Rational Design of a Genetic Finite State Machine: Combining Biology, Engineering, and Mathematics for Bio-Computer Research

Abstract

The recent success of biological engineering is due to a tremendous amount of research effort and the increasing number of market opportunities. Indeed, this has been partially possible due to the contribution of advanced mathematical tools and the application of engineering principles in genetic-circuit development. In this work, we use a rationally designed genetic circuit to show how models can support research and motivate students to apply mathematics in their future careers. A genetic four-state machine is analyzed using three frameworks: deterministic and stochastic modeling through differential and master equations, and a spatial approach via a cellular automaton. Each theoretical framework sheds light on the problem in a complementary way. It helps in understanding basic concepts of modeling and engineering, such as noise, robustness, and reaction–diffusion systems. The designed automaton could be part of a more complex system of modules conforming future bio-computers and it is a paradigmatic example of how models can assist teachers in multidisciplinary education.

Keywords

• mathematics
• synthetic biology
• education
• finite state machine
• noise
• cellular automaton