Coarse-graining bacteria colonies for modelling critical solute distributions in picolitre bioreactors for bacterial studies on single-cell level.

Microfluidic single-cell bioreactors have found widespread application to investigate growth and gene expression of microbial model organisms, but yet there are few attempts to systematically characterize different design and cultivation concepts. Quantitative measurements of critical solute concentrations, e.g. limiting nutrients, are not yet feasible within the typical volumes in the range of picolitres. A way to gain new insights about the mass transport within those volumes is by simulation, but the complex geometry resulting from the multitude of cells within a colony leads to time and resource consuming computational challenges. In this work, six different concepts for the model representation of cellular microcolonies within microfluidic monolayer growth chamber devices are compared. The Gini coefficient is proposed as new measure for inhomogeneity within cellular colonies. An example cell colony is represented by a single point source, a cylindrical volume with homogeneous reaction rates with and without adjusted diffusion coefficient, as point sources for each single cell and as rod-shaped, diffusion blocking, three-dimensional cells with varying shapes. Simulated concentration profiles across the chambers depended strongly on the chosen cell representation. The representation with the lowest degree of abstraction, three-dimensional cells, leads to complex geometries and high computational effort, but also gives a conservative and therefore preferable estimate for the cultivation conditions within a given cultivation chamber geometry. Interestingly, the cylindrical volume with adjusted diffusion coefficient gives similar results but requires far less computational effort. Therefore, it is proposed to use the three-dimensional cells for detailed studies and to determine parameters for the cylindrical volume with adjusted diffusion coefficient, which can then be used for experimental design, screening of parameter spaces, and similar applications.