Revision as of 15:32, 12 October 2014

iGEM ETH Zurich 2014

Whole cell model

Model

The whole cell model is the combination of the Quorum sensing, Integrase and XOR modules. The model shows the behaviour of the a single cell in response to incoming signals. The model enables us to understand the effect of leakiness, cross-talk and their combinations on the whole system.

Chemical Species

Name	Description
Lux-AHL	30C6-HSL is an acyl homoserine lactone which mainly binds to LuxR.
LuxR	Constitutively expressed regulator protein that can bind Lux-AHL and stimulate transcription of Bxb1.
RLux	LuxR and Lux-AHL complex which can dimerize.
DRLux	Dimerized form of RLux.
mRNA_Bxb1	mRNA of the Bxb1 integrase being transcribed by the Lux promoter.
Bxb1	Serine integrase that can fold into two conformations - Bxb1a and Bxb1b. We chose to use a common connotation for both conformations - Bxb1.
Las-AHL	30C12-HSL is an acyl homoserine lactone which mainly binds to LasR.
LasR	Constitutively expressed regulator protein that can bind Las-AHL and stimulate transcription of ΦC31.
RLas	LasR and Las-AHL complex which can dimerize.
DRLas	Dimerized form of RLas.
mRNA_ΦC31	mRNA of the ΦC31 integrase being transcribed by the Lux promoter.
ΦC31	Serine integrase that can fold into two conformations - ΦC31a and ΦC31b. We chose to use a common connotation for both conformations - ΦC31.
SI_Bxb1	Inactive DNA binding site for Bxb1. No dimer is bound to this site.
SA_Bxb1	Active DNA binding site for Bxb1. A dimer is bound to this site.
SF_Bxb1	Flipped DNA binding site for Bxb1. The site generated after recombination by integrase.
SI_ΦC31	Inactive DNA binding site for ΦC31. No dimer is bound to this site.
SA_ΦC31	Active DNA binding site for ΦC31. A dimer is bound to this site.
SF_ΦC31	Flipped DNA binding site for ΦC31. The site generated after recombination by integrase.
T_on,i	The number of terminators which are blocking the transcription of GFP and LuxI/LasI initially.
T_offBxb1	The number of terminators turned off by recombination due to Bxb1. Favours the transcription of GFP and LuxI.
T_offΦC31	The number of terminators turned off by recombination due to ΦC31. Favours the transcription of GFP and LuxI.
T_on,f	The number of terminators blocking the transcription of GFP and LuxI/LasI after recombination by Bxb1 and ΦC31. No transcription.
mRNA_GFP	mRNA for Green fluorescent protein which is produced when the cells are ON.
GFP	Green fluorescent protein which is produced when the cells are ON.
mRNA_LuxI	mRNA for LuxI which is produced when the cells are ON.
LuxI	Enzyme catalysing the production of Lux-AHL from SAM and ACP.
mRNA_LasI	mRNA for LasI which is produced when the cell are ON.
LasI	Enzyme catalysing the production of Las-AHL from SAM and ACP.

Reactions

For the Lux system

$$ \begin{align} &\rightarrow LuxR \\ Lux-AHL+LuxR & \leftrightarrow RLux\\ RLux+RLux &\leftrightarrow DRLux\\ DRLux+P_{luxOFF} & \leftrightarrow P_{luxON}\\ P_{luxON}&\rightarrow P_{luxON}+mRNA_{Bxb1}\\ mRNA_{Bxb1}&\rightarrow Bxb1\\ AHL &\rightarrow \\ LuxR &\rightarrow \\ RLux &\rightarrow\\ DRLux &\rightarrow\\ mRNA_{Bxb1} &\rightarrow\\ Bxb1 &\rightarrow \end{align}$$

For the Las system

\begin{align} &\rightarrow LasR \\ Las-AHL+LasR & \leftrightarrow RLas \\ RLas+RLas & \leftrightarrow DRLas\\ DRLas+P_{LasOFF} & \leftrightarrow P_{LasON}\\ P_{LasON}&\rightarrow P_{LasON}+mRNA_{\phi C31}\\ Las-AHL &\rightarrow \\ LasR &\rightarrow \\ RLas &\rightarrow\\ DRLas &\rightarrow\\ mRNA_{\phi C31} &\rightarrow \\ \phi C31 &\rightarrow \\ \end{align}

