Inter-Intra Molecular Dynamics as an Iterated Function System

TL;DR

This paper models the internal dynamics of molecules in crowded biological environments as an iterated function system, revealing how frequent interactions induce discrete, Cantor set-like states and stabilize multiple configurations.

Contribution

It introduces a self-consistent IFS framework to analyze molecular dynamics under frequent collisions, linking discrete state formation to biological systems.

Findings

Increased collision frequency leads to discrete state formation.

Discrete states resemble a Cantor set structure.

Interactions stabilize multiple molecular states.

Abstract

The dynamics of units (molecules) with slowly relaxing internal states is studied as an iterated function system (IFS) for the situation common in e.g. biological systems where these units are subjected to frequent collisional interactions. It is found that an increase in the collision frequency leads to successive discrete states that can be analyzed as partial steps to form a Cantor set. By considering the interactions among the units, a self-consistent IFS is derived, which leads to the formation and stabilization of multiple such discrete states. The relevance of the results to dynamical multiple states in biomolecules in crowded conditions is discussed.