Combinatorics in evolution: from rule-based systems to the thermodynamics of selectivities

Life on Earth uses quite specific and often universal chemical pathways, which have apparently been selected through evolution among many alternatives possible with the same or comparable mechanisms. Both network chemistry and Darwinian evolution are stochastic population processes, with natural associated entropy and information measures. The free recombination possible for elementary mechanisms, either in prebiotic chemistry or within evolutionary potential, produces a third combinatorics of possibilities to be filtered by selection. We would like to understand how statistical mechanics spans these three combinatorial levels, to learn for example whether there is a natural dimensional analysis of the costs of selection. In this study we use a rule-based model to generate "all possible" solutions to a biological problem of sugar-phosphate conversion, deriving the natural dissipaton costs and information geometry that constitute fitness criteria and separability of solutions. From these we show there is a minimum cost to select a subnetwork or single pathway from a network of prior possibilities, computed from the tilted generating function for the driven chemical ensemble.