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