Team:Manchester/Contribution

Contribution

Sarcosine Sensor

We designed and characterised a sarcosine sensor which we have added to the iGEM registry, and can be found here. Future iGEM teams can use this to express genes in response to sarcosine, an amino acid derivative. In our project we planned to use this sensor in a kill switch design which would make the survival of our bacteria dependent on a sarcosine-rich environment, the human urinary tract.

Lsr Promoter

We contributed to the previously characterised part LsrA promoter BBa_K117002. The LsrA promoter BioBrick can be important to many iGEM teams as it can be used to tie gene expression to common quorum sensing signal autoinducer-2 (AI-2). We added modelling equations from Hooshangi and Bentley, 2011 (linked here):

These equations allow future teams to model the expression of the Lsr promoter
To use these, teams must estimate a value of extracellular AI-2 concentration
For our own project, we assumed that the concentrations of Lsr operon proteins would be the same as if our protein was expressed under control of the Lsr promoter
We also created equations to model bacterial population and AI-2 production which can be found here
It should be mentioned that the concentration given is an intracellular concentration so any secreted proteins must undergo further modelling or assumptions

Variables

Symbol	Description	Initial Value
t	Time	0 minutes
[OP]	Lsr-operon concentration	0 M
[REG]	Lsr Regulator Cocnentration	0 M
[R]	LsrR Concentration	0 M
[A_p]	Intracellular Phosphorylated AI-2 concentration	0 M
[A_out]	Extracellular AI-2 Concentration	Estimate/model this uM

Parameters

Parameter	Description	Value	References
k_op	Lsr-synthesis rate	7 uM^-1 min^-1	[2]
k_r	LsrR synthesis rate	2 min^-1	[2]
k₁	Repression Coefficient (Lsr-operon)	0.2 uM	[2]
k₂	Repression coefficient (LsrR)	0.1 uM	[2]
k₃	AI-2/LsrR binding rate	0.5 uM^-1 min^-1	[2]
k₄	Repression coefficient (Lsr-regulator)	65 uM	[2]
k₅	REG/AI-2 interaction	0.0001 uM^-1 min^-1	[2]
k_f	AI-2 fluc through alternative pahways	0.01 uM^-1 min^-1	[2]
k_imp	AI-2 import via LasrABCD	0.01 uM^-1 min^-1	[2]
nOP	Cooperativity coefficient (Lsr-operon)	4	[2]
k_nR	class="model-th"Cooperativity coefficient (LsrR)	4	[2]
k_deg	Protein decay rate	0.02 min^-1	[2]

Equations

Equation 1

$$ \frac{d\left[OP\right]}{dt\ }\ =\ \frac{k_{op}}{1+\left(\frac{\left[R\right]}{k_{1}}\right)^{nOP}+\left(\frac{\left[REG\right]}{K_{4}}\right)^{nOP}}\ -\ k_{deg}\left[OP\right] $$

Equation 1 describes the rate of change of protein concentration produced by the Lsr promoter. Specifically this equation refers to the LsrABCD operon however in our model we assumed this concentration would be the same for our recombinant protein.

Equation 2

$$\frac{d\left[REG\right]}{dt}=\ \frac{k_{op}}{1+\left(\frac{\left[R\right]}{k_{1}}\right)^{nOP}+\left(\frac{\left[REG\right]}{K_{4}}\right)^{nOP}}\ -\ k_{deg}\left[REG\right]-k_{5}\left[Ap\right]\left[REG\right] $$

Equation 2 is describing the rate of change of a hypothetical Lsr-regulator molecule suggested to exist in the source literature. [2]

Equation 3

$$ \frac{d\left[R\right]}{dt}=\frac{k_{r}}{1+\left(\frac{\left[R\right]}{k_{2}}\right)^{nR}}\ -\ k_{deg}\left[R\right]\ -\ k_{3}\left[Ap\right]\left[R\right] $$

Equation 3 describes the rate of synthesis of LsrR

Equation 4

$$ \frac{d\left[Ap\right]}{dt}\ =\ k_{f}\left[A_{out}\right]+k_{imp}\left[OP\right]\left[A_{out}\right]-k_{3}\left[Ap\right]\left[R\right]-k_{5}\left[Ap\right]\left[REG\right] $$

This equation describes the concentration of phosphorylated AI-2 inside the cell. This is contributed to by flux of AI-2 through the LsrABCD channel complex and alternative pathways. Ap is depleted by AI-2 binding to the LsrR protein and the theoretical Lsr-regulator molecule.

Equation 5

$$\frac{d\left[A_{out}\right]}{dt}\ =\ k_{AI2}\cdot X-k_{f}\left[A_{out}\right]-k_{imp}\cdot\left[OP\right]\cdot A_{out}$$

Equation 5 gives us the rate of decrease of the exrracellular AI-2 concentration, this assumes that we have estimated an initial concentration of AI-2 which is not very realistic. In our model we added equations to decribe bacterial concentration and AI-2 production, further details can be found here:https://2021.igem.org/Team:Manchester/Model

Equation 6

$$\frac{d\left[ApG\right]}{dt}\ =\ k_{5}\left[Ap\right]\left[REG\right]\ -\ k_{deg}\left[ApG\right]$$

This equation gives us the rate of change of the Lsr-regulator/AI-2 complex.

Equation 7

$$ \frac{d\left[ApR\right]}{dt}\ =\ k_{3}\left[Ap\right]\left[R\right]-k_{deg}\left[ApR\right]$$

This equation gives us the rate of change of the LsrR/AI-2 complex.

please visit our model page for Dispersin B for more details