# Methylation Helps a Bacterium Adapt to Differing Concentrations

## Bacterial tumbling frequencies remain constant for different attractant concentrations

In the previous lesson, we explored the signal transduction pathway by which E. coli can change its tumbling frequency in response to a change in the concentration of an attractant. But the reality of cellular environments is that the concentration of an attractant can vary across several orders of magnitude. The cell therefore needs to detect not absolute concentrations of an attractant but rather relative changes.

E. coli detects relative changes in its concentration via adaptation to these changes. If the concentration of attractant remains constant for a period of time, then regardless of the absolute value of the concentration, the cell returns to the same background tumbling frequency. In other words, E. coli demonstrates robustness to the attractant concentration in maintaining its default tumbling behavior.

However, our current model is not able to address this adaptation. If the ligand concentration increases in the model, then phosphorylated CheY will plummet and remain at a low steady state.

In this lesson, we will investigate the biochemical mechanism that E. coli uses to achieve such a robust response to environments with different background concentrations. We will then expand the model we built in the previous lesson to replicate the bacterium’s adaptive response.

## Bacteria remember past concentrations using methylation

Recall that in the absence of an attractant, CheW and CheA readily bind to an MCP, leading to greater autophosphorylation of CheA, which in turn phosphorylates CheY. The greater the concentration of phosphorylated CheY, the more frequently the bacterium tumbles.

Signal transduction is achieved through phosphorylation, but E. coli maintains a “memory” of past environmental concentrations through a chemical process called methylation. In this reaction, a methyl group (-CH3) is added to an organic molecule; the removal of a methyl group is called demethylation.

Every MCP receptor contains four methylation sites, meaning that between zero and four methyl groups can be added to the receptor. On the plasma membrane, many MCPs, CheW, and CheA molecules form an array structure. Methylation reduces the negative charge on the receptors, stabilizing the array and facilitating CheA autophosphorylation. The more sites that are methylated, the higher the autophosphorylation rate of CheA, which means that CheY has a higher phosphorylation rate, and tumbling frequency increases.

Note that we now have two different ways that tumbling frequency can be elevated. First, if the concentration of an attractant is low, then CheW and CheA freely form a complex with the MCP, and the phosphorylation cascade passes phosphoryl groups to CheY, which interacts with the flagella and keeps tumbling frequency high. Second, an increase in MCP methylation can also boost CheA autophosphorylation and lead to an increased tumbling frequency.

Methylation of MCPs is achieved by an additional protein called CheR. When bound to MCPs, CheR methylates ligand-bound MCPs faster12, and so the rate of MCP methylation by CheR is higher if the MCP is bound to a ligand.3. Let’s consider how this fact affects a bacterium’s behavior.

Say that E. coli encounters an increase in attractant concentration. Then the lack of a phosphorylation cascade will mean less phosphorylated CheY, and so the tumbling frequency will decrease. However, if the attractant concentration levels off, then the tumbling frequency will flatten, while CheR starts methylating the MCP. Over time, the rising methylation will increase CheA autophosphorylation, bringing back the phosphorylation cascade and raising tumbling frequency back to default levels.

Just as the phosphorylation of CheY can be reversed, MCP methylation can be undone to prevent methylation from being permanent. In particular, an enzyme called CheB, which like CheY is phosphorylated by CheA, demethylates MCPs (as well as autodephosphorylates). The rate of an MCP’s demethylation is dependent on the extent to which the MCP is methylated. In other words, the rate of MCP methylation is higher when the MCP is in a low methylation state, and the rate of demethylation is faster when the MCP is in a high methylation state.3

The figure below adds CheR and CheB to provide a complete picture of the core pathways influencing chemotaxis. To model these pathways and see how our simulated bacterial system responds to different relative attractant concentrations, we will need to add quite a few molecules and reactions to our current model.

The chemotaxis signal-transduction pathway with methylation included. CheA phosphorylates CheB, which methylates MCPs, while CheR demethylates MCPs. Blue lines denote phosphorylation, grey lines denote dephosphorylation, green arrows denote methylation, and red arrows denote demethlyation. Image modified from Parkinson Lab’s illustrations.

## Combinatorial explosion and the need for rule-based modeling

We would like to add the methylation reactions discussed above to the model that we built in the previous lesson and see if this model can replicate the adaptation behavior of E. coli in the presence of a changing attractant concentration. Before incorporating the adaptation mechanisms in our BioNetGen model, we will first describe the reactions that BioNetGen will need.

We begin with considering the MCP complexes. In the phosphorylation tutorial, we identified two components relevant for reactions involving MCPs: a ligand-binding component l and a phosphorylation component Phos. The adaptation mechanism introduces two additional reactions: methylation of the MCP by CheR, and demethylation of the MCP by CheB.

We also need to include binding and dissociation reactions between the MCP and CheR because under normal conditions, most CheR are bound to MCP complexes.4 We will therefore introduce two additional components to the MCP molecules in addition to their phosphorylation components: r (denoting CheR-binding) and Meth (denoting methylation states). In our simulation, we will use three methylation levels (low, medium, and high) rather than five because these three states are most involved in the chemotaxis response to attractants.5

Imagine for a moment that we were attempting to specify every reaction that could take place in our model. To specify an MCP, we would need to tell the program whether it is bound to a ligand (two possible states), whether it is bound to CheR (two possible states), whether it is phosphorylated (two possible states), and which methylation state it is in (three possible states). Therefore, a given MCP has 2 · 2 · 2 · 3 = 24 total states.

