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-->M) 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(-) cdc25Delta, which are defective in progress through the latter half of the cell cycle (G2 and M phases). These cells exhibit "quantized" cycles (interdivision times clustering around 90, 160, and 230 min). We show that these quantized cycles are associated with a supercritical Hopf bifurcation in the mechanism, when the wee1 and cdc25 genes are disabled. (c) 2001 American Institute of Physics.