SMARTINI3 parametrization of multi-scale membrane models via unsupervised learning methods

In this study, we utilize genetic algorithms to develop a realistic implicit solvent ultra-coarse-grained (ultra-CG) membrane model comprising only three interaction sites. The key philosophy of the ultra-CG membrane model SMARTINI3 is its compatibility with realistic membrane proteins, for example, modeled within the Martini coarse-grained (CG) model, as well as with the widely used GROMACS software for molecular simulations. Our objective is to parameterize this ultra-CG model to accurately reproduce the experimentally observed structural and thermodynamic properties of Phosphatidylcholine (PC) membranes in real units, including properties such as area per lipid, area compressibility, bending modulus, line tension, phase transition temperature, density profile, and radial distribution function. In our example, we specifically focus on the properties of a POPC membrane, although the developed membrane model could be perceived as a generic model of lipid membranes. To optimize the performance of the model (the fitness), we conduct a series of evolutionary runs with diverse random initial population sizes (ranging from 96 to 384). We demonstrate that the ultra-CG membrane model we developed exhibits authentic lipid membrane behaviors, including self-assembly into bilayers, vesicle formation, membrane fusion, and gel phase formation. Moreover, we demonstrate compatibility with the Martini coarse-grained model by successfully reproducing the behavior of a transmembrane domain embedded within a lipid bilayer. This facilitates the simulation of realistic membrane proteins within an ultra-CG bilayer membrane, enhancing the accuracy and applicability of our model in biophysical studies.

Development of a bottom-up coarse-grained model for interactions of lipids with TiO 2 nanoparticles

Understanding interactions of inorganic nanoparticles with biomolecules is important in many biotechnology, nanomedicine, and toxicological research, however, the size of typical nanoparticles makes their direct modeling by atomistic simulations unfeasible. Here, we present a bottom-up coarse-graining approach for modeling titanium dioxide (TiO  2 ) nanomaterials in contact with phospholipids that uses the inverse Monte Carlo method to optimize the effective interactions from the structural data obtained in small-scale all-atom simulations of TiO  2 surfaces with lipids in aqueous solution. The resulting coarse-grained models are able to accurately reproduce the structural details of lipid adsorption on different titania surfaces without the use of an explicit solvent, enabling significant computational resource savings and favorable scaling. Our coarse-grained simulations show that small spherical TiO  2 nanoparticles ( r = 2 nm) can only be partially wrapped by a lipid bilayer with phosphoethanolamine headgroups, however, the lipid adsorption increases with the radius of the nanoparticle. The current approach can be used to study the effect of the size and shape of TiO  2 nanoparticles on their interactions with cell membrane lipids, which can be a determining factor in membrane wrapping as well as the recently discovered phenomenon of nanoquarantining, which involves the formation of layered nanomaterial-lipid structures.

Dynamic framework for large-scale modeling of membranes and peripheral proteins

In this chapter, we present a novel computational framework to study the dynamic behavior of extensive membrane systems, potentially in interaction with peripheral proteins, as an alternative to conventional simulation methods. The framework effectively describes the complex dynamics in protein-membrane systems in a mesoscopic particle-based setup. Furthermore, leveraging the hydrodynamic coupling between the membrane and its surrounding solvent, the coarse-grained model grounds its dynamics in macroscopic kinetic properties such as viscosity and diffusion coefficients, marrying the advantages of continuum- and particle-based approaches. We introduce the theoretical background and the parameter-space optimization method in a step-by-step fashion, present the hydrodynamic coupling method in detail, and demonstrate the application of the model at each stage through illuminating examples. We believe this modeling framework to hold great potential for simulating membrane and protein systems at biological spatiotemporal scales, and offer substantial flexibility for further development and parametrization.

