Response Theory for Non-Stationary Ligand-Receptor Interaction and a Solution to the Growth Signal Firing Problem

A nonlinear, microscopic response theory, with a solution to the growth signal firing problem, is derived from a non-stationary ligand receptor interaction. The predicted dose-response curve, which is a logistic type equation, is in striking agreement with the assessed growth data from the cell line ML4-144 of a leukemic Gibbon ape. The predicted slope, which is a non-trivial result, obtained only after summation over all orders of ligand-receptor interaction, agrees almost exactly with the experimentally assessed slope. As a direct consequence of the initial constraints, the intermolecular force becomes a function of the concentrations of the growth factor interleukin-2 and its receptor, and therefore changes sign at the definite number of receptor occupancies required to start DNA replication. This quantal threshold dynamics, concomitantly alternating with the reactant concentrations, constitutes the growth signal firing mechanism, and thereby clarifies one of the most elementary life functions which begins with the irrevocable decision to replicate DNA. The phenomenon of life is thus explained here in terms of “quantum” fluctuations, without which the transition of the S phase would not occur. The actual “quantum” of receptor activation could be identified only after a spontaneous symmetry breakdown of the model. Withdrawal from the cell cycle is explained in a similar way. Thus, in a first order approximation, the model proposed complies with all observanda and does not suffer from inconsistencies typical for stationary state type models such as a scale (EC50) defined by the affinity constant (K) which displaces the theoretically derived response curve from that assessed by several orders of magnitude.