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

A mapping of a macromolecule is a prescription to construct a simplified representation of the system in which only a subset of its constituent atoms is retained. As the specific choice of the mapping affects the analysis of all-atom simulations as well as the construction of coarse-grained models, the characterisation of the mapping space has recently attracted increasing attention. We here introduce a notion of scalar product and distance between reduced representations, which allows the study of the metric and topological properties of their space in a quantitative manner. Making use of a Wang-Landau enhanced sampling algorithm, we exhaustively explore such space, and examine the qualitative features of mappings in terms of their squared norm. 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, which mark the boundaries between qualitatively different reduced representations of the same molecule. Graphicabstract

Automated summary

The study introduces a method for calculating scalar product and distance between reduced representations of macromolecules, which allows for quantitative investigation of the metric and topological properties of their space. The research discovers the presence of discontinuous phase transitions in mapping space, marking the boundaries between qualitatively different reduced representations of the same molecule.