Temporally Coherent Backmapping of Molecular Trajectories From Coarse-Grained to Atomistic Resolution.

Coarse-graining offers a means to extend the achievable time and length scales of molecular dynamics simulations beyond what is practically possible in the atomistic regime. Sampling molecular configurations of interest can be done efficiently using coarse-grained simulations, from which meaningful physicochemical information can be inferred if the corresponding all-atom configurations are reconstructed. However, this procedure of backmapping to reintroduce the lost atomistic detail into coarse-grain structures has proven a challenging task due to the many feasible atomistic configurations that can be associated with one coarse-grain structure. Existing backmapping methods are strictly frame-based, relying on either heuristics to replace coarse-grain particles with atomic fragments and subsequent relaxation or parametrized models to propose atomic coordinates separately and independently for each coarse-grain structure. These approaches neglect information from previous trajectory frames that is critical to ensuring temporal coherence of the backmapped trajectory, while also offering information potentially helpful to producing higher-fidelity atomic reconstructions. In this work, we present a deep learning-enabled data-driven approach for temporally coherent backmapping that explicitly incorporates information from preceding trajectory structures. Our method trains a conditional variational autoencoder to nondeterministically reconstruct atomistic detail conditioned on both the target coarse-grain configuration and the previously reconstructed atomistic configuration. We demonstrate our backmapping approach on two exemplar biomolecular systems: alanine dipeptide and the miniprotein chignolin. We show that our backmapped trajectories accurately recover the structural, thermodynamic, and kinetic properties of the atomistic trajectory data.

Machine learning implicit solvation for molecular dynamics.

Accurate modeling of the solvent environment for biological molecules is crucial for computational biology and drug design. A popular approach to achieve long simulation time scales for large system sizes is to incorporate the effect of the solvent in a mean-field fashion with implicit solvent models. However, a challenge with existing implicit solvent models is that they often lack accuracy or certain physical properties compared to explicit solvent models as the many-body effects of the neglected solvent molecules are difficult to model as a mean field. Here, we leverage machine learning (ML) and multi-scale coarse graining (CG) in order to learn implicit solvent models that can approximate the energetic and thermodynamic properties of a given explicit solvent model with arbitrary accuracy, given enough training data. Following the previous ML-CG models CGnet and CGSchnet, we introduce ISSNet, a graph neural network, to model the implicit solvent potential of mean force. ISSNet can learn from explicit solvent simulation data and be readily applied to molecular dynamics simulations. We compare the solute conformational distributions under different solvation treatments for two peptide systems. The results indicate that ISSNet models can outperform widely used generalized Born and surface area models in reproducing the thermodynamics of small protein systems with respect to explicit solvent. The success of this novel method demonstrates the potential benefit of applying machine learning methods in accurate modeling of solvent effects for in silico research and biomedical applications.

Coarse graining molecular dynamics with graph neural networks.

Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at an atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it are consistent with the conclusions we would draw from a model at a finer level of detail. It has been proved that a force matching scheme defines a thermodynamically consistent coarse-grained model for an atomistic system in the variational limit. Wang et al. [ACS Cent. Sci. 5, 755 (2019)] demonstrated that the existence of such a variational limit enables the use of a supervised machine learning framework to generate a coarse-grained force field, which can then be used for simulation in the coarse-grained space. Their framework, however, requires the manual input of molecular features to machine learn the force field. In the present contribution, we build upon the advance of Wang et al. and introduce a hybrid architecture for the machine learning of coarse-grained force fields that learn their own features via a subnetwork that leverages continuous filter convolutions on a graph neural network architecture. We demonstrate that this framework succeeds at reproducing the thermodynamics for small biomolecular systems. Since the learned molecular representations are inherently transferable, the architecture presented here sets the stage for the development of machine-learned, coarse-grained force fields that are transferable across molecular systems.

Understanding membrane-active antimicrobial peptides.

Bacterial membranes represent an attractive target for the design of new antibiotics to combat widespread bacterial resistance to traditional inhibitor-based antibiotics. Understanding how antimicrobial peptides (AMPs) and other membrane-active agents attack membranes could facilitate the design of new, effective antimicrobials. AMPs, which are small, gene-encoded host defense proteins, offer a promising basis for the study of membrane-active antimicrobial agents. These peptides are cationic and amphipathic, spontaneously binding to bacterial membranes and inducing transmembrane permeability to small molecules. Yet there are often confusions surrounding the details of the molecular mechanisms of AMPs. Following the doctrine of structure-function relationship, AMPs are often viewed as the molecular scaffolding of pores in membranes. Instead we believe that the full mechanism of AMPs is understandable if we consider the interactions of AMPs with the whole membrane domain, where interactions induce structural transformations of the entire membrane, rather than forming localized molecular structures. We believe that it is necessary to consider the entire soft matter peptide-membrane system as it evolves through several distinct states. Accordingly, we have developed experimental techniques to investigate the state and structure of the membrane as a function of the bound peptide to lipid ratio, exactly as AMPs in solution progressively bind to the membrane and induce structural changes to the entire system. The results from these studies suggest that global interactions of AMPs with the membrane domain are of fundamental importance to understanding the antimicrobial mechanisms of AMPs.

