Team:Wageningen UR/Project/ModelingProj1

Short repetition of the Hasty construct used as base for our system

Fig.1: Basic oscillating genetic circuit as published by Danino & Hasty.

LuxI and AiiA can be expressed when a AHL-LuxR complex binds to the promoter region. The circuit uses both a positive and negative feedback loop to control the AHL concentration and therefore the expression of LuxI and AiiA. In the positive loop, LuxI generates more AHL, which then binds to LuxR

Mathematical model of the construct

Since our bio bricked oscillatory system is based on the design published by Danino et al. in the paper [http://www.nature.com/nature/journal/v463/n7279/abs/nature08753.html “A synchronized quorum of genetic clocks”], our first model of the system is a reproduction of the mathematical model in the supplementary information accompanying the publication mentioned. In their simulations, Danino et al. used the following set of delay differential equations, which we used as base for our simulation tool written in matlab.

Above: Set of delay differential equations derived by Danino et al. to model the oscillatory behaviour of the design using a positive and negative feedback loop.

The production of AiiA and LuxI depend on the internal AHL concentration in the single cell. The steps from gene to protein (transcription, translation, maturation etc.) are not modeled separately, but taken together in the following Hill function:

in which tau represents the time step between the relevant internal AHL concentration and the corresponding AiiA and LuxI, so that