Team:Pittsburgh/Model

What are we Modeling?

We focused on modeling the chemotactic response of E. coli and the effects photoswitchable Dronpa has on bacterial motility. When wild type E. coli are exposed to a chemical repellant, the main chemotaxis protein CheY will become phosphorylated by the autophosphorylated CheA. Next, the now phosphorylated CheY, (CheY~P) will be able to bind with high affinity to FliM, one of the proteins in the flagellar motor. This interaction between CheY~P and FliM is one of the main determinants behind the swimming versus tumbling behavior in bacteria.

We wanted to investigate this system because it is possible to compare the modeling results with experimental data obtained through microscopy videos. In addition, since the chemotaxis system has many aspects such as the reaction rates of kinase activity that we may not have considered, the model can give us more insight on potential research areas. Because our model is clearly based on certain rules that govern the interaction between the different chemotaxis proteins, we are able to use Rule Based Modeling.

What is Rule-Based Modeling and Our Model Design?

Rule-based modeling focuses on representing molecules as structured objects that interact with each other with set rules that can transform states of these objects (Faeder et al., 2009). For example, CheY would be a structured object that can interact with CheA and be transformed from an unphosphorylated to phosphorylated state.

In our model, the molecules we represented include the main chemotaxis protein CheY, CheA which undergoes autophosphorylation, the flagellar motor FliM, CheZ which dephosphorylates CheY~P, and phosphate to ensure we simulate a repellent bath like environment in our model. The rate constants and initial concentrations for the different components of our model were based off of the supplementary resources of the Sourjik paper (Sourjik and C.). The reaction rules were based off literature of the E. coli chemotaxis system with some modifications and assumptions we adapted to simplify and clarify the model. We have two forms of CheY, the native wild type and a mutant version. The wild type acts such that under a repellent condition, it will get phosphorylated by CheA, transform to the phosphorylated state and have high affinity to FliM. On the other hand, mutant CheY has been designed such that it always acts as if it is phosphorylated. Therefore, regardless whether or not there is repellent in the environment, mutant CheY always acts as if it is in the phosphorylated state. This is represented in our code by deactivating the CheZ dephosphorylation event for mutant CheY*. To simulate Dronpa’s photoswitchable dimerizing activity, we assumed rates lambda1 and lambda2 for dimerizing activity to allow us to see a change in behavior from a swimming trend to a tumbling trend. This allows us to observe trends in motility in all of our chemotaxis protein and Dronpa systems in comparison to one another.

We used the BioNetGen language (BNGL) developed by Dr. Jim Faeder which is based off of rule-based model to not only model the chemotactic response but also use the results and data obtained to be the basis for our interactive game.

Here is our reaction rules for our model.

System Overview

Contact Map

wt(wt~U~P~D)

wt is CheY and we have defined 3 states for it: it can be unphosphorylated (U), phosphorylated (P), or it can be dimerized (D) when 400nM light dimerizes Dronpa.

cheA(cheA~U~P)

cheA is CheA the protein responsible for autophosphoryation and we have defined 2 states for it: it can be unphosphorylated (U) or phosphorylated (P) Since we have have designed our model to be over saturated with phosphate, cheA should almost always be in the state of phosphorylated CheA to phosphorylate CheY

cheZ(cheZ)

cheZ is CheZ which is the protein responsible for dephosphorylation. In our model we have also utilized this ability to help define our mutant CheY. CheZ also has no other state it can transform into.

flag(S~U~F~FF~FFF)

flag is Flag which is the flagellar motor protein. We have defined 4 states for it: unbound (U), 1 FliM site bound by CheY-P (F), 2 FliM sites bound by CheY-P (FF), and 3 FliM sites bound by CheY-P (FFF).

p(p)

p is Phosphate groups with no other it can transform into.

