Modeling Stochastic Dynamics for Ratio Control of Bacteria Population

In recent years, synthetic biology has seen significant advancements. It represents a novel research area which combines engineering and biology proposing to create systems that do not exist in na- ture, by either synthesizing novel organisms or inserting artificial genetic circuits into living cells. Designing novel artificial genetic systems requires a suitable mathematical model enabling the study, analysis and simulation of the biological system before implementing in vivo experiments. Therefore, the first part of this thesis explores the wide range of possible modeling and simulation techniques, highlighting their differences through well-known examples. It focuses especially on realizing stochastic simulations of the genetic toggle switch, starting from its simplified determin- istic description. Among the current key challenges in synthetic biology emerges the co-existence of multiple popu- lations, in order to distribute the workload and the different functionalities. While several strategies exist to regulate the population sizes, different growth and division rates pose significant difficul- ties. Therefore, an innovative alternative approach considers only one population made of two phenotypically distinct subgroups, where each cell can change its phenotype under the control of an external input. In the literature two controllers have been proposed able to balance the numbers of these two subgroups, whose effectiveness has been validated using an Advanced Agent-Based Cell Simulator. Our work evaluates their performance on a stochastic model, yielding novel and different, yet at the same time promising and realistic, results. Further study is essential to refine the model and better understand the two approaches; however, we believe this thesis already provides a significant basis for the research in this area.