Van der Waals Perspective on Coarse-Graining: Progress toward Solving Representability and Transferability Problems

Abstract

Low-resolution coarse-grained (CG) models provide the necessary efficiency for simulating phenomena that are inaccessible to more detailed models. However, in order to realize their considerable promise, CG models must accurately describe the relevant physical forces and provide useful predictions. By formally integrating out the unnecessary details from an all-atom (AA) model, "bottom-up" approaches can, at least in principle, quantitatively reproduce the structural and thermodynamic properties of the AA model that are observable at the CG resolution. In practice, though, bottom-up approaches only approximate this "exact coarse-graining" procedure. The resulting models typically reproduce the intermolecular structure of AA models at a single thermodynamic state point but often describe other state points less accurately and, moreover, tend to provide a poor description of thermodynamic properties. These two limitations have been coined the "transferability" and "representability" problems, respectively. Perhaps, the simplest and most commonly discussed manifestation of the representability problem regards the tendency of structure-based CG models to dramatically overestimate the pressure. Furthermore, when these models are adjusted to reproduce the pressure, they provide a poor description of the compressibility. More generally, it is sometimes suggested that CG models are fundamentally incapable of reproducing both structural and thermodynamic properties. After all, there is no such thing as a "free lunch"; any significant gain in computational efficiency should come at the cost of significant model limitations. At least in the case of structural and thermodynamic properties, though, we optimistically propose that this may be a false dichotomy. Accordingly, we have recently re-examined the "exact coarse-graining" procedure and investigated the intrinsic consequences of representing an AA model in reduced resolution. These studies clarify the origin and inter-relationship of representability and transferability problems. Both arise as consequences of transferring thermodynamic information from the high resolution configuration space and encoding this information into the many-body potential of mean force (PMF), that is, the potential that emerges from an exact coarse-graining procedure. At least in principle, both representability and transferability problems can be resolved by properly addressing this thermodynamic information. In particular, we have demonstrated that "pressure-matching" provides a practical and rigorous means for addressing the density dependence of the PMF. The resulting bottom-up models accurately reproduce the structure, equilibrium density, compressibility, and pressure equation of state for AA models of molecular liquids. Additionally, we have extended this approach to develop transferable potentials that provide similar accuracy for heptane-toluene mixtures. Moreover, these potentials provide predictive accuracy for modeling concentrations that were not considered in their parametrizatio...

Coarse-grained Force Fields from the Perspective of Statistical Mechanics: Better Understanding the Origins of a MARTINI Hangover

“…ln ( ). [5][6]16 The PMF is in fact defined as a conditional free energy, so it must be decomposable into the two contributions We will calculate a midplane-projection of the pairwise PMF in a single leaflet and then its decomposition into the enthalpic and entropic contributions (see Methods for further computational details). 16 This decomposition of the PMF gives direct insight into the nature of the temperature dependence and provides a deeper understanding of the missing or incorrect entropic and enthalpic contributions to the MARTINI CG interactions compared with the underlying mapped atomistic scale results.…”

“…Representability issues in CG models, often more opaque, are related to the roles of resolution and the parameterization scheme in defining observables and calculating them. [6][7][8] We seek here to highlight the nature of representability as it applies to a particular lipid observable, the height fluctuation spectrum. The spectrum is calculated through a discrete Fourier transform of the midplane lipid bilayer shown below: [17][18]…”

“…Generally, the transferability problem relates to the application of a CG model to conditions away from the original parameterization conditions, and it limits their extensibility to different thermodynamic state points. [5][6] Separately, representability issues are rooted in key mathematical differences in the CG versus all-atom expressions. 7 Perhaps the most common example is that bottom-up CG models may incorrectly capture the pressure, isothermal compressibility, and/or certain other observables due to a difficulty in transitioning the definitions of observables between the all-atom and CG representations.…”

Molecular simulations of cellular processes

“…The number of beads and their positions within the molecule are chosen according to considerations about the spatiotemporal scales to be explored and the physicochemical features deemed important to the cellular processes (Tozzini 2005;Rudzinski and Noid 2014;Dunn et al 2016).…”

Multiscale Modeling Scheme for Simulating Polymeric Melts: Application to Poly(Ethylene Oxide)

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