Linear stability analysis of chemical mechanism, Listanalchem: A tool for the search of spontaneous mirror symmetry breaking

Homochirality, the phenomenon by which one of two virtually identical (non-superimposable mirror images) compounds is favored over the other in the chemistry of life, has been regarded as a requisite for the emergence of all living things on earth. Spontaneous mirror symmetry breaking has been proposed to produce the imbalance. Under this framework, Frank presented, in his foundational article "On spontaneous asymmetric synthesis", a simple chemical reaction network that displays spontaneous symmetry breaking for a specific set of reaction rates. Research has since focused on finding more complex and plausible models, each one with its advantages and disadvantages. Nevertheless, finding reaction rate values that make a model exhibit spontaneous symmetry breaking is a complex task, even for specially crafted models. LInear STability ANALysis of CHEmical Mechanism, Listanalchem, is a method and software for the search for appropriate reaction rates. It includes four different algorithms inspired by the analysis of Frank's network. Two classical algorithms are also included in Listanalchem: the Trace-Determinant plane and the Stoichiometric Network Analysis by Bruce Clarke. Listanalchem reads a chemical reaction network from plain text and runs one or more of the available algorithms according to the user selection. Listanalchem is tested and verified by studying classical, modified, and recent models proposed to explain the origin of biological homochirality.•Listanalchem allows a fast and reliable search for instability behavior in chemical mechanisms that pretend to explain spontaneous mirror symmetry breaking.•Listanalchem contains several model examples, including the most cited in the related literature.•Listanalchem is a tool that tests models that pretend to explain the origin of biological homochirality, helps find errors, and aids in designing new models.

Biological homochirality and stoichiometric network analysis: Variations on Frank’s model

Biological homochirality is modelled using chemical reaction mechanisms that include autocatalytic and inhibition reactions as well as input and output flows. From the mathematical point of view, the differential equations associated with those mechanisms have to exhibit bistability.  The search for those bifurcations can be carried out using stoichiometric network analysis. This algorithm simplifies the mathematical analysis and can be implemented in a computer programme, which can help us to analyse chemical networks. However, regardless of the reduction to linear polynomials, which is made possible by this algorithm, in some cases, the complexity and length of the polynomials involved make the analysis unfeasible. This problem has been partially solved by extending the stoichiometric matrix with rows that code the duality relations between the different reactions occurring in the network given as input. All these facts allow us to analyse 28 different network models, highlighting the basic requirements needed by a chemical mechanism to have spontaneous mirror symmetry breaking.