Constructing many-body dissipative particle dynamics models of fluids from bottom-up coarse-graining.

Since their emergence in the 1990s, mesoscopic models of fluids have been widely used to study complex organization and transport phenomena beyond the molecular scale. Even though these models are designed based on results from physics at the meso- and macroscale, such as fluid mechanics and statistical field theory, the underlying microscopic foundation of these models is not as well defined. This paper aims to build such a systematic connection using bottom-up coarse-graining methods. From the recently developed dynamic coarse-graining scheme, we introduce a statistical inference framework of explicit many-body conservative interaction that quantitatively recapitulates the mesoscopic structure of the underlying fluid. To further consider the dissipative and fluctuation forces, we design a novel algorithm that parameterizes these forces. By utilizing this algorithm, we derive pairwise decomposable friction kernels under both non-Markovian and Markovian limits where both short- and long-time features of the coarse-grained dynamics are reproduced. Finally, through these new developments, the many-body dissipative particle dynamics type of equations of motion are successfully derived. The methodologies developed in this work thus open a new avenue for the construction of direct bottom-up mesoscopic models that naturally bridge the meso- and macroscopic physics.

A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). II. Temperature transferability and structural properties at low temperature.

A number of studies have constructed coarse-grained (CG) models of water to understand its anomalous properties. Most of these properties emerge at low temperatures, and an accurate CG model needs to be applicable to these low-temperature ranges. However, direct use of CG models parameterized from other temperatures, e.g., room temperature, encounters a problem known as transferability, as the CG potential essentially follows the form of the many-body CG free energy function. Therefore, temperature-dependent changes to CG interactions must be accounted for. The collective behavior of water at low temperature is generally a many-body process, which often motivates the use of expensive many-body terms in the CG interactions. To surmount the aforementioned problems, we apply the Bottom-Up Many-Body Projected Water (BUMPer) CG model constructed from Paper I to study the low-temperature behavior of water. We report for the first time that the embedded three-body interaction enables BUMPer, despite its pairwise form, to capture the growth of ice at the ice/water interface with corroborating many-body correlations during the crystal growth. Furthermore, we propose temperature transferable BUMPer models that are indirectly constructed from the free energy decomposition scheme. Changes in CG interactions and corresponding structures are faithfully recapitulated by this framework. We further extend BUMPer to examine its ability to predict the structure, density, and diffusion anomalies by employing an alternative analysis based on structural correlations and pairwise potential forms to predict such anomalies. The presented analysis highlights the existence of these anomalies in the low-temperature regime and overcomes potential transferability problems.

A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). I. General theory and model.

Water is undoubtedly one of the most important molecules for a variety of chemical and physical systems, and constructing precise yet effective coarse-grained (CG) water models has been a high priority for computer simulations. To recapitulate important local correlations in the CG water model, explicit higher-order interactions are often included. However, the advantages of coarse-graining may then be offset by the larger computational cost in the model parameterization and simulation execution. To leverage both the computational efficiency of the CG simulation and the inclusion of higher-order interactions, we propose a new statistical mechanical theory that effectively projects many-body interactions onto pairwise basis sets. The many-body projection theory presented in this work shares similar physics from liquid state theory, providing an efficient approach to account for higher-order interactions within the reduced model. We apply this theory to project the widely used Stillinger-Weber three-body interaction onto a pairwise (two-body) interaction for water. Based on the projected interaction with the correct long-range behavior, we denote the new CG water model as the Bottom-Up Many-Body Projected Water (BUMPer) model, where the resultant CG interaction corresponds to a prior model, the iteratively force-matched model. Unlike other pairwise CG models, BUMPer provides high-fidelity recapitulation of pair correlation functions and three-body distributions, as well as N-body correlation functions. BUMPer extensively improves upon the existing bottom-up CG water models by extending the accuracy and applicability of such models while maintaining a reduced computational cost.

Coarse-graining involving virtual sites: Centers of symmetry coarse-graining.

