Team:USTC/Model/1
Abstract
It has been discovered that there are too many kinds of transfer protein in the membrane of E.coli, including the homologues of MtrCAB generated by our gene circuits and other intrinsic protein. To simplify the process of electron transfer from outer membrane to cystosol and prove the efficiency of our production, that is, MtrCAB conduits. We substitute resistances for MtrCAB and other transferring protein, which are located on the outer membrane, in the periplasm or across the internal membrane. Electrons can only transfer through the resistances. In the final achievement of this model, we can get the exact value of each kind of resistance and describe how much flux of electron conducted by MtrCAB conduits. In the end, our model has also provided a bright new method to detect the concentration of MtrCAB protein conveniently.
Description
If we simplify the protein as resistance in some way, we can see different kinds of protein transfer the electrons one by one, which represent resistances with different value connect in series.Similarly, the same kind of protein is simplified by resistances with the same value connect in parallel. Take MtrA as an example. thousands of MtrA located in the periplasm and each electron will go through the MtrA only once. So the close analogy with resistances in parallel can be made.
We can simplify the protein conduits:
Limited by the experimental condition, we cannot get the exact indispensable data from our own E.coli and MtrCAB system. We have to apply our model on the paper of Daniel E.Ross et al[1].Although the experiments is complished in Shewanella, but the resistance of the protein is supposed to be the same because our DNA part virtually originate from Shewanella. So we can apply the data bravely and check the identity of MtrCAB system in the same time. The data from that paper see Mtr current value(excel).
Assumption
part 1:circuit building
Assumption 1.1: Protein can be regarded as resistance.
There are a lot of identities between MtrCAB system and electric citcuit, that is the motivation for us to build this model. However the feasibility of replacement is still a hypothesis.
Assumption 1.2: the voltage of the same kind of protein is equal.
We assume the electron flux very in cell fluid, resulting in the isotropy of electron concentration to one cell.With this assumpption, same resistances can be connected in parallel.
Assumption 1.3:proteins of one kind are uniform in strcture.
Due to the same structure, the resistances of the protein is the same. Suppose the number of MtrA in one cell is N0, and the value of single MtrA resistance is R0, according to the formula of resistance in parallel, all the resistance of MtrA is:
In that way, we can count for the same kind of protein in one resistance.
Part 2: equation solving
Though the model is simplified, there are too many variables to solve the equation. To find out extra conditions, we have to make more assumptions.
Assumption 2.1:MtrC always connect to MtrB.
From the literature[2],we know that MtrB is essential to the stability of MtrC because MtrC is attached to MtrB by lipid. So that we can connect MtrC and MtrB into one resistance. Thus our varible is cut down.
Assumption 2.2:The resitivity, area density and the cross section area of the protein of one kind, including their homologues, are the same.
This assumption is based on the fact that protein MtrC, MtrA and CymA are all consist of peptides and hemes, which are very critical to electron transfer.Aditionally, the density of hemes in these protein is almost the same(Number of MtrC heme=10, MtrA heme=10, CymA heme=4).Cross sections of MtrCAB system are almost the same according to this illustration of size information [3]:
Equation and result
Assumption
Assumption
