Time Delays in a Genetic Positive-Feedback Circuit

Many principles of feedback control can be found implemented in complex biological networks. Dealing with transcription networks, positive feedbacks have been shown to frequently occur, providing biological toggle switches eventually leading a cell to its correct fate according to the proper stimulation. This note investigates the effects of delays related to the positive feedback of a basic transcription network. Motivation stems from the fact that, in spite of its toy-model features, the chosen transcription network is exploited to model the Tat feedback circuit that drives the HIV infected cells fate from active viral replication to latency. The delay is modeled by means of a cascade of transformations required to activate the transcription factor deputed to control: similar expedients are known to be exploited in cellular activities to schedule different biological functions at different timings. Our investigation is carried out by means of the stochastic approach, shown to be unavoidable to catch the noise-induced bimodality fashion of the circuit: by properly tuning the stochastic delay parameters, the regulatory circuit loses bimodality, and the transcription factor probability distribution converges to a Poisson distribution.