Glucose metabolism in Virtual Microbes

[ !! This is an old post from before the "dark-mode" days, so some of the images are unreadible unless you click for a preview !! ]

One of the most well-known carbon sources for bacterial growth is glucose, which converted into pyruvate in the process of glycolysis, which is then further processed in the TCA cycle (tricarboxylic acid cycle). Together, these pathways are among the most important chemical pathways for aerobic organisms, resulting both in the release of energy as well as building blocksused for the synthesis of amino acids and other essential metabolites required for growth. For microbes, growth is of course very directly related to reproduction, as every cell division results in a new (smaller) individual that again needs to grow. It is therefor no accident that both energy and building blocks are at the bedrock of the Virtual Microbe modelling platform. In the form of a user-defined artificial chemistry, Virtual Microbes have to synthesise both energy as well as building blocks, which are not directly available as a resource (see the tutorial if you are interested).

Although it is fun to come up with your own make-pretend metabolic universe, I here discuss my attempts to implement a simplified pathway of glycolysis and the TCA cycle, to see what things we might discover. As a footnote, I should add that my knowledge of metabolism is rather primitive, and many of the simplifications I make are likely very unrealistic. However, I'm gonna do this anyway in the spirit of "let's see what happens!".

For the first part in this series, I am mostly showing what is implemented, and how I accidentally converged on reality by "debugging" a very silly mistake in my initial biochemistry.

Virtual Glycolysis

The figure below shows you how I implemented the glycolysis pathway in four steps.

Virtual Glycolysis implementation

- Different metabolites are represented as blocks, with the number of squares representing the number of carbon atoms in the molecule. The energy carrier ATP is depicted as a red pentagon.

Note that many simplifications are made, such as lumping of reactions and metabolites, directly adding ATP from NADH/FADH2 that would normally be indirect via the electron transport chain, and the removal of ADP and inorganic phosphate, which are assumed to be abundantly available to synthesise ATP. Apart from all the simplifications, I did deliberately include the investment of 2 ATP per glucose, which is later rewarded with a payoff of 2x5=10 ATP per glucose, because.. well, that is just the way it is!

Virtual TCA cycle

For the tricarboxylic acid cycle (TCA cycle), I added onto glycolysis, the following reactions:

(initial) Virtual TCA Cycle

- Different metabolites are represented as

blocks, with the number of squares representing the number of carbon atoms in the molecule. The energy carrier ATP is depicted as a red pentagon.

Very similar simplifications to the ones with respect to glycolysis are made. In short, many well-known cascades of reactions are represented in a single reactions, all energy yields from NADH/FADH2 are immediately added to the ATP pool, etc.

Finally, note that the Virtual Microbes framework does not include reversible or spontaneous reactions. In other words: if the critters want any of these reactions to happen, they have to express proteins that catalyse it, and it can only go in the direction as drawn in the figures above.

What do they need to grow?

Of course, an actual microbe needs a lot of different metabolites to grow, and many of them are not in our current "metabolic universe". But let's ignore that for now. For growth, I here assigned the essential metabolites roughly based on work by Carlson et al., 2004 [efn_note] Carlson, Ross, and Friedrich Srienc. "Fundamental Escherichia coli biochemical pathways for biomass and energy production: identification of reactions." Biotechnology and bioengineering 85.1 (2004): 1-19. [/efn_note], which has recently also been succesfully applied to screen Elementary Flux Modes in E. coli [efn_note] Wortel, Meike T., et al. "Metabolic enzyme cost explains variable trade-offs between microbial growth rate and yield." PLoS computational biology 14.2 (2018): e1006010. [/efn_note]. See the image below:

Esstential metabolites for making building blocks

- Building blocks in Virtual Microbes are necessary to express proteins and grow the cells. All building blocks that are not used to synthesize proteins are available for growth.

After everything is setup as displayed above, I hand-crafted a cell that has genes to catalyse all the reactions depicted above. Note that these genes also have many parameters (Vmax, Ks, basal expression rates, etc.), which for now are all fixed on identical values for each gene.

A circle has no beginning..

What is wrong with the overview of reactions depicted above? At first glance, it really does look like the classic textbook representation of the central carbon metabolism. However, after trying to get Virtual Microbes to live in this universe for hours, I came to realise something is wrong here: 1Acetyl-CoA and 1 oxaloacetate are needed to enter the cycle, meaning that no matter how much glucose they consume, the cycle cannot be started from scratch. What's more, even if it could be started, the smallest amount of decay of oxaloacetate would inevitably slow things down: the TCA cycle will eventually deplete itself.

