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 membrane by means of all-atom molecular dynamics simulations is often hampered by sampling issues. A multiscale approach to conformational sampling was recently proposed by Bereau and Kremer (2016). It aims at accelerating the sampling of the atomistic conformational space by means of a systematic backmapping of coarse-grained snapshots. In this work, we first analyze the efficiency of this method by comparing its predictions for propanol insertion into a 1,2-Dimyristoyl-sn-glycero-3-phosphocholine membrane (DMPC) against reference atomistic simulations. The method is found 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 in affecting the reliability of the method in the case of a 1,2-Dioleoyl-sn-glycero-3-phosphocholine membrane (DOPC). We find that the accuracy of the results is tightly connected to the presence a good configurational overlap between the coarse-grained and atomistic models---a general requirement when developing multiscale simulation methods.Comment: 6 pages, 5 figure

Coarse-grained models for polymer solutions and colloid-polymer mixtures

Coarse-grained models are a very powerful ---and sometimes necessary--- tool in the analysis of the thermodynamic properties of macromolecular fluids. In these models, most of the original, microscopic degrees of freedom are integrated out and each macromolecule is mapped onto a set of effective sites, mutually interacting by means of appropriate intermolecular and intramolecular potentials. Depending on the number of sites n chosen, each macromolecule can be represented as a soft monoatomic molecule (n=1), or as a soft n-atomic molecule (n>1). The complexity of determining the complete set of effective interactions among the coarse-grained sites is such that an exact mapping is unfeasible in practice, hence approximations must be introduced, which always generate a lack of consistency between the original and the coarse-grained model. In this thesis, we apply coarse-graining strategies to the investigation of the universal, large scale and thermodynamic properties of polymer solutions and colloid-polymer mixtures, for two different polymer architectures: linear chains and star polymers. We begin the discussion by briefly summarizing the main concepts of statistical mechanics and polymer physics, in a general fashion. We then revise the formalism behind structure-based coarse-graining procedures, both single-site and multi-site, critically analyzing their limits of validity and the methods proposed in the literature to extend them. Thereafter, we determine the accuracy of coarse-grained, single-site mappings in reproducing the correct thermodynamic behavior of solutions of linear chains and colloid-linear chain mixtures, for different average polymer-to-colloid size ratios. In conclusion, we discuss coarse-grained models for star polymer solutions in good solvents. We introduce a new multi-site model for star polymers, whose validity should extend up to the semidilute regime, and compare its predictions for the thermodynamic properties of the system with those obtained by means of single-site models

Comparing different coarse-grained potentials for star polymers

We compare different coarse-grained models for star polymers. We find that phenomenological models inspired by the Daoud-Cotton model reproduce quite poorly the thermodynamics of these systems, even if the potential is assumed to be density dependent, as done in the analysis of experimental results. We also determine the minumum value fc of the functionality of the star polymer for which a fluid-solid transition occurs. By applying the Hansen-Verlet criterion we find 35 < fc < 40. This result is confirmed by an analysis based on the modified (reference) hypernetted chain method and is qualitatively consistent with previous work.Comment: 9 pages. In the new version, comments added and a few typos corrected. To appear in J. Chem. Phy

Integral-equation analysis of single-site coarse-grained models for polymer-colloid mixtures

We discuss the reliability of integral-equation methods based on several commonly used closure relations in determining the phase diagram of coarse-grained models of soft-matter systems characterized by mutually interacting soft and hard-core particles. Specifically, we consider a set of potentials appropriate to describe a system of hard-sphere colloids and linear homopolymers in good solvent, and investigate the behavior when the soft particles are smaller than the colloids, which is the regime of validity of the coarse-grained models. Using computer-simulation results as a benchmark, we find that the hypernetted-chain approximation provides accurate estimates of thermodynamics and structure in the colloid-gas phase in which the density of colloids is small. On the other hand, all closures considered appear to be unable to describe the behavior of the mixture in the colloid-liquid phase, as they cease to converge at polymer densities significantly smaller than those at the binodal. As a consequence, integral equations appear to be unable to predict a quantitatively correct phase diagram.Comment: 16 pages, 11 figures, 3 table

Coarse-graining polymer solutions: a critical appraisal of single- and multi-site models

We critically discuss and review the general ideas behind single- and multi-site coarse-grained (CG) models as applied to macromolecular solutions in the dilute and semi-dilute regime. We first consider single-site models with zero-density and density-dependent pair potentials. We highlight advantages and limitations of each option in reproducing the thermodynamic behavior and the large-scale structure of the underlying reference model. As a case study we consider solutions of linear homopolymers in a solvent of variable quality. Secondly, we extend the discussion to multi-component systems presenting, as a test case, results for mixtures of colloids and polymers. Specifically, we found the CG model with zero-density potentials to be unable to predict fluid-fluid demixing in a reasonable range of densities for mixtures of colloids and polymers of equal size. For larger colloids, the polymer volume fractions at which phase separation occurs are largely overestimated. CG models with density-dependent potentials are somewhat less accurate than models with zero-density potentials in reproducing the thermodynamics of the system and, although they presents a phase separation, they significantly underestimate the polymer volume fractions along the binodal. Finally, we discuss a general multi-site strategy, which is thermodynamically consistent and fully transferable with the number of sites, and that allows us to overcome most of the limitations discussed for single-site models.Comment: 23 pages, 9 figures, 4 table

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.Comment: 8 pages, 6 figures. Typos fixed, minor correction

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 non-uniform 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 an 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---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.Comment: 9 pages, 5 figure

On the search of minimum information loss in coarse-grained modelling of biomolecules

The computational resources required by atomistic simulations of biomolecular systems still limit their applicability to relatively short time and length scales, at odds with those typically characterising biological processes. By integrating out most of the microscopic degrees of freedom in favor of a description in terms of few sites interacting through effective potentials, coarse-grained (CG) models constitute a powerful instrument for broadening the class of accessible phenomena, at the same time providing accurate results [1]. Also an exact CG procedure, however, inherently comes at a price: a loss of information, quantified by an increase in entropy, arising when a system is observed through "CG glasses" [2]. Interestingly, this loss only depends on the mapping, i.e., the sites one employs to represent the system at the CG level, which are often a priori selected only based on physical intuition [3]. Several questions follow: how wide and diverse is the space of possible CG mappings of a biomolecule? Within this space, are there representations that minimise the information loss, and do these "privileged" mappings give hints on the underlying biological processes? In this work, we address these topics by first characterising the space of CG representations of a system through the definition of a distance between mappings. Subsequently, we develop a workflow enabling to estimate the increase in entropy of a protein arising from CG'ing. Finally, we show that minimising this quantity over the space of possible CG representations suggests a connection between the biological relevance of a chemical fragment composing the biomolecule and the amount of information it contains [4]. [1] R. Menichetti, A. Pelissetto and F. Randisi, J. Chem. Phys. 146, 244908 (2017).[2] J. F. Rudzinski and W. G. Noid, J. Chem. Phys. 135, 214101 (2011).[3] P. Diggins IV et al., J. Chem. Theory Comput. 15, 648 (2019).[4] M. Giulini, et al., J. Chem. Theory Comput. 16, 6795 (2020)