Introduction
An important parameter that determines the success of directional evolution is the time that the evolution system runs, which refers to the time scale within which we need to carry out and complete each experiment. There is no unified answer to this question, but it is entirely based on empirical results obtained through multiple experiments. It is not yet clear whether there is an optimal solution. Our iGEM modeling team attempts to answer this question through mathematical modeling.
Due to limited time, knowledge, and resources, our model construction is relatively simple:
1. According to the mutation data we have analyzed from the reference, we believe that the mutation rate grows linearly over time. So, we use a basic linear regression to model the growth of mutation rates.
2. However, this could be more complicated than we think. For example, the long-time behavior of the rate could follow an exponential model with respect to time, or an even more complex mathematical model such as the SI model or Michaelis-Menten kinetics, which are used in modeling long-time behavior in biological studies.
3. We implement the linear regression modeling. The codes and figures are shown in the following slides:
Results
Based on the simulation results, the rate for G>A mutation is faster than the rate for C>T mutation. It takes ~8 days to introduce 0.5 G>A mutation per kb. Within the same time interval, only 0.25 C>T mutation could be introduced.
This simulation modeling provides us with several useful guidance when using this directed-evolution system:
1. We can estimate the mutation rate of any interesting gene we want to mutate, with the help of two key parameters: the length of the gene and the time we run the system;
2. A low mutation rate gives us a big time window to catch the useful mutant among the whole population of the experimental cell samples;
3. As long as we successfully identify a super mutant, we can use this mutant as our new starting point to select the second mutation within this background.