A mapping space Odyssey: characterising the statistical and metric properties of reduced representations of macromolecules

TL;DR

This paper introduces a rigorous framework for analyzing simplified macromolecular representations using a metric space approach, revealing phase transitions that distinguish different levels of molecular detail.

Contribution

It proposes a novel scalar product and metric space for macromolecular mappings, linking their properties to thermodynamics and uncovering phase transitions in representation space.

Findings

Mapping space exhibits discontinuous phase transitions.

Quantitative relationship between representation complexity and thermodynamics.

A new framework for characterizing simplified molecular models.

Abstract

Simplified representations of macromolecules help in rationalising and understanding the outcome of atomistic simulations, and serve to the construction of effective, coarse-grained models. The number and distribution of coarse-grained sites bears a strict relation with the amount of information conveyed by the representation and the accuracy of the associated effective model; in this work, we investigate this relationship from the very basics: specifically, we propose a rigorous notion of scalar product among mappings, which implies a distance and a metric space of simplified representations. Making use of a Wang-Landau enhanced sampling algorithm, we exhaustively explore the space of mappings, quantifying their qualitative features in terms of their squared norm and relating them with thermodynamical properties of the underlying macromolecule. A one-to-one correspondence with an interacting lattice gas on a finite volume leads to the emergence of discontinuous phase transitions in mapping space that mark the boundaries between qualitatively different representations of the same molecule.