Coarse-Grained Modeling Using Neural Networks Trained on Structural Data

We propose a method of bottom-up coarse-graining, in which interactions within a coarse-grained model are determined by an artificial neural network trained on structural data obtained from multiple atomistic simulations. The method uses ideas of the inverse Monte Carlo approach, relating changes in the neural network weights with changes in average structural properties, such as radial distribution functions. As a proof of concept, we demonstrate the method on a system interacting by a Lennard-Jones potential modeled by a simple linear network and a single-site coarse-grained model of methanol-water solutions. In the latter case, we implement a nonlinear neural network with intermediate layers trained by atomistic simulations carried out at different methanol concentrations. We show that such a network acts as a transferable potential at the coarse-grained resolution for a wide range of methanol concentrations, including those not included in the training set.

Development of a Hybrid-Resolution Force Field for Peptide Self-Assembly Simulations: Optimizing Peptide-Peptide and Peptide-Solvent Interactions

Atomic descriptions of peptide self-assembly are crucial to an understanding of disease-related peptide aggregation and the design of peptide-assembled materials. Obtaining these descriptions through computer simulation is challenging because current force fields, which were not designed for this process and are often unable to describe correctly peptide self-assembly behavior and the sequence dependence. Here, we developed a framework using dipeptide aggregation as a model system to improve force fields for simulations of self-assembly. Aggregation-related structural properties were designed and used to guide the optimization of peptide-peptide and peptide-solvent interactions. With this framework, we developed a self-assembly force field, termed PACE-ASM, by reoptimizing a hybrid-resolution force field that was originally developed for folding simulation. With its applicability in folding simulations, the new PACE was used to simulate the self-assembly of two disease-related short peptides, Aβ_16-21 and PHF6, into β-sheet-rich cross-β amyloids. These simulations reproduced the crystal structures of Aβ_16-21 and PHF6 amyloids at near-atomic resolution and captured the difference in packing orientations between the two sequences, a task which is challenging even with all-atom force fields. Apart from cross-β amyloids, the self-assembly of emerging helix-rich cross-α amyloids by another peptide PSMα3 can also be correctly described with the new PACE, manifesting the versatility of the force field. We demonstrated that the ability of the PACE-ASM to model peptide self-assembly is based largely on its improved description of peptide-peptide and peptide-solvent interactions. This was achieved with our optimization framework that can readily identify and address the deficiency in describing these interactions.

Dual-potential approach for coarse-grained implicit solvent models with accurate, internally consistent energetics and predictive transferability

The dual-potential approach promises coarse-grained (CG) models that accurately reproduce both structural and energetic properties, while simultaneously providing predictive estimates for the temperature-dependence of the effective CG potentials. In this work, we examine the dual-potential approach for implicit solvent CG models that reflect large entropic effects from the eliminated solvent. Specifically, we construct implicit solvent models at various resolutions, R, by retaining a fraction 0.10 ≤ R ≤ 0.95 of the molecules from a simple fluid of Lennard-Jones spheres. We consider the dual-potential approach in both the constant volume and constant pressure ensembles across a relatively wide range of temperatures. We approximate the many-body potential of mean force for the remaining solutes with pair and volume potentials, which we determine via multiscale coarse-graining and self-consistent pressure-matching, respectively. Interestingly, with increasing temperature, the pair potentials appear increasingly attractive, while the volume potentials become increasingly repulsive. The dual-potential approach not only reproduces the atomic energetics but also quite accurately predicts this temperature-dependence. We also derive an exact relationship between the thermodynamic specific heat of an atomic model and the energetic fluctuations that are observable at the CG resolution. With this generalized fluctuation relationship, the approximate CG models quite accurately reproduce the thermodynamic specific heat of the underlying atomic model.

