Kinetics of Ligand Binding to Receptors in the Presence of Multiplicative Noise

The binding of ligands with receptors was theoretically studied in the case when the number of ligands in solution fluctuates under the influence of fluctuations of the external environment. A multiplicative stochastic differential equation has been obtained that describes the time change in the number of ligand-receptor complexes. The average number of ligand-receptor complexes and its variance were calculated. An isotherm of the binding of ligands to receptors was obtained. It has been shown that the presence of multiplicative noise leads to the fact that the process of binding of ligands to receptors becomes threshold—in the region of low concentrations of ligands at a certain ratio between the binding parameters and the intensity of the multiplicative noise, the formation of a ligand-receptor complex does not occur. It has been shown that with increasing ligand concentration, the relaxation time of the average number of ligand-receptor complexes decreases, and with increasing noise intensity it increases. It is also shown that at low values of the external noise intensity, the dispersion is proportional to the external noise intensity and increases linearly with increasing noise intensity.