A Review of Coarse-Grained Molecular Dynamics Techniques to Access Extended Spatial and Temporal Scales in Biomolecular Simulations

Perspective on Integrative Simulations of Bioenergetic Domains

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows

This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate's architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: (i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; (ii) It accelerates the prediction step by enabling adaptivity as the surrogate's evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0-[Formula: see text] scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1-[Formula: see text] shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations.

Polymer brushes for friction control: Contributions of molecular simulations

When polymer chains are grafted to solid surfaces at sufficiently high density, they form brushes that can modify the surface properties. In particular, polymer brushes are increasingly being used to reduce friction in water-lubricated systems close to the very low levels found in natural systems, such as synovial joints. New types of polymer brush are continually being developed to improve with lower friction and adhesion, as well as higher load-bearing capacities. To complement experimental studies, molecular simulations are increasingly being used to help to understand how polymer brushes reduce friction. In this paper, we review how molecular simulations of polymer brush friction have progressed from very simple coarse-grained models toward more detailed models that can capture the effects of brush topology and chemistry as well as electrostatic interactions for polyelectrolyte brushes. We pay particular attention to studies that have attempted to match experimental friction data of polymer brush bilayers to results obtained using molecular simulations. We also critically look at the remaining challenges and key limitations to overcome and propose future modifications that could potentially improve agreement with experimental studies, thus enabling molecular simulations to be used predictively to modify the brush structure for optimal friction reduction.

A Coarse-Grained Interaction Model for Sodium Dominant Montmorillonite

Montmorillonite is the main crystalline mineral present in bentonite. It is an absorbent, swelling material; the physical chemistry underlying its ability to absorb water and swell occurs at the nanoscale, governed by electrical double-layer interactions. In turn, absorption and swelling lead to important changes in the macroscopic transport properties of the clay. Mesoscale models can help us establish a link between these nanoscale processes and macroscale properties, notably by providing a detailed description of its pore network. Models on the scale of hundreds to thousands of nanometers are required, which cannot realistically be handled using traditional all-atom molecular dynamics simulations. This work presents a coarse-grained (CG) mesoscale model of sodium montmorillonite. In our model, montmorillonite platelets are represented by two types of particles: central nonhydrogen-bonded particles and edge hydrogen-bonding particles. The particle interactions are described by two-body potentials, which were optimized based on all-atom molecular dynamics simulations. Specifically, several potential mean force calculations involving dry and hydrated montmorillonite were performed, using the ClayFF potential to calculate interatomic forces. The CG model was validated by testing the scalability of the model, testing its ability to reproduce potentials of mean force reported elsewhere in the literature, and by comparing the calculated elastic properties of a system containing 1000 Na montmorillonite platelets to experimentally measured elastic properties of bentonite. The simulated elastic properties obtained using our mesoscale model agree with these experimental values.

A Review of Using Mathematical Modeling to Improve Our Understanding of Bacteriophage, Bacteria, and Eukaryotic Interactions

Phage therapy, the therapeutic usage of viruses to treat bacterial infections, has many theoretical benefits in the ‘post antibiotic era.’ Nevertheless, there are currently no approved mainstream phage therapies. One reason for this is a lack of understanding of the complex interactions between bacteriophage, bacteria and eukaryotic hosts. These three-component interactions are complex, with non-linear or synergistic relationships, anatomical barriers and genetic or phenotypic heterogeneity all leading to disparity between performance and efficacy in in vivo versus in vitro environments. Realistic computer or mathematical models of these complex environments are a potential route to improve the predictive power of in vitro studies for the in vivo environment, and to streamline lab work. Here, we introduce and review the current status of mathematical modeling and highlight that data on genetic heterogeneity and mutational stochasticity, time delays and population densities could be critical in the development of realistic phage therapy models in the future. With this in mind, we aim to inform and encourage the collaboration and sharing of knowledge and expertise between microbiologists and theoretical modelers, synergising skills and smoothing the road to regulatory approval and widespread use of phage therapy.

