\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "We discussed 2 hypothesis of when activation is preferred over repression.\n", "\n", "**a)** Devise an experimental way to discriminate among these models." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Problem 2: Model and Simulate\n", "\n", "

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Model the lac operon with activation and repression.\n", "\n", "**a)** Create a CRN model and find plausible parameters in literature. Which assumptions did you make and why?\n", "\n", "**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.\n", "\n", "**d)** Compare deterministic and stochastic simulations for one case. What do you observe?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Problem 3: Revisiting Problem 1\n", "\n", "

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having a working lac model, let's revisit Problem 1.\n", "\n", "**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?\n", "\n", "**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.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Problem 4: Michaelis-Menten and similar approximations\n", "\n", "

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**a)** Derive the Michaelis-Menten approximation for an enzyme E, substrate S, and product P.\n", "\n", "**b)** What is the difference to the activation / repression approximations that we used? Did you need to add an assumption?\n", "\n", "**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.\n", "\n", "**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." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "venv", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 4 }