On kinetics of phase transitions in cell membranes

Cell surface and cell division

A mathematical model of the regulation of cell division is suggested. The model is based on the hypothesis that the process giving rhythm to cell division is located in the cell membrane: i.e., the process of free-radical oxidation of membrane lipids. Much depends on the physical state of the membrane. In the membrane, phase transitions take place because of the changes in lipid composition. These transitions differ in normal and tumor cells: in normal cells they are sharp and hysteretic owing to the presence of a framework (membrane skeleton) on the surface of the membrane, while in tumor cells the integrity of the surface is violated so that the transitions are smooth. This model makes it possible to explain differences in the regulation of normal and cancer cell proliferation. Within the limits of the model, such phenomena as density dependent inhibition of growth, reverse transformation, influence of cyclic AMP and ions of Ca2+ on the cell cycle, the actions of serum and of proteases on the cycle, and so on, are explained. A rational scheme for the appearance of the selective damage found in tumor cells is proposed.

On the distribution of cell cycle generation times

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.