Stoichiometric network analysis of spontaneous mirror symmetry breaking in chemical reactions

We apply stoichiometric network analysis (SNA) to study enantioselective chemical reaction schemes, subject to various thermodynamic architectures, which may lead to spontaneous mirror symmetry breaking (SMSB). Stoichiometric matrices are used to calculate extreme currents or fluxes: the vector basis for the convex polyhedral cone of all stationary reaction rates. A major emphasis is given to the constraints that the rate constants must obey and how to express these in terms of the convex parameters and stationary inverse concentrations. We evaluate the corresponding Jacobians in terms of the constrained convex parameters and the inverse stationary concentrations and carry out stability analyses for the steady-state racemic configurations. A geometric visualization of SMSB is proposed, based on the structures of the convex cones, the angles between currents, and the cone's subspaces that result from enforcing the pertinent thermodynamic and chiral constraints.