Zum Mechanismus der biologischen 24StundenPeriodik The level (arithmetic average of all instantaneous values)of a selfsustained oscillation in general influences all properties of the oscillation, including period, amplitude and shape of the oscillation, and the rate of exchange of energy between the oscillator and its environment. Only when the nonlinear damping factor does not depend on the instantaneous value of the oscillating function, but only on the amplitude of the oscillation, are the other properties independent of the average level. The differential equations describing selfsustained oscillations cannot be solved exactly, but methods of approximation are applicable. Numerical solutions to several different forms of the equations will be discussed.

Fundamental Limits and Tradeoffs in Autocatalytic Pathways This paper develops some basic principles to study autocatalytic networks and exploit their structural properties in order to characterize their inherent fundamental limits and tradeoffs. In a dynamical system with autocatalytic structure, the systemu0027s output is necessary to catalyze its own production. Our study has been motivated by a simplified model of a glycolysis pathway. First, the properties of this class of pathways are investigated through a network model, which consists of a chain of enzymatically catalyzed intermediate reactions coupled with an autocatalytic component. We explicitly derive a hard limit on the minimum achievable xe2x84x92_2 gain disturbance attenuation and a hard limit on its minimum required output energy. Then, we show how these resulting hard limits lead to some fundamental tradeoffs between transient and steadystate behavior of the network and its net production.