A compartmental reaction-diffusion cell cycle model
The paper presents a model that describes the triggering of an S phase mechanism for DNA synthesis, important in setting the reproduction time of the cell. The S phase is preceded by the \(G_ 1\) phase whose time length is the main determinant of the length of the cell cycle. The model presented is based on the generation of epigenetic oscillations due to genetic control by repression. It is an intricate coupling between the size and shape of the growing cell and the biochemical reaction - diffusion processes in the cell that determine the initiation of the epigenetic oscillations, hence the S phase triggering mechanism. The eukaryotic cell, considered as a system consisting of two compartments, the nucleus and the cytoplasm, is modeled by a system of equations with boundary conditions. The main numerical results obtained in the special idealized case where the cell and its nucleus are spherically shaped are presented. The restriction to spherical shapes was made in order to simplify the computations which are quite time- consuming. Further work on differently shaped cells is done in Section 3. Section 2 contains a description of the mathematical analysis of the model and a detailed study of the dependence of the critical stability curve when the diffusion rates are varied as well as when the cell is viewed as a three-, two- or one-dimensional spatial domain. The results for the dependence of the critical stability curve on the cell volume are presented. These results form the basis for the triggering mechanism that was described. The mathematical analysis of the model indicates that the proposed triggering mechanism is in qualitative agreement with the observed behaviour of the cell cycle under variations of different pertinent parameters. In the final section, extensions of the work to current models as well as to more elaborate models currently pursued are discussed.
scientific article; zbMATH DE number 4191451