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Model Mathematics

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Component: environment

Component: FAt

FAt = \{\begin{matrix} FA2 if time \geq tA \\ FA1 otherwise \end{matrix}

Component: FBt

FBt = \{\begin{matrix} FB2 if time \geq tB \\ FB1 otherwise \end{matrix}

Component: F0t

F0t = FAt + FBt

Component: c15

\frac{d}{d time} (c15) = \frac{p0}{V2} (c015 - c15) + p16 c16 + p17 c17 + pAA15 pp - ((p15 c19 + p18 + \frac{p19 c19}{p20 + c15} + p29) c15)

Component: c16

\frac{d}{d time} (c16) = (\frac{p0}{V2} (c016 - c16) + p15 c15 c19 - (p16 c16)) + pAA16 pp

Component: c17

\frac{d}{d time} (c17) = (\frac{p0}{V2} (c017 - c17) + p1 s1 c1 + p2 s2 c2 + p3 s3 c3 + p4 s4 c4 + p5 s5 c5 + p6 s6 c6 + p7 s7 c7 + p8 s8 c8 + p9 s9 c9 + p14 s14 c14 + p18 c15 + p26 c18 - ((p17 + p25 c19 + p28) c17)) + pAA17 pp

Component: c18

\frac{d}{d time} (c18) = (\frac{p0}{V2} (c018 - c18) + p25 c17 c19 - (p26 c18)) + pAA18 pp

Component: c19

\frac{d}{d time} (c19) = \frac{p0}{V2} (c019 - c19) + p11 s11 c11 + p12 s12 c12 + p13 c13 s13 + p10 c10 s10 + p23 (1 - gt) c17 + p16 c16 + p26 c18 - ((\frac{p19 c15}{p20 + c15} + p15 c15 + p25 c17) c19)

Component: c20

\frac{d}{d time} (c20) = \frac{p0}{V2} (c020 - c20) + \frac{p19 c15}{p20 + c15} c19

Component: c21

\frac{d}{d time} (c21) = \frac{p0}{V2} (c021 - c21) - (p21 c21)

Component: c22

\frac{d}{d time} (c22) = \frac{p0}{V2} (c022 - c22) - (p22 c22)

Component: c23

\frac{d}{d time} (c23) = (\frac{p0}{V2} (c023 - c23) + p21 c21 + p22 c22 - (p23 c23)) + \frac{p31 c15}{p20 + c15} c19

Component: c24

\frac{d}{d time} (c24) = \frac{p0}{V2} (c024 - c24) + 2 p30 p23 c23 + \frac{p32 c15}{p20 + c15} c19 - (p24 c24)

Component: pp

pp = \{\begin{matrix} p33 if time < t1 \\ 0 otherwise \end{matrix}

Component: gt

gt = \{\begin{matrix} 0 if time < 3 \\ p27 otherwise \end{matrix}

Component: c1

\frac{d}{d time} (c1) = (\frac{p0}{V2} (c01 - c1) - (p1 c1)) + pAA1 pp

Component: c2

\frac{d}{d time} (c2) = (\frac{p0}{V2} (c02 - c2) - (p2 c2)) + pAA2 pp

Component: c3

\frac{d}{d time} (c3) = (\frac{p0}{V2} (c03 - c3) - (p3 c3)) + pAA3 pp

Component: c4

\frac{d}{d time} (c4) = (\frac{p0}{V2} (c04 - c4) - (p4 c4)) + pAA4 pp

Component: c5

\frac{d}{d time} (c5) = (\frac{p0}{V2} (c05 - c5) - (p5 c5)) + pAA5 pp

Component: c6

\frac{d}{d time} (c6) = (\frac{p0}{V2} (c06 - c6) - (p6 c6)) + pAA6 pp

Component: c7

\frac{d}{d time} (c7) = (\frac{p0}{V2} (c07 - c7) - (p7 c7)) + pAA7 pp

Component: c8

\frac{d}{d time} (c8) = (\frac{p0}{V2} (c08 - c8) - (p8 c8)) + pAA8 pp

Component: c9

\frac{d}{d time} (c9) = (\frac{p0}{V2} (c09 - c9) - (p9 c9)) + pAA9 pp

Component: c10

\frac{d}{d time} (c10) = (\frac{p0}{V2} (c010 - c10) - (p10 c10)) + pAA10 pp

Component: c11

\frac{d}{d time} (c11) = (\frac{p0}{V2} (c011 - c11) - (p11 c11)) + pAA11 pp

Component: c12

\frac{d}{d time} (c12) = (\frac{p0}{V2} (c012 - c12) - (p12 c12)) + pAA12 pp

Component: c13

\frac{d}{d time} (c13) = (\frac{p0}{V2} (c013 - c13) - (p13 c13)) + pAA13 pp

Component: c14

\frac{d}{d time} (c14) = (\frac{p0}{V2} (c014 - c14) - (p14 c14)) + pAA14 pp

Component: c01

\frac{d}{d time} (c01) = \frac{FAt}{V1} CA1 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c01) - (\frac{p0}{V1} (c01 - c1))