Extension of the CAVS model to the simulation of helical peptides in a membrane environment

Considering the effect of peptide insertion on the dipole potential of the lipid membrane, we extend the CAVS coarse-grained (CG) model to the simulation of helical peptides in a membrane environment. In this approach, the CG scheme for a peptide backbone is similar to the treatment in the united-atom model, while we treated the side chain of an amino acid by grouping 1-3 heavy atoms into a CG unit. The CAVS CG force field for peptides is optimized by reproducing the experimental results for the backbone (φ, ψ) distribution and predicting the PMF profiles of transferring organic molecules in a lipid bilayer membrane obtained from all-atom simulations. The CAVS simulation of a helical peptide in a phosphatidylcholine (PC) lipid bilayer revealed that the insertion of a peptide increases the dipole potential of the PC lipid bilayer, in which the peptide and its neutralized ions make a significant contribution. Finally, we carried out the CAVS simulation for five different helical peptides in the PC lipid bilayer to explore the behavior of peptide tilt, showing excellent agreement with the all-atom simulations. Our work suggests that the peptide tilt should relieve the deformation stress from the lipid bilayer, and the peptide aggregation could reduce the peptide tilt by resisting the deformation stress from the surrounding lipids.

Molecular Dynamics Simulations of Adenosine Receptors: Advances, Applications and Trends

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Adenosine receptors (ARs) are transmembrane proteins that belong to the G protein-coupled receptors (GPCRs) superfamily and mediate the biological functions of adenosine. To date, four AR subtypes are known, namely A1, A2A, A2B and A3 that exhibit different signaling pathways, tissue localization, and mechanisms of activation. Moreover, the widespread ARs and their implication in numerous physiological and pathophysiological conditions had made them pivotal therapeutic targets for developing clinically effective agents.

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The crystallographic success in identifying the 3D crystal structures of A2A and A1 ARs has dramatically enriched our understanding of their structural and functional properties such as ligand binding and signal transduction. This, in turn, has provided a structural basis for a larger contribution of computational methods, particularly molecular dynamics (MD) simulations, toward further investigation of their molecular properties and designing bioactive ligands with therapeutic potential. MD simulation has been proved to be an invaluable tool in investigating ARs and providing answers to some critical questions. For example, MD has been applied in studying ARs in terms of ligand-receptor interactions, molecular recognition, allosteric modulations, dimerization, and mechanisms of activation, collectively aiding in the design of subtype selective ligands.

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In this review, we focused on the advances and different applications of MD simulations utilized to study the structural and functional aspects of ARs that can foster the structure-based design of drug candidates. In addition, relevant literature was briefly discussed which establishes a starting point for future advances in the field of drug discovery to this pivotal group of drug targets.

Computational insights into lipid assisted peptide misfolding and aggregation in neurodegeneration

An overview of recent advances in computational investigation of peptide–lipid interactions in neurodegeneration – Alzheimer's, Parkinson's and Huntington's disease.

Coarse-grained simulations of polyelectrolyte complexes: MARTINI models for poly(styrene sulfonate) and poly(diallyldimethylammonium)

We present simulations of aqueous polyelectrolyte complexes with new MARTINI models for the charged polymers poly(styrene sulfonate) and poly(diallyldimethylammonium). Our coarse-grained polyelectrolyte models allow us to study large length and long time scales with regard to chemical details and thermodynamic properties. The results are compared to the outcomes of previous atomistic molecular dynamics simulations and verify that electrostatic properties are reproduced by our MARTINI coarse-grained approach with reasonable accuracy. Structural similarity between the atomistic and the coarse-grained results is indicated by a comparison between the pair radial distribution functions and the cumulative number of surrounding particles. Our coarse-grained models are able to quantitatively reproduce previous findings like the correct charge compensation mechanism and a reduced dielectric constant of water. These results can be interpreted as the underlying reason for the stability of polyelectrolyte multilayers and complexes and validate the robustness of the proposed models.

