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Analysis of the Model
The TCA Cycle
The file 1_TCA.ka models the electron transfer between the TCA cycle and the quinol QH2. This process starts with the absorption of glucose by the TCA cycle and passes through Complex I and Complex II before it reaches the quinol.
The above graph shows the amounts of glucose, Complex I and Complex II as the electron transfer between the TCA cycle and the quinol goes on.
This is an idealized plot of the TCA cycle given optimum conditions. The actual model doesn’t work as cleanly as this, because adding the realistic external constraint seriously affects all involved parameters and also injects a great deal of randomness. Reality generally has a nasty habit of ruining clear and concise approaches. However we include this because it presents a good, if idealised, overview of the working of the TCA cycle.
The Electron Transport Chain
File 3_MtrABC.ka:
In this file the passage of the electrons through the periplasm is modelled.
First the passage through the inner membrane occurs with the reaction between NapC and mtrA, then mtrA moves through the periplasm itself, eventually reaching an mtrB attached to the outer membrane to which it transfers the electrons it’s carrying. Additionally, when moving through the periplasm, mtrA can encounter soluble Iron molecules which will also accept electrons.
Here we can see that, "mtrCAB_electrons_from_SolubleIron" is significantly larger than "mtrCAB_electrons_from_mtrB". As it turns out, the bulk of the produced electric current is via soluble Iron present in the periplasm. Noticing this we made a second model where MtrBC is absent and therefore we can have more mtrA agents. The "mtrA_electrons_from_SolubleIron" is even larger, as expected, but though the number of mtrAs has almost doubled(from 2100 to 4000), the growth in electron rate is ~1.4 It’s clear that the extra mtrAs suffer from diminishing returns.
File 4_UFe.ka:
This file models the transfer of iron from the outer membrane of the cell to it’s final acceptor, insoluble iron. mtrC is always connected to a mtrB, so for the purpose of this model we consider them a single agent.
If a particle of insoluble iron comes close enough to the mtrC then the electron can be directly transferred. Intercellular Flavin can also pick up the electrons from mtrC and then separately connect to insoluble iron particles. Since the number of mtrCs is quite small the Flavin transfer mechanism is important.
Here we can see the amount of electrons transferred directly to insoluble iron vs. the amount transferred via Flavin. We also test what happens when the insoluble iron particle count is significantly increased by using smaller particles. Specifically, we look at micrometer sized particles and nanometer sized particles. As expected, the rates are higher with the nanoParticles, but considering there are more than 1000x more particles of nanometer size the difference isn’t as dramatic as one might assume. The small number of mtrC agents is likely the limiting step here.
Here we can see that similar to the number of insoluble iron particles, the number of Flavins can also have a big effect on the electron transfer rate. We show the direct mtrC-InsolubleIron rate as well as flavin-InsolubleIron rates for various different quantities of added Flavin.
File 5.ka
This model is a concatenation of models 3 and 4 taking care that the mtrA-mtrBC reaction is accurate and also rewriting some other aspects so that it will be compatible with models 1 & 2.
We look at the model both with the previous values and with 10X more NapC, which brings its behaviour more in line with that expected from Shewanella.
Here we see the familiar relationship between amount of electrons transferred directly through mtrC and those transferred through Flavin. We can also see that increasing the NapC to 10X the normal quantity scales up all rates by roughly the same amount.
The effect of the added NapC is more pronounced in the periplasm. Here originally the rate between electrons given to soluble iron and those given to mtrB is ~9, but with 10X NapC it becomes almost ~20, which is what would be expected from Shewanella.
Conclusion and Future work
This model is a close approximation of the underlying biological system. It incorporates a lot of experimental work and has been verified against yet more research results, showing very promising results.
The next step is to use this model to try to better understand the biological underpinnings of the system. Specifically, we plan to do a series of sensitivity analysis type tests and see how varying the different parameters affects the results. In this fashion we can gain insight into which biological subsystems offer the most promise, thus hopefully reducing the work that needs to be undertaken in the lab.
Furthermore additions to the model trying to boost the electron output or perhaps replicate some other complex behaviour could first be tried in the model. This again will work as a preliminary step which will support or cast doubt upon the biological validity of the proposed addition and will, at the very least, raise some interesting questions about the working of any new proposed system.
* All graphs are aggregated over 50 runs of the model. They show the mean and the standard deviation of the curve. Many thanks to Donal Stewart for providing the tool which made aggregating all the hundreds of text files painless and actually fun!
