Team:TU Delft-Leiden/Modeling/Curli/Reflection

Critical reflection on our model

We have successfully created a model that simulates a measurement in the way that we envisioned it. We are fairly confident that the system will show some of the behaviour that we modelled. We think that it is valuable to be critical on our own workings. Also we want you to know that we understand the strong and weak points of our model. Therefore we have made a short list of things that could be improved in further adaptations of the model.

We went in the gene level to a simplified model that was just about the creation of curli. However, we have not taken into account for instance maturation of the CsgB. It might as well be that our response is delayed. Luckily we found that CsgB fastens the production of CsgA [1].

Another point that is interesting to look at, is the restraining of the amount of CsgB that is permitted on the cell surface. We don't know what exactly happens on the cell level, since this is unknown. In order to still have adequately long wires we had to decrease the CsgB production drastically.

However, this makes the system especially sensitive to leakage of CsgB. Unfortunately, the experiments that we have performed show that the promoter we use is especially leaky. This means that there will most likely already form curli before the promoter is activated. The steep increase in the amount of Curli that is observed will then probably not happen. Instead, the curli are just formed over time. If this is true, then we strongly doubt that there will be any noticeable difference between a weakly and strong induced promoter at all. Only switching on or off the CsgB production is in our opinion not a good idea. From our colony model it seems that the abundance of CsgA is necessary.

Modelling the cell level was maybe hardest of all. The kinetics of the curli adding remains largely unknown to us. We tried to keep it as simple as possible, and still have some useful information to give to the colony level. Our first intention was to actually model each wire and look at the percolation between the wires. Then look at the conductance as function of the radius due to the percolation in between the wires. We even created the code that could find clusters of curli fibres. In this end this seemed infeasible. For instance, we don't know the exact thickness of the wires. We cannot incorporate physical interactions between the wires, since this would be computationally too heavy.

We also made the assumption that curli can only grow and never break. In literature [2] we've found that the assumption that the starting point of the curli is random is not true. It appears that they are clustered. However, distinguishing between the radial axis of the cell would make it very complicated for the colony model. For the same reason we made the assumption that our E. Coli are spherical rather than rod-shaped. This would increase the variation per cell. However, from the percolation simulations we see that the individual cell variations have small influence on the outcome. Therefore we still think that at our simplifications might give reasonable results.

In the colony model we regret that we had to scale down the cell density. The memory necessary to find the resistance between \( N \) cells goes with \( N^2 \). Simulation times increase even more drastically. For higher cell densities we expect a similar characteristic response, but with a higher conductance. It might also be nice to see what would happen if cells are permitted to lie on top of each other, thereby increasing the dimension to three. But then again, physical interactions are hard to incorporate in a model.

A more fundamental difference between our model and reality is that we look at connection from one cell to another. In reality, it is the stuff in between the cells that makes it conductive or not. The electrons won't go through the cells.

References

[1] Hammer ND Chapman MR, The C-terminal repeating units of CsgB direct bacterial functional amyloid nucleation, J Mol Biol 2012 sep 21

[2] Epstein EA Chapman MR, Spatial clustering of the curlin secretion lipoprotein requires curli fiber assembly, J Bacteriol. 2009 Jan