Modeling mutant distribution in a stressed Escherichia coli bacteria population using experimental data

In this paper we propose a statistical physics approach to experimental results on bacterial mutations (\textit{Escherichia coli}). We get scaling laws that describe some generic traits and suggest some features of the underlying dynamical structure for the considered evolution process. Our main assumption is that the evolution dynamics could be visualized as a random walk on a fitness landscape whose topological structure is analogous to the structure of energy landscape potentials used in Physics and Chemistry. Then we relate the generic distribution of local minima attraction basins to the number of bacterial mutations and we discuss the comparison with experimental results.