Differential Equations

Rate of Change of Wild-type-CheY-Dronpa-Monomeric over Time

Rate of Change of Wild-type-CheY-Dronpa-Monomeric-Phosphorylated over Time

Rate of Change of Wild-type-CheY-Dronpa-Monomeric-FliM bounded over Time

Rate of Change of Wild-type-CheY-Monomeric-Phosphorylated-FliM bounded over Time

Rate of Change of Mutant-CheY-Dronpa-Monomeric over Time

Rate of Change Mutant-CheY-Dronpa-Monomeric-FliM bounded over Time

Variables

Assumptions for Simplicity and Clarity

Assumption #1: CheY-P binding onto Flag directly affects motor bias.

-E.coli actually have another protein, Flim, that CheY-P binds onto first, and the FliM from the CheY-P~FliM complex binds onto Flag. However we chose not to directly model FliM for simplicity and clarity of our model. Instead, we have created binding sites on the structured object Flag represented as FliM.

Assumption #2: Flag has 3 FliM protein binding sites which CheY-P can bind onto to affect motor bias.

-E.coli’s Flag technically has 34 FliMs which CheY-P would bind onto. However, based off literature, we found that in E.coli when greater than 2/3 of the 34 FliMs are bounded by CheY, it greatly increases the motor bias towards tumbling. To simplify this, we made Flag just had 3 FliM sites where CheY-P can bind and when greater than two out of the three of the designed spots of FliM are bound by CheY-P, it will increase the motor bias towards tumbling.

Assumption #3: Cells are in a repellent bath.

-We oversaturated the environment with 0.5M of phosphate so under normal circumstances the E.coli CheY should always be phosphorylated and lead to motor bias towards tumbling.

Assumption #5: Average volume of cell is 1.4x10^-15L.

-We based this value off Sourjik (2002) literature value

(Bai 2010)

Model Results

Tumbling One Bound

“Tumbling One Bound” is when 1 CheY-P is bound to FliM, (S~F). (Molecules Tumbling_one flag(S~F)) According with our assumption, when less than 2/3 of the spots in FliM are bound, there is motor biased towards running instead of tumbling. Therefore, comparing the “Tumbling One Bound” graph with the “Running” graph, high concentration of CheY-P~FliM correlates to more running compared to later in the timescale. “Tumbling One Bound” eventually peaks at around 2E+01 seconds for our four constructs, Wt CheY, Wt CheY Dronpa, Mut CheY, and Mut CheY Dronpa.

Initially there was a spike for “Tumbling One Bound” which compares to the initial states of the Michaelis-Menten equation, V0 = Vmax [S]/(Km + [S]). In this initial linear state, there is increase in concentration of CheY-P bound to FliM (S~F) similar to the the Michaelis-Menten equation when there is a high concentration of enzyme with a low concentration of substrate. In our model, the “enzyme” would be CheY, the “substrate” would be the phosphate, and the “product” would be S~F, 1 CheY-P binding onto FliM. Since in the beginning of the reaction, all of the CheY are unphosphorylated, there is relatively higher concentration of free CheY compared to later in time. Therefore the limitation of product formation, is limited by amount of phosphate. However, as time increases, the original linear and fast formation rate of S~F slows down because more and more CheY are already phosphorylated. Their active site is not available to bind phosphate groups to create more CheY-P which binds to FliM to create S~F. Another reason for decrease of formation of one CheY-P bound to FliM is that since CheY-P have a much higher affinity towards FliM compared to CheY, the probability by which FliM gets bound to more CheY-P is very high.

Therefore, with increasing time, a total of 2 or even 3 CheY-P can bound to FliM (S~FF, S~FFF) or the original CheY-P~FliM entity dissociates apart. In both cases, the concentration of the state of 1 CheY-P bound to FliM (S~F) decreases, which is reflected in our model.

Tumbling Two Bound

“Tumbling Two Bound” is when 2 CheY-P are bound to FliM, (S~FF). (Molecules Tumbling_two flag(S~FF)). Compared to “Tumbling One Bound” and “Full Tumbling (3 bound)”, the maximum concentration for all the four constructs is much lower. S~FF is the intermediate state where there is flexibility to fully turn motor bias to tumbling or drop down to S~F for higher bias towards running. We see that the the graphs are less smooth probably because of it is subjected to two rapidly changing concentrations that are already at very low concentrations. If the ODE solver we used in our BNG model had better resolution, we would not be seeing thee artifacts.

