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

Abstract

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.

Predicting unfolding thermodynamics and stable intermediates for alanine-rich helical peptides with the aid of coarse-grained molecular simulation

“…In this regard, a number of 4 beads-per-amino acid (4bAA) CG models have been previously proposed and studied in order to capture the configurational and aggregation behavior of peptides and proteins in solution [7,16,22]. 4bAA models have primarily been designed to capture qualitative structural features of polypeptide unfolding and self-assembly – e.g., the transition between helix and coil configurations for natively helical polypeptides, the existence of local conformations during unfolding, and the formation of tertiary structures for long poly-peptides [7,16,22].…”

“…4bAA models have primarily been designed to capture qualitative structural features of polypeptide unfolding and self-assembly – e.g., the transition between helix and coil configurations for natively helical polypeptides, the existence of local conformations during unfolding, and the formation of tertiary structures for long poly-peptides [7,16,22]. Previous work from some of the present authors showed that 4bAA models can help one understand the molecular scale interactions that affect the unfolding and self-assembly of Ala-rich peptides in the context of polymer-peptide interactions [7].…”

“…An earlier model was based on that from Bereau and Deserno, which was originally designed to capture structural details of membrane protein assembly [16]. Separately, previous work has shown that the 4bAA level of CG modeling provides an optimal balance between molecular detail, computational accuracy, and computational burden when (poly)peptide unfolding and aggregation are of interest [22]. …”

“…Even though qualitative structural features of the unfolding process are reasonably well captured, the quantitative details such as unfolding free energy values, midpoint unfolding temperatures (T m ), and unfolding enthalpy values obtained from molecular simulations (both CG and atomistic) typically do not match those obtained experimentally [7,16,22–25]. Furthermore, it is common to use molecular simulations in a “hindsight” manner, where the experimental behavior is already known and the simulations are intended to give molecular-scale insight that is beyond the capabilities of the experiment, or to help confirm or refute hypotheses that were based on interpretation of the experimental data.…”

Molecular Dynamics Simulation of High Density DNA Arrays

“…On the CG level, the DNA molecule is typically modeled with three sites per nucleotide [50,[91][92][93][94]. The interactions between CG beads can be obtained either with a top-down approach, i.e., fitted to reproduce key experimental data, especially thermodynamic properties, or with the bottom-up approach, employing methods such as inverse Monte Carlo [95], iterative Boltzmann inversion (IBI) [96], force matching [97][98][99], and relative entropy [100][101][102]. Recently, also the popular MARTINI force field [103] was extended to DNA [104].…”