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We have uncovered that the non-equilibrium network dynamics and globalproperties are determined by two essential features: the potential landscapeand the flux landscape. We have found that the funneled potential landscape iscrucial for the stability of the states on the cell cycle, however, thestabilities of the oscillation states cannot guarantee the stable directionalflows. We have uncovered that the funneled flux landscape is important for theemergence and maintenance of the stable limit cycle oscillation flow. This workwill allow us to identify the key factors and structure elements of thenetworks in determining the stability, speed and robustness of the fissionyeast cell cycle oscillations. We see that the nonequilibriumness characterizedby the degree of detailed balance breaking from the energy pump quantified bythe flux is the cause of the energy dissipation for initiating and sustainingthe replications essential for the origin and evolution of life. Regulating thecell cycle speed is crucial for designing the prevention and curing strategy ofcancer.

Funneled Potential and Flux Landscapes Dictate the Stabilities of both the States and the Flow: Fission Yeast Cell Cycle