Resolution limit of data-driven coarse-grained models spanning chemical space

Broad chemical transferability in structure-based coarse-graining

Compared to top-down coarse-grained (CG) models, bottom-up approaches are capable of offering higher structural fidelity. This fidelity results from the tight link to a higher-resolution reference, making the CG model chemically specific. Unfortunately, chemical specificity can be at odds with compound-screening strategies, which call for transferable parametrizations. Here we present an approach to reconcile bottom-up, structure-preserving CG models with chemical transferability. We consider the bottom-up CG parametrization of 3,441 C7O2 small-molecule isomers. Our approach combines atomic representations, unsupervised learning, and a large-scale extended-ensemble force-matching parametrization. We first identify a subset of 19 representative molecules, which maximally encode the local environment of all gas-phase conformers. Reference interactions between the 19 representative molecules were obtained from both homogeneous bulk liquids and various binary mixtures. An extended-ensemble parametrization over all 703 state points leads to a CG model that is both structure-based and chemically transferable. Remarkably, the resulting force field is on average more structurally accurate than single-state-point equivalents. Averaging over the extended ensemble acts as a mean-force regularizer, smoothing out both force and structural correlations that are overly specific to a single state point. Our approach aims at transferability through a set of CG bead types that can be used to easily construct new molecules, while retaining the benefits of a structure-based parametrization.

Data-driven discovery of cardiolipin-selective small molecules by computational active learning

Subtle variations in the lipid composition of mitochondrial membranes can have a profound impact on mitochondrial function. The inner mitochondrial membrane contains the phospholipid cardiolipin, which has been demonstrated to act as a biomarker for a number of diverse pathologies. Small molecule dyes capable of selectively partitioning into cardiolipin membranes enable visualization and quantification of the cardiolipin content. Here we present a data-driven approach that combines a deep learning-enabled active learning workflow with coarse-grained molecular dynamics simulations and alchemical free energy calculations to discover small organic compounds able to selectively permeate cardiolipin-containing membranes. By employing transferable coarse-grained models we efficiently navigate the all-atom design space corresponding to small organic molecules with molecular weight less than ≈500 Da. After direct simulation of only 0.42% of our coarse-grained search space we identify molecules with considerably increased levels of cardiolipin selectivity compared to a widely used cardiolipin probe 10-N-nonyl acridine orange. Our accumulated simulation data enables us to derive interpretable design rules linking coarse-grained structure to cardiolipin selectivity. The findings are corroborated by fluorescence anisotropy measurements of two compounds conforming to our defined design rules. Our findings highlight the potential of coarse-grained representations and multiscale modelling for materials discovery and design.

Automated Coarse-Grained Mapping Algorithm for the Martini Force Field and Benchmarks for Membrane-Water Partitioning

With a view to high-throughput simulations, we present an automated system for mapping and parameterizing organic molecules for use with the coarse-grained Martini force field. The method scales to larger molecules and a broader chemical space than existing schemes. The core of the mapping process is a graph-based analysis of the molecule's bonding network, which has the advantages of being fast, general, and preserving symmetry. The parameterization process pays special attention to coarse-grained beads in aromatic rings. It also includes a method for building efficient and stable frameworks of constraints for molecules with structural rigidity. The performance of the method is tested on a diverse set of 87 neutral organic molecules and the ability of the resulting models to capture octanol-water and membrane-water partition coefficients. In the latter case, we introduce an adaptive method for extracting partition coefficients from free-energy profiles to take into account the interfacial region of the membrane. We also use the models to probe the response of membrane-water partitioning to the cholesterol content of the membrane.

Data-driven equation for drug-membrane permeability across drugs and membranes

Drug efficacy depends on its capacity to permeate across the cell membrane. We consider the prediction of passive drug-membrane permeability coefficients. Beyond the widely recognized correlation with hydrophobicity, we additionally consider the functional relationship between passive permeation and acidity. To discover easily interpretable equations that explain the data well, we use the recently proposed sure-independence screening and sparsifying operator (SISSO), an artificial-intelligence technique that combines symbolic regression with compressed sensing. Our study is based on a large in silico dataset of 0.4 × 10⁶ small molecules extracted from coarse-grained simulations. We rationalize the equation suggested by SISSO via an analysis of the inhomogeneous solubility-diffusion model in several asymptotic acidity regimes. We further extend our analysis to the dependence on lipid-membrane composition. Lipid-tail unsaturation plays a key role but surprisingly contributes stepwise rather than proportionally. Our results are in line with previously observed changes in permeability, suggesting the distinction between liquid-disordered and liquid-ordered permeation. Together, compressed sensing with analytically derived asymptotes establish and validate an accurate, broadly applicable, and interpretable equation for passive permeability across both drug and lipid-tail chemistry.

Physics-Inspired Structural Representations for Molecules and Materials

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

Machine learning of free energies in chemical compound space using ensemble representations: Reaching experimental uncertainty for solvation

Free energies govern the behavior of soft and liquid matter, and improving their predictions could have a large impact on the development of drugs, electrolytes, or homogeneous catalysts. Unfortunately, it is challenging to devise an accurate description of effects governing solvation such as hydrogen-bonding, van der Waals interactions, or conformational sampling. We present a Free energy Machine Learning (FML) model applicable throughout chemical compound space and based on a representation that employs Boltzmann averages to account for an approximated sampling of configurational space. Using the FreeSolv database, FML's out-of-sample prediction errors of experimental hydration free energies decay systematically with training set size, and experimental uncertainty (0.6 kcal/mol) is reached after training on 490 molecules (80% of FreeSolv). Corresponding FML model errors are on par with state-of-the art physics based approaches. To generate the input representation for a new query compound, FML requires approximate and short molecular dynamics runs. We showcase its usefulness through analysis of solvation free energies for 116k organic molecules (all force-field compatible molecules in the QM9 database), identifying the most and least solvated systems and rediscovering quasi-linear structure-property relationships in terms of simple descriptors such as hydrogen-bond donors, number of NH or OH groups, number of oxygen atoms in hydrocarbons, and number of heavy atoms. FML's accuracy is maximal when the temperature used for the molecular dynamics simulation to generate averaged input representation samples in training is the same as for the query compounds. The sampling time for the representation converges rapidly with respect to the prediction error.

Swarm-CG: Automatic Parametrization of Bonded Terms in MARTINI-Based Coarse-Grained Models of Simple to Complex Molecules via Fuzzy Self-Tuning Particle Swarm Optimization

We present Swarm-CG, a versatile software for the automatic iterative parametrization of bonded parameters in coarse-grained (CG) models, ideal in combination with popular CG force fields such as MARTINI. By coupling fuzzy self-tuning particle swarm optimization to Boltzmann inversion, Swarm-CG performs accurate bottom-up parametrization of bonded terms in CG models composed of up to 200 pseudo atoms within 4-24 h on standard desktop machines, using default settings. The software benefits from a user-friendly interface and two different usage modes (default and advanced). We particularly expect Swarm-CG to support and facilitate the development of new CG models for the study of complex molecular systems interesting for bio- and nanotechnology. Excellent performances are demonstrated using a benchmark of 9 molecules of diverse nature, structural complexity, and size. Swarm-CG is available with all its dependencies via the Python Package Index (PIP package: swarm-cg). Demonstration data are available at: www.github.com/GMPavanLab/SwarmCG.

Is preservation of symmetry necessary for coarse-graining?

This work investigates if preserving the symmetry of the underlying molecular graph of a given molecule when choosing a coarse-grained (CG) mapping significantly affects the CG model accuracy.