Consistent and Transferable Force Fields for Statistical Copolymer Systems at the Mesoscale

The statistical trajectory matching (STM) method was applied successfully to derive coarse grain (CG) models for bulk properties of homopolymers. The extension of the methodology for building CG models for statistical copolymer systems is much more challenging. We present here the strategy for developing CG models for styrene-butadiene-rubber, and we compare the quality of the resulting CG force fields on the structure and thermodynamics at different chemical compositions. The CG models are used through the use of a genuine mesoscopic method called the dissipative particle dynamics method and compared to high-resolution molecular dynamics simulations. We conclude that the STM method is able to produce coarse-grained potentials that are transferable in composition by using only a few reference systems. Additionally, this methodology can be applied on any copolymer system.

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.

Unfolding the prospects of computational (bio)materials modeling

In this perspective communication, we briefly sketch the current state of computational (bio)material research and discuss possible solutions for the four challenges that have been increasingly identified within this community: (i) the desire to develop a unified framework for testing the consistency of implementation and physical accuracy for newly developed methodologies, (ii) the selection of a standard format that can deal with the diversity of simulation data and at the same time simplifies data storage, data exchange, and data reproduction, (iii) how to deal with the generation, storage, and analysis of massive data, and (iv) the benefits of efficient "core" engines. Expressed viewpoints are the result of discussions between computational stakeholders during a Lorentz center workshop with the prosaic title Workshop on Multi-scale Modeling and are aimed at (i) improving validation, reporting and reproducibility of computational results, (ii) improving data migration between simulation packages and with analysis tools, (iii) popularizing the use of coarse-grained and multi-scale computational tools among non-experts and opening up these modern computational developments to an extended user community.

Relative entropy indicates an ideal concentration for structure-based coarse graining of binary mixtures

Many methodological approaches have been proposed to improve systematic or bottom-up coarse-graining techniques to enhance the representability and transferability of the derived interaction potentials. Transferability describes the ability of a coarse-grained (CG) model to be predictive, i.e., to describe a system at state points different from those chosen for parametrization. Whereas the representability characterizes the accuracy of a CG model to reproduce target properties of the underlying reference or fine-grained model at a given state point. In this article, we shift the focus away from methodological aspects and rather raise the question whether we can overcome the disadvantages of a given method in terms of representability and transferability by systematically selecting the state point at which the CG model gets parametrized. We answer this question by applying the inverse Monte Carlo (IMC) approach-a structure-based coarse-graining method-to derive effective interactions for binary mixtures of simple Lennard-Jones (LJ) particles, which are different in size. For such simple systems we indeed can identify a concentration where the derived potentials show the best performance in terms of structural representability and transferability. This specific concentration is identified by computing the relative entropy which quantifies the information loss between different IMC models and the reference LJ model at varying mixture compositions. Further, we show that an IMC model for mixtures of n-hexane and n-perfluorohexane shows the same trend in transferability as the IMC models for the LJ system. All derived models are more transferable in the direction of increasing concentration of the larger-sized compound.

Maximizing the absorption of small cosolutes inside neutral hydrogels: steric exclusion versus hydrophobic adhesion

In this work the equilibrium absorption of nanometric cosolutes (which could represent drugs, reactants, small globular proteins and other kind of biomacromolecules) inside neutral hydrogels is studied. We specially focus on exploring, for different swelling states, the competition between the steric exclusion induced by the cross-linked polymer network constituting the hydrogel, and the solvent-induced short-range hydrophobic attraction between the polymer chains and the cosolute particle. For this purpose, the cosolute partition coefficient is calculated by means of coarse-grained grand canonical Monte Carlo simulations, and the results are compared to theoretical predictions based on the calculation of the excluded and binding volume around the polymer chains. For small hydrophobic attractions or large cosolute sizes, the steric repulsion dominates, and the partition coefficient decreases monotonically with the polymer volume fraction, ϕ_m. However, for large enough hydrophobic attraction strength, the interplay between hydrophobic adhesion and the steric exclusion leads to a maximum in the partition coefficient at certain intermediate polymer density. Good qualitative and quantitative agreement is achieved between simulation results and theoretical predictions in the limit of small ϕ_m, pointing out the importance of geometrical aspects of the cross-linked polymer network, even for hydrogels in the swollen state. In addition, the theory is able to predict analytically the onset of the maximum formation in terms of the details of the cosolute-monomer pair interaction, in good agreement with simulations too. Finally, the effect of the many-body attractions between the cosolute and multiple polymer chains is quantified. The results clearly show that these many-body attractions play a very relevant role determining the cosolute binding, enhancing its absorption in more than one order of magnitude.

