Chemical reactions inside cells are generally considered to happen within fixed-size compartments. However, cells and their compartments are highly dynamic. Thus, such stringent geometrical assumptions may not reflect biophysical reality, and can highly bias conclusions from simulation studies. In this work, we present an intuitive algorithm for particle-based diffusion in and on moving boundaries, for both point particles and spherical particles. We first benchmark our proposed stochastic method against solutions of partial differential equations in appropriate scenarios, and further demonstrate that moving boundaries can give rise to super-diffusive motion as well as time-inhomogeneous reaction rates. Finally, we conduct a numerical experiment representing photobleaching of diffusing fluorescent proteins in dividing Saccharomyces cerevisiae cells to demonstrate that moving boundaries might cause important effects neglected in previously published studies of cell compartmentalization.
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