Nonlocal growth and kinetic roughening in biological systems: bacterial colonies and cell aggregates

The morphology of biological systems, such as bacterial colonies or cell aggregates, depends to a great extent on the environmental conditions, e.g. the nutrient density or the mobility. In case of a high density of nutrients, morphologies correspond to the Kardar-Parisi-Zhang (KPZ) universality class, where growth is only determined by the local environment.

In this work we will present two alternative routes to introduce non-local effects in the known models to study the morphology of such aggregates. The first model is continuous, and adds to the KPZ equation a non-local term which depends on the shadowing angle, i.e. the angle under which each point of the interface can see the exterior of the aggregate. The theoretical results have been compared to experimental profiles obtained with B. subtilis and E. coli [Silvia N. Santalla et al., Phys. Rev. E 98, 012407 (2018)].

A second model is based on the inclusion of non-local effects in the Eden model. In this model, the probability that a new cell will be appended at a certain point depends on the local density of nutrients and, again, on the shadowing angle [Silvia N. Santalla and Silvio C. Ferreira, Phys. Rev. E 98, 022405 (2018)].

In both models we obtain a long-term Family-Vicsek preasymptotic scaling with non-universal exponents characterizing the interface, thus explaining the previous observations by several research teams of different scaling exponents, even purportedly related to the quenched-KPZ class, which we can effectively rule out.