Coarse-Grained Molecular Models of Water: A Review

The Sphingosine and Phytosphingosine Ceramide Ratio in Lipid Models Forming the Short Periodicity Phase: An Experimental and Molecular Simulation Study

The lipids located in the outermost layer of the skin, the stratum corneum (SC), play a crucial role in maintaining the skin barrier function. The primary components of the SC lipid matrix are ceramides (CERs), cholesterol (CHOL), and free fatty acids (FFAs). They form two crystalline lamellar phases: the long periodicity phase (LPP) and the short periodicity phase (SPP). In inflammatory skin conditions like atopic dermatitis and psoriasis, there are changes in the SC CER composition, such as an increased concentration of a sphingosine-based CER (CER NS) and a reduced concentration of a phytosphingosine-based CER (CER NP). In the present study, a lipid model was created exclusively forming the SPP, to examine whether alterations in the CER NS:CER NP molar ratio would affect the lipid organization. Experimental data were combined with molecular dynamics simulations of lipid models containing CER NS:CER NP at ratios of 1:2 (mimicking a healthy SC ratio) and 2:1 (observed in inflammatory skin diseases), mixed with CHOL and lignoceric acid as the FFA. The experimental findings show that the acyl chains of CER NS and CER NP and the FFA are in close proximity within the SPP unit cell, indicating that CER NS and CER NP adopt a linear conformation, similarly as observed for the LPP. Both the experiments and simulations indicate that the lamellar organization is the same for the two CER NS:CER NP ratios while the SPP NS:NP 1:2 model had a slightly denser hydrogen bonding network than the SPP NS:NP 2:1 model. The simulations show that this might be attributed to intermolecular hydrogen bonding with the additional hydroxide group on the headgroup of CER NP compared with CER NS.

EXCOGITO, an Extensible Coarse-Graining Toolbox for the Investigation of Biomolecules by Means of Low-Resolution Representations

Bottom-up coarse-grained (CG) models proved to be essential to complement and sometimes even replace all-atom representations of soft matter systems and biological macromolecules. The development of low-resolution models takes the moves from the reduction of the degrees of freedom employed, that is, the definition of a mapping between a system's high-resolution description and its simplified counterpart. Even in the absence of an explicit parametrization and simulation of a CG model, the observation of the atomistic system in simpler terms can be informative: this idea is leveraged by the mapping entropy, a measure of the information loss inherent to the process of coarsening. Mapping entropy lies at the heart of the extensible coarse-graining toolbox, EXCOGITO, developed to perform a number of operations and analyses on molecular systems pivoting around the properties of mappings. EXCOGITO can process an all-atom trajectory to compute the mapping entropy, identify the mapping that minimizes it, and establish quantitative relations between a low-resolution representation and the geometrical, structural, and energetic features of the system. Here, the software, which is available free of charge under an open-source license, is presented and showcased to introduce potential users to its capabilities and usage.

Construction of Multiscale Dissipative Particle Dynamics (DPD) Models from Other Coarse-Grained Models

We present a general scheme for converting coarse-grained models into Dissipative Particle Dynamics (DPD) models. We build the corresponding DPD models by analogy with the de novo DPD coarse-graining scheme suggested by Groot and Warren (J. Chem. Phys., 1997). Electrostatic interactions between charged DPD particles are represented though the addition of a long-range Slater Coulomb potential as suggested by González-Melchor et al. (J. Chem. Phys., 2006). The construction is illustrated by converting MARTINI models for various proteins into a DPD representation, but it not restricted to the usual potential form in the MARTINI model-viz., Lennard-Jones potentials. We further extended the DPD scheme away from the typical use of homogeneous particle sizes, therefore faithfully representing the variations in the particle sizes seen in the underlying MARTINI model. The accuracy of the resulting construction of our generalized DPD models with respect to several structural observables has been benchmarked favorably against all-atom and MARTINI models for a selected set of peptides and proteins, and variations in the scales of the coarse-graining of the water solvent.

Coarse-Graining with Equivariant Neural Networks: A Path Toward Accurate and Data-Efficient Models

Machine learning has recently entered into the mainstream of coarse-grained (CG) molecular modeling and simulation. While a variety of methods for incorporating deep learning into these models exist, many of them involve training neural networks to act directly as the CG force field. This has several benefits of which the most significant is accuracy. Neural networks can inherently incorporate multibody effects during the calculation of CG forces, and a well-trained neural network force field outperforms pairwise basis sets generated from essentially any methodology. However, this comes at a significant cost. First, these models are typically slower than pairwise force fields, even when accounting for specialized hardware, which accelerates the training and integration of such networks. The second and the focus of this paper is the need for a considerable amount of data to train such force fields. It is common to use 10s of microseconds of molecular dynamics data to train a single CG model, which approaches the point of eliminating the CG model's usefulness in the first place. As we investigate in this work, this "data-hunger" trap from neural networks for predicting molecular energies and forces can be remediated in part by incorporating equivariant convolutional operations. We demonstrate that, for CG water, networks that incorporate equivariant convolutional operations can produce functional models using data sets as small as a single frame of reference data, while networks without these operations cannot.

