Biologic: Gene circuits and feedback in an introductory physics sequence for biology and premedical students

Abstract

Two synthetic gene circuits -- the genetic toggle switch and the repressilator -- are analyzed quantitatively and discussed in the context of an educational module on gene circuits and feedback that constitutes the final topic of a year-long introductory physics sequence, aimed at biology and premedical undergraduate students. The genetic toggle switch consists of two genes, each of whose protein product represses the other's expression, while the repressilator consists of three genes, each of whose protein product represses the next gene's expression. Analytic, numerical, and electronic treatments of the genetic toggle switch shows that this gene circuit realizes bistability. A simplified treatment of the repressilator reveals that this circuit can realize sustained oscillations. In both cases, a "phase diagram" is obtained, that specifies the region of parameter space in which bistability or oscillatory behavior, respectively, occurs.