Table 3.

Delay constraints.

Number	Delay Constraints
1	${\delta }_{FOXO}^{+}\le \left|{\delta }_{mTORC1}^{-}\right|+\left|{\delta }_{Akt}^{-}\right|$
2	$\left|{\delta }_{FOXO}^{-}\right|\le {\delta }_{Akt}^{+}+{\delta }_{mTORC1}^{+}$
3	$\left|{\delta }_{PI3K}^{-}\right|\le {\delta }_{mTORC1}^{+}+\left|{\delta }_{Akt}^{-}\right|$
4	$\pi (FOXO)+\left|{\delta }_{PI3K}^{-}\right|\le ,\pi (Akt)+\pi (mTORC1)$
5	$\pi (FOXO)+\pi (PI3K)\le \pi (Akt)+\pi (mTORC1)+{\delta }_{mTORC2}^{+}$
6	${\delta }_{FOXO}^{+}+\left|{\delta }_{PI3K}^{-}\right|\le \pi (mTORC1)+\left|{\delta }_{Akt}^{-}\right|$
7	$\pi (FOXO)+\pi (PI3K)\le \pi (mTORC2)+{\delta }_{Akt}^{+}+{\delta }_{mTORC1}^{+}$
8	${\delta }_{PI3K}^{+}+{\delta }_{FOXO}^{+}\le {\delta }_{Akt}^{+}+\pi (mTORC2)$
9	$\pi (PI3K)+{\delta }_{FOXO}^{+}\le {\delta }_{Akt}^{+}+\pi (mTORC2)+{\delta }_{mTORC1}^{+}$

Delay Constraints of the selected cycle characterizing its invariance kernel. δ⁺ represents production (activation) delay while δ⁻ represents degradation (inhibition) delay. Notation π(e) refers to the sum of production and degradation delays of the entity e.