Mustafin A T, Volkov E I
Biosystems. 1982;15(2):111-26. doi: 10.1016/0303-2647(82)90025-9.
The problem of whether the cell cycle is a deterministic or probabilistic process is widely discussed in the current literature (P. Nurse, Nature, 286, pp. 9-10, 1980). In this report the question of fluctuations of cell cycle period is treated in the limits of the membrane model of cell division regulation. The parametric analysis of the equations set both for normal and tumour cells is carried out. We describe the bifurcation parameters in the neighbourhood of which the system can amplify the small fluctuations. The presence of white noise in parameters describing the lipids and antioxidants influxes into membrane is examined by methods of Marcovian processes and also by direct stochastic computer simulation. The equation for the distribution function of generation times is obtained and the increase of dispersion and mean cycle time during the changes of those parameters which would be connected with cell culture density is calculated. The influence of parameter fluctuations upon the cycle period for both normal and tumour cells is compared in the framework of model assumptions. The ratio of dispersion of generation time distribution to mean period value for an ensemble of tumour cells is shown to be several times greater than that for normal ones. In the discussion the problem of the presence of a premitotical (G02) resting state and of the possibility of its experimental detection is considered.
细胞周期是一个确定性过程还是概率性过程的问题在当前文献中得到了广泛讨论（P. 纳斯，《自然》，第286卷，第9 - 10页，1980年）。在本报告中，细胞周期时长波动问题是在细胞分裂调控的膜模型框架内进行探讨的。对正常细胞和肿瘤细胞的方程组进行了参数分析。我们描述了系统能够放大微小波动的附近的分岔参数。通过马尔可夫过程方法以及直接的随机计算机模拟，研究了描述脂质和抗氧化剂流入细胞膜的参数中白噪声的存在情况。得到了世代时间分布函数的方程，并计算了与细胞培养密度相关的那些参数变化期间离散度和平均周期时间的增加情况。在模型假设的框架内，比较了参数波动对正常细胞和肿瘤细胞周期时长的影响。结果表明，肿瘤细胞群体的世代时间分布离散度与平均周期值之比比正常细胞群体的该比值大几倍。在讨论中，考虑了有丝分裂前（G02）静止状态的存在问题及其实验检测的可能性。
