Problem 1: Designing Experiments

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We discussed 2 hypothesis of when activation is preferred over repression.

a) Devise an experimental way to discriminate among these models.

Problem 2: Model and Simulate

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Model the lac operon with activation and repression.

a) Create a CRN model and find plausible parameters in literature. Which assumptions did you make and why?

c) Think of simulations (and resulting figures) to demonstrate activation, repression, and combinations of both. Run simulations and discuss their outcomes for plausibility and implications for the cell.

d) Compare deterministic and stochastic simulations for one case. What do you observe?

Problem 3: Revisiting Problem 1

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Having a working lac model, let's revisit Problem 1.

a) Why do you think both activation and repression are used in the lac operon? Is this consistent with what you found in Problem 1?

b) Run a deterministic and stochastic simulation to see if the occupation theory has an impact and under which parameters (e.g., binding/unbinding rates). Discuss your observations.

Problem 4: Michaelis-Menten and similar approximations

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a) Derive the Michaelis-Menten approximation for an enzyme E, substrate S, and product P.

b) What is the difference to the activation / repression approximations that we used? Did you need to add an assumption?

c) For the approximations that we derived in the 1st lecture: Challenge the approximation (for Hill coefficient 1) and show where it holds and where it breaks in simulations. You can use deterministic or stochastic simulations to make this point. Hint: Changing $k^+$ and $k^-$ while keeping $K_d$ constant.

d) For the approximations that we derived in the 1st lecture: Can you modify the system for Hill coefficients larger than 1. What would be a CRN that results in such an approximation? Give a mathematical proof.