Kinetics and Mechanisms of Pressure-Induced Ice Amorphization and Polyamorphic Transitions in a Machine-Learned Coarse-Grained Water Model

Water glasses have attracted considerable attention due to their potential connection to a liquid-liquid transition in supercooled water. Here we use molecular simulations to investigate the formation and phase behavior of water glasses using the machine-learned bond-order parameter (ML-BOP) water model. We produce glasses through hyperquenching of water, pressure-induced amorphization (PIA) of ice, and pressure-induced polyamorphic transformations. We find that PIA of polycrystalline ice occurs at a lower pressure than that of monocrystalline ice and through a different mechanism. The temperature dependence of the amorphization pressure of polycrystalline ice for ML-BOP agrees with that in experiments. We also find that ML-BOP accurately reproduces the density, coordination number, and structural features of low-density (LDA), high-density (HDA), and very high-density (VHDA) amorphous water glasses. ML-BOP accurately reproduces the experimental radial distribution function of LDA but overpredicts the minimum between the first two shells in high-density glasses. We examine the kinetics and mechanism of the transformation between low-density and high-density glasses and find that the sharp nature of these transitions in ML-BOP is similar to that in experiments and all-atom water models with a liquid-liquid transition. Transitions between ML-BOP glasses occur through a spinodal-like mechanism, similar to ice crystallization from LDA. Both glass-to-glass and glass-to-ice transformations have Avrami-Kolmogorov kinetics with exponent n = 1.5 ± 0.2 in experiments and simulations. Importantly, ML-BOP reproduces the competition between crystallization and HDA→LDA transition above the glass transition temperature T_g, and separation of their time scales below T_g, observed also in experiments. These findings demonstrate the ability of ML-BOP to accurately reproduce water properties across various regimes, making it a promising model for addressing the competition between polyamorphic transitions and crystallization in water and solutions.

Equilibrium states corresponding to targeted hyperuniform nonequilibrium pair statistics

The Zhang-Torquato conjecture [G. Zhang and S. Torquato, Phys. Rev. E, 2020, 101, 032124.] states that any realizable pair correlation function g₂(r) or structure factor S(k) of a translationally invariant nonequilibrium system can be attained by an equilibrium ensemble involving only (up to) effective two-body interactions. To further test and study this conjecture, we consider two singular nonequilibrium models of recent interest that also have the exotic hyperuniformity property: a 2D "perfect glass" and a 3D critical absorbing-state model. We find that each nonequilibrium target can be achieved accurately by equilibrium states with effective one- and two-body potentials, lending further support to the conjecture. To characterize the structural degeneracy of such a nonequilibrium-equilibrium correspondence, we compute higher-order statistics for both models, as well as those for a hyperuniform 3D uniformly randomized lattice (URL), whose higher-order statistics can be very precisely ascertained. Interestingly, we find that the differences in the higher-order statistics between nonequilibrium and equilibrium systems with matching pair statistics, as measured by the "hole" probability distribution, provide measures of the degree to which a system is out of equilibrium. We show that all three systems studied possess the bounded-hole property and that holes near the maximum hole size in the URL are much rarer than those in the underlying simple cubic lattice. Remarkably, upon quenching, the effective potentials for all three systems possess local energy minima (i.e., inherent structures) with stronger forms of hyperuniformity compared to their target counterparts. Our methods are expected to facilitate the self-assembly of tunable hyperuniform soft-matter systems.

Stability and Metastability of Liquid Water in a Machine-Learned Coarse-Grained Model with Short-Range Interactions

Coarse-grained water models are ∼100 times more efficient than all-atom models, enabling simulations of supercooled water and crystallization. The machine-learned monatomic model ML-BOP reproduces the experimental equation of state (EOS) and ice-liquid thermodynamics at 0.1 MPa on par with the all-atom TIP4P/2005 and TIP4P/Ice models. These all-atom models were parametrized using high-pressure experimental data and are either accurate for water's EOS (TIP4P/2005) or ice-liquid equilibrium (TIP4P/Ice). ML-BOP was parametrized from temperature-dependent ice and liquid experimental densities and melting data at 0.1 MPa; its only pressure training is from compression of TIP4P/2005 ice at 0 K. Here we investigate whether ML-BOP replicates the experimental EOS and ice-water thermodynamics along all pressures of ice I. We find that ML-BOP reproduces the temperature, enthalpy, entropy, and volume of melting of hexagonal ice up to 400 MPa and the EOS of water along the melting line with an accuracy that rivals that of both TIP4P/2005 and TIP4P/Ice. We interpret that the accuracy of ML-BOP originates from its ability to capture the shift between compact and open local structures to changes in pressure and temperature. ML-BOP reproduces the sharpening of the tetrahedral peak of the pair distribution function of water upon supercooling, and its pressure dependence. We characterize the region of metastability of liquid ML-BOP with respect to crystallization and cavitation. The accessibility of ice crystallization to simulations of ML-BOP, together with its accurate representation of the thermodynamics of water, makes it promising for investigating the interplay between anomalies, glass transition, and crystallization under conditions challenging to access through experiments.

