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.

Natural algorithms We provide further evidence that the study of complex selforganizing systems can benefit from an algorithmic perspective. The subject has been traditionally viewed through the lens of physics and control theory. Using tools typically associated with theoretical computer science, we settle an old question in theoretical ecology: bounding the convergence of bird flocks. We bound the time to reach steady state by a toweroftwos of height linear in the number of birds. We prove that, surprisingly, the toweroftwos growth is intrinsic to the model. This unexpected result demonstrates the merits of approaching biological dynamical systems as natural algorithms and applying algorithmic techniques to them.