Each rod is one bacterium in a Petri-dish colony. Susceptible cells (green) carry no resistance gene; resistant cells (red) carry a plasmid that neutralizes the antibiotic's target. Resistance arises two ways: rare spontaneous mutation, and conjugation — direct plasmid transfer from a resistant donor to a susceptible neighbor, the main real-world route of horizontal gene transfer between bacteria.
Logistic growth with selection, each generation:
dS/dt = r·S·(1-N/K) − k·C·m(class,gram)·S − h·S·(R/N) − μ·S
dR/dt = r·f·R·(1-N/K) + h·S·(R/N) + μ·S
N = S+R (carrying capacity K) r = growth rate C = antibiotic concentration
k = kill constant m = gram/class permeability factor h = conjugation rate
μ = mutation rate f = fitness cost of carrying resistance (f < 1, plasmids cost energy)
- Antibiotic class — cell-wall drugs (penicillins) hit Gram-positive cells hardest since their thick peptidoglycan wall is the direct target; the Gram-negative outer membrane blocks much of the drug. Protein- and DNA-synthesis inhibitors cross both envelopes and act broadly.
- Concentration — kill rate above the minimum inhibitory concentration (MIC); below MIC, susceptible cells simply grow slower rather than dying.
- Gram-positive / Gram-negative — switches cell-wall structure and the class-specific permeability factor
m used above.
- Conjugation rate — probability per generation that a resistant cell transfers its plasmid to a susceptible neighbor on contact; this is why resistance can spread even with zero new mutations.
This is exactly why finishing a prescribed antibiotic course matters: a sub-lethal concentration selectively kills susceptible cells while resistant survivors — seeded by mutation or conjugation — are left to repopulate the colony unopposed.