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From 2010.igem.org

Contents 1 Questions for the modelers 1.1 Known from literature 1.2 TODOs for modelers 1.3 Further questions 1.4 Answers so far 1.4.1 Answers from the Spiro (1997) model 1.4.2 Answers from Rao (2004) model

Questions for the modelers

Known from literature

• The tumbling frequency is a function of the concentration of phosphorylated CheY (and possibly also of the unphosphorylated one, so either CheYp or CheYp/CheY is important):

• time not tumbling / total time = bias = f(CheYp)

• We know the tumbling frequency over time for big step inputs of the ligand:

• bias(t) = bias(t, stepHeight)

• In every model we know or can easily obtain the change in CheYp for a big step inputs of ligands.

--> We can estimate the CheYp concentration necessary to get a bias of one (=not tumbling anymore). We can also estimate the CheYp concentration to get at least once in a while tumbling. We can do this for every model.

TODOs for modelers

• Implement a model.

• Estimate the threshold for CheYp, for which the bias is high enough so that we basically don't get any tumbling. This can be done by giving a high step input of ligands on the model and following the next steps.

• For the high step input, the concentration of CheYp should reduce significantly for at least 30s, but maybe for several minutes (depends on the model).

• Just "guess" the threshold value: In the step input simulation, CheYp should be below this value for a few dozens of seconds, but then return to its original value (or to a value close to its original value -> adaptation).

• Calculate Delta: Delta = Original value CheYp - threshold.

• Short explanation: We want to construct a light input so, that putting on the red light (far red light), the CheYp concentration is reduced far enough, so that the bias is close to one (=no tumbling anymore). We can reformulate this: We want to construct a light input, so that putting on the red light (far red light) has a similar response in the CheYp concentration than giving a high step input of ligands on the system, for which we know that tumbling is basically completely repressed (bias=1). We can further reformulate this: Turning on the red light (far red light) should reduce CheYp for at least Delta

• Implement the light input. Lets assume we construct the light input by fusing PIF3 to CheR. For all other Che proteins the algorithm is basically the same.

• Since we know not enough about the necessary parameters, we just assume that putting on the light input reduces the CheR concentration for 50%.

• We now make the simulations which give us the answer if a light input is useful: First, we equilibrate the model. This means for a constant value of ligands we simulate the model until it reaches its steady state values which I denote with x0.

• We save x0.

• Now we change our model file: At the beginning of the model file we just multiply the state representing CheR with 0.5. E.g. let's assume that the states of the model are denoted by x and the 15th element of x is the state representing CheR. Then we add the line x(15) = 0.5 * x(15) at the beginning of the model.m file.

• We start a simulation with the initial conditions x0 obtained by equilibrating the model (see above).

• We plot the time line of CheYp. Then we plot a line representing the value Threshold (Original value CheYp - Delta). Then we print this plot, because this is our main result and the other people in the team are interested in exactly that plot.

• Now we just look if and how long CheYp stays below the threshold.

• The input is good, if CheYp stays below the threshold for a significant amount of time (>30s).

• We estimate the time the time CheYp needs to fall below the threshold (=activation time), how long it stays below the threshold (= straight swimming time) and how far we come below this threshold (=robustness).

As a short summary: By applying the algorithm we now know if CheR is a good input. But wait, we are not done yet. If CheR is a good input depends on several things. One of the most important things is the (constant) ligand concentration. The biological background: CheR methylases the receptor. The receptor is "more methylased" for a higher ligand concentration. Thus, removing CheR will have different effects for different ligand concentrations (or, even simpler: If no receptor is methylased anyway, removing the methylase CheR will probably have no effect). Thus, we have to do the following:

• Repeat the experiment for different constant concentrations of ligands. So first set the ligand concentration, equilibrate the model and then do the experiment by reducing CheR to 50%.

• Next, we are of course interested how long it takes to get CheYp back to its original value by turning on the far red (red) light. Thus:

• Save the final steady state value of the experiment where you reduced CheR to 50%. I will denote this state as x1.

• Remove the line where you reduced CheR to 50% (=set it again to 100%). Run a second simulation which is initialized with x1.

• Measure the time CheYp needs to get above the threshold again. Save and print the respective plots.

OK, now we have the information we need for CheR. Now do the same for CheB, CheZ and CheY. But be carefull: In most models e.g. CheB can be in to states, phosphorylated and not phosphorylated: CheB_t = CheB + CheBp. Of course, in the experiment you have to reduce BOTH, the phosphorylated and unphosphorylated form, by 50%. The same is true for CheY. For some inputs CheYp will increase rather than decrease (probably for CheB and CheZ). This is not a problem, because then we would just activate going straight forward with far red light and tumbling with red light (inverse logic). The problem can thus be easily solved by just increasing the initial concentration of e.g. CheB. But this shouldn't be your concern, yet. The important thing for you is just: When we put red light on, does the concentration of CheYp increase or decrease for Delta. • The direction is not intereseting.

So, happy modeling.

Remark: For the simulations you can basically look in how I did it for the Spiro (1997) model (see files). I did it a little bit more automatized and furthermore included already the light actiation/deactivation part in more detail. However, I yet didn't model exactly the binding process.

Further questions

How strong should be the promoter of the genes (=how much protein-expression/minute do we need)? Probably should be answered before: how big are the degradation constants of the respective genes and mRNAs? How big is the translation rate? How much should we overexpress the anker protein (e.g. PhyB-GBD) compared to the Che-fusion protein (e.g. PIF3-CheR)?

Answers so far

Answers from the Spiro (1997) model

This model basically predicts that we can go for all Che proteins (CheR, B, Y and Z). For CheR and CheY the concentration of CheYp drops more than Delta, for CheB and CheZ it increases more than Delta. For all Che proteins the concentrations stay like forever below/above the threshold, until we deactivate them with far-red light. The best results I obtained for assuming a high ligand concentration (saturation, so that the methylation level of the receptors is high). For CheY and CheZ the reaction times were (as expected), much faster than for CheB and CheR. However, for these proteins the reaction times were still fast enough. I already showed the plots in the last meetings.

Answers from Rao (2004) model

The predictions are identical to the previous model (Spiro 1997)