Component: c02

\frac{d}{d time} (c02) = \frac{FAt}{V1} CA2 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c02) - (\frac{p0}{V1} (c02 - c2))

Component: c03

\frac{d}{d time} (c03) = \frac{FAt}{V1} CA3 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c03) - (\frac{p0}{V1} (c03 - c3))

Component: c04

\frac{d}{d time} (c04) = \frac{FAt}{V1} CA4 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c04) - (\frac{p0}{V1} (c04 - c4))

Component: c05

\frac{d}{d time} (c05) = \frac{FAt}{V1} CA5 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c05) - (\frac{p0}{V1} (c05 - c5))

Component: c06

\frac{d}{d time} (c06) = \frac{FAt}{V1} CA6 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c06) - (\frac{p0}{V1} (c06 - c6))

Component: c07

\frac{d}{d time} (c07) = \frac{FAt}{V1} CA7 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c07) - (\frac{p0}{V1} (c07 - c7))

Component: c08

\frac{d}{d time} (c08) = \frac{FAt}{V1} CA8 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c08) - (\frac{p0}{V1} (c08 - c8))

Component: c09

\frac{d}{d time} (c09) = \frac{FAt}{V1} CA9 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c09) - (\frac{p0}{V1} (c09 - c9))

Component: c010

\frac{d}{d time} (c010) = \frac{FAt}{V1} CA10 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c010) - (\frac{p0}{V1} (c010 - c10))

Component: c011

\frac{d}{d time} (c011) = \frac{FAt}{V1} CA11 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c011) - (\frac{p0}{V1} (c011 - c11))

Component: c012

\frac{d}{d time} (c012) = \frac{FAt}{V1} CA12 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c012) - (\frac{p0}{V1} (c012 - c12))

Component: c013

\frac{d}{d time} (c013) = \frac{FAt}{V1} CA13 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c013) - (\frac{p0}{V1} (c013 - c13))

Component: c014

\frac{d}{d time} (c014) = \frac{FAt}{V1} CA14 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c014) - (\frac{p0}{V1} (c014 - c14))

Component: c015

\frac{d}{d time} (c015) = \frac{FAt}{V1} CA15 + \frac{FBt}{V1} CB15 - (\frac{F0t}{V1} c015) - (\frac{p0}{V1} (c015 - c15))

Component: c016

\frac{d}{d time} (c016) = \frac{FAt}{V1} CA16 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c016) - (\frac{p0}{V1} (c016 - c16))

Component: c017

\frac{d}{d time} (c017) = \frac{FAt}{V1} CA17 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c017) - (\frac{p0}{V1} (c017 - c17))

Component: c018

\frac{d}{d time} (c018) = \frac{FAt}{V1} CA18 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c018) - (\frac{p0}{V1} (c018 - c18))

Component: c019

\frac{d}{d time} (c019) = \frac{FAt}{V1} CA19 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c019) - (\frac{p0}{V1} (c019 - c19))

Component: c020

\frac{d}{d time} (c020) = \frac{FAt}{V1} CA20 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c020) - (\frac{p0}{V1} (c020 - c20))

Component: c021

\frac{d}{d time} (c021) = \frac{FAt}{V1} CA21 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c021) - (\frac{p0}{V1} (c021 - c21))

Component: c022

\frac{d}{d time} (c022) = \frac{FAt}{V1} CA22 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c022) - (\frac{p0}{V1} (c022 - c22))

Component: c023

\frac{d}{d time} (c023) = \frac{FAt}{V1} CA23 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c023) - (\frac{p0}{V1} (c023 - c23))

Component: c024

\frac{d}{d time} (c024) = \frac{FAt}{V1} CA24 + \frac{FBt}{V1} CB1 - (\frac{F0t}{V1} c024) - (\frac{p0}{V1} (c024 - c24))

Component: model_parameters

Source: Derived from workspace Dynamics of amino acid metabolism of primary human liver cells in 3D bioreactors at changeset 6b155b15f687.

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Dynamic Model of Amino Acid and Carbohydrate Metabolism in Primary Human Liver Cells