TOPOLOGICAL AND NONLINEAR PROPERTIES OF LIGAND-RECEPTOR SYSTEMS
M. Bounias, A. Bonaly · Journal of Biological Systems · 1996
Ligand-receptor (L-R) interactions involving substrate-enzyme and hormone-receptor systems, obey complex processes. Many parameters are not easily addressed in classical kinetic approaches; most are generally based on the probabilistic mass-action law and equilibrium constants. We describe the system in terms of tessellation of the reactional space with balls B(x, Γ) centered on the reactive species and whose radius (Γ), used as a scaling unit, is derived from the Hausdorff distance η=dist(L, R). This value is altered by a set of corrective terms representing interactions with inert and non-reactive species present in the medium, the influence of particular cell factors including heterogeneous phase conditions, and metabolic dissipation of the product. Topological properties have been studied for nonlinear pairing function governing the distance between two species, and the fractal dimension of the system is linked with its Bouligand-Minkowski dimension. The set of instant state equations of the system includes a chain of transfer matrices accounting for the linear phase of catalytic functions. An alternative set of iterative functions providing a complete metric description of the system in its topological definition space, exhibits similarities with the equations of the Mandelbrot sets family. Experimental confirmation that the major parameters (Vmax, S50 and Hill coefficient) are polyphasic functions of time rather than constants was obtained for honeybees haemolymph α-glucosidases.