## Conjugation Rate

**ODE of the Conjugation Model**

R: Recipient cell,

D: Donor cell,

T: Transconjugant cell.

The growth rates of the recipient, donor, and transconjugant cells are φR, , and , respectively.

γ is the conjugation rate, which is the parameter of interest for calculation.

The conjugation rate calculation is referred to in the *Journal of General Microbiology*, 136, 2319-2325 (1990).

We generalized to the case where all growth rates are different to calculate conjugation rate γ. The generalized equation is as follows:

where T, R and N are the transconjugant, recipient and the total cell concentration [CFU/ml] at the stationary phase.

β = γ / φ, where γ is the conjugation rate and φ is the overall growth rate.

σ0 is the initial ratio of donor and the total cells, D(0)/N(0).

αT, αR and αD are the rations of each growth rate divided by the overall growth rate φ, namely φΤ/φ, φR/φ and φD/φ, respectively.

However, the equation containing the conjugation rate γ is transcendental, meaning there is no analytical solution for γ. Therefore, simply consider the special case where all growth rates are identical, namely αT = αR = αD = 1. The resulting equation from this simplification is consistent with the equation reported in the above reference.

The last equation was used to evaluate the conjugation rate γ.