Metabolic diversity in cell populations: probability densities over the flux polytope

Even in clonal populations, cells appear to be strongly heterogeneous in terms of, e.g., protein levels, RNA levels, sizes at birth or division, interdivision times and elongation rates. Part of this variability is likely due to the inherent stochasticity of gene expression at the level of single cells. It is however known that heterogeneous populations may possess an evolutionary advantage, for instance in variable environments or under stress. Despite appearing to be at odds with the idea of optimality presented in the previous chapters, metabolic diversity can be described and modeled within the constraint-based framework introduced in the previous chapters. Specifically, a statistical representation of heterogeneous populations can be obtained by defining suitable probability distributions on the flux polytope. This chapter addresses • the different sources of variation that affect microbial metabolism along with the mechanisms that may favor higher variability, • the methods devised to represent heterogeneous microbial populations within the framework of constraint- based models, and • how these approaches connect to the optimality scenario presented in the previous chapters.