Stoichiometric network analysis of spontaneous mirror symmetry breaking in chemical reactions

Abstract

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.

Chemical Basis of Biological Homochirality during the Abiotic Evolution Stages on Earth

“…For reasonable reaction rate constants and reaction parameters (not specified here) in this example instability of the racemic branch occurs for n > 1.6 and SMSB for n ≥ 1.7. Non-integer values of n correspond to the simplification of complex autocatalytic networks [56], which leads to the same dynamic change of the solution species.…”

“…However, enantioselective autocatalysis may also fulfill condition (3) for several different compositions. Autocatalytic reaction networks capable of yielding species/enantiomer selection have been previously reviewed [3,46,47,[56][57][58]. In addition to the networks cited/discussed therein, we must include the recently reported enantioselective hypercycle [50,59], which is highly significant due to its coincidence with the replicators of the nucleic acid and protein domain [60].…”

“…This is because the autocatalytic functionality of (5) can only emerge if reaction (4) is operative. Reaction (4) can start for initial conditions without any D and L. The first order autocatalysis (5), also called quadratic autocatalysis, cannot lead to species selection [56] (between D and L in SMSB), i.e., the entropy production needed to achieve the instability of the racemic branch is not high enough. This is because the kinetic/dynamic sigmoidal curve of growth implicit in autocatalytic processes (n > 0; see the meaning of n in Figure 2) is needed, as well as a super-exponential growth (n > 1) is necessary for species selection.…”

Spontaneous mirror symmetry breaking and origin of biological homochirality

“…refs. [27,44,53]) and stoichiometric network analysis (SNA) for the stability analysis of the final stationary states [54]. Figure 5 shows the SMSB in the simulation of a hypercyclic autocatalytic reaction network in a CSTR.…”

Stoichiometric network analysis of a reaction system with conservation constraints

“…1,21,22 The overall process can be represented as a linear combination of several elementary reaction pathways known as extreme currents E i and they all contribute to the steady-state values of reaction rates. The contributions of the extreme currents E i , denoted as the current rates j i , are the components of the corresponding current rate vector j, whereas the extreme currents E i are the columns of the extreme current matrix E. 1,2,6,17,18,[20][21][22][23][24] Thus,…”