Biomolecular Binding under Confinement: Statistical Predictions of Steric Influence in Absence of Long‐Distance Interactions

Abstract

We propose a theoretical model for the influence of confinement on biomolecular binding at the single-molecule scale at equilibrium, based on the change of the number of microstates (localization and orientation) upon reaction. Three cases are discussed: DNA sequences shorter and longer than the single strain DNA Kuhn length and spherical proteins, confined into a spherical container (liposome, droplet, etc.). The influence of confinement is found to be highly dependent on the molecular structure and significant for large molecules (relative to container size).

Statistical mechanics of dimerizations and its consequences for small systems

“…[4][5][6][7][8][9][10][11][12] Different explanations were put forward that include conformational changes of the unbound molecule(s), non-fluorescent bindings, and missed events due to transient interactions. 13,14 Several theoretical studies proposed that small systems, attributed to be stochastic in nature, are characterized by equilibrium constants different than that observed for a macroscopic system, which attributed to be deterministic. [15][16][17][18][19][20][21][22] Sizedependent equilibrium constant was also advocated by introducing 'nanoconfinement entropic effects on chemical equilibrium' applied only to systems with small number of molecules.…”

Statistical predictions on the encapsulation of single molecule binding pairs into sized-dispersed nanocontainers

“…2,8,31 However, an important application of single molecule encapsulation is the confinement of two types of molecules that can bind to each other. 2,31,[35][36][37][38] In such a case, the simple calculation above does not account for the effect of the binding constant in bulk solution, which is important to determine the probability that the molecular binding pair will be encapsulated together. There appears to be no statistical treatment of this situation, and no description of the effect that the size distribution of the container may have.…”