Kernel-Based Machine Learning for Efficient Simulations of Molecular Liquids

Current machine learning (ML) models aimed at learning force fields are plagued by their high computational cost at every integration time step. We describe a number of practical and computationally efficient strategies to parametrize traditional force fields for molecular liquids from ML: the particle decomposition ansatz to two- and three-body force fields, the use of kernel-based ML models that incorporate physical symmetries, the incorporation of switching functions close to the cutoff, and the use of covariant meshing to boost the training set size. Results are presented for model molecular liquids: pairwise Lennard-Jones, three-body Stillinger-Weber, and bottom-up coarse-graining of water. Here, covariant meshing proves to be an efficient strategy to learn canonically averaged instantaneous forces. We show that molecular dynamics simulations with tabulated two- and three-body ML potentials are computationally efficient and recover two- and three-body distribution functions. Many-body representations, decomposition, and kernel regression schemes are all implemented in the open-source software package VOTCA.

Designing exceptional gas-separation polymer membranes using machine learning

The field of polymer membrane design is primarily based on empirical observation, which limits discovery of new materials optimized for separating a given gas pair. Instead of relying on exhaustive experimental investigations, we trained a machine learning (ML) algorithm, using a topological, path-based hash of the polymer repeating unit. We used a limited set of experimental gas permeability data for six different gases in ~700 polymeric constructs that have been measured to date to predict the gas-separation behavior of over 11,000 homopolymers not previously tested for these properties. To test the algorithm's accuracy, we synthesized two of the most promising polymer membranes predicted by this approach and found that they exceeded the upper bound for CO₂/CH₄ separation performance. This ML technique, which is trained using a relatively small body of experimental data (and no simulation data), evidently represents an innovative means of exploring the vast phase space available for polymer membrane design.

Inserting Small Molecules across Membrane Mixtures: Insight from the Potential of Mean Force

Small solutes have been shown to alter the lateral organization of cell membranes and reconstituted phospholipid bilayers; however, the mechanisms by which these changes happen are still largely unknown. Traditionally, both experiment and simulation studies have been restricted to testing only a few compounds at a time, failing to identify general molecular descriptors or chemical properties that would allow extrapolating beyond the subset of considered solutes. In this work, we probe the competing energetics of inserting a solute in different membrane environments by means of the potential of mean force. We show that these calculations can be used as a computationally efficient proxy to establish whether a solute will stabilize or destabilize domain phase separation. Combined with umbrella-sampling simulations and coarse-grained molecular dynamics simulations, we are able to screen solutes across a wide range of chemistries and polarities. Our results indicate that for the system under consideration, preferential partitioning and therefore effectiveness in altering membrane phase separation are strictly linked to the location of insertion in the bilayer (i.e., midplane or interface). Our approach represents a fast and simple tool for obtaining structural and thermodynamic insight into the partitioning of small molecules between lipid domains and its relation to phase separation, ultimately providing a platform for identifying the key determinants of this process.

Molecular dynamics trajectories for 630 coarse-grained drug-membrane permeations

The permeation of small-molecule drugs across a phospholipid membrane bears much interest both in the pharmaceutical sciences and in physical chemistry. Connecting the chemistry of the drug and the lipids to the resulting thermodynamic properties remains of immediate importance. Here we report molecular dynamics (MD) simulation trajectories using the coarse-grained (CG) Martini force field. A wide, representative coverage of chemistry is provided: across solutes-exhaustively enumerating all 105 CG dimers-and across six phospholipids. For each combination, umbrella-sampling simulations provide detailed structural information of the solute at all depths from the bilayer midplane to bulk water, allowing a precise reconstruction of the potential of mean force. Overall, the present database contains trajectories from 15,120 MD simulations. This database may serve the further identification of structure-property relationships between compound chemistry and drug permeability.

Probing Nanoparticle/Membrane Interactions by Combining Amphiphilic Diblock Copolymer Assembly and Plasmonics

Understanding the interactions between nanoparticles (NPs) and boundaries of cells is crucial both for their toxicity and therapeutic applications. Besides specific receptor-mediated endocytosis of surface-functionalized NPs, passive internalization is prompted by relatively unspecific parameters, such as particle size and charge. Based on theoretical treatments, adhesion to and bending of the cell membrane can induce NP wrapping. Experimentally, powerful tools are needed to selectively probe possible membrane-NP motifs at very dilute conditions and avoid dye labeling. In this work, we employ surface resonance-enhanced dynamic light scattering, surface plasmon resonance, electron microscopy, and simulations for sensing interactions between plasmonic AuNPs and polymersomes. We distinguish three different interaction scenarios at nanomolar concentrations by tuning the surface charge of AuNPs and rationalize these events by balancing vesicle bending and electrostatic/van der Waals AuNP and vesicle adhesion. The clarification of the physical conditions under which nanoparticles passively translocate across membranes can aid in the rational design of drugs that cannot exploit specific modes of cellular uptake and also elucidates physical properties that render nanoparticles in the environment particularly toxic.

