Multiple-transition cell cycle models that exhibit transition probability kinetics

Cell cycle models that allow multiple random transitions and asymmetric cell division may exhibit a property that has been used to support the transition probability model of the cell cycle: that the absolute value of the difference between sibling cell inter-mitotic times varies from one sibling pair to another and is described by an exponential statistical distribution. Three models that show this property are described, each of which postulates the existence of objects that are partitioned between daughter cells during cell division and whose number influences the duration of the subsequent cell cycle, e.g., surface receptors for growth factors or transcriptional complexes that are carried by sister chromatids. In the first model, sibling cells receive identical numbers of the objects, which are used to perform multiple random transitions that constitute part of the cell cycle. The second model is like the first, except that the partitioning of objects between the newly-formed sibling cells is random. The third model is also like the first, except that all of the objects are passed to one of the sibling cells. These results show that the general mechanisms that are responsible for the dispersion of inter-mitotic times, the correlation between sibling generation times and the apparently exponentially distributed difference between sibling generation times, could be a combination of unequal cell division, multiple random cell cycle transitions and heterogeneity of mitotic cells.