Multifaceted Computational Modeling in Glycoscience

Glycoscience assembles all the scientific disciplines involved in studying various molecules and macromolecules containing carbohydrates and complex glycans. Such an ensemble involves one of the most extensive sets of molecules in quantity and occurrence since they occur in all microorganisms and higher organisms. Once the compositions and sequences of these molecules are established, the determination of their three-dimensional structural and dynamical features is a step toward understanding the molecular basis underlying their properties and functions. The range of the relevant computational methods capable of addressing such issues is anchored by the specificity of stereoelectronic effects from quantum chemistry to mesoscale modeling throughout molecular dynamics and mechanics and coarse-grained and docking calculations. The Review leads the reader through the detailed presentations of the applications of computational modeling. The illustrations cover carbohydrate-carbohydrate interactions, glycolipids, and N- and O-linked glycans, emphasizing their role in SARS-CoV-2. The presentation continues with the structure of polysaccharides in solution and solid-state and lipopolysaccharides in membranes. The full range of protein-carbohydrate interactions is presented, as exemplified by carbohydrate-active enzymes, transporters, lectins, antibodies, and glycosaminoglycan binding proteins. A final section features a list of 150 tools and databases to help address the many issues of structural glycobioinformatics.

Conservative Potentials for a Lattice-Mapped, Coarse-Grain Scheme with Fuzzy Switching Functions

We extend our previous work (Luo, S.; Thachuk, M. J. Phys. Chem. A 2021, 125, 64866497) on determining conservative potentials for lattice-like, coarse-grain (CG) mapping schemes to the case where the boundaries between different spatial regions are not sharply defined but are fuzzy. In other words, the system is divided into interpenetrating "subcells" such that atomistic particles continuously change their memberships as they move through space. This is done by using fuzzy switching functions to define overlapping regions between subcells with fractional particle occupations. In this case, a full mass matrix is required to describe the system, and its off-diagonal elements are nonzero and contribute to the CG potential. As the overlapping region increases in size, we observe the mass distribution transitions from a discrete spectrum, through an intermediate state, and finally to a continuous Gaussian-like function. We interpret this as a quantitative measure for signaling when a continuum-theory description of the system is appropriate. Nonzero correlations among all CG variables are calculated and are found to depend strongly on the degree of overlap. In particular, those for the diagonal mass elements decrease in magnitude, and there exists a specific value of the overlap for which the correlations are zero. Other correlations are strong only when the overlap is quite large, so there is a trade-off between the complexity of the interactions in the system and the degree of fuzziness between the subcells. However, if the number of particles in a subcell is large enough and the overlap is moderate, then the CG potential is found to be well-approximated by a generalized quadratic function. These results demonstrate the transition between atomistic and continuum resolutions in a system and have implications for designing CG schemes with mixed atomistic and continuum character.

The Critical Diameter for Continuous Evaporation Is between 3 and 4 nm for Hydrophilic Nanopores

Evaporation studies of water using classical molecular dynamics simulations are largely limited due to their high computational expense. This study addresses that issue by developing coarse-grained molecular dynamics models based on Morse potential. Models are optimized based on multi-temperature and at room temperature using machine learning techniques like Genetic Algorithm, Nelder-Mead algorithm, and Strength Pareto Evolutionary Algorithm. The multi-temperature-based model named as Morse-D is found to be more accurate than the single temperature model in representing the water properties at higher temperatures. Using this Morse-D water model, evaporation from hydrophilic nanopores with pore diameter varying from 2 to 5 nm is studied. Our results show that the critical diameter to initiate continuous evaporation at nanopores lies between 3 and 4 nm. A maximum heat flux of 21.3 kW/cm² is observed for a pore diameter of 4.5 nm and a maximum mass flow rate of 16.2 ng/s for a pore diameter of 5 nm. The observed heat flux is an order of magnitude times larger than the currently reported values from experiments in the literature for water, which indicates that we need to focus on nanoscale evaporation to enhance the critical heat flux.

Assembly and Analysis of Cell-Scale Membrane Envelopes

The march toward exascale computing will enable routine molecular simulation of larger and more complex systems, for example, simulation of entire viral particles, on the scale of approximately billions of atoms─a simulation size commensurate with a small bacterial cell. Anticipating the future hardware capabilities that will enable this type of research and paralleling advances in experimental structural biology, efforts are currently underway to develop software tools, procedures, and workflows for constructing cell-scale structures. Herein, we describe our efforts in developing and implementing an efficient and robust workflow for construction of cell-scale membrane envelopes and embedding membrane proteins into them. A new approach for construction of massive membrane structures that are stable during the simulations is built on implementing a subtractive assembly technique coupled with the development of a structure concatenation tool (fastmerge), which eliminates overlapping elements based on volumetric criteria rather than adding successive molecules to the simulation system. Using this approach, we have constructed two "protocells" consisting of MARTINI coarse-grained beads to represent cellular membranes, one the size of a cellular organelle and another the size of a small bacterial cell. The membrane envelopes constructed here remain whole during the molecular dynamics simulations performed and exhibit water flux only through specific proteins, demonstrating the success of our methodology in creating tight cell-like membrane compartments. Extended simulations of these cell-scale structures highlight the propensity for nonspecific interactions between adjacent membrane proteins leading to the formation of protein microclusters on the cell surface, an insight uniquely enabled by the scale of the simulations. We anticipate that the experiences and best practices presented here will form the basis for the next generation of cell-scale models, which will begin to address the addition of soluble proteins, nucleic acids, and small molecules essential to the function of a cell.

