A Markovian framework to study the evolution of complexity and resilience in chemical organizations

Chemical Organization Theory (COT) is a framework to study the relation between structure and stability in reaction networks. It combines structural and stoichiometric conditions underlying self-production, and identifies a class of subnetworks on each reaction network, so-called organizations, that can be mapped to the possible limit sets that exhibit dynamical stability.

So far, organizations have been applied as a model for the emergence of autopoietic systems in biochemistry and other areas, but there is currently no systematic study on how organizations can become more complex. Here we formalize the dynamics of transitions between organizations as a Markov process where nodes of the process graph are organizations and transition probabilities reflect the probability of transition from one organization to another. Hence, the structural evolution of a reaction network is seen as a random walk in the graph of organizations.

We introduce the terms local and global resilience to describe organizations that have a tendency to resist perturbations or are more likely to be visited on a random walk. This allows a more sophisticated investigation of the influence of structural properties on the evolution of chemical organisations.