Inferring the Topology of Gene Regulatory Networks: An Algebraic Approach to Reverse Engineering - Mathematical Concepts and Methods in Modern Biology - page 80

x1

x3

x2

FIGURE 3.5
Wiring diagram for Exercise 3.5.

1 1 0

0 0 1

FIGURE 3.6
Partial state space for Exercise 3.6.

already been phosphorylated (1) or not (0) before the interaction. Furthermore, we
want f 1 to indicate the absence/presence of protein A right after the interaction and
f 2 to point out whether protein B has been phosphorylated or not.

1. Explain why f 1 should depend on x 1 only, while f 2 must depend on both x 1
and x 2 .
2. Do you find the following Boolean model reasonable? Correct it if necessary.

f 1 = x 1 ,

f 2 = x 1 OR x 2 .

3. Convert the above Boolean functions into polynomials over Z 2 .