Overlapping hydration shells in salt solutions causing non-monotonic Soret coefficients with varying concentration

We develop an intuitive picture that overlapping hydration shells in salt solutions cause non-monotonic Soret coefficients with varying concentration.

Solvent-scaling as an alternative to coarse-graining in adaptive-resolution simulations: The adaptive solvent-scaling (AdSoS) scheme

A new approach termed Adaptive Solvent-Scaling (AdSoS) is introduced for performing simulations of a solute embedded in a fine-grained (FG) solvent region itself surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, the AdSoS scheme is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by an s-dependent modulation of the atomic masses and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. This scaling approach offers a number of advantages compared to traditional coarse-graining: (i) the CG parameters are immediately related to those of the FG model (no need to parameterize a distinct CG model); (ii) nearly ideal mixing is expected for CG variants with similar s-values (ideal mixing holding in the limit of identical s-values); (iii) the solvent relaxation timescales should be preserved (no dynamical acceleration typical for coarse-graining); (iv) the graining level N_G (number of FG molecules represented by one CG molecule) can be chosen arbitrarily (in particular, N_G = s³ is not necessarily an integer); and (v) in an adaptive-resolution scheme, this level can be varied continuously as a function of the position (without requiring a bundling mechanism), and this variation occurs at a constant number of particles per molecule (no occurrence of fractional degrees of freedom in the buffer layer). By construction, the AdSoS scheme minimizes the thermodynamic mismatch between the different regions of the adaptive-resolution system, leading to a nearly homogeneous scaled solvent density s³ρ. Residual density artifacts in and at the surface of the boundary layer can easily be corrected by means of a grid-based biasing potential constructed in a preliminary pure-solvent simulation. This article introduces the AdSoS scheme and provides an initial application to pure atomic liquids (no solute) with Lennard-Jones plus Coulomb interactions in a slab geometry.

Conservative Potentials for a Lattice-Mapped Coarse-Grained Scheme

The conservative potential, arising from a coarse-grain (CG) mapping scheme for nonbonded atomistic particles, is studied. This is a bottom-up approach from first-principles that maps atomistic particles to fluid element-like subcells whose centers lie on a regular, cubic lattice. Unlike standard CG mapping schemes, the current one uses dynamic labeling which on-the-fly changes the CG labels of the particles. The subcells can also be different sizes and shapes, in principle. Equilibrium atomistic molecular dynamics trajectories for different Lennard-Jones fluids are calculated and converted to CG ones, from which CG probability distribution functions are calculated. Correlation studies show position and mass CG variables are uncoupled in a given subcell, as are different vector components of position. Furthermore, the strongest coupling occurs with neighboring cells in specific directions, and the resulting distribution is well described by a multivariate Gaussian. This implies the CG potential has a generalized quadratic form, whose derivative can be determined analytically. A microscopic rationalization is provided for the signs and relative magnitudes of different correlation coefficients, and in some cases, a connection is made with bulk properties of the fluid. We argue the generalized quadratic form should be robust to changes in the particulars of the CG scheme, as well as the nature of the atomistic intermolecular potential. Only a few potential parameters need to be calculated from the underlying atomistic system. This is significant because it indicates the transferability of this form to other, more complex systems. This transferability will be tested in future work, where mapping schemes with fuzzy boundaries will be considered.

Emergence of Nontrivial Spin Textures in Frustrated Van Der Waals Ferromagnets

In this work, first principles ground state calculations are combined with the dynamic evolution of a classical spin Hamiltonian to study the metamagnetic transitions associated with the field dependence of magnetic properties in frustrated van der Waals ferromagnets. Dynamically stabilized spin textures are obtained relative to the direction of spin quantization as stochastic solutions of the Landau-Lifshitz-Gilbert-Slonczewski equation under the flow of the spin current. By explicitly considering the spin signatures that arise from geometrical frustrations at interfaces, we may observe the emergence of a magnetic skyrmion spin texture and characterize the formation under competing internal fields. The analysis of coercivity and magnetic hysteresis reveals a dynamic switch from a soft to hard magnetic configuration when considering the spin Hall effect on the skyrmion. It is found that heavy metals in capped multilayer heterostructure stacks host field-tunable spiral skyrmions that could serve as unique channels for carrier transport. The results are discussed to show the possibility of using dynamically switchable magnetic bits to read and write data without the need for a spin transfer torque. These results offer insight to the spin transport signatures that dynamically arise from metamagnetic transitions in spintronic devices.