Coarse-Grained Modeling of Nucleic Acids Using Anisotropic Gay-Berne and Electric Multipole Potentials

In this work, we attempt to apply a coarse-grained (CG) model, which is based on anisotropic Gay-Berne and electric multipole (EMP) potentials, to the modeling of nucleic acids. First, a comparison has been made between the CG and atomistic models (AMBER point-charge model) in the modeling of DNA and RNA hairpin structures. The CG results have demonstrated a good quality in maintaining the nucleic acid hairpin structures, in reproducing the dynamics of backbone atoms of nucleic acids, and in describing the hydrogen-bonding interactions between nucleic acid base pairs. Second, the CG and atomistic AMBER models yield comparable results in modeling double-stranded DNA and RNA molecules. It is encouraging that our CG model is capable of reproducing many elastic features of nucleic acid base pairs in terms of the distributions of the interbase pair step parameters (such as shift, slide, tilt, and twist) and the intrabase pair parameters (such as buckle, propeller, shear, and stretch). Finally, The GBEMP model has shown a promising ability to predict the melting temperatures of DNA duplexes with different lengths.

Dynamic force matching: A method for constructing dynamical coarse-grained models with realistic time dependence

Coarse-grained (CG) models of molecular systems, with fewer mechanical degrees of freedom than an all-atom model, are used extensively in chemical physics. It is generally accepted that a coarse-grained model that accurately describes equilibrium structural properties (as a result of having a well constructed CG potential energy function) does not necessarily exhibit appropriate dynamical behavior when simulated using conservative Hamiltonian dynamics for the CG degrees of freedom on the CG potential energy surface. Attempts to develop accurate CG dynamic models usually focus on replacing Hamiltonian motion by stochastic but Markovian dynamics on that surface, such as Langevin or Brownian dynamics. However, depending on the nature of the system and the extent of the coarse-graining, a Markovian dynamics for the CG degrees of freedom may not be appropriate. In this paper, we consider the problem of constructing dynamic CG models within the context of the Multi-Scale Coarse-graining (MS-CG) method of Voth and coworkers. We propose a method of converting a MS-CG model into a dynamic CG model by adding degrees of freedom to it in the form of a small number of fictitious particles that interact with the CG degrees of freedom in simple ways and that are subject to Langevin forces. The dynamic models are members of a class of nonlinear systems interacting with special heat baths that were studied by Zwanzig [J. Stat. Phys. 9, 215 (1973)]. The properties of the fictitious particles can be inferred from analysis of the dynamics of all-atom simulations of the system of interest. This is analogous to the fact that the MS-CG method generates the CG potential from analysis of equilibrium structures observed in all-atom simulation data. The dynamic models generate a non-Markovian dynamics for the CG degrees of freedom, but they can be easily simulated using standard molecular dynamics programs. We present tests of this method on a series of simple examples that demonstrate that the method provides realistic dynamical CG models that have non-Markovian or close to Markovian behavior that is consistent with the actual dynamical behavior of the all-atom system used to construct the CG model. Both the construction and the simulation of such a dynamic CG model have computational requirements that are similar to those of the corresponding MS-CG model and are good candidates for CG modeling of very large systems.

Liposomal nanohybrid cerasomes for mitochondria-targeted drug delivery

Mitochondrial dysfunctions cause numerous human disorders and the development of mitochondria-targeted nanocarriers for drug delivery has aroused great attention. Herein, we report the synthesis of a liposomal nanohybrid cerasome modified with triphosphonium (TPP) for drug delivery to the mitochondrial matrix. The cerasomes were observed to possess an average size of about 38 nm in diameter, and the theoretical simulation of GBEMP mapping demonstrated that the amphiphilic organotrialkoxysilanes were stable as a bilayer equilibrium conformation after self-assembly. The cerasomes showed good stability, excellent biocompatibility and sustainable drug release behavior. Moreover, the TPP-targeted cerasomes resulted in greater drug accumulation in mitochondria, thus leading to a greater antitumor effect as compared to non-targeted cerasomes by using doxorubicin as a modal drug. The specific accumulation of TPP-targeted cerasomes within mitochondria was also confirmed by using JC-1 as the fluorescent probe to analyze the mitochondrial transmembrane potential change.

