Emergence of bimodal cell population responses from the interplay between analog single-cell signaling and protein expression noise

Birtwistle, Marc R; Rauch, Jens; Kiyatkin, Anatoly; Aksamitiene, Edita; Dobrzyński, Maciej; Hoek, Jan B; Kolch, Walter; Ogunnaike, Babatunde A; Kholodenko, Boris N

doi:10.1186/1752-0509-6-109

Table 1 Kinetic description of the ERK signaling cascade

From: Emergence of bimodal cell population responses from the interplay between analog single-cell signaling and protein expression noise

N	Reaction	Rate	Kinetic
			constant*
1	MAP3K → pMAP3K	$v_{1} = \frac{k_{1}^{cat} \cdot [R a s - G T P] \cdot [M A P 3 K] / K_{m 1}}{(1 + [M A P 3 K] / K_{m 1})} \cdot g (F_{a})$	$k_{1}^{cat} = 0.2$ ; $K_{m 1} = 50$
2	pMAP3K → MAP3K	$v_{2} = \frac{V_{max 2} \cdot [p M A P 3 K] / K_{m 2}}{(1 + [p M A P 3 K] / K_{m 2})}$	$V_{max 2} = 5$ ; $K_{m 2} = 50$
3	MAP2K → pMAP2K	$v_{3} = \frac{k_{3}^{cat} \cdot [p M A P 3 K] \cdot [M A P 2 K] / K_{m 3}}{(1 + [M A P 2 K] / K_{m 3} + [p M A P 2 K] / K_{m 4})}$	$K_{3}^{cat} = 1$ ; $K_{m 3} = 130$
4	pMAP2K → ppMAP2K	$v_{4} = \frac{k_{4}^{cat} \cdot [p M A P 3 K] \cdot [p M A P 2 K] / K_{m 4}}{(1 + [M A P 2 K] / K_{m 3} + [p M A P 2 K] / K_{m 4})}$	$k_{4}^{cat} = 5$ ; $K_{m 4} = 50$
5	ppMAP2K → pMAP2K	$v_{5} = \frac{V_{max 5} \cdot [p p M A P 2 K] / K_{m 5}}{(1 + [p p M A P 2 K] / K_{m 5} + [p M A P 2 K] / K_{m 6} + [M A P 2 K] / K_{i 1})}$	$V_{max 5} = 250$ ; $K_{m 5} = 100$
6	pMAP2K → MAP2K	$v_{6} = \frac{V_{max 6} \cdot [p M A P 2 K] / K_{m 6}}{(1 + [p p M A P 2 K] / K_{m 5} + [p M A P 2 K] / K_{m 6} + [M A P 2 K] / K_{i 1})}$	$V_{max 6} = 250$ ; $K_{m 6} = 100$ ; $K_{i 1} = 80$
7	MAPK → pMAPK	$v_{7} = \frac{k_{7}^{cat} \cdot [p p M A P 2 K] \cdot [M A P K] / K_{m 7}}{(1 + [M A P K] / K_{m 7} + [p M A P K] / K_{m 8})}$	$k_{7}^{cat} = 1$ ; $K_{m 7} = 50$
8	pMAPK → ppMAPK	$v_{8} = \frac{k_{8}^{cat} \cdot [p p M A P 2 K] \cdot [p M A P K] / K_{m 8}}{(1 + [M A P K] / K_{m 7} + [p M A P K] / K_{m 8})}$	$k_{8}^{cat} = 20$ ; $K_{m 8} = 50$
9	ppMAPK → pMAPK	$v_{9} = \frac{V_{max 9} \cdot [p p M A P K] / K_{m 9}}{(1 + [p p M A P K] / K_{m 9} + [p M A P K] / K_{m 10} + [M A P K] / K_{i 2})}$	$V_{max 9} = 380$ ; $K_{m 9} = 10$
10	pMAPK → MAPK	$v_{10} = \frac{V_{max 10} \cdot [p M A P K] / K_{m 10}}{(1 + [p p M A P K] / K_{m 9} + [p M A P K] / K_{m 10} + [M A P K] / K_{i 2})}$	$V_{max 10} = 50$ ; $K_{m 10} = 18 K_{i 2} = 100$
11	Feedback	$g (F_{a}) = \frac{(1 + F_{a} \cdot {([p p M A P K] / K_{a})}^{2})}{(1 + {([p p M A P K] / K_{a})}^{2})}$	$K_{a} = 100$ ; $F_{a} = 5; 1; 0.5 (PF; US; NF)$

* Maximal rates, Michaelis and catalytic constants are expressed in [nM/s], [nM], and [s^-1], respectively. Total protein concentrations are [MAPK3]_total = 200nM, [MAPK2]_total = 200nM, and [MAPK]_total = 360nM.

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ISSN: 1752-0509

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