. Author manuscript; available in PMC: 2008 Apr 28.

Published in final edited form as: Syst Biol (Stevenage). 2006 Jul;153(4):236–246. doi: 10.1049/ip-syb:20050090

5.2.1) Differential Equations of the three-gene regulatory network.

Transcripts

\frac{d [MD]}{dt} = - kDMD \times MD + kRPD \times PD + kR F_{2} PD \times F_{2} PD

\frac{d [ME]}{dt} = - kDME \times ME + kRPE \times PE + kR D_{2} PE \times D_{2} PE

\frac{d [MF]}{dt} = - kDMF \times MF + kRPF \times PF + kREQPF \times EQPF

Proteins

\frac{d [D]}{dt} = - kDegD \times D + kTD \times MD - 2 [k D_{2} \times D \times D] + 2 [kU D_{2} \times D_{2}]

\frac{d [E]}{dt} = - kDE \times E + kTE \times ME - kEQ \times E \times Q + kUEQ \times EQ

\frac{d [F]}{dt} = - kDF \times F + kTF \times MF - 2 [K F_{2} \times F \times F] + 2 [kU F_{2} \times F_{2}]

Dimers/Heterodimers

\frac{d [EQ]}{dt} = KEQ \times E \times Q - kUEQ \times EQ - kDEQ \times EQ - kPF \times EQ \times PF + kUPF \times EQPF

\frac{d [F_{2}]}{dt} = k F_{2} \times F \times F - kU F_{2} \times F_{2} - kD F_{2} \times F_{2} - kPD \times F_{2} \times PD + kUPD \times F_{2} PD

\frac{d [D_{2}]}{dt} = k D_{2} \times D \times D - kU D_{2} \times D_{2} - kD D_{2} \times D_{2} - kPE \times D_{2} \times PE + kUPE \times D_{2} PE

Bound Promoters

\frac{d [D_{2} PE]}{dt} = kPE \times D_{2} \times PE - kUPE \times D_{2} PE

\frac{d [F_{2} PD]}{dt} = kPD \times F_{2} \times PD - kUPD \times F_{2} PD

\frac{d [EQPF]}{dt} = kPF \times EQ \times PF - kUPF \times EQPF