Coarse-grained (CG) models allow efficient molecular simulation by reducing the degrees of freedom in the system. To recapitulate important physical properties, including many-body correlations at the CG resolution, an appropriate mapping from the atomistic to CG level is needed. Symmetry exhibited by molecules, especially when aspherical, can be lost upon coarse-graining due to the use of spherically symmetric CG effective potentials. This mismatch can be efficiently amended by imposing symmetry using virtual CG sites. However, there has been no rigorous bottom-up approach for constructing a many-body potential of mean force that governs the distribution of virtual CG sites. Herein, we demonstrate a statistical mechanical framework that extends a mapping scheme of CG systems involving virtual sites to provide a thermodynamically consistent CG model in the spirit of the principle of maximum entropy. Utilizing the extended framework, this work defines a center of symmetry (COS) mapping and applies it to benzene and toluene systems such that the planar symmetry of the aromatic ring is preserved by constructing two virtual sites along a normal vector. Compared to typical center of mass (COM) CG models, COS CG models correctly recapitulate radial and higher order correlations, e.g., orientational and three-body correlations. Moreover, we find that COS CG interactions from bulk phases are transferable to mixture phases, whereas conventional COM models deviate between the two states. This result suggests a systematic approach to construct more transferable CG models by conserving molecular symmetry, and the new protocol is further expected to capture other many-body correlations by utilizing virtual sites.

Coarse-graining of many-body path integrals: Theory and numerical approximations.

Feynman's imaginary time path integral approach to quantum statistical mechanics provides a theoretical formalism for including nuclear quantum effects (NQEs) in simulation of condensed matter systems. Sinitskiy and Voth [J. Chem. Phys. 143, 094104 (2015)] have presented the coarse-grained path integral (CG-PI) theory, which provides a reductionist coarse-grained representation of the imaginary time path integral based on the quantum-classical isomorphism. In this paper, the many-body generalization of the CG-PI theory is presented. It is shown that the N interacting particles obeying quantum Boltzmann statistics can be represented as a system of N pairs of classical-like pseudoparticles coupled to each other analogous to the pseudoparticle pair of the one-body theory. Moreover, we present a numerical CG-PI (n-CG-PI) method applying a simple approximation to the coupling scheme between the pseudoparticles due to numerical challenges of directly implementing the full many-body CG-PI theory. Structural correlations of two liquid systems are investigated to demonstrate the performance of the n-CG-PI method. Both the many-body CG-PI theory and the n-CG-PI method not only present reductionist views of the many-body quantum Boltzmann statistics but also provide theoretical and numerical insight into how to explicitly incorporate NQEs in the representation of condensed matter systems with minimal additional degrees of freedom.

Quantum theory of multiscale coarse-graining.

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.

Mesoscopic coarse-grained representations of fluids rigorously derived from atomistic models.

Mesoscopic models are widely used to study complex organization and transport phenomena in chemical and biological systems. Defining a rigorous procedure by which a mesoscopic coarse-grained (CG) representation for a fluid can be constructed from an atomistic fine-grained (FG) model is a long-standing question in the field. The connection of these CG models with the FG level of description, which might be built by CG mappings from the FG model, is often unclear. The present paper introduces a new CG mapping scheme that uses dynamically self-consistent smooth centroidal Voronoi tessellation to address this challenging problem. The new mapping scheme is applied to the coarse-graining of supercritical Lennard-Jones fluid systems at different CG resolutions under both quiescent conditions and non-equilibrium shear flow. The method generates continuous, stable, and ergodic CG trajectories and quantitatively captures the slow collective motions of the underlying FG fluids. A parameterization of the CG models from the mapped CG trajectory is then developed based on the Mori-Zwanzig formalism. The Generalized Langevin Equation describes the dynamics of CG variables, and the parameterized result is shown to reproduce the structural and dynamical correlations of the CG system. The new dynamical mapping scheme and the parameterization protocol open up an avenue for direct bottom-up construction of mesoscopic models of fluids in a Lagrangian description.

Molecular transport through membranes: Accurate permeability coefficients from multidimensional potentials of mean force and local diffusion constants.