Multiscale polarizable coarse-graining water models on cluster-level electrostatic dipoles

The development of a coarse-grained (CG) water model is increasingly important in CG studies of biological processes. In this work, we developed a generic CG force field of liquid water on cluster-level electrostatic dipoles. An exponential term is introduced in the non-bonded potential to adjust the well depth. The whole force field is parametrized on the AMOEBA simulation and then refined on the experimental density, dielectric permittivity and isothermal compressibility. The new CG water force field is suitable for the construction of multi-resolution water models and here the N_C = 4/5/10 systems are taken as examples. The results show that the N_C = 4/5/10 models can correctly reproduce the density and relative dielectric permittivity. The models can well predict the pressure-density/density-temperature relationships close to the all-atom or experiment results. However, the new models behave differently from other CG models in several water properties such as the air-water surface tension. Through dipole distributions, two representative polarizable configurations are captured after the N_C = 4/5/10 systems are dynamically equilibrated. Besides, the N_C = 4 model is coupled with the Martini Na⁺/Cl^- models to predict ion-relevant radial distribution functions in comparison to the Martini result. Lastly, CPU tests suggest that the new CG models can enhance simulation efficiency by factors of 20-42, compared to the TIP3P force field. The newly proposed polarizable water force field is practical and transferable and can be flexibly extended to higher coarse-graining of liquid water.

Development of accurate coarse-grained force fields for weakly polar groups by an indirect parameterization strategy

Coarse-grained (CG) molecular dynamics simulations are widely used to predict morphological structures and interpret mechanisms of mesoscopic behavior between the scope of traditional experiments and all-atom simulations. However, most current CG force fields (FFs) are not precise enough, especially for polar molecules or functional groups. A main obstacle in developing accurate CG FFs for polar molecules is the freezing problem met at room temperature. In this work, we introduce an indirect parametrization strategy for weakly polar groups by considering their short-chain homologs to avoid freezing. Here, a polar group containing three to four heavy atoms is mapped into one CG bead that is connected to one alkyl bead composed of three or four carbons. The CG beads interact via 4-parameter nonbonded Morse potentials and harmonic bonded potentials. An efficient meta-multilinear interpolation parameterization algorithm, as recently developed by us, is used to rigorously optimize the force parameters. Satisfactory accuracy is witnessed in terms of the density, heat of vaporization, surface tension, and solvation free energy of the homologs of twelve polar molecules, all deviating from the experiment by less than 5%. The transferability of the current FF is indicated by the predicted density, heat of vaporization, and end-to-end distance distributions of fatty acid methyl esters composed of multiple functional groups parameterized in this work.

Renormalization group theory of molecular dynamics

Large scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have enabled large scale calculations, macroscopic analyses are still not realizable. Here, we present renormalized molecular dynamics (RMD), a renormalization group of MD in thermal equilibrium derived by using the Migdal–Kadanoff approximation. The RMD method improves the computational efficiency drastically while retaining the advantage of MD. The computational efficiency is improved by a factor of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{n(D+1)}$$\end{document}2n(D+1) over conventional MD where D is the spatial dimension and n is the number of applied renormalization transforms. We verify RMD by conducting two simulations; melting of an aluminum slab and collision of aluminum spheres. Both problems show that the expectation values of physical quantities are in good agreement after the renormalization, whereas the consumption time is reduced as expected. To observe behavior of RMD near the critical point, the critical exponent of the Lennard-Jones potential is extracted by calculating specific heat on the mesoscale. The critical exponent is obtained as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu =0.63\pm 0.01$$\end{document}ν=0.63±0.01. In addition, the renormalization group of dissipative particle dynamics (DPD) is derived. Renormalized DPD is equivalent to RMD in isothermal systems under the condition such that Deborah number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$De\ll 1$$\end{document}De≪1.

Rotational dynamics of proteins in nanochannels: role of solvent's local viscosity

Viscosity variation of solvent in local regions near a solid surface, be it a biological surface of a protein or an engineered surface of a nanoconfinement, is a direct consequence of intermolecular interactions between the solid body and the solvent. The current coarse-grained molecular dynamics study takes advantage of this phenomenon to investigate the anomaly in a solvated protein's rotational dynamics confined using a representative solid matrix. The concept of persistence time, the characteristic time of structural reordering in liquids, is used to compute the solvent's local viscosity. With an increase in the degree of confinement, the confining matrix significantly influences the solvent molecule's local viscosity present in the protein hydration layer through intermolecular interactions. This effect contributes to the enhanced drag force on protein motion, causing a reduction in the rotational diffusion coefficient. Simulation results suggest that the direct matrix-protein non-bonded interaction is responsible for the occasional jump and discontinuity in orientational motion when the protein is in very tight confinement.