Say that we are simulating the simple reaction of a ligand binding to an MCP, which we originally wrote as T + LTL. We now need this reaction to include 12 of the 24 states, the ones corresponding to the MCP being unbound to the ligand. Our previously simple reaction would become 12 different reactions, one for each possible unbound state of the complex molecule T. And if the situation were just a little more complex, with the ligand molecule L having n possible states, then we would have 12n reactions. Imagine trying to debug a model in which we had accidentally incorporated a typo when transcribing just one of these reactions!

In other words, as our model grows, with multiple different states for each molecule involved in each reaction, the number of reactions we need to represent the system grows very fast; this phenomenon is called combinatorial explosion and means that building realistic models of biochemical systems at scale can be daunting.

A major benefit of using a rule-based modeling language such as the one developed by BioNetGen is that it circumvents combinatorial explosion by consolidating many reactions into a single rule. For example, when modeling ligand-MCP binding, we can summarize the 12 different reactions with the rule “a free ligand molecule binds to an MCP that is not bound to a ligand molecule.” In the BioNetGen language, this rule is represented by the same one-line expression as it was in the previous lesson:

LigandReceptor: L(t) + T(l) <-> L(t!1).T(l!1) k_lr_bind, k_lr_dis


We will not bog down the text with a full specification of all the rules needed to add methylation to our model while avoiding combinatorial explosion. If you’re interested in the details, please follow our tutorial.

## Bacterial tumbling is robust to large sudden changes in attractant concentration

In the figures that follow, we plot the concentration over time of each molecule for different values of l0, the initial concentration of ligand. From what we have learned about E. coli, we should see the concentration of phosphorylated CheY (and therefore the bacterium’s tumbling frequency) drop before returning to its original equilibrium. But will our simulation capture this behavior?

First, we add a relatively small amount of attractant, setting l0 equal to 10,000. The system returns so quickly to an equilibrium in phosphorylated CheY that it is difficult to imagine that the attractant has had any effect on tumbling frequency.

Molecular concentrations (in number of molecules in the cell) over time (in seconds) in a BioNetGen chemotaxis simulation with 10,000 initial attractant ligand particles.

If instead l0 is equal to 100,000, then we obtain the figure below. After an initial drop in the concentration of phosphorylated CheY, it returns to equilibrium after a few minutes.

Molecular concentrations (in number of molecules in the cell) over time (in seconds) in a BioNetGen chemotaxis simulation with 100,000 initial attractant ligand particles.

When we increase l0 by another factor of ten to 1 million, the initial drop is more pronounced, but the system returns just as quickly to equilibrium. Note how much higher the concentration of methylated receptors are in this figure compared to the previous figure; however, there are still a significant concentration of receptors with low methylation, indicating that the system may be able to handle an even larger jolt of attractant.

Molecular concentrations (in number of molecules in the cell) over time (in seconds) in a BioNetGen chemotaxis simulation with one million initial attractant ligand particles.

When we set l0 equal to 10 million, we give the system this bigger jolt. Once again, the model returns to its previous CheY equilibrium after a few minutes.

Molecular concentrations (in number of molecules in the cell) over time (in seconds) in a BioNetGen chemotaxis simulation with ten million initial attractant ligand particles.

Finally, with l0 equal to 100 million, we see what we might expect: the steepest drop in phosphorylated CheY yet, but a system that is able to return to equilibrium.

Molecular concentrations (in number of molecules in the cell) over time (in seconds) in a BioNetGen chemotaxis simulation with 100 million initial attractant ligand particles.

Our model, which is built on real reaction rate parameters, provides compelling evidence that the E. coli chemotaxis system is robust to changes in its environment across several orders of magnitude of attractant concentration. This robustness has been observed in real bacteria67, as well as replicated by other computational simulations8.

Aren’t bacteria magnificent?

However, our work is not done. We have simulated E. coli adapting to a single sudden change in its environment, but life is about responding to continual change. So in the next lesson, we will further examine how our simulated bacterium responds in an environment in which the ligand concentration is changing constantly.

If you find chemotaxis biology as interesting as we do, then we suggest the following resources.

1. Amin DN, Hazelbauer GL. 2010. Chemoreceptors in signaling complexes: shifted conformation and asymmetric coupling. Available online

2. Terwilliger TC, Wang JY, Koshland DE. 1986. Kinetics of Receptor Modification - the multiply methlated aspartate receptors involved in bacterial chemotaxis. The Journal of Biolobical Chemistry. Available online

3. Spiro PA, Parkinson JS, and Othmer H. 1997. A model of excitation and adaptation in bacterial chemotaxis. Biochemistry 94:7263-7268. Available online 2

4. Lupas A., and Stock J. 1989. Phosphorylation of an N-terminal regulatory domain activates the CheB methylesterase in bacterial chemotaxis. J Bio Chem 264(29):17337-42. Available online

5. Boyd A., and Simon MI. 1980. Multiple electrophoretic forms of methyl-accepting chemotaxis proteins generated by stimulus-elicited methylation in Escherichia coli. Journal of Bacteriology 143(2):809-815. Available online

6. Shimizu TS, Delalez N, Pichler K, and Berg HC. 2005. Monitoring bacterial chemotaxis by using bioluminescence resonance energy transfer: absence of feedback from the flagellar motors. PNAS. Available online

7. Krembel A., Colin R., Sourijik V. 2015. Importance of multiple methylation sites in Escherichia coli chemotaxis. Available online

8. Bray D, Bourret RB, Simon MI. 1993. Computer simulation of phosphorylation cascade controlling bacterial chemotaxis. Molecular Biology of the Cell. Available online