BPS2026 – Small confinement volume and reaction rates

In the standard elementary theory of reaction kinetics, the rate of product formation does not depend upon the volume confining the reaction; it only depends on average concentrations and constant rate parameters. However, even in simple reactions such as A + B = C, several volume and spatially related factors could affect rates, such as localized depletion zones, a bias toward rebinding immediately after release, large stochastic fluctuations of local concentrations with low reactant numbers, and reflection at the outer boundary. We employ a stochastic molecular simulation approach to see if confinement of A and B into a very small volume affects the rate of production of C. For simplicity, the geometry is a small spherical target A (radius a) centered in a reflecting shell (radius b where b > a) with reactant B diffusing in the intermediate space. An analytical theory for such a simple setup can be quite complex, often involving mathematical series that only slowly converge. In our simulations, whenever a molecule of B encounters the surface of A, it may bind with a specified on-probability and remains bound for a time determined by a constant off-probability per unit time. Successful binding is allowed to occur only if the target A is not already bound with another B (i.e., a target A accommodates only one B at a time). After either an unsuccessful binding attempt or a recently released successful binding, B resumes its random diffusion starting from near the surface of A. Starting from zero occupancy at time t = 0, our stochastic simulations show an increasing rate of occupancy of A vs. time t as the confinement volume is made small (while always keeping the concentration of B constant). The relevance to prebiotic reaction kinetics in abiotically generated small volumes, and to small-volume subcellular organelles are discussed.