Stationary Distributions and Condensation in Autocatalytic Reaction Networks

Quasi-Stationary Distributions for a Class of Autocatalytic Chemical Reactions

Product-form stationary distributions for deficiency zero chemical reaction networks.

We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled system with mass-action kinetics admits a complex balanced equilibrium. Feinberg's deficiency zero theorem then implies that such a distribution exists ...

Tensor Approximation of Stationary Distributions of Chemical Reaction Networks

We prove that the stationary distribution of a system of reacting species with a weaklyreversible reaction network of zero deficiency in the sense of Feinberg admits tensor-structured approximation of complexity which scales linearly with respect to the number of species and logarithmically in the maximum copy numbers as well as in the desired accuracy. Our results cover the classical mass-acti...

Autocatalytic sets in polymer networks with variable catalysis distributions

Abstract. All living systems – from the origin of life to modern cells – rely on a set of biochemical reactions that are simultaneously self-sustaining and autocatalytic. This notion of an autocatalytic set has been formalized graph-theoretically (as ‘RAF’), leading to mathematical results and polynomialtime algorithms that have been applied to simulated and real chemical reaction systems. In t...

On RAF Sets and Autocatalytic Cycles in Random Reaction Networks

The emergence of autocatalytic sets of molecules seems to have played an important role in the origin of life context. Although the possibility to reproduce this emergence in laboratory has received considerable attention, this is still far from being achieved. In order to unravel some key properties enabling the emergence of structures potentially able to sustain their own existence and growth...