Water in Nanopores and Biological Channels: A Molecular Simulation Perspective

This Review explores the dynamic behavior of water within nanopores and biological channels in lipid bilayer membranes. We focus on molecular simulation studies, alongside selected structural and other experimental investigations. Structures of biological nanopores and channels are reviewed, emphasizing those high-resolution crystal structures, which reveal water molecules within the transmembrane pores, which can be used to aid the interpretation of simulation studies. Different levels of molecular simulations of water within nanopores are described, with a focus on molecular dynamics (MD). In particular, models of water for MD simulations are discussed in detail to provide an evaluation of their use in simulations of water in nanopores. Simulation studies of the behavior of water in idealized models of nanopores have revealed aspects of the organization and dynamics of nanoconfined water, including wetting/dewetting in narrow hydrophobic nanopores. A survey of simulation studies in a range of nonbiological nanopores is presented, including carbon nanotubes, synthetic nanopores, model peptide nanopores, track-etched nanopores in polymer membranes, and hydroxylated and functionalized nanoporous silica. These reveal a complex relationship between pore size/geometry, the nature of the pore lining, and rates of water transport. Wider nanopores with hydrophobic linings favor water flow whereas narrower hydrophobic pores may show dewetting. Simulation studies over the past decade of the behavior of water in a range of biological nanopores are described, including porins and β-barrel protein nanopores, aquaporins and related polar solute pores, and a number of different classes of ion channels. Water is shown to play a key role in proton transport in biological channels and in hydrophobic gating of ion channels. An overall picture emerges, whereby the behavior of water in a nanopore may be predicted as a function of its hydrophobicity and radius. This informs our understanding of the functions of diverse channel structures and will aid the design of novel nanopores. Thus, our current level of understanding allows for the design of a nanopore which promotes wetting over dewetting or vice versa. However, to design a novel nanopore, which enables fast, selective, and gated flow of water de novo would remain challenging, suggesting a need for further detailed simulations alongside experimental evaluation of more complex nanopore systems.

Dissipative particle dynamics model of homogalacturonan based on molecular dynamics simulations

In this study we present an alternative dissipative particle dynamics (DPD) parametrization strategy based on data extracted from the united-atom molecular simulations. The model of the homogalacturonan was designed to test the ability of the formation of large-scale structures via hydrogen bonding in water. The extraction of coarse-grained parameters from atomistic molecular dynamics was achieved by means of the proposed molecule aggregation algorithm based on an iterative nearest neighbour search. A novel approach to a time-scale calibration scheme based on matching the average velocities of coarse-grained particles enabled the DPD forcefield to reproduce essential structural features of homogalacturonan molecular chains. The successful application of the proposed parametrization method allowed for the reproduction of the shapes of radial distribution functions, particle velocities and diffusivity of the atomistic molecular dynamics model using DPD force field. The structure of polygalacturonic acid molecules was mapped into the DPD force field by means of the distance and angular bond characteristics, which closely matched the MD results. The resulting DPD trajectories showed that randomly dispersed homogalacturonan chains had a tendency to aggregate into highly organized 3D structures. The final structure resembled a three-dimensional network created by tightly associated homogalacturonan chains organized into thick fibres.

A Surface Site Interaction Point Method for Dissipative Particle Dynamics Parametrization: Application to Alkyl Ethoxylate Surfactant Self-Assembly

Dissipative particle dynamics (DPD) is a coarse-grained approach to the simulation of large supramolecular systems, but one limitation has been that the parameters required to describe the noncovalent interactions between beads are not readily accessible. A first-principles computational method has been developed so that bead interaction parameters can be calculated directly from ab initio gas-phase molecular electrostatic potential surfaces of the molecular fragments that represent the beads. A footprinting algorithm converts the molecular electrostatic potential surfaces into a discrete set of surface site interaction points (SSIPs), and these SSIPs are used in the SSIMPLE (surface site interaction model for the properties of liquids at equilibrium) algorithm to calculate the free energies of transfer of one bead into a solution of any other bead. The bead transfer free energies are then converted into the required DPD interaction parameters for all pairwise combinations of different beads. The reliability of the parameters was demonstrated using DPD simulations of a range of alkyl ethoxylate surfactants. The simulations reproduce the experimentally determined values of the critical micelle concentration and mean aggregation number well for all 22 surfactants studied.

An Atomistic Molecular Dynamics Study of Titanium Dioxide Adhesion to Lipid Bilayers

Titanium dioxide (TiO₂) nanoparticles are found in an array of consumer and industrial products, and human exposure to these nanoparticles involves interaction with biological membranes. To understand the effect of the membrane lipid composition on bilayer perturbation by TiO₂, we performed all-atom molecular dynamics simulations of nanosized TiO₂ interacting with three single component bilayers differing only in their headgroup composition: the zwitterionic DOPC, which is overall neutral containing negatively charged phosphate and positively charged choline in its head, DOPG, which is overall anionic containing negatively charged phosphate and neutral glycerol, and the anionic DOPS, containing negatively charged phosphate attached to the hydroxyl side-chain of the amino acid, serine containing negatively charged carboxyl and positively charged ammonium. The nanoparticle adheres to all three bilayers causing a negative curvature on their top leaflet. However, the local deformation of DOPG was more pronounced than DOPC and DOPS. The anionic DOPG, which is the thinnest of the three bilayers, interacted most strongly with the TiO₂. DOPS has the next strongest interaction; however, its high bending modulus enables it to resist deformation by the nanoparticle. DOPC has the weakest interaction with the nanoparticle of the three as it has the highest bending modulus and its zwitterionic head groups have strong cohesive interactions. We also observed a nonuniform response of the bilayers: the orientational order of the lipids near the nanoparticle decreases, while that of the lipids away from the nanoparticle increases. The overall thickness and bending modulus of DOPG increased upon contact with the nanoparticle owing to overall stiffening of the bilayer despite local softening, while the average structural and mechanical properties of DOPC and DOPS remain unchanged, which can be explained in part by the greater bilayer bending elasticicty of DOPC and DOPS. The above findings suggest that regions of biological membranes populated by anionic lipids with weaker bending elasticity will be more susceptible to perturbation by TiO₂ nanoparticles than zwitterionic-rich regions.

