Difference between revisions of "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]:

Assumption 2.3:MtrB have no resistance.

In fact, there is a pore in the middle of MtrB so that electron and get it through freely. We supposed that the pore has no resistance,that means, the resistivity of the pore is zero.

With assumption2,3 we can deduce that the resistance of MtrA,MtrC,CymA including their homologues,is in proportion to the length of the protein.According to the measurement in the figure above, it is 9:8.5:1.3. Suppose the proportionality coefficient is k, we have:

Among them:

Equation and result

As we only care about the efficiency of MtrCAB system, getting the proportion among all the protein is enough .Thus we'll suppose the voltage casually as V0=1mV.

Here are the KVL equations in different strains of Shewanella.

Solve those equations with current value(excel), so far we have:

Here, the proportionality coefficient k is remained, that means, it can only be measured in experiment. In fact, the physical meaning of k is clearly defined by the expression of resistance:

So that:

ρ represent the resistivity of protein and S is the cross section area. They are all measurable and availible.

Data Processing

According to the circuit model introduced before ,Mtr CAB protein can be regarded as resistance in parallel or in series .In the sake of applying the model in our system, We tested the electricity of our E.coli to estimate the efficiency of our system.

Here is the current measured in average in our system:

Engineered cell refers to our E.coli with plasmid transformed. We can see that WT conduct the current easier than the engineered E.coli because of metabolic pressure .Now we can abstract our system as electric circuit model.

Resistance replace the protein listed below:

In the same way, we have KVL equation:

Then we get the solution:

The efficiency is:

Conclusion

Apparently, this number is far less than MtrCAB system works in Shewanella. electrons transfered via our system is not account for the majority, which represent a great potential to perfect the our Mtr system.

There is another possibility exists that E.coli can not adopt Mtr system as naturally as Shewanella , There may have some other mechanism shaping MtrCAB protein remained to explore.