Toxicity and death

We model death as a stochastic process depending on an intrinsic death rate r = 0.03, which is potentially increased when internal metabolite concentrations reach a toxic threshold. This cumulative toxic effect e_tox is computed over all internal metabolites M and the current lifetime τ of a microbe as:

with the toxic effect function f(m, t) for the concentration of metabolite m at time t with metabolite-specific toxicity threshold tox_m

This toxic effect increases the death rate d of microbes starting at the intrinsic death rate r:

where s scales the toxic effect. Microbes that survive after an update cycle retain the toxic level they accumulated so far. Cells can also die from starvation. When they are unable to produce enough biomass product to maintain the slowly decaying volume of the cell and cell size drops below a predefined threshold size, cells are automatically marked for death.