Statistics of Reaction Flux and Dynamical Activity Associated with a Diffusion-Influenced Ligand-Binding Reaction

In this paper, we consider a macromolecule with two competitive binding sites where a ligand can bind to and gives rise to a unicyclic reaction network consisting of four states-(i) a single state with both binding sites vacant, (ii) two states with one bound site and one free binding site, and (iii) an another single state with both sites occupied. We obtain probability densities of the time-integrated current along the clockwise direction and the dynamical activity or mean number of jumps between different states for finite times at a fast diffusion limit. On the other hand, in the diffusion-limited case, ligand diffusion between the two binding sites directly connects the mono-ligated states-changing the reaction scheme. Addition of the new reaction channel alters the precision of ligand occupancy to a single site, the mean dynamical activity, and the mean entropy production rate. All of these quantities are calculated with varying degrees of competition between the two sites for ligands, and we find that increase in the competition between the two sites decreases all above-mentioned additive functionals. The upper bound of precision associated with a single-site ligand occupancy for a diffusion-influenced reaction network is set by the mean dynamical activity (mean entropy production rate) at small (large) ligand concentrations at the steady-state limit.