Full Tumbling (3 bound)

“Full Tumbling (3 bound)” is when 3 CheY-P are bound to FliM, (S~FFF). (Molecules Tumbling_two flag(S~FFF)) This is only case where based off our assumption there is true motor bias towards tumbling because there are more than two out of the three designated sites of FliM bound by CheY. Comparing Full Tumbling to Running, as tumbling increases, running decreases which matches our prediction. This graph also show the characteristic sigmoidal aspect associated with cooperativity. The small degree of the sigmoidal curve corresponds to what was reported in the the Sourjik and Berg (2002) paper, where they found that phosphorylated CheY cooperativity is much less compared to the cooperativity in motor response. However there is still slight cooperation as shown in the Hill coefficient of CheY-P and FliM, 1.8+/- 0.3 (Sourjik and C.) which is demonstrated in our model.

Eventually all the constructs reach a similar maximum amount of tumbling because tumbling is limited by the interaction between CheY-P and FliM. Even though we had oversaturated the environment with phosphate to encourage CheY-P state, the cell holds a steady concentration of CheY and FliM so once the equilibrium of CheY and CheY-P is reached, that is the maximum number of CheY-P that can bind onto FliM at any one given time.

Running

Running is any state when there is 2 out of the 3 or less designed sites on FliM not bounded by FliM. Similar to the “Full Tumbling” graph, there is also slight cooperativity demonstrated. As each additional CheY-P bind onto FliM, there is a slight cooperativity effect and an increase in motor bias towards tumbling.

Effect our Model has on our Project?

Through modeling our chemotaxis system we were able to gain a better understanding of this complex process in bacteria. This model enabled us to compare our results from microscopy and also be the basis of our game to allow for a larger audience to understand how the photoswitchable Dronpa can control bacteria movement.

From our simulation we were able to see more nuanced details of bacterial motility that could not be seen through assays such as swarm plates or microscopy. With both of those assays, it is only possible to see the final outcome, tumbling or swimming. However there are details such as motor biased from more than 2 CheY-P bound to FliM that would not have been observable since this is at the molecular level of systems. In our model, we have clear reaction rules that define the interactions and transformation of states so that all possible forms of our molecules are defined and considered in the model. Therefore our model showcased that there may be unexpected results such as Wt-CheY-Dronpa or Wild type CheY having slower response to tumbling compared to mutants. In our microscopy and swarm assays, we initially had the thought that since wild type CheY is the native state which CheY is in bacteria, they must have been adapted to be most efficient to deal with the different environments bacteria are in. However, with our model, Mut-CheY-Dronpa and Mut CheY actually had a faster response to tumbling which may allude to confounding variables that we may not be able to consider in our wet-lab experiments. This is valuable insight to us as we further explore areas to look into for bacterial motility control especially if we wish to develop optically controlled bacteria into the therapeutic field.

The model also helped us with the design of our game. By obtaining data from simulations that can consider more aspects of the chemotaxis system then data from wet-lab, we can make the game more interactive, demonstrate more complexities of the biological system, more realistic to what scientist are researching in the field of bacterial motility.

Although our model has simplifications and assumptions that may not necessarily be the most realistic case of bacterial chemotaxis, it has simplified and clarified the process to manageable parts that all audiences, from biologist to the general public can understand.

Resources

Bai, F., R.W. Branch, D.V. Nicolau, T. Pilizota, B.C. Steel, P.K. Maini, and R.M.B. Berry. Conformational Spread as a Mechanism for Cooperativity in the Bacterial Flagellar Switch. Science. 327:685-689.

Faeder, J.R., M.L. Blinov, and W.S. Hlavacek. 2009. Rule-Based Modeling of Biochemical Systems with BioNetGen. In Systems Biology. I.V. Maly, editor. Humana Press, Totowa, NJ. 113-167.

Nelson, David L., et al. Lehninger Principles of Biochemistry. W.H. Freeman, 2017.

Sourjik, V., and B.H. C. Binding of the Excherichia coli response regulator CheY to its target measured in vivo by fluorescence resonance energy transfer. PNAS. 99:12669-12674.

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