Equations

Applying mass action kinetic laws, we obtain the following set of differential equations. $$\begin{align*} \frac{d[Lux-AHL]}{dt} &= k_{-RLux}[R_{Lux}]-k_{RLux}[Lux-AHL][LuxR]-d_{Lux-AHL}[Lux-AHL]\\ \frac{d[LuxR]}{dt} &= \alpha_{LuxR} -k_{RLux}[Lux-AHL][LuxR] + k_{-RLux}[RLux] - d_{LuxR}[LuxR] \\ \frac{d[RLux]}{dt} &= k_{RLux}[Lux-AHL][LuxR] - k_{-RLux}[RLux] - 2 k_{DRLux} [RLux]^2 + 2 k_{-DRLux} [DRLux] - d_{RLux} [RLux] \\ \frac{d[DRLux]}{dt} &= k_{DRLux} [RLux]^2 - k_{-DRLux} [DRLux] - d_{DRLux} [DRLux] \\ \frac{d[P_{LuxON}]}{dt} &= k_{P_{LuxON}} [P_{LuxOFF}][DRLux] - k_{-P_{LuxON}} [P_{LuxON}]\\ \frac{d[mRNA_{Bxb1}]}{dt} &= L_{P_{Lux}} + k_{mRNA_{Bxb1}} [P_{LuxON}] - d_{mRNA_{Bxb1}} [mRNA_{Bxb1}]\\ \frac{d[Bxb1]}{dt} &= k_{mRNA_{Bxb1}} [mRNA_{Bxb1}] - d_{Bxb1}[Bxb1]\\ \end{align*}$$

@@ Line 167: / Line 167: @@
 <html><article id="Dynamics"></html>
-== Characterization: K<sub>mLux</sub> and K<sub>mLas</sub> ==
+== Dynamics ==
-=== Data ===
+=== Ideal case ===
-For the Quorum sensing module we used established experimentally determined parameters for the rate of formation of RLux (reference). Since, in the literature the other parameters were estimated or fitted to their data, we decided to determine the parameters specific to our system. Hence, we used our data for the remaining parameters. Our data was mainly a transfer function of normalized GFP concentration as a function of input Lux-AHL concentrations. (link to data)
-=== Assumptions ===
+=== With Leakiness ===
-From the original set of reactions, we reduce the rate of production of mRNA<sub>Bxb1</sub> as a Hill function of RLux instead of Mass action kinetics in terms of P<sub>LuxON</sub>  and P<sub>LuxOFF</sub>.
-Assumption A
+=== With Leakiness and Crosstalk ===
-We assumed that the dimerization of RLux to DRLux is quick. Quasi steady state approximation (QSSA)  as follows
-$$\frac{d[DRLux]}{dt} = k_{DRLux} [RLux]^2 - k_{-DRLux} [DRLux] - d_{DRLux} [DRLux] \approx 0\\$$
-Assumption B
-Further, from literature, we found that DRLux is specific to DNA and the dissociation constant is low (k<sub>m</sub> = 0.1nM) {Reference}.  Therefore, we using QSSA again,
-$$\frac{d[P_{LuxON}]}{dt} = k_{P_{LuxON}} [P_{LuxOFF}][DRLux] - k_{-P_{LuxON}} [P_{LuxON}] \approx 0\\$$
-Solving, we get the rate of production of mRNA<sub>Bxb1</sub> as
-$$\frac{d[mRNA_{Bxb1}]}{dt} = L_{P_{Lux}} + \frac{K_{mRNA_{Bxb1}}RLux^2}{K_{mLux} + RLux^2 }- d_{mRNA_{Bxb1}} [mRNA_{Bxb1}]\\$$
-where
-$$K_{mLux} = \frac {k_{-P_{LuxON}}}{k_{P_{LuxON}}}.\frac {k_{-DRLux} + d_{DRLux}}{k_{DRLux}}$$
-is a lumped parameter which we fitted to our data.
-Similarly, lumped parameter K<sub>mLas</sub> was derived for the las system and fitted to a transfer function of normalized GFP concentration as a function of input Las-AHL.
-<!--Further,
-$$K_{mRNA_{Bxb1}} = k_{mRNA_{Bxb1}} P_{LuxTOT}$$ which we assumed. -->
-=== Parameter fitting ===
-We used MEIGO Toolbox to fit the parameters to the transfer functions.
-=== Range of validity of the assumptions ===
-These assumptions hold true for all input Lux-AHL and Las-AHL concentrations.
-<html></article></html>
-<html><article id="Leakiness"></html>
-<html></article></html>
-<html><article id="Cross-talk"></html>
 <html></article></html>
 {{:Team:ETH Zurich/tpl/foot}}

Team:ETH Zurich/modeling/whole

From 2014.igem.org

Revision as of 15:32, 12 October 2014

Whole cell model

Model

Chemical Species

Reactions

Equations

Dynamics

Ideal case

With Leakiness

With Leakiness and Crosstalk

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