Equilibrium probability distribution for number of bound receptor-ligand complexes

The phenomenon of molecular binding, where two molecules, referred to as a receptor and ligand, bind together form ligand-receptor complex, is ubiquitous in biology essential for the accurate functioning all life-sustaining processes. probability single forming complex with any one L surrounding ligand molecules at thermal equilibrium can be derived from partition function obtained Gibbs-Boltzmann distribution. We extend this approach system consisting R receptors ligands derive density p r ; , find bound receptor-ligand complexes equilibrium. This extension allows us illustrate aspects problem which are not apparent problem, namely, (a) symmetry expected distribution number under exchange (b) chemical kinetic equations has an exact correspondence maximum probable value expression L. fluctuations present practically relevant sensing application benefits knowledge ( ).