Team:Wageningen UR/Project/ModelingProj1

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(→Modeling synchronized oscillations)
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'''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.   
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'''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.  }}
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{|
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|'''A'''||:||AiiA
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|-
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|'''I'''||:||LuxI
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|-
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|'''Hi'''||:||internal AHL
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|-
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|'''He'''||:||external AHL
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|}
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'''A:'''  AiiA
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{{:Team:Wageningen_UR/Templates/Style | text= __NOTOC__
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'''I:'''  LuxI
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'''Hi:'''  internal AHL
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'''He:''' external AHL
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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:  }}
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:  }}

Revision as of 18:35, 11 September 2011

Building a Synchronized Oscillatory System

Modeling synchronized oscillations

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.

Equations hasty WUR.png


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:

Equations2 hasty WUR.png

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

Equations3 hasty WUR.png

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