The Theory of Ultra-Coarse-Graining. 2. Numerical Implementation

The increasing interest in the modeling of complex macromolecular systems in recent years has spurred the development of numerous coarse-graining (CG) techniques. However, many of the CG models are constructed assuming that all details beneath the resolution of CG degrees of freedom are fast and average out, which sets limits on the resolution of feasible coarse-grainings and on the range of applications of the CG models. Ultra-coarse-graining (UCG) makes it possible to construct models at any desired resolution while accounting for discrete conformational or chemical changes within the CG sites that can modulate the interactions between them. Here, we discuss the UCG methodology and its numerical implementation. We pay particular attention to the numerical mechanism for including state transitions between different conformations within CG sites because this has not been discussed previously. Using a simple example of 1,2-dichloroethane, we demonstrate the ability of the UCG model to reproduce the multiconfigurational behavior of this molecular liquid, even when each molecule is modeled with only one CG site. The methodology can also be applied to other molecular liquids and macromolecular systems with time scale separation between conformational transitions and other intramolecular motions and rotations.

An Anisotropic Coarse-Grained Model for Proteins Based On Gay-Berne and Electric Multipole Potentials

Gay–Berne anisotropic potential has been widely used to evaluate the nonbonded interactions between coarse-grained particles being described as elliptical rigid bodies. In this paper, we are presenting a coarse-grained model for twenty kinds of amino acids and proteins, based on the anisotropic Gay–Berne and point electric multipole (EMP) potentials. We demonstrate that the anisotropic coarse-grained model, namely GBEMP model, is able to reproduce many key features observed from experimental protein structures (Dunbrack Library), as well as from atomistic force field simulations (using AMOEBA, AMBER, and CHARMM force fields), while saving the computational cost by a factor of about 10–200 depending on specific cases and atomistic models. More importantly, unlike other coarse-grained approaches, our framework is based on the fundamental intermolecular forces with explicit treatment of electrostatic and repulsion-dispersion forces. As a result, the coarse-grained protein model presented an accurate description of nonbonded interactions (particularly electrostatic component) between hetero/homodimers (such as peptide–peptide, peptide–water). In addition, the encouraging performance of the model was reflected by the excellent correlation between GBEMP and AMOEBA models in the calculations of the dipole moment of peptides. In brief, the GBEMP model given here is general and transferable, suitable for simulating complex biomolecular systems.

Effects of Molecular Dynamics Thermostats on Descriptions of Chemical Nonequilibrium

The performance of popular molecular dynamics (MD) thermostat algorithms in constant temperature simulations of equilibrium systems is well-known. This is not the case, however, in the context of nonequilibrium chemical systems, such as chemical reactions or nanoscale self-assembly processes. In this work, we investigate the effect of popular thermostat algorithms on the "natural" (i.e., Hamiltonian) dynamics of a nonequilibrium, chemically reacting system. By comparing constant-temperature quantum mechanical MD (QM/MD) simulations of carbon vapor condensation using velocity scaling, Berendsen, Andersen, Langevin, and Nosé-Hoover chain thermostat algorithms with natural NVE simulations, we show that efficient temperature control and reliable reaction dynamics are mutually exclusive in such a system. This problem may be circumvented, however, by placing the reactive system in an inert He atmosphere, which is itself described using NVT MD. We demonstrate that both realistic temperature control and dynamics consistent with natural NVE dynamics can then be obtained simultaneously. In essence, the thermal energy created by the natural dynamics of the NVE subsystem is drained by the thermostat acting on the NVT atmosphere, without adversely affecting the dynamics of the reactive system itself.