Estimating the permeability coefficient of small molecules through lipid bilayer membranes plays an important role in the development of effective drug candidates. In silico simulations can produce acceptable relative permeability coefficients for a series of small molecules; however, the absolute permeability coefficients from simulations are usually off by orders of magnitude. In addition to differences between the lipid bilayers used in vitro and in silico, the poor convergence of permeation free energy profiles and over-simplified diffusion models have contributed to these discrepancies. In this paper, we present a multidimensional inhomogeneous solubility-diffusion model to study the permeability of a small molecule drug (trimethoprim) passing through a POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) lipid bilayer. Our approach improves the permeation model in three ways: First, the free energy profile (potential of mean force, PMF) is two-dimensional in two key coordinates rather than simply one-dimensional along the direction normal to the bilayer. Second, the 2-D PMF calculation has improved convergence due to application of the recently developed transition-tempered metadynamics with randomly initialized replicas, while third, the local diffusivity coefficient was calculated along the direction of the minimum free energy path on the two-dimensional PMF. The permeability is then calculated as a line integral along the minimum free energy path of the PMF. With this approach, we report a considerably more accurate permeability coefficient (only 2-5 times larger than the experimental value). We also compare our approach with the common practice of computing permeability coefficients based only on the translation of the center of mass of the drug molecule. Our paper concludes with a discussion of approaches for minimizing the computational cost for the purpose of more rapidly screening a large number of drug candidate molecules.

Dynamics of ethyl cellulose nanoparticle self-assembly at the interface of a nematic liquid crystal droplet.

Design and fabrication of many next-generation liquid crystal (LC)-based devices rely on nematic LC domains in the form of drops or emulsions. In addition to surfactants, solid nanoparticles may be used to stabilize LC-in-water Pickering emulsions, possibly adding new dimensions to device functionality. In this work we quantitatively study the adsorption of ethyl cellulose (EC) nanoparticles, as a colloid model system, on the 4-cyano-4'-pentylbiphenyl (5CB)-water interface via a series of dynamic interfacial tension measurements. It is found that the planar alignment of 5CB molecules at the interface with water is unaffected by particle adsorption, but a significant reduction of the interfacial tension over time occurs. It is also found that adsorption of EC nanoparticles to the LC-water interface is irreversible and results in close hexagonal packing. This study demonstrates a systematic approach to quantitatively investigate the effect of nanoparticles on the stabilization of LC emulsions.

Effects of repulsive interaction on the electric double layer of an imidazolium-based ionic liquid by molecular dynamics simulation.

The effects of repulsive interaction on the electric double layer (EDL) and differential capacitance (Cd) of an ionic liquid (IL) 1-butyl-3-methyl-imidazolium hexafluorophosphate (BMIM(+)/PF6(-)) on the graphite electrode were studied by molecular dynamics (MD) simulations. The strength of repulsive interaction was studied by manually tuning the parameter lambda (λ) with λ = 1.00 for normal Lennard-Jones interaction and smaller λ for stronger repulsion between IL and the electrode. When λ changes from 1.00 to 0.25, the dependence of Cd on potential (Cd-U) curves at different repulsions is asymmetrically camel-shaped with higher Cd at the negative polarization than that at the positive due to the thinner effective thickness of EDL from the specific adsorption of BMIM(+). Such a trend is opposite in the case of λ = 0.05. Apart from that, the maximum of Cd at the negative polarization monotonically decreases with increasing repulsion. On the other hand, the maximum of Cd at the positive polarization first increases with increasing repulsion, due to the more effective screening of PF6(-) by weakening the specific adsorption of BMIM(+) as λ changes from 1.00 to 0.75, and then it decreases with increasing repulsion.

Temperature effects on the capacitance of an imidazolium-based ionic liquid on a graphite electrode: a molecular dynamics simulation.

Temperature-dependent electric double layer (EDL) and differential capacitance-potential (C(d)-U) curves of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM(+)/PF6(-)) were studied on a graphite electrode by molecular dynamics simulations. It was found that all C(d)-U curves were asymmetric camel-shaped with higher C(d) at negative polarization, attributed to the specific adsorption of BMIM(+). In addition, the maxima of Cd at the negative polarization decrease monotonically with temperature due to the thicker EDL, whereas at the positive polarization they gradually increase from 450 to 550 K and decrease at 600 K. Such temperature effects at positive polarization may be understood in terms of the competition between two aspects: the weakening specific adsorption of BMIM(+) allows more effective screening to the positive charge and overall increasing EDL thickness. Although the former dominates from 450 to 550 K, the latter becomes dominant at 600 K.

Coupling a recombinant oxidase to catalase through specific noncovalent interaction to improve the oxidation of 5-hydroxymethylfurfural to 2,5-furandicarboxylic acid.

