Compare a simple model of negative autoregulation to one without autoregulation:
(i) Assume that the basal transcription rates β and β0 vary between cells, following a Gaussian distribution with σ/µ = 0.1. Simulate time courses of both models for 100 different "cells" using the following parameters: β = 2, β0 = 1,γ = 1,K = 1. Plot the nonregulated and auto regulated systems in two separate plots. Comment on the variation you see in the time courses.
(ii) Calculate the deterministic steady state for both models above. How does variation in the basal transcription rate β or β0 enter into the steady state? Relate it to what you see in part (i).