Stochastic or Not? Method To Predict and Quantify the Stochastic Effects on the Association Reaction Equilibria in Nanoscopic Systems

The stochastic nature of chemical reaction and impact of the stochasticity on their evolution is soundly documented. Both theoretical predictions and emerging experimental evidence indicate the influence of stochastic effects on the equilibrium state of association reaction. In this work simple mathematical formulas are introduced to estimate these effects. First, the dependence of the ratio of observed reactants (apparent association constant, equivalent of macroscopic association constant in stochastic analysis) on the volume and the number of molecules of reagents is discussed and the limiting factors of this effect are shown. Next, the apparent association constant is approximated for nanoscale systems by closed-form formulas derived for this purpose. Finally, an estimation for the macroscopic constant value from the apparent one is provided and validated on the published experimental data. This work was inspired by chemical reactions occurring in biological compartments, but the results can be used for all systems belonging to the stochastic regime of chemical reactions.