MODELING AND ANALYSIS OF TIME-LAGS IN SOME BASIC PATTERNS OF CELL-PROLIFERATION

In this paper, we present a systematic approach for obtaining qualitat ively and quantitatively correct mathematical models of some biologica l phenomena with time-lags. Features of our approach are the developme nt of a hierarchy of related models and the estimation of parameter va lues, along with their non-linear biases and standard deviations, for sets of experimental data. We demonstrate our method of solving parame ter estimation problems for neutral delay differential equations by an alyzing some models of cell growth that incorporate a time-lag in the cell division phase. We show that these models are more consistent wit h certain reported data than the classic exponential growth model. Alt hough the exponential growth model provides estimates of some of the g rowth characteristics, such as the population-doubling time, the time- lag growth models can additionally provide estimates of: (i) the fract ion of cells that are dividing, (ii) the rate of commitment of cells t o cell division, (iii) the initial distribution of cells in the cell c ycle, and (iv) the degree of synchronization of cells in the (initial) cell population.