
2
Mathematical Models and
Design Specifications in
Synthetic Gene Networks
2.1 Mathematical Models of Synthetic Gene Networks
First consider a simple cross-inhibition network shown in Figure 2.1. This
network is synthesized with two genes, a and b, that code for two repressor
proteins, A and B. More specifi cally, protein B represses the expression of
gene a, whereas protein A represses the expression of gene b, and at higher
concentration, the expression of its own gene. Protein degradations are
not regulated. This synthetic system can be modeled by the following
differential equations (Batt et al. 2007, Chen and Wu 2009).
a b
a
x
1
()
ba
rx
()
2aa
rx
b