Team:ETH Zurich/modeling/qs

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== Alternative Design==
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== Alternative Design ==
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As cross-talk is a burning issue in quorum sensing, we thought about a theoretical solution. [https://2014.igem.org/Team:Edinburgh Edinburgh iGEM team 2014]also worked on communication between ''E. coli''. They developed new communication channels via metabolic wiring. By assuming that quorum sensing molecules would not cross-talk with metabolites, we used their idea to develop a model on molecular level. The idea is finally to combine our whole-cell model and their idea on metabolites.
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Metabolic wiring is based on the fact that when a ressource is at disposal, a cell will produce an enzyme to break it down to smaller pieces. There is often a chain of metabolites. Using the fact that metabolites can diffuse through the membrane, this can allow communication (for more information, please see the [[https://2014.igem.org/Team:Edinburgh Edinburgh iGEM team 2014] wiki).
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=== Chemical Species ===
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The species' names are generic because the implementation with particular metabolites implies biological considerations on cell growth and medium used.
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{| class="wikitable"
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|-
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! Name
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! Description
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|-
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|'''A'''
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|Metabolite
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|-
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|'''B'''
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|Metabolite
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|-
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|'''Enz'''
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|Enzyme that catalyzes the transformation from A to B
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|-
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|'''[A,Enz]'''
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|Complex made of metabolite A and enzyme Enz
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|-
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|'''P_A'''
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|Promoter induced by A. It can be either on or off (rescued or not)
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|}
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=== Reactions ===
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$$\begin{align*}
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&\rightarrow A \\
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A + P_{Aoff} &\rightarrow P_{Aon} \\
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P_{Aon} &\rightarrow P_{Aon} + Enz \\
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A + Enz &\leftrightarrow [A.Enz] \\
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[A.Enz] &\rightarrow B \\
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A &\rightarrow \\
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B &\rightarrow \\
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[A.Enz] &\rightarrow \\
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Enz &\rightarrow
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\end{align*}$$
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=== Parameters ===
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{| class="wikitable"
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|-
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! Name
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! Description
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|-
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|'''α<sub>A</sub>'''
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|Production rate of metabolite A
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|-
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|'''d<sub>A</sub>'''
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|Degradation rate of metabolite A
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|-
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|'''α<sub>Enz</sub>'''
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|Production rate of enzyme Enz
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|-
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|'''d<sub>Enz</sub>'''
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|Degradation rate of enzyme Enz
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|-
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|'''α<sub>B</sub>'''
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|Production rate of metabolite B
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|-
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|'''d<sub>B</sub>'''
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|Degradation rate of metabolite B
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|-
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|'''K<sub>d</sub>'''
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|Parameter of the Michaelis-Menten function modeling the action of enzyme Enz on the substrate, metabolite A, in order to produce metabolite B
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|-
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|'''n'''
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|Hill coefficient for the Hill function modeling the activation of the transcription of enzyme Enz with metabolite A as inducer
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|-
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|'''K<sub>A</sub>'''
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|Activation concentration for the Hill function modeling the activation of the transcription of enzyme Enz with metabolite A as inducer
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|}
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Parameters are not well-known.
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=== Deterministic Model ===
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We derived this model doing the following assumptions:
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;'''Assumption 1'''
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:The induction of the promoter $P_A$ by A is supposed to follow an Hill function.
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;'''Assumption 2'''
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:The enzyme-based reaction from A to B is supposed to follow a Michaelis-Menten function.
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$$\begin{align}
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\frac{d[A]}{dt} &= \alpha_A - \beta_{A} [A] \\
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\frac{d[Enz]}{dt} &= \alpha_{Enz} \frac{[A]^n}{K_{A}^n + [A]^n} - \beta_{Enz} [Enz] \\
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\frac{d[B]}{dt} &= \alpha_B \frac{[Enz] [A]}{K_d + [A]} - \beta_{B} [B]
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\end{align}$$
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=== Application to our project ===
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Populations of bacteria will grow into a medium, which provide them metabolite A. The metabolite B will serve as communicating signal, like LasAHL or LuxAHL. It will be an input for the logic construct. As soon as metabolite B is being made available to the cell, the cell will produce the input for the logic construct.
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<br/>
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Moreover, one type of cell will produce B as output. Therefore, the output of the logic gate signal will correspond to the production (or absence of production) of the enzyme Enz, so that the A contained in the medium can be transformed to B. Enz will play the same role as LasI or LuxI in our original model.
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<br/>
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We separate the promoter activating the production of the enzyme with the production of the enzyme itself. Moreover, cells sense B and want to produce B. In our modules, we have to remplace equations in the sensing module and in the production module.
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;'''Sensing Module'''
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:For example, B would induce the production of the integrase, Bxb1.
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$$
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\begin{align*}
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\frac{d[B]}{dt} &= \alpha_B - \beta_{B} [B] \\
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\frac{d[Bxb1]}{dt} &= \alpha_{Enz} \frac{[B]^n}{K_{B}^n + [B]^n} - \beta_{Bxb1} [Bxb1]
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\end{align*}
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$$
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;'''Production Module'''
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:Here, output<sub>logic</sub> is the output of the logic factorized in one term.
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$$\begin{align*}
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\frac{d[Enz]}{dt} &= output_{logic} - \beta_{Enz} [Enz] \\
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\frac{d[B]}{dt} &= \alpha_B \frac{[Enz] [A]}{K_d + [A]} - \beta_{B} [B]
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\end{align*}
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$$
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=== Simulations ===
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We implemented this solution in our [https://2014.igem.org/Team:ETH_Zurich/modeling#Alternative_Design whole-cell model]. As no parameter is none, we assumed their values to be in the range of standard rates. It gave a possible valid result.
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Revision as of 13:07, 15 October 2014

iGEM ETH Zurich 2014