Mathematical method for determining the average number of times ligands are bound to cells

James Bogert
Northern Arizona University

Through flow cytometry, it has become feasible to measure the percent of surface receptors occupied on a cell and the percent of a multivalent ligand in the solution that is bound to a cell. From these results, it is possible to determine the equilibrium constants for ligand-receptor aggregates. From these equilibrium constants, one calculate the distribution of receptor aggregates on the surface of the cell, which can then be manipulated to give the average number of receptors that are bound to each ligand. However, this information does not shed any light on the rate constants associated with the ligand-receptor chemical bonds. We hypothesized that the same average number of receptors bound to each ligand can be calculated taking advantage of the ligand-receptor rate constants. In fact we were able to derive a mathematical method for determining the average number of times each ligand is bound (within a certain error range) given the half life of a ligand-receptor bond, and the time it takes to liberate a certain fraction of the ligand in the presence of an inhibitor. This method has applications to research in many areas of biochemistry, microbiology, and immunology. We will begin conducting experiments utilizing a rapid mixing device attached to a cytometer, the data of which will be cross-checked against our mathematical predictions. The data collected from these experiments can be applied to the model and help us gain better understanding of ligand receptor interactions.