Implicit solvent systematic coarse-graining of dioleoylphosphatidylethanolamine lipids: From the inverted hexagonal to the bilayer structure

Lamellar and hexagonal lipid structures are of particular importance in the biological processes such as membrane fusion and budding. Atomistic simulations of formation of these phases and transitions between them are computationally prohibitive, hence development of coarse-grained models is an important part of the methodological development in this area. Here we apply systematic bottom-up coarse-graining to model different phase structures formed by 1,2-dioleoylphosphatidylethanolamine (DOPE) lipid molecules. We started from atomistic simulations of DOPE lipids in water carried out at two different water/lipid molar ratio corresponding to the lamellar L_α and inverted hexagonal H_II structures at low and high lipid concentrations respectively. The atomistic trajectories were mapped to coarse-grained trajectories, in which each lipid was represented by 14 coarse-grained sites. Then the inverse Monte Carlo method was used to compute the effective coarse-grained potentials which for the coarse-grain model reproduce the same structural properties as the atomistic simulations. The potentials derived from the low concentration atomistic simulation were only able to form a bilayer structure, while both L_α and H_II lipid phases were formed in simulations with potentials obtained at high concentration. The typical atomistic configurations of lipids at high concentration combine fragments of both lamellar and non-lamellar structures, that is reflected in the extracted coarse-grained potentials which become transferable and can form a wide range of structures including the inverted hexagonal, bilayer, tubule, vesicle and micellar structures.

Systematic Coarse-Grained Lipid Force Fields with Semiexplicit Solvation via Virtual Sites

Despite the central role of lipids in many biophysical functions, the molecular mechanisms that dictate macroscopic lipid behavior remain elusive to both experimental and computational approaches. As such, there has been much interest in the development of low-resolution, implicit-solvent coarse-grained (CG) models to dynamically simulate biologically relevant spatiotemporal scales with molecular fidelity. However, in the absence of solvent, a key challenge for CG models is to faithfully emulate solvent-mediated forces, which include both hydrophilic and hydrophobic interactions that drive lipid aggregation and self-assembly. In this work, we provide a new methodological framework to incorporate semiexplicit solvent effects through the use of virtual CG particles, which represent structural features of the solvent-lipid interface. To do so, we leverage two systematic coarse-graining approaches, multiscale coarse-graining (MS-CG) and relative entropy minimization (REM), in a hybrid fashion to construct our virtual-site CG (VCG) models. As a proof-of-concept, we focus our efforts on two lipid species, 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) and 1,2-dipalmitoyl- sn-glycero-3-phosphocholine (DPPC), which adopt a liquid-disordered and gel phase, respectively, at room temperature. Through our analysis, we also present, to our knowledge, the first direct comparison between the MS-CG and REM methods for a complex biomolecule and highlight each of their strengths and weaknesses. We further demonstrate that VCG models recapitulate the rich biophysics of lipids, which enable self-assembly, morphological diversity, and multiple phases. Our findings suggest that the VCG framework is a powerful approach for investigation into macromolecular biophysics.

Systematic hierarchical coarse-graining with the inverse Monte Carlo method

We outline our coarse-graining strategy for linking micro- and mesoscales of soft matter and biological systems. The method is based on effective pairwise interaction potentials obtained in detailed ab initio or classical atomistic Molecular Dynamics (MD) simulations, which can be used in simulations at less accurate level after scaling up the size. The effective potentials are obtained by applying the inverse Monte Carlo (IMC) method [A. P. Lyubartsev and A. Laaksonen, Phys. Rev. E 52(4), 3730-3737 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. An in-house software package MagiC is developed to obtain the effective potentials for arbitrary molecular systems. In this work we compute effective potentials to model DNA-protein interactions (bacterial LiaR regulator bound to a 26 base pairs DNA fragment) at physiological salt concentration at a coarse-grained (CG) level. Normally the IMC CG pair-potentials are used directly as look-up tables but here we have fitted them to five Gaussians and a repulsive wall. Results show stable association between DNA and the model protein as well as similar position fluctuation profile.

