Mathematical modeling for the design of evolution experiments to study the genetic instability of metabolically engineered photosynthetic microorganisms

Engineering the metabolism of photosynthetic microorganisms with the aim of converting CO₂ and water, by exploiting solar energy, into end-products of commercial value is a rising interest in the biotechnology field. The producing host that carries a genetic modification not associated with competitive fitness advantage usually experiences a production burden (i.e., a metabolic burden related to product synthesis), leading to genetic instability and abortive production phenotype. The genetic instability of these engineered strains is a major hindrance to the spreading of large-scale photosynthetic cell factory processes. This genetic instability can be studied by means of evolution experiments, which are often time-consuming. In these experiments, the cell population is subjected to a long-term culturing during which the possible variation of the number of producers and of cells that lose the production traits, here defined as retro-mutants, is recorded. Here, a mathematical model that describes the dynamics of retro-mutants into a population of metabolically engineered photosynthetic microorganisms has been developed. The model has been used to simulate evolution experiments, conducted both in continuous (chemostat and turbidostat) and semi-continuous (serial batch transfer) culturing modes. These simulations allowed identifying the set of operative parameters for each cultivation mode that optimizes an evolution experiment in terms of experimental time needed to detect the arising of retro-mutants. Moreover, it has been found that in a scale of number of microbial generations only two parameters, precisely the production burden and the mutation rate, are determinant for the appearance of retro-mutants. These parameters are intrinsic features of any metabolically engineered strain and do not depend on the adopted cultivation system or on the microbial growth kinetics characteristics. This result further extends the applicability of the model also to non-photosynthetic metabolically engineered microorganisms.