MATHEMATICAL MODELLING OF CELLULAR RESPONSES TO EXTERNAL SIGNALS

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Abstract
An empirical mathematical model is proposed to describe the response (growth rate, metabolic activity etc.) of a cell population to various intensities of an external signal (hormone, antibody, pharmacon etc.). The model is based on the assumption that the signal causes the target system to pass consecutively through i=1, …, N distinct population states having response coefficients Ri. Describing the interaction of the system with the signal according to the rules of chemical kinetics by two phenomenological parameters (k - sensitivity, n - cooperativity index) one arrives at a series expansion for Ri which is linear in the Ri’s but nonlinear with respect to k and n (“R-decomposition”). The pattern of expansion coefficients Ri is characteristic of a given signal and can be used to reveal similarities in the responses of the cell population to various signals. A user-friendly microcomputer program has been developed to fit the model equation to experimental data by means of constraint nonlinear regression analysis and to determine all characteristic curve parameters (number and location of extremal values, inflection points etc.). The robustness and benefit of the model is demonstrated by applications to various types of “exotic” dose-reponse-curves obtained from a neutral-red assay of fibroblasts. Similarities between response curves are studied.

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