Application of Mathematical Modeling to Analysis of Nerves Growth Factor Interaction with Platelets

In our previous work (N. D. Chekalina et al. Bull. Exp. Biol. Med., 1996, 121, 295–297 [Russian]) we demonstrated the impossibility of applying Scatchard plots to analysis of the interaction of nerve growth factor (NGF) and platelet due to the nonlinearity of these plots. In the present study we assumed that the cause of nonlinear Scatchard plots is a nonequilibrium interaction of NGF and platelets. With this assumption we used mathematical modeling to define the parameters of the interaction of NGF with platelets. We show that our assumption makes it possible to describe experimental data with a maximal error of 7% using a model with one type of noncooperative binding site and one type of ligand. Due to the maximal error value we did not take into account more complicated models of ligand–receptor interaction. The conjugate gradient method was used to define the parameters of NGF interaction with platelets. The concentration of binding sites found is 18.7 fmol/106 cells, and the dissociation constant is 38.4 nM.