To test this idea, I added an extra reaction which can produce oxaloacetate from the primary resource. With a limited understanding of the details of this metabolism, I decided to add the possibility of converting pyruvate into oxaloacetate. Does this extra addition, that is not even in most of the textbooks, make any sense? Well... a quick Google search assured me that, not only does it make sense, it is actually an essential reaction for real organisms. An enzyme called pyruvate carboxylase indeed converts pyruvate (plus co2 and atp) into oxaloacetate. It appears that, even though I was merely "lucky" picking the correct substrate (e.g. it also works if you do the same with g3p), the model debugged my primitive understanding of metabolism. So, here's the updated "metabolic universe":

Virtual Glycolysis and TCA Cycle

- Different metabolites are represented as

blocks, with the number of squares representing the number of carbon atoms in the molecule. The energy carrier ATP is depicted as a red pentagon (as only a little pyruvate needs to be coverted to oxaloacetate, I assume in this figure that merely 1 less atp is now produced per glucose)

The changes depicted above solved the problem immediately: the engine of the TCA cycle was purring and my Virtual Microbes grew.. kind of. They appeared to be experiencing periods of growth… and periods of stagnation. They are growing in waves:

Virtual Microbes growing in waves

Why are the Virtual Microbes growing in waves? There are two reasons this could be the case. Firstly, they are growing on a limited influx of resource. Perhaps the current critters are actually over-exploiting their environment, and can only grow there where no cells were growing a moment before. Although this is the most plausible explanation, it actually takes quite some time for the cells to start growing again, even when the resource (glucose) is pretty high (not shown). What is this supposed kick-start problem?

The danger of a turbo design?

To study if the growth in waves shown above is only due to direct resource limitation, I decided to grow these cells in batch culture. This revealed that, under certain conditions, the internal metabolism of the cells could no longer be started even when glucose concentrations are refreshed:

Virtual Microbes in batch culture can display "growth arrest"

Note that the cells from the figure above are not simply ATP depleted. Instead, other metabolites and their relative ratios appear to be the limiting factor. I have not yet fully grasped the physiological details of this phenomenon, but I did find some literature that displays similar dynamics [efn_note] Teusink, Bas, et al. "The danger of metabolic pathways with turbo design." Trends in biochemical sciences 23.5 (1998): 162-169. [/efn_note] [efn_note] Mulukutla, Bhanu Chandra, et al. "Bistability in glycolysis pathway as a physiological switch in energy metabolism." PloS one 9.6 (2014): e98756. [/efn_note] [efn_note] van Heerden, Johan H., et al. "Lost in transition: start-up of glycolysis yields subpopulations of nongrowing cells." Science343.6174 (2014): 1245114. [/efn_note]. In these articles it is shown that upper glycolysis (i.e. the investment phase)can outpace lower glycolysis (i.e. thepayoff phase), resulting in an alternative, low-yield steady state. Indeed, as can be seen from the Figure above, some glucose is actually consumed by the cells even in their state of "growth arrest". They are not completely failing to metabolise, but are doing so at an incredibly limited rate (not shown).

Despite showing the same phenomenon, not all details are likely identical in Virtual Microbes and the work by van Heerden et al. (2014). Firstly, inorganic phosphate limitations are shown to be a key variable in the work by van Heerden, but these metabolites are assumed to be non-limiting for Virtual Microbes. In other words, this comparison cannot be fully made. However, the problem with the so-called unbalanced design of glycolysis is clearly present in my simulations so far. To be continued.. ;)

What's next?

So, what is next? Well, because Virtual Microbes is a platform designed to simulate eco-evolutionary dynamics, it makes sense to start adding evolution to the mix! As a preliminary, something interesting I stumbled upon is that the starting clone (with genes to catalyse all reactions) was quickly invaded by mutants that have high growth rates but lower ATP yield. These mutants have lost the genes to catalyse the reactions for the second half of the TCA cycle, therefor retaining more of the other essential metabolites (see Figure below).

When the system is simulated with mutations, high growth rate mutants invade, and eventually take over the population.

This type of metabolism is actually very much convergent with what was found as the Elementary Flux Mode for high growth rates (Wortel et al., 2018). I had actually expected a spatial system such as Virtual Microbes to have enough higher-level selection (kin/group) to avoid this loss of yield, but it turns out this isn't the case. I plan to study this, and some other interesting ideas, in the future.

To wrap up, up until now the Virtual implementation of glycolysis and the TCA cycle are, at least in terms of their dynamics, converging with the literature. Any future discoveries might therefore even be relevant in the non-Virtual world.