Scaling laws in microbial growth

Microbial growth and division are fundamental processes shaping organisms’ life cycle. Mathematical models of such biological processes have been developed, but several questions remain open, especially when focusing on single-cell lineages. The development of new microfluidic devices, combining single-molecule microscopy and automated image analysis, allows to track individual cells and their quantities of interest for many generations. Furthermore, recent discoveries of scaling laws hint at the existence of universal growth laws, not yet formulated. In this thesis work we hypothesize that cells operate in the vicinity of a critical point and we therefore aim at describing temporal and size scaling of lineages both from a theoretical and an empirical point of view. Our first step is indeed an analytical one, carried out with the purpose of putting the problem in the proper theoretical framework. Simulations are coded in order to explore the behavior of the system at different distances from the critical point. They are based on various models having different numbers of traits which range from 1 to 2, but belonging to the same universality class. Finally, we want to probe the proposed theoretical results by making use of available cell data from two different experiments and comparing them to the predictions of our model. Analysis’ results are presented both for the numerical approach and for the comparison with experimental data. We show how simulations confirm the hypothesized scalings and clarify exponents upon which different theoretical results can be found in literature. Furthermore, the moment scaling we find in experimental data is consistent with the criticality hypothesis. To corroborate this result we infer the control parameters of a particular model from the universality class with the aid of Bayesian Inference (BI) and find that they are indeed close to the critical point. Data quality shows to be an hurdle in probing the scaling of the autocorrelation length ξ with respect to <m>. No clear behaviour arises indeed from the analysis.