On the role of conserved moieties in shaping the robustness and production capabilities of reaction networks

Abstract

We study a simplified, solvable model of a fully-connected metabolic network with constrained quenched disorder to mimic the conservation laws imposed by stoichiometry on chemical reactions. Within a spin-glass type of approach, we show that in presence of a conserved metabolic pool the flux state corresponding to maximal growth is stationary independently of the pool size. In addition, and at odds with the case of unconstrained networks, the volume of optimal flux configurations remains finite, indicating that the frustration imposed by stoichiometric constraints, while reducing growth capabilities, confers robustness and flexibility to the system. These results have a clear biological interpretation and provide a basic, fully analytical explanation to features recently observed in real metabolic networks.

Optimal Fluxes, Reaction Replaceability, and Response to Enzymopathies in the Human Red Blood Cell

“…In particular, there exists a value ρ ⋆ of ρ , representing the maximum metabolic production rate compatible with the stoichiometric constraints, above which no suitable flux vectors exist. The presence of conserved metabolic pools [ 25 ] implies ρ ⋆ = 1 [ 26 ], so that in metabolic networks optimal steady state fluxes correspond to the solutions of…”

Boolean constraint satisfaction problems for reaction networks

“…Hence the presence of metabolite pools imply that ρ * = 1 in real metabolic networks. This results has been generalized in [56] where conserved pools are studied rigorously in simplified reaction networks.…”

Von Neumann’s growth model: Statistical mechanics and biological applications

“…The continuous line marks the separation between the regions with g = 0 (stationary regime) and g < 0 (contracting regime). The expanding regime lies on the = 0 axis (n > 1) and is represented by a green strip [26].…”

“…One obtains: and g < 0 (contracting regime). The expanding regime lies on the = 0 axis (n > 1) and is represented by a green strip [26].…”