Mathematical model of the cell division cycle of fission yeast

Abstract

Much is known about the genes and proteins controlling the cell cycle of fission yeast. Can these molecular components be spun together into a consistent mechanism that accounts for the observed behavior of growth and division in fission yeast cells? To answer this question, we propose a mechanism for the control system, convert it into a set of 14 differential and algebraic equations, study these equations by numerical simulation and bifurcation theory, and compare our results to the physiology of wild-type and mutant cells. In wild-type cells, progress through the cell cycle ͑G1→S→G2→M͒ is related to cyclic progression around a hysteresis loop, driven by cell growth and chromosome alignment on the metaphase plate. However, the control system operates much differently in double-mutant cells, wee1 Ϫ cdc25⌬, which are defective in progress through the latter half of the cell cycle ͑G2 and M phases͒. These cells exhibit ''quantized'' cycles ͑interdivision times clustering around 90, 160, and 230 min͒. We show that these quantized cycles are associated with a supercritical Hopf bifurcation in the mechanism, when the wee1 and cdc25 genes are disabled. © 2001 American Institute of Physics. ͓DOI: 10.1063/1.1345725͔To reproduce itself, a cell must replicate all of its components and divide into two nearly identical daughter cells. During this cycle, the cell's deoxyribonucleic acid "DNA…, which stores its genetic information, must be replicated precisely, and the two copies of each DNA molecule "called sister chromatids… must be segregated accurately to the daughter cells " Fig. 1…. In eukaryotic cells, these two steps, called DNA replication and mitosis, occur during distinct temporal phases of the cell cycle "S phase and M phase… separated by gaps "G1 and G2…. Maintaining the correct order of events is the responsibility of the cell cycle engine. 1 Over the past 20 years, molecular biologists have uncovered many components of this engine. Cellcycle genes from one species can often replace their counterparts in other species, even between yeast and human cells, indicating that the cell cycle engine is an ancient and highly conserved mechanism among eukaryotes. From such discoveries, we can now construct schematic diagrams of the cell cycle engine in many different species, 2,3 but how can we be sure that a diagram is consistent with the overall physiology of cell division in any particular species? Biochemical reaction kinetics, in combination with the modern theory of nonlinear dynamical systems, provide just the tool we need to derive the physiological consequences of complex molecular regulatory networks. We illustrate this tool by associating some unusual features of the fission yeast cell cycle to bifurcations in the system of equations describing its cell cycle engine.

Optimizing periodicity and polymodality in noise-induced genetic oscillators

“…Therefore detailed mathematical models with a relatively large number of biochemical components (on the order of 10) have been proposed to explain this behavior [8]. In those models, period skipping arises already at the deterministic level (i.e., in the absence of sources of heterogeneity and inhomogeneity) [9], while noise is sometimes considered [10] to reproduce the level of irregularity observed in the experiments. Other striking examples of polymodal cycles * jordi.g.ojalvo@upc.edu embedded in an otherwise oscillatory dynamics were reported long ago in sensory neurons [11] and bacterial motility [12].…”

A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications

“…Although the nature of that relationship is very subtle [3,43] there is a consensus that relevant oscillations typically occur in the presence of Hopf bifurcations, and considerable work has been done to investigate various chemical and biological systems with respect to Hopf bifurcation fixed points [24,42,44,55,67].…”

The regulatory network of cell-cycle progression is fundamentally different in plants versus yeast or metazoans

“…This inhibition of Cdk1 activity by Wee1 and its release by Cdc25 fulfill a fundamental function during metazoan cell cycle control ensures the unidirectionality of the cell cycle. 8,9 The underlying molecular mechanism for this is a wiring of Cdk1 with Cdc25 or Wee1 by positive this notion by a detailed structure-function analysis. Our data demonstrate that the regulatory connection between these three components is not conserved and that plants must have evolved different mechanisms to stably progress through a mitotic cycle and arrest the cell cycle upon DNA damage.…”