Team:Edinburgh/Modelling/Kappa/Analysis

Analysis of the Sub-models

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.


Figure 1. This graph shows the amounts of Complex I and Complex II as the electron transfer between the TCA cycle and the quinol goes on.

The amount of Complex I with NADH together with the amount of Complex I without NADH gives us the total amount of Complex I. This is why the two corresponding graphs shown above are “complementary”.
The same can be said about the amount of Complex II with succinate and the amount of Complex II without succinate.

When working on the TCA cycle, we started with an “ideal” model. What we mean is that there was no restriction on the total amount of agents or tokens of any kind. However, this is never the case in reality where the electron transfer process takes place in the limits of a cell.

Even so, it is useful to consider such an ideal model in order to study the interaction between the different elements of the system when there are no restrictions.


Figure 2. Idealised electron transfer system

Figure 2 presents such an idealised model. In it we can again see the “complimentary” property of the tuples (Complex I with NADH, Complex I without NADH) and (Complex II with succinate, Complex II without succinate).

The Electron Transport Chain

File 3_MtrABC.ka:

In this file we model the passage of the electrons through the periplasm.

First, the electron transfer through the inner membrane occurs with the reaction between NapC and mtrA. Then mtrA moves through the periplasm, eventually reaching an mtrB attached to the outer membrane to which it transfers the electrons it is carrying. Additionally, when moving through the periplasm, mtrA can encounter soluble Iron molecules which will also accept electrons.In this file the passage of the electrons through the periplasm is modelled.


Figure 3.

As shown in Figure 3, "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. Inter-cellular 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.


Figure 4.

Figure 4 shows 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.


Figure 5.

The number of Flavins can also have a big effect on the electron transfer rate, as seen in figure 5. 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.


Figure 6.

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.
Figure 7.

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.



So far we saw how isolated sub-systems work on their own. Next why consider the electron transfer system as a whole.

* 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!