Stochasticity of the transfer of reactant molecules between nano-reactors affecting the reversible association A + B ⇆ C

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Abstract
Theoretical analysis and computer simulations (Monte Carlo and numerical integration of differential equations) indicate that the statistical effect of a small number of reacting molecules is affected by transfer of reagent molecules between nanoreactors (droplets in this study). As a model reaction, a simple reversible association A + B ⇆ C was chosen, which was studied previously without reagent transfer processes. For sufficiently fast exchange of reactant molecules and a sufficiently high number of nanoreactors, the studied systems virtually do not differ from large volume systems if overall kinetics and thermodynamics of the chemical process are concerned. However, if either reagent molecule exchange is not fast or the number of exchanging nanoreactors is low, then the stochastic effect is clearly visible, influencing the kinetics of reaching reaction equilibrium. In systems with a low number of nanoreactors, the apparent (average) equilibrium constant is affected as well. The distribution of reactant molecules in the nanoreactors is governed by stochastic processes, dependent on stochastic rate constants of all processes, chemical as well as physical (transfer of molecules outside and into droplets). When accumulation of reactant molecules in the continuous phase cannot be neglected, then the partition coefficients of reactants between the continuous and dispersed phases have to be taken into account. Distributions of reactant molecules described in the paper for systems composed of few nanoreactors can be especially important for some biochemical processes in living cells or devised corresponding artificial reactors. If the reactant molecules predominate in a continuous phase, then the kinetics and overall conversion of reversible association may be significantly affected by the presence of the dispersed phase and its catalytic behavior can be observed. It has been shown that Monte Carlo simulations, applying a devised simple algorithm, give reliable results, allowing theoretical studies of nanoscale-droplet systems.
Funding Information
  • National Science Centre (2018-2019)

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