Direct route to reproducing pair distribution functions with coarse-grained models via transformed atomistic cross correlations

Coarse-grained (CG) models are often parameterized to reproduce one-dimensional structural correlation functions of an atomically detailed model along the degrees of freedom governing each interaction potential. While cross correlations between these degrees of freedom inform the optimal set of interaction parameters, the correlations generated from the higher-resolution simulations are often too complex to act as an accurate proxy for the CG correlations. Instead, the most popular methods determine the interaction parameters iteratively while assuming that individual interactions are uncorrelated. While these iterative methods have been validated for a wide range of systems, they also have disadvantages when parameterizing models for multicomponent systems or when refining previously established models to better reproduce particular structural features. In this work, we propose two distinct approaches for the direct (i.e., noniterative) parameterization of a CG model by adjusting the high-resolution cross correlations of an atomistic model in order to more accurately reflect correlations that will be generated by the resulting CG model. The derived models more accurately describe the low-order structural features of the underlying AA model while necessarily generating inherently distinct cross correlations compared with the atomically detailed reference model. We demonstrate the proposed methods for a one-site-per-molecule representation of liquid water, where pairwise interactions are incapable of reproducing the true tetrahedral solvation structure. We then investigate the precise role that distinct cross-correlation features play in determining the correct pair correlation functions, evaluating the importance of the placement of correlation features as well as the balance between features appearing in different solvation shells.

Evidence of information limitations in coarse-grained models

Developing accurate coarse-grained (CG) models is critical for addressing long time and length scale phenomena with molecular simulations. Here, we distinguish and quantify two sources of error that are relevant to CG models in order to guide further methods development: "representability" errors, which result from the finite basis associated with the chosen functional form of the CG model and mapping operator, and "information" errors, which result from the limited kind and quantity of data supplied to the CG parameterization algorithm. We have performed a systematic investigation of these errors by generating all possible CG models of three liquids (butane, 1-butanol, and 1,3-propanediol) that conserve a set of chemically motivated locality and topology relationships. In turn, standard algorithms (iterative Boltzmann inversion, IBI, and multiscale coarse-graining, MSCG) were used to parameterize the models and the CG predictions were compared with atomistic results. For off-target properties, we observe a strong correlation between the accuracy and the resolution of the CG model, which suggests that the approximations represented by MSCG and IBI deteriorate with decreasing resolution. Conversely, on-target properties exhibit an extremely weak resolution dependence that suggests a limited role of representability errors in model accuracy. Taken together, these results suggest that simple CG models are capable of utilizing more information than is provided by standard parameterization algorithms, and that model accuracy can be improved by algorithm development rather than resorting to more complicated CG models.

Bottom-up derived flexible water model with dipole and quadrupole moments for coarse-grained molecular simulations

A bottom-up CG water model is developed to capture the electrostatic multipoles, structural correlation and thermodynamics of water.

Implicit-solvent coarse-grained modeling for polymer solutions via Mori-Zwanzig formalism

We present a bottom-up coarse-graining (CG) method to establish implicit-solvent CG modeling for polymers in solution, which conserves the dynamic properties of the reference microscopic system. In particular, tens to hundreds of bonded polymer atoms (or Lennard-Jones beads) are coarse-grained as one CG particle, and the solvent degrees of freedom are eliminated. The dynamics of the CG system is governed by the generalized Langevin equation (GLE) derived via the Mori-Zwanzig formalism, by which the CG variables can be directly and rigorously linked to the microscopic dynamics generated by molecular dynamics (MD) simulations. The solvent-mediated dynamics of polymers is modeled by the non-Markovian stochastic dynamics in GLE, where the memory kernel can be computed from the MD trajectories. To circumvent the difficulty in direct evaluation of the memory term and generation of colored noise, we exploit the equivalence between the non-Markovian dynamics and Markovian dynamics in an extended space. To this end, the CG system is supplemented with auxiliary variables that are coupled linearly to the momentum and among themselves, subject to uncorrelated Gaussian white noise. A high-order time-integration scheme is used to solve the extended dynamics to further accelerate the CG simulations. To assess, validate, and demonstrate the established implicit-solvent CG modeling, we have applied it to study four different types of polymers in solution. The dynamic properties of polymers characterized by the velocity autocorrelation function, diffusion coefficient, and mean square displacement as functions of time are evaluated in both CG and MD simulations. Results show that the extended dynamics with auxiliary variables can construct arbitrarily high-order CG models to reproduce dynamic properties of the reference microscopic system and to characterize long-time dynamics of polymers in solution.

