  In this letter, we analyze a genetic toggle switch recently studied in the
literature where the expression of two repressor proteins can be tuned by
controlling two different inputs, namely the concentration of two inducer
molecules in the growth medium of the cells. Specifically, we investigate the
dynamics of this system when subject to pulse-width modulated (PWM) input. We
provide an analytical model that captures qualitatively the experimental
observations reported in the literature and approximates its asymptotic
behavior. We also discuss the effect that the system parameters have on the
prediction accuracy of the model. Moreover, we propose a possible external
control strategy to regulate the mean value of the fluorescence of the reporter
proteins when the cells are subject to such periodic forcing.