Comparison of the Effects of Daptomycin on Bacterial and Model Membranes.

Daptomycin is a phosphatidylglycerol specific, calcium-dependent membrane-active antibiotic that has been approved for the treatment of Gram-positive infections. A recent Bacillus subtilis study found that daptomycin clustered into fluid lipid domains of bacterial membranes and the membrane binding was correlated with dislocation of peripheral membrane proteins and depolarization of membrane potential. In particular, the study disproved the existence of daptomycin ion channels. Our purpose here is to study how daptomycin interacts with lipid bilayers to understand the observed phenomena on bacterial membranes. We performed new types of experiments using aspirated giant vesicles with an ion leakage indicator, making comparisons between daptomycin and ionomycin, performing vesicle-vesicle transfers, and measuring daptomycin binding to fluid phase versus gel phase bilayers and bilayers including cholesterol. Our findings are entirely consistent with the observations for bacterial membranes. In addition, daptomycin is found to cause ion leakage through the membrane only if its concentration in the membrane is over a certain threshold. The ion leakage caused by daptomycin is transient. It occurs only when daptomycin binds the membrane for the first time; afterward, they cease to induce ion leakage. The ion leakage effect of daptomycin cannot be transferred from one membrane to another. The level of membrane binding of daptomycin is reduced in the gel phase versus the fluid phase. Cholesterol also weakens the membrane binding of daptomycin. The combination of membrane concentration threshold and differential binding is significant. This could be a reason why daptomycin discriminates between eukaryotic and prokaryotic cell membranes.

Comparative Study of the Condensing Effects of Ergosterol and Cholesterol.

Cholesterol, due to its condensing effect, is considered an important regulator of membrane thickness. Other sterols, due to their structural similarities to cholesterol, are often assumed to have a universal effect on membrane properties similar to the condensing effect of cholesterol, albeit possibly to different degrees. We used x-ray diffraction to investigate this assumption. By the combination of lamellar diffraction and grazing-angle scattering, we measured the membrane thickness and the tilt-angle distribution of the lipid's hydrocarbon chains. This method is sensitive to phase separation, which is important for examining the miscibility of sterols and phospholipids. Mixtures of ergosterol or cholesterol with dimyristoylphosphatidylcholine, palmitoyloleoylphosphatidylcholine, and dioleoylphosphatidylcholine were systematically studied. We found that mixing ergosterol with phospholipids into a single phase became increasingly difficult with higher sterol concentrations and also with higher concentrations of unsaturated lipid chains. The only condensing effect of ergosterol was found in dimyristoylphosphatidylcholine, although the effect was less than one-third of the effect of cholesterol. Unlike cholesterol, ergosterol could not maintain a fixed electron density profile of the surrounding lipids independent of hydration. In dioleoylphosphatidylcholine and palmitoyloleoylphosphatidylcholine, ergosterol made the membranes thinner, opposite to the effect of cholesterol. In all cases, the tilt-angle variation of the chain diffraction was consistent with the membrane thickness changes measured by lamellar diffraction, i.e., a thickening was always associated with a reduction of chain tilt angles. Our findings do not support the notion that different sterols have a universal behavior that differs only in degree.

Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics.

Machine-learned coarse-grained (CG) models have the potential for simulating large molecular complexes beyond what is possible with atomistic molecular dynamics. However, training accurate CG models remains a challenge. A widely used methodology for learning bottom-up CG force fields maps forces from all-atom molecular dynamics to the CG representation and matches them with a CG force field on average. We show that there is flexibility in how to map all-atom forces to the CG representation and that the most commonly used mapping methods are statistically inefficient and potentially even incorrect in the presence of constraints in the all-atom simulation. We define an optimization statement for force mappings and demonstrate that substantially improved CG force fields can be learned from the same simulation data when using optimized force maps. The method is demonstrated on the miniproteins chignolin and tryptophan cage and published as open-source code.

Machine learning coarse-grained potentials of protein thermodynamics.

A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.

Machine learned coarse-grained protein force-fields: Are we there yet?

The successful recent application of machine learning methods to scientific problems includes the learning of flexible and accurate atomic-level force-fields for materials and biomolecules from quantum chemical data. In parallel, the machine learning of force-fields at coarser resolutions is rapidly gaining relevance as an efficient way to represent the higher-body interactions needed in coarse-grained force-fields to compensate for the omitted degrees of freedom. Coarse-grained models are important for the study of systems at time and length scales exceeding those of atomistic simulations. However, the development of transferable coarse-grained models via machine learning still presents significant challenges. Here, we discuss recent developments in this field and current efforts to address the remaining challenges.

Machine Learning of Coarse-Grained Molecular Dynamics Force Fields.

Atomistic or ab initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force-matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multibody terms that emerge from the dimensionality reduction.