From quantum to subcellular scales: multi-scale simulation approaches and the SIRAH force field

Modern molecular and cellular biology profits from astonishing resolution structural methods, currently even reaching the whole cell level. This is encompassed by the development of computational methods providing a deep view into the structure and dynamics of molecular processes happening at very different scales in time and space. Linking such scales is of paramount importance when aiming at far-reaching biological questions. Computational methods at the interface between classical and coarse-grained resolutions are gaining momentum with several research groups dedicating important efforts to their development and tuning. An overview of such methods is addressed herein, with special emphasis on the SIRAH force field for coarse-grained and multi-scale simulations. Moreover, we provide proof of concept calculations on the implementation of a multi-scale simulation scheme including quantum calculations on a classical fine-grained/coarse-grained representation of double-stranded DNA. This opens the possibility to include the effect of large conformational fluctuations in chromatin segments on, for instance, the reactivity of particular base pairs within the same simulation framework.

Energy storage analysis of R125 in UIO-66 and MOF-5 nanoparticles: A molecular simulation study

The efficiency of thermodynamic cycles can be improved by using the optimized working fluid. In the present paper, classic molecular dynamics simulations and grand canonical Monte Carlo were employed to examine the thermal energy storage characteristicsof R125/UIO-66 and R125/MOF-5 nanofluids. The results indicate that the adsorption of R125 in MOF-5 is larger than that in UIO-66. Also, the thermal energy storage capacity of R125 was strengthened by mixing with UIO-66 or MOF-5 nanoparticles. In addition, the R125/UIO-66 mixtures can store less energy than that of R125/MOF-5 mixtures except the temperature difference is 30 K to 50 K.

On the growth of argon clusters on a weak adsorbent decorated with patches

Much attention has been paid to understanding the clustering mechanism of water adsorbed on carbonaceous adsorbents. Adsorbed water forms clusters around strong sites, such as functional groups and surface defects, and these clusters then coalesce if the strong sites are sufficiently close to each other. Simulations of water adsorption are notoriously time consuming because of the slow relaxation of the strongly-directional hydrogen bonds. Our objective in this paper is to gain a better insight into clustering and coalescence of water, without incurring large computing overheads. To this end we have chosen argon as an adsorbate, and a substrate that is a very weak adsorbent for argon. To mimic functional groups, the substrate surface is decorated with strongly adsorbing patches. The adsorbate forms nano-clusters with convex surfaces at pressures greater than the saturation vapour pressure. When these clusters are sufficiently close to each other, they coalescence to form larger fused clusters, and there is a decrease in the equilibrium pressure. The relationship between the radius of curvature of the developed nano-clusters and the equilibrium pressure follows the functional form of the Kelvin equation, but the energy parameterγv_M is smaller than the bulk value, implying that the clusters have a smaller cohesive energy.

Machine learning coarse grained models for water

An accurate and computationally efficient molecular level description of mesoscopic behavior of ice-water systems remains a major challenge. Here, we introduce a set of machine-learned coarse-grained (CG) models (ML-BOP, ML-BOP_dih, and ML-mW) that accurately describe the structure and thermodynamic anomalies of both water and ice at mesoscopic scales, all at two orders of magnitude cheaper computational cost than existing atomistic models. In a significant departure from conventional force-field fitting, we use a multilevel evolutionary strategy that trains CG models against not just energetics from first-principles and experiments but also temperature-dependent properties inferred from on-the-fly molecular dynamics (~ 10's of milliseconds of overall trajectories). Our ML BOP models predict both the correct experimental melting point of ice and the temperature of maximum density of liquid water that remained elusive to-date. Our ML workflow navigates efficiently through the high-dimensional parameter space to even improve upon existing high-quality CG models (e.g. mW model).

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.

Interaction of deoxyribonucleic acid with deoxyribonucleic acid-binding protein from starved cells: cluster formation and crystal growing as a model of initial stages of nucleoid biocrystallization

The paper represents the study of interaction between deoxyribonucleic acid (DNA) and deoxyribonucleic acid-binding protein from starved cells (DPS) cluster formation and crystal growing within a cell. This study is a part of the project that includes European Synchrotron Radiation Facility (ESRF) investigations of in vivo and in vitro nanocrystallization processes of Escherichia coli (E. coli) nucleoid under stress condition combined with theoretical molecular dynamics approaches. Nucleoid biocrystallization is an adaptive mechanism of bacterial cells under stress. It is poorly understood at the present time. Understanding crystal formation process is a very important for molecular biology, pharmacology and other areas. In the simulation part the coarse-grained modeling of various combinations of the following molecules was used: DPS proteins (from 1 to 108 DPS dodecamers in simulation box), short DNA fragments with a length of 24 base pairs (b.p., from 1 to 100 DNA fragments in simulation box) and a part of pBluescript SK(+) plasmide with a length of 161 b.p., in the presence of ions. We defined structural, energetic and dynamic properties of DPS-DPS and DPS-DNA complexes in clusters and crystals that allow us to predict crystal formation and the structure of these crystals in experimental systems.  Communicated by Ramaswamy H. Sarma.

On the nature and use of models in network neuroscience

Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behaviour. As the space of its applications grows, so does the diversity of meanings of the term network model. This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. In this Review, we examine the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along the following three primary dimensions: from data representations to first-principles theory; from biophysical realism to functional phenomenology; and from elementary descriptions to coarse-grained approximations. Third, we draw on biology, philosophy and other disciplines to establish validation principles for these models. We close with a discussion of opportunities to bridge model types and point to exciting frontiers for future pursuits.