Departamento de Matemática Aplicada
Universidad Complutense de Madrid
Replicating cell populations create three dimensional organisms of diverse shapes. Elucidating how those different geometries arise is an intriguing question that has motivated many theories. Small cellular systems, such as bacterial biofilms, seem to develop from the interplay between cellular and mechanical processes. B. subtilis biofilms growing on air/agar interfaces spread while absorbing water and creating wrinkles, that evolve into a network of channels circulating water and nutrients. Stiffness gradients due to cellular division, death, and swelling govern the observed wrinkled patterns. Föppl–Von Kármán equations for the biofilm, coupled to stochastic cellular processes and to the agar substratum, allow us to reproduce branching wrinkles and wrinkled coronas. While wrinkle branching is associated with advancing compression fronts, wrinkled coronas are related to a stiffness reduction due to swelling, as shown in D.R Espeso, B Einarsson, A Carpio, Physical Review E, 91, 022710, 2015
Submerged biofilms grow on liquid/solid interfaces. They take oxygen and nutrients from the surrounding fluid and may alter the substratum they attach to. Depending on the strength of the flow, the concentration of nutrients, the type of nutrient and the bacterial strain, biofilms grow into the fluid forming different patterns. The presence of geometric constraints affects these filamentary structures. In cilyndrical flow circuits we have discovered that helical instabilities develop and biofilms wrap around the walls forming helices that do not interfere with the flow, as shown in D.R. Espeso, A. Carpio, E. Martínez-García, V. de Lorenzo Scientific Reports 6, 27170 (2016). The formation of these structures can be reproduced by discrete rod models coupled to the flow.
In straight channels streamers and ripples are commonly observed.
Biofilm washed out Ripples moving dowstream
Streamers eventually eroded Groups of mounds
The procedure to produce these in silico films is explained in Biofilm growth on rugose surfaces, D Rodriguez, B Einarsson, A Carpio, Physical Review E, 86, 061914, 2012.