previously found for x(m) = 0. We estimate the position of the liquid-liquid critical point to be at T = 193 K, P = 96 MPa, and ρ = 1.003 g/cm(3). When the methanol mole fraction is doubled to x(m) = 0.10 no liquid-liquid transition is observed, indicating its possible disappearance at this concentration. We also study the water-water and water-methanol structure in the two solutions. We find that down to low temperature methanol can be incorporated into the water structure for both x(m) = 0.05 and x(m) = 0.10.

Lattice Boltzmann implementation of the three-dimensional Ben-Naim potential for water-like fluids

We develop a three-dimensional lattice Boltzmann (LB) model accounting for directional interactions between water-like molecules, based on the so-called Ben-Naim (BN) potential [A. Ben-Naim, Molecular Theory of Water and Aqueous Solutions: Part I: Understanding Water (World Scientific Publishing Company, 2010); "Statistical mechanics of 'waterlike' particles in two dimensions. I. Physical model and application of the Percus-Yevick equation," J. Chem. Phys. 54, 3682 (1971)]. The water-like molecules are represented by rigid tetrahedra, with two donors and two acceptors at the corners and interacting with neighboring tetrahedra, sitting on the nodes of a regular lattice. The tetrahedra are free to rotate about their centers under the drive of the torque arising from the interparticle potential. The orientations of the water molecules are evolved in time via an overdamped Langevin dynamics for the torque, which is solved by means of a quaternion technique. The resulting advection-diffusion-reaction equation for the quaternion components is solved by a LB method, acting as a dynamic minimizer for the global energy of the fluid. By adding thermal fluctuations to the torque equation, the model is shown to reproduce some microscopic features of real water, such as an average number of hydrogen bonds per molecules (HBs) between 3 and 4, in a qualitative agreement with microscopic water models. Albeit slower than a standard LB solver for ordinary fluids, the present scheme opens up potentially far-reaching scenarios for multiscale applications based on a coarse-grained representation of the water solvent.