Team:TU-Delft/BandAid

Band Aid

The Band Aid Modeling is related to the final application of our project. Specifically, we are going to use a band aid in which E.coli will be added. By locating the band aid on the wound, the S.aureus should be detected and killed(Figure 1).

                                                                        Figure 1: Band Aid Application

As, it is already known, S.aureus is a pathogenic bacterium that utilises quorum sensing (QS), a cell-to-cell signalling mechanism, to enhance its ability to cause disease[1]. The communication is succeeded through small peptides known as AIPs. We engineered the receiver part of S.aureus to E.coli in order to be able for the last to detect AIPs produced by S.aureus.

The main purpose in the band aid modeling is to answer questions like these mentioned underneath:

1. Is it possible the AIPs to pass through the membrane in order to be feasible for the E.coli to detect MRSA?
2. If the MRSA is detected, is the amount of the produced peptide enough to kill it ?
3. What is the maximum diameter of the pores in the membrane so as only the AIPs and the peptides to pass through?
4. How many pores are necessary in order to be possible for the peptide to be released?

Differential Equations

Our model consists of two Populations:

1. Sender: The S.aureus Population
2. Receiver: The E.coli Population

For our model we made the aforementioned assumptions:

1. The S.aureus population grows exponentially according to the equation:
   
2. The E.coli population is constant.
3. Membrane assumed in 47mm diameter and 0.1μm pore size.
4. Flux equals to pore size * number of holes * Diffusion.
5. No hydrophobic/hydrophilic interactions of the membrane are taken into account.

The differential equations related to each population are represented below.

Sender: S.aureus Population

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Figure 2:Sender

Receiver: E.coli Population

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Parameters

Parameter	Value	Description	Units	Reference
s	0.02	Ratio of basal to QS transcription	Molecules cells-1s-1	[1][2]
u	0.05	mRNA transcription rate	Molecules cells-1s-1	[1][2]
l	1	protein degradation	sec-1	[1][2]
f	1	agrA activation	Molecules-1cm3s-1	[1][2]
g1	1	unbinding AIP from AgrC	s-1	[1][2]
ks	0.1	AgrD loss through AIP production		[1][2]
ka	102	AIP production	Molecules-1cm3s-1	[1][2]
la	1	Natural AIP degradation	s-1	[1][2]
h	0.1	receptor loss through AIP binding		[1][2]
gij	1	AIP from Population i unbinding from Population j		[1][2]
bij	1	AIP binding from Population i to Population j		[1][2]
ba	1	Ratio of cognate AIP binding in Population 2 to Population 1		[1][2]
r	/2/3600	growth rate		[1][2]
K	1	capacity		[1][2]
D	8e-4	diffusion coefficient of the membrane		[1][2]
A	20000	Area of the membrane		[1][2]
pore size	0.22	membrane pore size	0.001	[1][2]

Variables

Variable	Description	Reference
Mi	mRna concentration in Population i	[1][2]
Ai	agrA concentration in Population i	[1][2]
Si	agrD concentration in Population i	[1][2]
ai	AIP concentration in Population i	[1][2]
Ri	agrC concentration in Population i	[1][2]
Pi	Proportion of cells that are upregulated in S.aureus population	[1][2]

Results