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.

Conjugation rate calculator

Concentration Calculation