Skip to main content
Complex Adaptive Systems Modeling

Table 3 Constraints for the invariant cycle

From: On the modeling and analysis of the biological regulatory network of NF-\({\kappa }\)B activation in HIV-1 infection

Cycle no.

000\(\rightarrow\)100\(\rightarrow\)110\(\rightarrow\)010\(\rightarrow\)011\(\rightarrow\)001\(\rightarrow\)000

Constraints

1

\(\delta ^+_{NFKB010}+|\delta ^-_{NFKB001}|+2|\delta ^-_{TNF-A011}|=\delta ^+_{HIV000} +|\delta ^-_{HIV110}|\)

2

\(\delta ^+_{TNF-A100}\)+\(|\delta ^-_{TNF-A011}|\) \(\le \delta ^+_{HIV000}\)+\(|\delta ^-_{HIV110}|\)

3

\(\delta ^+_{HIV000}+|\delta ^-_{HIV110}|+\le \delta ^+_{NFKB110}+|\delta ^-_{NFKB001}|+2|\delta ^-_{TNF-A011}|\)

4

\(\delta ^+_{HIV011}\ge |\delta ^-_{TNF-A011}|\)

5

\(\delta ^+_{NFKB011}\ge |\delta ^-_{TNF-A011}|\)

6

\(\delta ^+_{HIV001}\ge |\delta ^-_{NFKB001}|+2|\delta ^-_{TNF-A011}|\)

7

\(\delta ^+_{TNF-A001}\ge |\delta ^-_{NFKB001}|+|\delta ^-_{TNF-A011}|\)

8

\(\delta ^+_{HIV000}\le \delta ^+_{NFKB000}\)+\(|\delta ^-_{NFKB001}|\)+\(2|\delta ^-_{TNF-A011}|\)

9

\(\delta ^+_{HIV000}\le \delta ^+_{TNF-A000}\)+\(|\delta ^-_{TNF-A011}|\)

10

\(\delta ^+_{HIV000}\ge |\delta ^-_{NFKB001}|+2|\delta ^-_{TNF-A011}|\)

11

\(\delta ^+_{TNF-A100}\)+\(|\delta ^-_{TNF-A 011}| \le \delta ^+_{HIV000}\)+ \(|\delta ^-_{HIV100}|\)

12

\(\delta ^+_{TNF-A100}\le \delta ^+_{NFKB100}\)+\(|\delta ^-_{NFKB001}|\)+\(|\delta ^-_{TNF-A011}|\)

13

\(\delta ^+_{HIV000}\le \delta ^+_{TNF-A100}\)+\(|\delta ^-_{TNF-A011}|\)

  1. The conjunction of constraints 1–13 characterize the invariance kernel. The violation of these constraints could take system towards stable steady state
Back to article page