Bacterial Chemotaxis Part 2
We previously published a post about a model of bacterial chemotaxis in which we discussed the chemotaxis behavior in an individual E. coli, its biological function, and the mechanical forces that drive it. Using a model described by Dr. Brian Ingalls, we provided a program that would simulate bacterial chemotaxis behavior. When we design models of biological systems we want to not only capture the behavior involved, but also the biological forces that make it work.
How does Bacterial Chemotaxis work?
Now that we have seen the model’s behavior, we can look at the biology that drives it. Biologically there are two types of signals that will induce the running behavior of chemotaxis in a bacterium: an attractive source of nutrition or a repulsive molecule, here we use glucose in the environment to give the bacterium an attractant. Recall that an E. coli also has two modes of movement: running and tumbling. When the bacterium tumbles it moves in no particular direction; when it is running it is moving in an oriented manner toward or away from a stimulus. Each of these movements is controlled by an interesting circuit of molecular interactions.
Let’s cover two important molecular players in this model. First, we have the active chemotaxis receptor complex, which affects the flagellar motor and drives the E. coli’s tumbling behavior. Next we have our ligand that serves as our chemoattractant. Binding of the chemoattractant to the receptor turns off the tumbling signal, resulting in its running behavior. Using this simple chemoattractant sensing event, E. coli has built its molecular circuits to accomplish two tasks: to sense the elevation of the local chemoattractant level and move towards it, as well as to stop and tumble when there is no elevation of the chemoattractant level. This ability to stop and tumble with no elevation of the chemoattractant allows the E. coli to explore its environment until it detects another increase in the chemoattractant concentration.
To accomplish the alternating movement of running and tumbling the bacterium has to not only sense the elevation of the chemoattractant level, but also replenish the active tumbling signal that had been reduced after binding to the chemoattractant (Figure 1). There are some interesting molecular dynamics at play that our E. coli uses to move to the higher chemoattractant sources.
Figure 1: Input and output of the bacterial chemotaxis pathway. Elevating levels of the chemoattractant (input; L, red) results in a drop in tumbling signal, represented by the activity level of the chemoattractant receptor (output; Am, yellow). Note, the recovery of the tumbling signal during the period of constant ligand level. Ultimately, E. coli bacterium would end up moving from a location of low chemoattractant to higher chemoattractant.
Molecular Interactions Driving Bacterial Chemotaxis
In the model discussed in the post, three ‘proteins’ work together to accomplish the modulation and replenishment of the tumbling signaling activity of the chemotaxis receptor complex through regulating the methylation state of the receptor: CheA, CheBP, and CheR. CheR methylates CheA; CheB demethylates CheA; Methylated CheA is the active version of CheA that produces a tumbling signal, its secondary kinase activity phosphorylates CheB, activating it. This creates a negative feedback loop to keep CheA methylation level and CheB phosphorylation level in check and reset to the steady state of the model even after perturbation as long as the total concentrations of CheA, CheB and CheR in the system remain unchanged. This can be simply stated using L++ by declaring simple reactions associated with each of these proteins.
Consider the code shown in Figure 2. In the code we have designated the proteins in the model as well as the reactions that they facilitate, allowing us to specify the reactions required to create the negative feedback loop that forms between CheA and CheB. In the code, protein Am carries out reaction pt to phosphorylate protein B while protein BP carries out two reactions, mt1 and mt2, to remove methyl groups on various states of protein A.
protein R
{
reaction mt1(A -> Am, kcat=1, KM=1e-10nM);
reaction mt2(AL -> AmL, kcat=1, KM=1e-10nM);
}
protein BP
{
reaction mt1(Am -> A, kcat=200, KM=1nM);
reaction mt2(AmL -> AL, kcat=1, KM=1nM);
}
protein Am
{
reaction pt(B -> BP, k=0.05e9, krev=0.005);
}
reaction lb1(Am + L -> AmL, k=1e9, krev=1);
reaction lb2(A + L -> AL, k=1e9, krev=1);
R = 5nM, B = 0.1nM, A = 500nM;
L[0:100] = 20nM, L[100:200] = 40nM, L[200:300] = 80nM;Figure 2. The graphical and text-based L++ code representations of bacterial chemotaxis. Each of our key proteins is defined in the code, CheA as protein Am, CheR as protein R, and CheB as protein BP. With each definition of the protein we included their respective functions in the chemotaxis system.
It may not be obvious as to how this negative feedback system is sufficient to drive the bacterial chemotaxis, so let’s walk through the sequence of molecular events during the bacterial chemotaxis and analyze the flow of molecules (Figure 3).
Figure 3. The flow of molecules after the disruption of the steady state by a chemoattractant binding to the tumbling signal receptor. Am’s concentration is largely affected by both a reduction after an increase in the ligand in the environment, as well as the methylation of A and the disassociation of the ligand from AmL (Orange). Reduction of Am similarly causes a reduction of BP in the system and a pause of the tumble signal (Purple); however, restoration of Am similarly restores BP and the tumbling signal (Blue).
In its exploration of its environment an E. coli will eventually tumble into an area in which the concentration of L is higher than it previously was, allowing for free receptors on Am to bind. Remember when we mentioned that Am binding to L deactivates it? We call this new inactive Am AmL to indicate that it is bound to L. Now we have the drop in Am below the threshold level in the system that we saw in the analog signal earlier, and as expected we will see the tumbling signal get turned off as the E. coli starts running and exploring its environment in a more directed manner. This also causes a cascade that is required to return the tumbling signal to its active state to allow our E. coli to start surveying its environment again.
In addition to the tumbling signal being reduced as the concentration of AmL increases, less BP is also made as there is not a sufficient level of Am in the system to phosphorylate B. The reduction in BP, in tandem with an unchanged level of R, results in an increase in Am methylation to bring the system back to balance. Some of the bound L also falls off, and the reverse reaction of AmL to Am also contributes to the restoration of the Am levels required to maintain the steady state. Logically, BP will also be restored in the system as the Am levels return to their state that is sufficient to induce the tumbling behavior.
So far we have seen the kinase activity of Am as it activates Protein B via phosphorylation, but we have not needed BP’s activity yet. Once an active Am has been deactivated due to the binding of a chemoattractant (AmL), the protein can slowly be restored to its basal form. Protein BP removes the methyl group and the ligand will fall off of the receptor when it is no longer needed, leaving the cell with an inactive Protein A that can be recycled into the system through Protein R’s methylation. Each of these proteins is recruited by the others in a manner similar to how the gears in a clock interact in such a way that the movement of one affects the movement of the others.
Chemotaxis: Moving On
In our previous post about bacterial chemotaxis we discussed how we can design a program using L++ to generate the chemotaxis behavior. We hope that this has shed some light on how we can apply quantitative models in biological contexts to generate accurate simulations of behaviors in living organisms. With the foundations laid out we can start to consider how to further expand on this behavior. An environment is not usually so simple that there is a single ligand for the bacterium to interact with. How could we introduce ligands of differing nutritional value? Or what might this model look like if we included a chemical repellant in the E. coli’s environment? We are already working on additional behaviors of E. coli bacteria as we build our first virtual organism. Check back in soon for our post detailing the biological and virtual dynamics of E. coli cell division.
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