Nazarenko V G
Biofizika. 1976 Mar-Apr;21(2):352-6.
A model of homogenous cell population is analysed, the mitotic activity of which is controled by an inhibitor produced by the cells themselves. While deducing the model it is assumed that the inhibitor concentration is proportional to the population density at some preceding time moment. The density change in time is described by a delay differential equation: dx/dt=alpha x/(1+x(v)(t--0))--x. According to this equation oscillation of cell number may be observed in the population with an increase of the critical value of delay in the mechanism of mitotic activity inhibition. The oscillation period determined analytically in linear approximation equals the quadruplicated time of delay. Numerical integration of the model has shown that the period observed is close to the calculated one.
分析了一个均匀细胞群体模型，其有丝分裂活性由细胞自身产生的一种抑制剂控制。在推导该模型时，假设抑制剂浓度与前一时刻的群体密度成正比。时间上的密度变化由一个延迟微分方程描述：dx/dt = αx/(1 + x(v)(t - 0)) - x。根据这个方程，随着有丝分裂活性抑制机制中延迟临界值的增加，群体中可能会观察到细胞数量的振荡。在线性近似下解析确定的振荡周期等于延迟时间的四倍。该模型的数值积分表明，观察到的周期与计算值接近。
