CS178 Homework 6

Modify the Matlab code provided in “geneticnetwork.m” to plot continuous and stepwise
representations of the network defined by the following Boolean equations:

G0’=not G1
G1’=not G0

Use the initial state G0=0 and G1=0.
You should only need to modify two functions, “sig_system” and “step_system.”
Machines with Matlab installed are located in the Hughs Computer Cluster on the lower
floor of the science library.

Question 1:
What are the step and sigmoid equations that you used in the Matlab program?
Describe the difference between the stepwise (piecewise linear) function and the fully
continuous graphs.

Question 2:
a) What values of kappa and gamma cause the system to reach the steady state G0=1,
G1=0?
b) What values cause it to reach G0=0, G1=1?
c) Do any values of kappa and gamma cause the system to reach the state G0=1, G1=1?
Would it be likely that a real genetic network would reach this state?

Question 3:
“geneticnetwork.m” includes step and sigmoid systems approximated by the Boolean
functions G0’= G1, G1’=not G0. The Boolean system gives rise to a cycle of states [0,0]-
>[0,1]->[1,1]->[1,0].
Does this cycle occur in the continuous system? If not, does the Boolean system
adequately approximate the behavior of the continuous function? Why or why not?