title: Looking for chemical reaction networks exhibiting a drift along a manifold of marginally stable states.
abstract: I recently reported some examples of mass-action equations that have a continuous manifold of marginally stable stationary states [Brogioli, D., 2010. Marginally stable chemical systems as precursors of life. Phys. Rev. Lett. 105, 058102; Brogioli, D., 2011. Marginal stability in chemical systems and its relevance in the origin of life. Phys. Rev. E 84, 031931]. The corresponding chemical reaction networks show nonclassical effects, i.e. a violation of the mass-action equations, under the effect of the concentration fluctuations: the chemical system drifts along the marginally stable states. I proposed that this effect is potentially involved in abiogenesis. In the present paper, I analyze the mathematical properties of mass-action equations of marginally stable chemical reaction networks. The marginal stability implies that the mass-action equations obey some conservation law; I show that the mathematical properties of the conserved quantity characterize the motion along the marginally stable stationary state manifold, i.e. they allow to predict if the fluctuations give rise to a random walk or a drift under the effect of concentration fluctuations. Moreover, I show that the presence of the drift along the manifold of marginally stable stationary-states is a critical property, i.e. at least one of the reaction constants must be fine tuned in order to obtain the drift.
authors.affiliation: Dipartimento di Medicina Sperimentale, Università degli Studi di Milano - Bicocca, Via Cadore 48, Monza (MI) 20052, Italy. doriano.brogioli@unimib.it
authors.forename: Doriano
authors.initials: D
authors.lastname: Brogioli
mesh_terms: D000465:Algorithms; D002384:Catalysis; D055598:Chemical Phenomena; D008390:Markov Chains; D008956:Models, Chemical; D000069497:Origin of Life