  For over two decades, Flux Balance Analysis (FBA) has been successfully used
for predicting growth rates and intracellular reaction rates in microbiological
metabolism. An aspect that is often omitted from this analysis, is segregation
or heterogeneity between different cells. In this work, we propose an extended
FBA method to model cell size distributions in balanced growth conditions.
Hereto, a mathematical description of the concept of balanced growth in terms
of cell mass distribution is presented. The cell mass distribution, quantified
by the Number Density Function (NDF), is affected by cell growth and cell
division. An optimization program is formulated in a general manner in which
the NDF, average cell culture growth rate and reaction rates per cell mass are
treated as optimization variables. As qualitative proof of concept, the
methodology is illustrated on a core carbon model of Escherichia coli under
aerobic growth conditions. This illustrates feasibility and applications of
this method, while indicating some shortcomings intrinsic to the simplified
biomass structuring and the time invariant approach.