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.

Microscopic reweighting for nonequilibrium steady-state dynamics

Computer simulations generate trajectories at a single, well-defined thermodynamic state point. Statistical reweighting offers the means to reweight static and dynamical properties to different equilibrium state points by means of analytic relations. We extend these ideas to nonequilibrium steady states by relying on a maximum path entropy formalism subject to physical constraints. Stochastic thermodynamics analytically relates the forward and backward probabilities of any pathway through the external nonconservative force, enabling reweighting both in and out of equilibrium. We avoid the combinatorial explosion of microtrajectories by systematically constructing pathways through Markovian transitions. We further identify a quantity that is invariant to dynamical reweighting, analogous to the density of states in equilibrium reweighting.

Controlled exploration of chemical space by machine learning of coarse-grained representations

The size of chemical compound space is too large to be probed exhaustively. This leads high-throughput protocols to drastically subsample and results in sparse and nonuniform datasets. Rather than arbitrarily selecting compounds, we systematically explore chemical space according to the target property of interest. We first perform importance sampling by introducing a Markov chain Monte Carlo scheme across compounds. We then train a machine learning (ML) model on the sampled data to expand the region of chemical space probed. Our boosting procedure enhances the number of compounds by a factor 2 to 10, enabled by the ML model's coarse-grained representation, which both simplifies the structure-property relationship and reduces the size of chemical space. The ML model correctly recovers linear relationships between transfer free energies. These linear relationships correspond to features that are global to the dataset, marking the region of chemical space up to which predictions are reliable; this is a more robust alternative to the predictive variance. Bridging coarse-grained simulations with ML gives rise to an unprecedented database of drug-membrane insertion free energies for 1.3 million compounds.

Drug-Membrane Permeability across Chemical Space

Unraveling the relation between the chemical structure of small druglike compounds and their rate of passive permeation across lipid membranes is of fundamental importance for pharmaceutical applications. The elucidation of a comprehensive structure-permeability relationship expressed in terms of a few molecular descriptors is unfortunately hampered by the overwhelming number of possible compounds. In this work, we reduce a priori the size and diversity of chemical space to solve an analogous-but smoothed out-structure-property relationship problem. This is achieved by relying on a physics-based coarse-grained model that reduces the size of chemical space, enabling a comprehensive exploration of this space with greatly reduced computational cost. We perform high-throughput coarse-grained (HTCG) simulations to derive a permeability surface in terms of two simple molecular descriptors-bulk partitioning free energy and pK a. The surface is constructed by exhaustively simulating all coarse-grained compounds that are representative of small organic molecules (ranging from 30 to 160 Da) in a high-throughput scheme. We provide results for acidic, basic, and zwitterionic compounds. Connecting back to the atomic resolution, the HTCG predictions for more than 500 000 compounds allow us to establish a clear connection between specific chemical groups and the resulting permeability coefficient, enabling for the first time an inverse design procedure. Our results have profound implications for drug synthesis: the predominance of commonly employed chemical moieties narrows down the range of permeabilities.

Automated detection of many-particle solvation states for accurate characterizations of diffusion kinetics

Discrete-space kinetic models, i.e., Markov state models, have emerged as powerful tools for reducing the complexity of trajectories generated from molecular dynamics simulations. These models require configuration-space representations that accurately characterize the relevant dynamics. Well-established, low-dimensional order parameters for constructing this representation have led to widespread application of Markov state models to study conformational dynamics in biomolecular systems. On the contrary, applications to characterize single-molecule diffusion processes have been scarce and typically employ system-specific, higher-dimensional order parameters to characterize the local solvation state of the molecule. In this work, we propose an automated method for generating a coarse configuration-space representation, using generic features of the solvation structure-the coordination numbers about each particle. To overcome the inherent noisy behavior of these low-dimensional observables, we treat the features as indicators of an underlying, latent Markov process. The resulting hidden Markov models filter the trajectories of each feature into the most likely latent solvation state at each time step. The filtered trajectories are then used to construct a configuration-space discretization, which accurately describes the diffusion kinetics. The method is validated on a standard model for glassy liquids, where particle jumps between local cages determine the diffusion properties of the system. Not only do the resulting models provide quantitatively accurate characterizations of the diffusion constant, but they also reveal a mechanistic description of diffusive jumps, quantifying the heterogeneity of local diffusion.