Multiscale coarse-grained modelling of chromatin components: DNA and the nucleosome

To model large biomolecular systems, such as cell and organelles an atomistic description is not currently achievable and is not generally practical. Therefore, simplified coarse-grained (CG) modelling becomes a necessity. One of the most important cellular components is chromatin, a large DNA-protein complex where DNA is highly compacted. Recent progress in coarse graining modelling of the major chromatin components, double helical DNA and the nucleosome core particle (NCP) is presented. First, general principles and approaches allowing rigorous bottom-to-top generation of interaction potentials in the CG models are presented. Then, recent CG models of DNA are reviewed and their adequacy is benchmarked against experimental data on the salt dependence of DNA flexibility (persistence length). Furthermore, a few recent CG models of the NCP are described and their application for studying salt-dependent NCP-NCP interaction is discussed. An example of a multiscale approach to CG modelling of chromatin is presented where interactions and self-assembly of thousands of NCPs in solution are observed.

Force Field Development for Lipid Membrane Simulations

With the rapid development of computer power and wide availability of modelling software computer simulations of realistic models of lipid membranes, including their interactions with various molecular species, polypeptides and membrane proteins have become feasible for many research groups. The crucial issue of the reliability of such simulations is the quality of the force field, and many efforts, especially in the latest several years, have been devoted to parametrization and optimization of the force fields for biomembrane modelling. In this review, we give account of the recent development in this area, covering different classes of force fields, principles of the force field parametrization, comparison of the force fields, and their experimental validation. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

A Solvent-Mediated Coarse-Grained Model of DNA Derived with the Systematic Newton Inversion Method

We present a new class of coarse-grained (CG) force fields (FFs) for B-DNA with explicit ions suited for large-scale mesoscale simulations at microsecond-micrometer scale using a wide spectrum of particle simulation methods from molecular dynamics to dissipative particle dynamics. The effective solvent-mediated pairwise interactions making up the FFs are obtained by inverting radial distribution functions and other particle-particle distributions obtained from all-atom simulations of numbers of octadecamer DNA fragments from the Ascona B-DNA library. The inverse Monte Carlo (IMC) method, later known as Newton inversion (NI) (Lyubartsev, A. P.; Laaksonen, A. Phys. Rev. E, 1995, 52, 3730-3737), was used together with the iterative Boltzmann inversion (IBI) scheme to compute the effective CG potentials. We show that this systematic structure-based approach is capable of providing converged potentials that accurately reproduce the structural features of the underlying atomistic system within a few percents of relative difference. We also show that a simple one-site-per-nucleotide model with 10 intramolecular pair interaction potentials is able to reproduce key features of DNA, for example, the persistence length and its dependence on the ionic concentration, experimentally determined around 50 nm at physiological salt concentration.

Coarse-grained molecular dynamics simulation of self-assembly and surface adsorption of ionic surfactants using an implicit water model

We perform coarse-grained molecular dynamics simulations for sodium dodecyl sulfate (SDS) surfactant using a modification of the Dry Martini force field (Arnarez et al. 2014) with implicit water. After inclusion of particle mesh Ewald (PME) electrostatics, an artificially high dielectric constant for water (ε(r) = 150), and reparameterization, we obtain structural and thermodynamic properties of SDS micelles that are close to those obtained from the standard Martini force field with explicit water, which in turn match those of atomistic simulations. The gains in computational efficiency obtained by removing explicit water allow direct simulations of the self-assembly of SDS in solution. We observe surfactant exchange among micelles and micelle fission and fusion and obtain realistic, equilibrated micelle size distributions at modest computational cost, as well as a transition to cylindrical micelles at high surfactant concentration or with added salt. We further apply this parametrized force field to study the adsorption of SDS onto hydrophobic surfaces and calculate the adsorption kinetics and equilibrium adsorption isotherm. The greatly increased speed of computation of surfactant self-assembly made possible by this Dry Martini method should allow future simulation of competitive adsorption of multiple surfactant species to surfaces, as well as simulation of micellar shape transitions.