Bottom-Up Informed and Iteratively Optimized Coarse-Grained Non-Markovian Water Models with Accurate Dynamics

Coarse-grained simulation of water: A comparative study and overview

In spite of the tremendous increase in computational power over the last few decades, the problem of simulating atomistic systems containing large amounts of water molecules over longer lengths and time scales still remains. In this respect, the coarse-grained (CG) force field reduces the computational cost and, therefore, allows simulations of larger systems for longer times. However, the specific scope of the different CG water models is more limited compared to their atomistic counterparts. In this context, we conducted a comparative study on the molecular physical structure, thermodynamic, and dynamic properties of bulk water systems using six distinct CG water models and all-atom (AA) simulations. The six CG simulation procedures involved modeling with three variants of the water model coming from the MARTINI force field, one from the SPICA force field, and the two Iterative Boltzmann Inversion (IBI) derived potentials from the AA simulations. The AA simulations have been performed using the SPC/E and TIP4P force fields. The IBI models, namely SPC/E-IBI and TIP4P-IBI, depict the structural features in close agreement with the atomistic samples. The explicit number of water molecules in the first coordination shell for the three MARTINI models and the SPICA force field is in excellent agreement with the SPC/E and TIP4P values. The ensuing simulated densities for the various water models align significantly with the literature data, indicating the reliability of our approach. The SPC/E and SPICA models stand out in predicting the enthalpy of vaporization among the all-atom and CG force fields, respectively. The two all-atom models and their IBI equivalents are better at representing the isobaric specific heat capacity compared to the other models. The isothermal compressibility is reproduced comprehensively by the SPC/E force field followed by TIP4P, while SPICA is the better choice within the CG models. With respect to the dynamics of the system, the diffusion coefficient of the SPICA force field is in perfect agreement with the experimental data, even better than the atomistic samples. The overall scores of the different models, indicative of their relative performances compared to the other models, have also been computed.

Predicting the Spurious Acceleration of Coarse-Grained Molecular Dynamics from Molecular Fluid Structure

Reproducing dynamical properties, such as diffusion coefficients, in coarse-grained (CG) molecular dynamics simulations can be challenging due to the loss of fine-grained details, such as atomic vibrations and local motions of particles in the parent all-atom (AA) system. In this study, we present a predictive tool for the mobility acceleration factor, defined as ratio of the CG diffusion coefficient to the AA diffusion coefficient. According to the well-established Green-Kubo formalism, the diffusion coefficient is related to integral of the velocity autocorrelation function. As integral of the velocity autocorrelation function is influenced by the particle's acceleration, key parameters affecting the acceleration differences between an AA molecule and its corresponding CG bead are identified to develop a predictive model. By conducting AA and CG simulations on 20 liquid hydrocarbons with varying masses and sizes, their mobility acceleration factors are determined, the largest being 62.78. This data is then used to fit a nonlinear functional form as the predictive model. The identified molecular descriptors for the predictive model are easy to calculate for new molecules, enabling the model to be readily applied to predict the mobility acceleration factor for different molecules in CG simulations.

Cross-correlations in the fluctuation-dissipation relation influence barrier-crossing dynamics

The Generalized Langevin Equation has been successfully used to model and understand the conformational dynamics of molecules in solution. However, recent works have demonstrated that, in these kinds of applications, the usual fluctuation-dissipation relation connecting the statistics of the random force to the memory kernel could contain a cross-correlation term. In this work, we systematically explore the origins of this cross-correlation term and argue that it plays a role, particularly in the folding dynamics of biopolymers. Finally, we propose an approximation for the cross-correlation term within the usual fluctuation-dissipation relation.

