Team:TU Delft-Leiden/Modeling/Curli

Curli Model

Gene Level Modeling

We will start with modelling the expression of Curli on the gene level. Proteins that are dedicated to curli formation are the CsgA/B/D/E/F/G [1]. CsgA is the main building block of the curli. When produced this is secreted out of the cell by the csgEFG complex. In the absence of CsgB there is no curli formation, since the CsgA proteins remain unpolymerized. CsgB is the starting block of the curli fibrils, likes piles under a house, that connect the cell membrane to the first CsgA. Once this is placed on the cell surfaced, the CsgA can polymerize onto the starting curli fibril. In the constructs we produce, CsgA is continuously produced. The CsgB promoter, on the other hand is in our design activated by a landmine promoter, activated by either TNT or DNT. In our design, the curli are first grown in a medium. During this time, they produce CsgA. Hence, there is an initial concentration CsgA present in the system when the CsgB promoter is activated. The csgEFG operon encodes four accessory proteins required for the curli assembly. Overexpression of these genes is not needed [bron?] for curli formation.

Extended gene level modeling

to be written

Analytical gene level modeling

Though the model as described above, providing that all rates are known, has a more accurate (though still simplified) representation of the curli assembly system, we have chosen decrease the complexity further to the bare essentials. Most of the production rates and kinetic constants cannot be found in literature. Measuring the accurate rates is, within the scope of this project, unfeasible for many reasons. First of all, we think that the secretion of the proteins is not a rate limiting step. We are interested in the CsgA/B production and curli formation. The scope in which we expect the system to respond is in the order of hours. If secretion were the rate limiting step, it would mean that many CsgA/B units are piled up inside the bacteria. One might raise the question whether it is justified that the growth of new subunits is independent of the length of the curli, since the CsgA is secreted at the edge of the cell distance and has to ‘travel’ towards the end of the curli fibrils. This would suggest that the assumption used in deterministic modelling that all concentrations are homogeneous is not justified. A quick calculation shows that after one second, the displacement of a spherical particle with radius r=10nm due to Brownian motion in liquid water at room temperature using equation 0 is 6.6 μm; many times the bacterial radius! Hence the diffusion is not rate limiting.