Accurate Structure-Based Coarse Graining Leads to Consistent Barrier-Crossing Dynamics

Structure-based coarse graining of molecular systems offers a systematic route to reproduce the many-body potential of mean force. Unfortunately, common strategies are inherently limited by the molecular mechanics force field employed. Here, we extend the concept of multisurface dynamics, initially developed to describe electronic transitions in chemical reactions, to accurately sample the conformational ensemble of a classical system in equilibrium. In analogy to describing different electronic configurations, a surface-hopping scheme couples distinct conformational basins beyond the additivity of the Hamiltonian. The incorporation of more surfaces leads systematically toward improved cross-correlations. The resulting models naturally achieve consistent long-time dynamics for systems governed by barrier-crossing events.

Engineering Proteins at Interfaces: From Complementary Characterization to Material Surfaces with Designed Functions

Once materials come into contact with a biological fluid containing proteins, proteins are generally—whether desired or not—attracted by the material's surface and adsorb onto it. The aim of this Review is to give an overview of the most commonly used characterization methods employed to gain a better understanding of the adsorption processes on either planar or curved surfaces. We continue to illustrate the benefit of combining different methods to different surface geometries of the material. The thus obtained insight ideally paves the way for engineering functional materials that interact with proteins in a predetermined manner.

In silico screening of drug-membrane thermodynamics reveals linear relations between bulk partitioning and the potential of mean force

The partitioning of small molecules in cell membranes-a key parameter for pharmaceutical applications-typically relies on experimentally available bulk partitioning coefficients. Computer simulations provide a structural resolution of the insertion thermodynamics via the potential of mean force but require significant sampling at the atomistic level. Here, we introduce high-throughput coarse-grained molecular dynamics simulations to screen thermodynamic properties. This application of physics-based models in a large-scale study of small molecules establishes linear relationships between partitioning coefficients and key features of the potential of mean force. This allows us to predict the structure of the insertion from bulk experimental measurements for more than 400 000 compounds. The potential of mean force hereby becomes an easily accessible quantity-already recognized for its high predictability of certain properties, e.g., passive permeation. Further, we demonstrate how coarse graining helps reduce the size of chemical space, enabling a hierarchical approach to screening small molecules.

Structural-kinetic-thermodynamic relationships identified from physics-based molecular simulation models

Coarse-grained molecular simulation models have provided immense, often general, insight into the complex behavior of condensed-phase systems but suffer from a lost connection to the true dynamical properties of the underlying system. In general, the physics that is built into a model shapes the free-energy landscape, restricting the attainable static and kinetic properties. In this work, we perform a detailed investigation into the property interrelationships resulting from these restrictions, for a representative system of the helix-coil transition. Inspired by high-throughput studies, we systematically vary force-field parameters and monitor their structural, kinetic, and thermodynamic properties. The focus of our investigation is a simple coarse-grained model, which accurately represents the underlying structural ensemble, i.e., effectively avoids sterically-forbidden configurations. As a result of this built-in physics, we observe a rather large restriction in the topology of the networks characterizing the simulation kinetics. When screening across force-field parameters, we find that structurally accurate models also best reproduce the kinetics, suggesting structural-kinetic relationships for these models. Additionally, an investigation into thermodynamic properties reveals a link between the cooperativity of the transition and the network topology at a single reference temperature.

Efficient potential of mean force calculation from multiscale simulations: Solute insertion in a lipid membrane

The determination of potentials of mean force for solute insertion in a lipid membrane by means of all-atom molecular dynamics simulations is often hampered by sampling issues. Recently, a multiscale method has been proposed to leverage the conformational ensemble of a lower-resolution model as starting point for higher resolution simulations. In this work, we analyze the efficiency of this method by comparing its predictions for propanol insertion into a lipid membrane against conventional atomistic umbrella sampling simulation results. The multiscale approach is confirmed to provide accurate results with a gain of one order of magnitude in computational time. We then investigate the role of the coarse-grained representation. We find that the accuracy of the results is tightly connected to the presence of a good configurational overlap between the coarse-grained and atomistic models-a general requirement when developing multiscale simulation methods.