Modulating Coarse-Grained Dynamics by Perturbing Free Energy Landscapes

We introduce an approach to describe the long-time dynamics of multiatomic molecules by modulating the free energy landscape (FEL) to capture dominant features of the energy-barrier crossing dynamics of the all-atom (AA) system. Notably, we establish that the self-diffusion coefficient of coarse-grained (CG) systems can be accurately delineated by enhancing conservative force fields with high-frequency perturbations. Using theoretical arguments, we show that these perturbations do not alter the lower-order distribution functions, thereby preserving the structure of the AA system after coarse-graining. We demonstrate the utility of this approach using molecular dynamics simulations of simple molecules in bulk with distinct dynamical characteristics with and without time scale separations as well as for inhomogeneous systems where a fluid is confined in a slit-like nanochannel. Additionally, we also apply our approach to more powerful many-body potentials optimized by using machine learning (ML).

A Gauss-Newton method for iterative optimization of memory kernels for generalized Langevin thermostats in coarse-grained molecular dynamics simulations

In molecular dynamics simulations, dynamically consistent coarse-grained (CG) models commonly use stochastic thermostats to model friction and fluctuations that are lost in a CG description. While Markovian, i.e., time-local, formulations of such thermostats allow for an accurate representation of diffusivities/long-time dynamics, a correct description of the dynamics on all time scales generally requires non-Markovian, i.e., non-time-local, thermostats. These thermostats typically take the form of a Generalized Langevin Equation (GLE) determined by a memory kernel. In this work, we use a Markovian embedded formulation of a position-independent GLE thermostat acting independently on each CG degree of freedom. Extracting the memory kernel of this CG model from atomistic reference data requires several approximations. Therefore, this task is best understood as an inverse problem. While our recently proposed approximate Newton scheme allows for the iterative optimization of memory kernels (IOMK), Markovian embedding remained potentially error-prone and computationally expensive. In this work, we present an IOMK-Gauss-Newton scheme (IOMK-GN) based on IOMK that allows for the direct parameterization of a Markovian embedded model.

Synthetic Force-Field Database for Training Machine Learning Models to Predict Mobility-Preserving Coarse-Grained Molecular-Simulation Potentials

Balancing accuracy and efficiency is a common problem in molecular simulation. This tradeoff is evident in coarse-grained molecular dynamics simulation, which prioritizes efficiency, and all-atom molecular simulation, which prioritizes accuracy. Despite continuous efforts, creating a coarse-grained model that accurately captures both the system's structure and dynamics remains elusive. In this article, we present a data-driven approach for constructing coarse-grained models that aim to describe both the structure and dynamics of the system equally well. While the development of machine learning models is well-received in the scientific community, the significance of dataset creation for these models is often overlooked. However, data-driven approaches cannot progress without a robust dataset. To address this, we construct a database of synthetic coarse-grained potentials generated from unphysical all-atom models. A neural network is trained with the generated database to predict the coarse-grained potentials of real liquids. We evaluate their quality by calculating the combined loss of structural and dynamical accuracy upon coarse-graining. When we compare our machine learning-based coarse-grained potential with the one from iterative Boltzmann inversion, the machine learning prediction turns out better for all eight hydrocarbon liquids we studied. As all-atom surfaces turn more nonspherical, both ways of coarse-graining degrade. Still, the neural network outperforms iterative Boltzmann inversion in constructing good quality coarse-grained models for such cases. The synthetic database and the developed machine learning models are freely available to the community, and we believe that our approach will generate interest in efficiently deriving accurate coarse-grained models for liquids.

Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties

The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.

Force renormalization for probes immersed in an active bath

Langevin equations or generalized Langevin equations (GLEs) are popular models for describing the motion of a particle in a fluid medium in an effective manner. Here we examine particles immersed in an inherently nonequilibrium fluid, i.e., an active bath, which are subject to an external force. Specifically, we consider two types of forces that are highly relevant for microrheological studies: A harmonic, trapping force and a constant, "drag" force. We study such systems by molecular simulations and use the simulation data to extract an effective GLE description. We find that within this description, in an active bath, the external force in the GLE is not equal to the physical external force, but rather a renormalized external force, which can be significantly smaller. The effect cannot be attributed to the mere temperature renormalization, which is also observed.