Stochastic description of the ligand-receptor interaction of biologically active substances at extremely low doses.

Signalling molecules can be effective at extraordinarily low concentrations (down to attomolar levels). To handle such cases, probabilistic methods have been used to describe the formal kinetics of action of biologically active substances in these low doses, although it has been necessary to review what is meant by such a term. The mean numbers of transformed/degraded molecules and their dispersions were calculated for the possible range of ligand-receptor binding schemes. We used both analytical equations and numerical simulations to calculate the coefficients of variation (ratio of standard deviation to mean) and demonstrated that the distribution of the coefficient is highly dependent on the reaction scheme. It may, therefore, be used as an additional factor for discriminating between cooperative and noncooperative models of ligand-receptor interaction over extreme ranges of ligand dilution. The relevance to signalling behaviour is discussed.