Problem 1 - Hill Function (10 marks) The hill function can be used to describe processes that involve cooperative binding events (see page 72). Demonstrate graphically in MATLAB that the process becomes more switch-like as the Hill coefficient increases (switch like means on-off behavior). In other words, the higher n becomes the closer the system resembles a step response. Briefly discuss, using solutions for different values of n, what this means for process behavior for a system undergoing inhibition. Give an example found in biology and provide a reference. 72 This approximation is formalized in the Hill function [X]" ([X]/K)" 1+([X]/K)"K" +[X]" Y = Y n=1 n=2 n=4, X Xn Kn+Xn Y = Figure 3.10 Hill functions. As the Hill coefficient n increases, the sigmoidal curve becomes more switch-like. When the Hill coefficient is 1, the curve is hyperbolic.