To model bacterial growth we consider a general limiting resource R and each bacteria incorporate R with individual parameters following a Michaelis-Menten dynamic throughout a growth function G(R)= c * u(R) where c represents the resource incorporation efficiency associated with a plasmid cost and u(R) is the uptake funcion defined as (R)=(Vmax*R)/(Km+R) with Vmax representing maximun incorporation rate and Km the half saturation constant.
To consider the action of antibiotics the model were parameterized with the respectives MICs for each genotype and antibiotic, and estimated the per plasmid resistance profiles.
Under this assumptions a simple realization consists en the following logistic: bacteria incorporates resource which trasforms to ATP and when is reaches a critical amount they undergo division. Upon division, the energy is divided between mother and daughter and the plasmids are segregated following a Poisson process. Then plasmids replicate untill they reach a random Normal(μ, \(\sigma\) ).
As b-lactams antibiotics affects directly in growth, we consider that bacteria growing faster are more likely to be killed, so we established ATP gained threshold to which we apply noise. And we consider the antibiotic ambient concentration vs the resistance profile to decide whether a bacteria lives or dies applying noise.
We iterate this process to each bacteria in the population for each moment of time to make our in silico single experiments. With this model we have been able to reproduce dose-respose, evolutionary and chemostat like experiments.