Surveying the energy landscape of coarse-grained mappings

Abstract

Simulations of soft materials often adopt low-resolution coarse-grained (CG) models. However, the CG representation is not unique and its impact upon simulated properties is poorly understood. In this work, we investigate the space of CG representations for ubiquitin, which is a typical globular protein with 72 amino acids. We employ Monte Carlo methods to ergodically sample this space and to characterize its landscape. By adopting the Gaussian network model as an analytically tractable atomistic model for equilibrium fluctuations, we exactly assess the intrinsic quality of each CG representation without introducing any approximations in sampling configurations or in modeling interactions. We focus on two metrics, the spectral quality and the information content, that quantify the extent to which the CG representation preserves low-frequency, large-amplitude motions and configurational information, respectively. The spectral quality and information content are weakly correlated among high-resolution representations but become strongly anticorrelated among low-resolution representations. Representations with maximal spectral quality appear consistent with physical intuition, while low-resolution representations with maximal information content do not. Interestingly, quenching studies indicate that the energy landscape of mapping space is very smooth and highly connected. Moreover, our study suggests a critical resolution below which a “phase transition” qualitatively distinguishes good and bad representations.

EXCOGITO, an Extensible Coarse-Graining Toolbox for the Investigation of Biomolecules by Means of Low-Resolution Representations

“…The notions of norm, cosine, and distance for coarse-grained representations have been introduced in ref , where these basic quantities have been employed to characterize the metric properties of the mapping space of specific proteins. In that work, it was shown that the mapping space is extremely diverse; that the mappings in it can be grouped according to features that correlate with the structure of the underlying protein; and that in this space a phase transition occurs that is analogous to a gas–liquid phase transition on the lattice, as it was observed by other authors as well. , …”

“…Recent works ,,,, have emphasized the fundamental importance of the mapping between high- and low-resolution descriptions of a system, whose origins are to be found in the renormalization group approach to critical phenomena. While significant efforts have been directed toward developing CG force fields, one can observe in the literature a notable gap in the examination of the properties of mappings themselves, which nonetheless a few authors have started to address.…”

“…This approach relies on a simple yet powerful idea, namely, that by losing resolution , e.g., by looking at the system in terms of fewer atoms than the total, we gain information about the processes that take place at a more global scale. Since a few years, this idea is put forward by various authors; ,,,− here, we do not aim to review the results obtained so far nor to discuss the theoretical and practical aspects of its implementation. Rather, we illustrate the software that we developed to put this idea to work.…”

“…More specifically, given a mapping as the selection of a particular subgroup of elements (the retained atoms) from a set (the whole molecule), we can ask ourselves questions about the total number of mappings, the amount of them sharing the same qualitative and quantitative features, and the relationship that exists between mapping groups with given features and the structural properties of the system on which the selection takes place. These questions have been addressed in various recent works; − here, we only report those results obtained by some of us through the application of the methods implemented in EXCOGITO.…”

“…In that work, it was shown that the mapping space is extremely diverse; that the mappings in it can be grouped according to features that correlate with the structure of the underlying protein; and that in this space a phase transition occurs that is analogous to a gas−liquid phase transition on the lattice, as it was observed by other authors as well. 35,36 Recently, the concepts of mapping space metric have been applied by Giulini and co-workers to the analysis of interface residues in protein complexes. 39 By exploiting the equivalence between protein-specific interfaces and coarse-grained mappings, eqs 17 and 18 can be used to quantify the similarity between different interfaces and to cluster them in binding surfaces.…”