Team:Imperial College London/Modelling/Protein Display/Detailed Description

1. Identification of all active and relevant elements of the isolated part of the system.
2. Identification of interactions between the identified elements.
3. Determining the threshold concentration of Auto Inducing Peptide (AIP) needed for activation of the receptor.
4. Determining the volume of the cell wall.
5. Defining a control volume around the bacterial cell (after cleavage, the surface protein will float around in the extracellular environment).
6. Determining the importance of localised concentrations in a control volume.
7. Determining the surface protein production to estimate the maximum abundance on the bacterial surface.
8. Final version of equations

1. The surface protein consists of a cell wall binding domain, a linker and AIP (Auto Inducing Peptide). It is expressed by constitutive gene expression. It was assumed that the bacteria would be fully grown before carrying out the detection so the cell wall would be covered with as many surface proteins as the cell can maintain.
2. Schistosoma elastase (enzyme released by the parasite) cleaves the AIP from the cell wall binding domain at the linker site. In the laboratory, we used TEV protease as we could not get hold of Schistosoma elastase, so the model was adjusted appropriately (TEV enzyme kinetic parameters were used).
3. The ComD receptor is activated by a sufficiently high AIP concentration. Once activated, ComD signals into the cell to activate the colour response.

Apart from the proteins being expressed from genes, there was only one more chemical reaction identified in this part of the system. This is the cleavage of proteins, which is an enzymatic reaction:

• Substrate (S) = Protein
• Enzyme (E) = TEV (Protease)
• Product (P) = Peptide

The optimal peptide concentration required to activate ComD is 10 ng/ml [1]. This is the threshold value for ComD activation. However, the minimum concentration of peptide to give a detectable activation is 0.5ng/ml.
The threshold for the minimal activation of the receptor is c_th=4.4658×10^-9 mol/L. Click on the button below to uncover the conversion from ng/ml to mol/L.

Initially, we defined a control volume assuming that bacteria would grow in close colonies on the plate. We realized that our initial choice of control volume was not accurate, since our bacteria are meant to be used in suspension so we had to reconsider this issue. If you wish to have a look at our initial working, click on the button below.

Initial Choice of Control Volume

This control volume is considered to be wrong, but the details were kept for reference.
Control volume initial choice
The control volume: The inner boundary is determined by the bacterial cell (proteins after being displayed and cleaved cannot diffuse back into bacterium). The outer boundary is more time scale dependent. We have assumed that after mass cleavage of the display-proteins by TEV, many of these AIPs will bind to the receptors quite quickly (eg. 8 seconds). Our volume is determined by the distance that AIPs could travel outwards by diffusion within that short time. In this way, we are sure that the concentration of AIPs outside our control volume after a given time is approximately 0. This approach is not very accurate and can lead us to false negative conclusions (as in reality there will be a concentration gradient, with the highest concentration on the cell wall).

Control volume (Volume of B. subtilis to be excluded. x indicates the distance travelled by AIPs from the surface in time t).

Difussion distance was calculated using Fick's 1^st Law: x=√2Dt, where: x - diffusion distance, D - diffusion constant, t - time of diffusion
D_average = 10.7×10^-11 m²s^-1 for a protein in agarose gel for pH=5.6 [3]
t = 8s (arbitrarily chosen)
This gives: x = 4.14×10^-5m
The control volume can be calculated by adding 2x to the length and the diamter of the cell.
This gives a control volume (CV) = 4.81×10^-7m³

Calibration curve relating cell concentration to optical density at 600nm (OD600).

The graph shows values of CFU/ml for different optical densities. The range of CFU/ml is therefore between 0.5×10⁸ - 5×10⁸.
In this calculation, we assumed that only one cell will grow and become one colony (i.e. no more than one cell will form no more than one colony). Therefore, the maximum number of cells in 1ml of solution is 5×10⁸. Taking the volume of 1 ml = 10^-3 dm³ and dividing by the (maximum) number of cells in 1ml gives the average control volume (CV) around each cell: 2×10^-12 dm³/cell. For simplicity, we choose the control volume to be cubic. Taking the third root of this value gives the length of each side of the control volume.

Side length of cubic Control volume is y = 1.26×10^-4 dm = 1.26×10^-5 m.

• AIPs being very close to the cell surface will have an equal probability of heading back towards the bacterium as diffusing away from it (since the cell is a lot bigger than the AIPs).
• It is likely that there will be some chemical interactions between AIPs and the bacterium which could be attracting the AIPs to the host bacterium (e.g. electrostatic attraction could be possible).

• This paper mentions that each cell displays 2.4×10⁵ peptides. [2]
• 2.4×10⁵ molecules = 2.4×10⁵/6.02×10²³ mol = 0.398671×10^-18 mol
• Volume of ''B.subtilis'' cell wall: 0.32×10^-15m³
• Concentration = [mol/L]
• c = 1.24×10^-3 mol/L. This is the concentration of protein that will be displayed on a single cell of B.sub.

Production of protein by transcription and translation.

1. Havarstein, L., Coomaraswamy, G. & Morrison, D. (1995) An unmodified heptadecapeptide pheromone induces competence for genetic transformation in Streptococcus pneumoniae. Proc. Natl. [Online] 92, 11140-11144. Available from: http://ukpmc.ac.uk/backend/ptpmcrender.cgi?accid=PMC40587&blobtype=pdf [Accessed 27th August 2010]
2. Kobayashi, G. et al (2000) Accumulation of an artificial cell wall-binding lipase by Bacillus subtilis wprA and/or sigD mutants. FEMS Microbiology Letters. [Online] 188(2000), 165-169. Available from: http://onlinelibrary.wiley.com/doi/10.1111/j.1574-6968.2000.tb09188.x/pdf [Accessed 27th August 2010]
3. Gutenwik, J., Nilsson, B. & Axelsson, A. (2003) Determination of protein diffusion coefficients in agarose gel with a diffusion cell. Biochemical Engineering Journal. [Online] 19(2004), 1-7. Available from: http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V5N-4B3MXDC-2-K&_cdi=5791&_user=217827&_pii=S1369703X03002377&_origin=search&_coverDate=07%2F01%2F2004&_sk=999809998&view=c&wchp=dGLzVtb-zSkzS&md5=c17d0e7320f03931006f9b1a10a438b9&ie=/sdarticle.pdf [Accessed August 20th 2010]
4. Imperial College London (2008) Biofabricator Subtilis - Designer Genes. [Online] Available from: https://2008.igem.org/Imperial_College/18_September_2008 [Accessed 1st September 2010]
5. Graham L. L. & Beverisge T. J. (1993) Structural Differentiation of the Bacillus subtilis 168 Cell Wall. Journal of Bacteriolofy. [Online] 5(1994), 1413-1420. Available from: http://jb.asm.org/cgi/reprint/176/5/1413?ijkey=27dafbac7e23dee50390d3fe67d9d1bab0c6f48c [Accessed October 26th 2010]