Heterogeneity Induced Effective Repulsion and Its Effects on Equilibrium Binding Fraction of a Divalent Receptor

We have discussed the effects of microscopic interactions on the shape of plot for the simple receptor model with two heterogeneous binding sites. It is straightforward to generalize the present discussion for the more complex interaction models in which an arbitrary number of bound substrate molecules interact with an arbitrary microscopic potential. Research in this direction is currently under going on. Binding of substrate molecules to a limited number of receptors or binding sites is a ubiquitous phenomenon commonly observed across diverse fields of science. When the binding affinity of binding sites to substrate molecules is homogeneous and the interactions between the bound substrate molecules are negligible, the dependence of the equilibrium fraction of the bound sites on the substrate concentration can be described by the classic Langmuir's model. However, microscopic interactions between substrate molecules in a receptor and heterogeneous affinities of binding sites to substrate molecules make the shape of adsorption isotherm of the receptor significantly distinct from the Langmuir isotherm. Numerous systems of receptors or surfaces were reported to be heterogeneous. The interaction of antibodies with antigens, the gaseous adsorption onto carbon materials and metal-organic framework, and the solute adsorption at heterogeneous interface, constitute only a very few examples of molecular binding to receptors with a distributed affinity. A variety of different theoretical models have been proposed to provide quantitative descriptions of adsorption isotherms of systems with various binding affinity distributions