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Table 1 Kinetic equations used in the model. Reactions 1, 2, and 3 are reversible Henri-Michaelis-Menten reactions with one substrate and one product. Reaction 4 is an irreversible Henri-Michaelis-Menten reaction with one substrate and one product. Reaction 5 is a mass action reaction with 2 substrates and one product.

From: Parameter estimation for stiff equations of biosystems using radial basis function networks

Reaction number kinetic equation
1 d [ X 2 ] d t = ( K 11 K 12 [ X 1 ] K 13 K 14 [ X 2 ] ) [ E 1 ] K 14 [ X 2 ] + K 12 [ X 1 ] + K 14 K 12 ( K 21 K 22 [ X 2 ] K 23 K 24 [ X 3 ] ) [ E 2 ] K 24 [ X 3 ] + K 22 [ X 2 ] + K 24 K 22 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@A493@
2 d [ X 3 ] d t = ( K 21 K 22 [ X 2 ] K 23 K 24 [ X 3 ] ) [ E 2 ] K 24 [ X 3 ] + K 22 [ X 2 ] + K 24 K 22 ( K 31 K 32 [ X 3 ] K 33 K 34 [ X 4 ] ) [ E 3 ] K 34 [ X 4 ] + K 32 [ X 3 ] + K 34 K 32 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@A4C9@
3 d [ X 4 ] d t = ( K 31 K 32 [ X 3 ] K 33 K 34 [ X 4 ] ) [ E 3 ] K 34 [ X 4 ] + K 32 [ X 3 ] + K 34 K 32 K 41 [ X 4 ] [ E 4 ] K 42 + [ X 4 ] + K 52 [ X 6 ] K 51 [ X 4 ] [ E 2 ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@9B12@
4 d [ X 5 ] d t = K 41 [ X 4 ] [ E 4 ] K 42 + [ X 4 ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdsgaKjabcUfaBjabdIfaynaaBaaaleaacqaI1aqnaeqaaOGaeiyxa0fabaGaemizaqMaemiDaqhaaiabg2da9maalaaabaGaem4saS0aaSbaaSqaaiabisda0iabigdaXaqabaGccqGGBbWwcqWGybawdaWgaaWcbaGaeGinaqdabeaakiabc2faDjabcUfaBjabdweafnaaBaaaleaacqaI0aanaeqaaOGaeiyxa0fabaGaem4saS0aaSbaaSqaaiabisda0iabikdaYaqabaGccqGHRaWkcqGGBbWwcqWGybawdaWgaaWcbaGaeGinaqdabeaakiabc2faDbaaaaa@4CAF@
5 d [ X 6 ] d t = K 51 [ X 4 ] [ E 2 ] K 52 [ X 6 ] d [ E 2 ] d t = K 52 [ X 6 ] K 51 [ X 4 ] [ E 2 ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@6C8D@