A modified version of a previously developed mathematical model [Obeyesekere et al., Cell Prolif. (1997)] of the G1-phase of the cell cycle is presented. This model describes the regulation of the G1-phase that includes the interactions of the nuclear proteins, RB, cyclin E, cyclin D, cdk2, cdk4 and E2F. The effects of the growth factors on cyclin D synthesis under saturated or unsaturated growth factor conditions are investigated based on this model. The solutions to this model (a system of nonlinear ordinary differential equations) are discussed with respect to existing experiments. Predictions based on mathematical analysis of this model are presented. In particular, results are presented on the existence of two stable solutions, i.e., bistability within the G1-phase. It is shown that this bistability exists under unsaturated growth factor concentration levels. This phenomenon is very noticeable if the efficiency of the signal transduction, initiated by the growth factors leading to cyclin D synthesis, is low. The biological significance of this result as well as possible experimental designs to test these predictions are presented.

© 2 0 0 3 L a n d e s B i o s c i e n c e . N o t f o r d i s t r i b u t i o n . Report Theoretical and Experimental Evidence for Hysteresis in Cell Proliferation ABSTRACTWe propose a mathematical model for the regulation of the G1-phase of the mammalian cell cycle taking into account interactions of cyclin D/cdk4, cyclin E/cdk2, Rb and E2F. Mathematical analysis of this model predicts that a change in the proliferative status in response to a change in concentrations of serum growth factors will exhibit the property of hysteresis: the concentration of growth factors required to induce proliferation is higher than the concentration required to maintain proliferation. We experimentally confirmed this prediction in mouse embryonic fibroblasts in vitro. In agreement with the mathematical model, this indicates that changes in proliferative mode caused by small changes in concentrations of growth factors are not easily reversible. Based on this study, we discuss the importance of proliferation hysteresis for cell cycle regulation.

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In this work we present a mathematical approach to elucidate possible mechanisms involving mdm2 in the regulation of the cell cycle. It has been experimentally shown that the over-expression of MDM2 leads to uncoupling of DNA synthesis with mitosis resulting in polyploidy cells with multiple copies of their genomes. The function of MDM2 that uncouples the DNA synthesis phase (S) and the Mitosis phase (M) is unclear. To answer this question, we first formulate a mathematical model of the dynamics of the cell cycle regulatory proteins during the DNA synthesis phase and mitosis. This model is then tested for bifurcation that produces period doubling cascades that we relate to the biological event of polyploidy. The model formulation, the underlying biology, and the bifurcation results to delineate the unknown function of MDM2 are presented. Based on reproducing the known experimental result of polyploidy in MDM2 overexpressed cells, we propose several possible functions of mdm2, i.e., possible interactions with the other cell cycle regulating proteins that will result in uncoupling the S and M phases. We conclude that the most likely unknown function of MDM2 leading to the uncoupling of the S and M phases is an obstruction of the activation of Cdc25C by MDM2.

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