Sample size dependence of tagged molecule dynamics in steady-state networks with bimolecular reactions: Cycle times of a light-driven pump

TL;DR

This study investigates how the size of steady-state reaction networks influences the dynamics of tagged molecules, revealing robustness in cycle times due to rate-determining unimolecular processes, with implications for small chemical systems.

Contribution

It introduces a framework for simulating tagged molecule dynamics in both macroscopic and small-volume stochastic regimes, applied to a light-driven supramolecular pump.

Findings

Average cycle times are robust against system size.

Unimolecular rate processes stabilize small-system behavior.

Cycle completion times are unaffected by molecular fluctuations.

Abstract

Here, steady-state reaction networks are inspected from the viewpoint of individual tagged molecules jumping among their chemical states upon the occurrence of reactive events. Such an agent-based viewpoint is useful for selectively characterizing the behavior of functional molecules, especially in the presence of bimolecular processes. We present the tools for simulating the jump dynamics both in the macroscopic limit and in the small-volume sample where the numbers of reactive molecules are of the order of few units with an inherently stochastic kinetics. The focus is on how an ideal spatial "compartmentalization" may affect the dynamical features of the tagged molecule. Our general approach is applied to a synthetic light-driven supramolecular pump composed of ring-like and axle-like molecules that dynamically assemble and disassemble, originating an average ring-through-axle directed motion under constant irradiation. In such an example, the dynamical feature of interest is the completion time of direct/inverse cycles of tagged rings and axles. We find a surprisingly strong robustness of the average cycle times with respect to the system's size. This is explained in the presence of rate-determining unimolecular processes, which may, therefore, play a crucial role in stabilizing the behavior of small chemical systems against strong fluctuations in the number of molecules.