Bayesian calibration of coarse-grained forces: Efficiently addressing transferability

Generating and calibrating forces that are transferable across a range of state-points remains a challenging task in coarse-grained (CG) molecular dynamics. In this work, we present a coarse-graining workflow, inspired by ideas from uncertainty quantification and numerical analysis, to address this problem. The key idea behind our approach is to introduce a Bayesian correction algorithm that uses functional derivatives of CG simulations to rapidly and inexpensively recalibrate initial estimates f0 of forces anchored by standard methods such as force-matching. Taking density-temperature relationships as a running example, we demonstrate that this algorithm, in concert with various interpolation schemes, can be used to efficiently compute physically reasonable force curves on a fine grid of state-points. Importantly, we show that our workflow is robust to several choices available to the modeler, including the interpolation schemes and tools used to construct f0. In a related vein, we also demonstrate that our approach can speed up coarse-graining by reducing the number of atomistic simulations needed as inputs to standard methods for generating CG forces.

Evaluation of mapping schemes for systematic coarse graining of higher alkanes

Different levels of coarse-graining are introduced to study the thermodynamic and structural properties of higher alkanes.

The impact of resolution upon entropy and information in coarse-grained models

By eliminating unnecessary degrees of freedom, coarse-grained (CG) models tremendously facilitate numerical calculations and theoretical analyses of complex phenomena. However, their success critically depends upon the representation of the system and the effective potential that governs the CG degrees of freedom. This work investigates the relationship between the CG representation and the many-body potential of mean force (PMF), W, which is the appropriate effective potential for a CG model that exactly preserves the structural and thermodynamic properties of a given high resolution model. In particular, we investigate the entropic component of the PMF and its dependence upon the CG resolution. This entropic component, SW, is a configuration-dependent relative entropy that determines the temperature dependence of W. As a direct consequence of eliminating high resolution details from the CG model, the coarsening process transfers configurational entropy and information from the configuration space into SW. In order to further investigate these general results, we consider the popular Gaussian Network Model (GNM) for protein conformational fluctuations. We analytically derive the exact PMF for the GNM as a function of the CG representation. In the case of the GNM, -TSW is a positive, configuration-independent term that depends upon the temperature, the complexity of the protein interaction network, and the details of the CG representation. This entropic term demonstrates similar behavior for seven model proteins and also suggests, in each case, that certain resolutions provide a more efficient description of protein fluctuations. These results may provide general insight into the role of resolution for determining the information content, thermodynamic properties, and transferability of CG models. Ultimately, they may lead to a rigorous and systematic framework for optimizing the representation of CG models.

Transferability of a coarse-grained atactic polystyrene model: the non-bonded potential effect

In this paper, we construct an efficient and simple coarse grained (CG) model for atactic polystyrene (PS) by using a 1 : 1 mapping scheme at 463 K and 1 atm pressure and derive the corresponding bonded and non-bonded potentials in the CG force field (FF) via a direct Boltzmann inversion approach and a combined structure-based and thermodynamic quantities-based CG method, respectively.

Recent advances in transferable coarse-grained modeling of proteins

Computer simulations are indispensable tools for studying the structure and dynamics of biological macromolecules. Biochemical processes occur on different scales of length and time. Atomistic simulations cannot cover the relevant spatiotemporal scales at which the cellular processes occur. To address this challenge, coarse-grained (CG) modeling of the biological systems is employed. Over the last few years, many CG models for proteins continue to be developed. However, many of them are not transferable with respect to different systems and different environments. In this review, we discuss those CG protein models that are transferable and that retain chemical specificity. We restrict ourselves to CG models of soluble proteins only. We also briefly review recent progress made in the multiscale hybrid all-atom/CG simulations of proteins.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.