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'''Fig.1:''' ''Basic oscillating genetic circuit as published by Danino & Hasty.'' | '''Fig.1:''' ''Basic oscillating genetic circuit as published by Danino & Hasty.'' | ||
Fig.1: Basic oscillating genetic circuit as published by Danino & Hasty.
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.
| A | : | AiiA |
| I | : | LuxI |
| Hi | : | internal AHL |
| He | : | external AHL |
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
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