Text S2. Module 2: Kinetic equations for the phosphorylation-dephosphorylation reactions of the HSF1 trimer-HSE complex (HH). We consider the stepwise dual ...
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Text S2 Module 2: Kinetic equations for the phosphorylation-dephosphorylation reactions of the HSF1 trimer-HSE complex (HH) We consider the stepwise dual phosphorylation-dephosphorylation reactions of the complex HH as module 2. The kinetic equations of the phosphorylation-dephosphorylation reactions of the complex HH by the kinase and phosphatase are given as follows: HH + M K3 HHM K3 HHp + M K3 HHpM K3
R13 = k13 [HHpppM K3] R14 = k14 [HHpppp][P P 5] − k−14 [HHppppP P 5]
(28) (29)
R15 = k15 [HHppppP P 5]
(30)
R16 = k16 [HHpppP P 5] − k−16 [HHppp][P P 5] R17 = k17 [HHppp][P P 5] − k−17 [HHpppP P 5S]
(31) (32)
R18 = k18 [HHpppP P 5S] R19 = k19 [HHppP P 5] − k−19 [HHpp][P P 5]
(33) (34)
R20 = k23 [HHp][P P 5] − h−23 [HHpP P 5S] R21 = k24 [HHpP P 5S]
(35) (36)
R22 = k11 [HHP P 5] − h66 [P P 5][HH] R23 = k20 [HHpp][P P 5] − k−20 [HHppP P 5S]
(37) (38)
R24 = k21 [HHppP P 5S] R25 = k22 [HHpP P 5] − k−22 [HHp][P P 5]
(39) (40)
In the above equations, HH is the HSF13S:HSE complex; HHp ,HHpp ,HHppp ,and HHpppp are the mono, di, tri, and tetra-phosphorylated complex; MK3 is the kinase; PP5 is a phosphatase, a co-chaperone; PP5S is the activated phosphatase formed during the dephosphorylation; and the rest of the dynamical variables are the complexes of MK3 or PP5A. The kinetic equation for the production of mRNA90 from tetra phosphorylated HHpppp is given as follows: k
HHpppp −−26 → mRN A90 + HH + 4P i
(41)
The corresponding rate equation is: R26 =
k26 [HHpppp ]
(42)
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Rate equations for the phosphorylation-dephosphorylation reactions of trimer HSF1-HSE complex, (HH) d[HH] dt d[HHp] dt d[HHpp] dt d[HHppp] dt d[HHpppp] dt d[HHM K3] dt d[HHpM K3] dt d[HHppM K3] dt d[HHpppM K3] dt d[HHppppP P 5] dt d[HHpppP P 5] dt d[HHpppP P 5S] dt d[HHppP P 5] dt d[HHppP P 5S] dt d[HHpP P 5] dt d[HHpP P 5S] dt d[HHP P 5] dt
