While developing PREDCEL in the lab, we simultaneously developed it in silico so that both sides could benefit from each other. One of the most important parameter of phage assisted directed evolution experiments like PREDCEL and PACE is the phage titer itself. If the phage titer drops washout can occur and the experiment has to be restarted with the disadvantage of loosing library complexity. If the phage titer increases too much, the multiplicity of infection (MOI), that means the amount of phage relative the the amount of E. coli rises too. If fore example the MOI is 10 and an E. coli can only be infected by one phage, nine out of ten phages will not infect an E. coli and thus will not evolve, but still make up most of the phage population.

Modelling concentrations in one Lagoon

Here the concentrations \(c\) of uninfected E. coli, infected E. coli and phage producing E. coli as well as the M13 phage are modelled. They are denoted with the subscripts \(_{u}\), \(_{i}\), \(_{p}\) and \(_{P}\). If the whole E. coli population is referred to, \(c_{E}\) is used. If an arbitrary E. coli population is meant, the subscript \(_{e}\) is used. The phage concentration \(c_{P}\) refers to the free phage only, phage that are contained in an E. coli they infected are not included. The used parameters include the time \(t\), the affinity of phage for E. coli \(k\), the duration between infection of an E. coli and the first phage leaving the E. coli \(t_{P}\). The three different E. coli populations each have a generation time \(t\) that is denoted with their subscript. The fitness of a phage population is \(f\).