## Multiplicity of infection (MOI)

The multiplicity of infection (abbreviated MOI) is the average number of phage per bacterium. The MOI is determined by simply dividing the number of phage added (ml added x PFU/ml) by the number of bacteria added (ml added x cells/ml). The average number of phage per bacterium in the population could be 0.1, 1, 2, 10, etc, depending upon how you set up the experiment.

Although the MOI tells you the average number of phage per bacterium, the actual number of phage that infect any given bacterial cell is a statistical function. For example, if the MOI is 1, some cells will get infected with one phage but some cells may be infected with 0 phage and other cells infected with two phage. The proportion of cells in a population infected by a specific number of phage (n) can be calculated from the Poisson distribution.

where:

m = multiplicity of infection (MOI)
n = number of phage infecting a cell
P(n) = probability cell will be infected with n phage

The results agree with what you would expect by simple common sense -- at a low MOI most cells will be infected with fewer phage and at a high MOI most cells will be infected with more phage. The proportion of cells in a population that are infected with 0, 1, 2, ...,20 phage when infected with an MOI of 0.1, 1, 2, or 10 is shown in the figure below.

This information can be very useful form many experiments that use phage. For example, when doing transductions you may want to ensure that the bacterial recipients get no more than one phage particle to avoid lysis of the transductants, when screening for lysogens you may want to ensure that the bacteria are infected with many phage to favor the lysogenic pathway, etc.