Modeling of Nanomachine/Micromachine Crowds: Interplay between the Internal State and Surroundings

The
activity of biological cells is primarily based on chemical
reactions and typically modeled as a reaction-diffusion system. Cells
are, however, highly crowded with macromolecules, including a variety
of molecular machines such as enzymes. The working cycles of these
machines are often coupled with their internal motion (conformational
changes). In the crowded environment of a cell, motion interference
between neighboring molecules is not negligible, and this interference
can affect the reaction dynamics through machine operation. To simulate
such a situation, we propose a reaction-diffusion model consisting
of particles whose shape depends on an internal state variable, for
crowds of nano- to micromachines. The interference between nearby
particles is naturally introduced through excluded volume repulsion.
In the simulations, we observed segregation and flow-like patterns
enhanced by crowding out of relevant molecules, as well as molecular
synchronization waves and phase transitions. The presented model is
simple and extensible for diverse molecular machinery and may serve
as a framework to study the interplay between the mechanical stress/strain
network and the chemical reaction network in the cell. Applications
to more macroscopic systems, e.g., crowds of cells, are also discussed.