5-Hydroxymethylfurfural oxidase (HMFO) can catalyze both hydroxyl and aldehyde oxidations. It catalyzes 5-hydroxymethylfurfural into 2,5-furandicarboxylic acid. However, the application of HMFO encountered two problems: the expressed HMFO in Escherichia coli. is largely in the form of inclusion bodies, and the by-product of H2O2 has a negative effect on HMFO stability. To solve these problems, recombinant HMFO was generated by fusing the C-terminus to an elastin-like polypeptide (ELP). ELP-HMFO can be expressed with significantly reduced inclusion bodies. ELP-HMFO exhibited improved stability and tolerance toward H2O2. Further recombination is carried out by fusing the N-terminus of HMFO to a glutamic acid-rich leucine zipper motif (ZE). Similarly, recombinant catalase (CAT) is generated by fusing the N-terminus to ELP and fusing the C-terminus to an arginine-rich leucine zipper motif (ZR). ELP-HMFO-ZE can interact specifically with ZR-CAT-ELP, ascribing to the coiled-coil association of ZE and ZR. ELP-HMFO-ZE#ZR-CAT-ELP coordinates the respective catalytic activities of the two enzymes. ELP-HMFO-ZE catalyzes the oxidation of HMF, and the generated hydrogen peroxide is decomposed by ZR-CAT-ELP into H2O and oxygen. During the oxidation of HMF, the cofactor FAD of HMFO is reduced, and molecular oxygen is needed to reoxidize the reduced FAD. The evolved oxygen from the decomposing of H2O2 can just meet the requirement, which can be diffused efficiently from ZR-CAT-ELP to ELP-HMFO-ZE due to the short distance between the two enzymes.

Ultra-Coarse-Grained Liquid State Models with Implicit Hydrogen Bonding.

Coarse-graining (CG) methodologies have been widely used to extend the time and length scales of computer simulations by averaging over the atomistic details beneath the resolution of the CG models. Despite the efficiency of CG models, important configurational information during a given process may be lost at the CG resolution. One example of this is the topology of the hydrogen bonding network in the liquid state. When the functional group that participates in hydrogen bonding (e.g., -OH in methanol) is coarse-grained into one CG site, the effective interactions of the resultant CG model are usually derived from an averaged overall trajectory and, thus, do not take into account the hydrogen bonding interactions and topologies that are present at the all-atom resolution. In order to overcome this challenge, the present study develops new ultra-coarse-grained (UCG) models that include internal states within the CG sites that participate in hydrogen bonding, where each state represents a specific configuration such as the hydrogen bonding donor or acceptor. Internal states of the UCG beads are modeled to remain in quasi-equilibrium, and the degree of mixing is controlled by utilizing the effective local density of the UCG sites. In particular, we consider two groups of UCG models with different types of hydrogen bonding motifs: chain-like and ring-like. Using five different liquid systems that contain the same fundamental functional groups as biomolecules, we demonstrate the ability of the UCG models to reproduce the structural properties that originate from the configurations beneath the resolution of the UCG model. This proposed approach can also be applied to other liquids with such specific and directional interactions, or even to complex biomolecular systems in which hydrogen bonding is critical.

A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes.

The size of ions significantly influences the electric double layer structure of room temperature ionic liquid (IL) electrolytes and their differential capacitance (Cd). In this study, we extended the mean-field theory (MFT) developed independently by Kornyshev (2007J. Phys. Chem. B 111 5545-57) and Kilic, Bazant, and Ajdari (2007 Phys. Rev. E 75 021502) (the KKBA MFT) to take into account the asymmetric 1:1 IL electrolytes by introducing an additional parameter ξ for the anion/cation volume ratio, besides the ionic compressibility γ in the KKBA MFT. The MFT of asymmetric ions becomes KKBA MFT upon ξ = 1, and further reduces to Gouy-Chapman theory in the γ → 0 limit. The result of the extended MFT demonstrates that the asymmetric ILs give rise to an asymmetric Cd, with the higher peak in Cd occurring at positive polarization for the smaller anionic size. At high potential, Cd decays asymptotically toward KKBA MFT characterized by γ for the negative polarization, and characterized by ξγ for the positive polarization, with inverse-square-root behavior. At low potential, around the potential of zero charge, the asymmetric ions cause a higher Cd, which exceeds that of Gouy-Chapman theory.