Oscillations in MAPK cascade triggered by two distinct designs of coupled positive and negative feedback loops

BMC Research Notes

Table 3 After addition of the nuclear components, ‘S1’ and ‘S2’ were renamed as ‘S1n’ and ‘S2n’ respectively

Reaction number in models S1n and S2n	Reaction	Flux equation	Parameter value
11]	MK ↔ MK-n	k11_f.MK - k11_b.MK-n	k11_f = 10.34 sec^-1
11]	MK ↔ MK-n	k11_f.MK - k11_b.MK-n	k11_b = 2.86 sec^-1
12]	P3-n gene → PreP3mRNA	$\frac{V 12 . {({M K}^{* } - n)}^{n 12}}{{(K 12)}^{n 12} + {({M K}^{ *} - n)}^{n 12}}$	V12 = 29.24 nmol/sec
			K12 = 169 nmol/ml
			n12 = 3.97
13]	PreP3mRNA→P3mRNA	k13. PreP3mRNA	k13 = 0.022 sec^-1
14]	P3mRNA → ɸ	k14.P3mRNA	k14 = 0.0078 sec^-1
15]	P3mRNA → P3-c	k15.P3mRNA	k15 = 0.0012 sec^-1
16]	P3-c ↔ P3-n	k16_f.P3-c - k16_b.P3-n	k16_f = 22.56 sec^-1
16]	P3-c ↔ P3-n	k16_f.P3-c - k16_b.P3-n	k16_b = 15.4 sec^-1
17]	P3-c → ɸ	k17.P3-c	k17 = 0.00025 sec^-1
18]	P3-n → ɸ	k18.P3-n	k18 = 0.00025 sec^-1
19]	MK ↔ MK-n	k19_f.MK - k19_b.MK-n	k19_f = 10.34 sec^-1
19]	MK ↔ MK-n	k19_f.MK - k19_b.MK-n	k19_b = 2.86 sec^-1
20]	MK* ↔ MK*-n	k20_f.MK* - k20_b.MK*-n	k20_f = 10.34 sec^-1
20]	MK* ↔ MK*-n	k20_f.MK* - k20_b.MK*-n	k20_b = 2.86 sec^-1
21]	MK*-n → MK-n	$\frac{k 21 . (P 3 - n) . \frac{({M K}^{* } - n)}{K 21}}{1 + \frac{{M K}^{ } - n}{K 21} + \frac{{M K}^{} - n}{K 22}}$	k21 = 0.68 sec^-1
			K21 = 10300 nmol/ml
			K22 = 87 nmol/ml
22]	MK*-n → MK-n	$\frac{k 22 . (P 3 - n) . \frac{({M K}^{} - n)}{K 22}}{1 + \frac{{M K}^{} - n}{K 22} + \frac{{M K}^{* *} - n}{K 21}}$	k22 = 0.31 sec^-1
			K21 = 10300 nmol/ml
			K22 = 87 nmol/ml

Table shows the reactions and flux equations in both S1n and S2n are shown in Table3. Reactions 1–10 in S1n and S2n were identical to that given in Table2 for S1 and S2 respectively. Reactions and flux equations shown in this table are common for both S1n and S2n. Reactions 21 and 22 were built from the original mass action reactions ([10], by assuming steady state condition of the enzyme-substrate complexes, which were used to calculate Km value for reactions 21 and 22. In the reactions, ki_f and ki_b where i = 11, 16, 19, 20 are the forward and backward reaction rates of the respective reactions. The parameter values ki, where i = 13, 14, 15, 17, 18, 21, 22 are the catalytic rates of the respective reactions. Ki, i = 12, 21, 22 are the Km values of the respective reactions. V12 is the maximum velocity of the reaction 12.

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