You are here: Home / Exposures / Hoefnagel, Starrenburg, Martens, Hugenholtz, Kleerebezem, Van Swam, Bongers, Westerhoff, Snoep, 2002 / Metabolic engineering of lactic acid bacteria, the combined approach: kinetic modelling, metabolic control and experimental analysis

Model Mathematics

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Component: environment

Component: PYR

\frac{d}{d time} (PYR) = V_GLYC - (V_LDH + V_PDH + 2.0 V_ALS)

Component: ACP

\frac{d}{d time} (ACP) = V_PTA - V_ACK

Component: ACAL

\frac{d}{d time} (ACAL) = V_ACALDH - V_ADH

Component: ACLAC

\frac{d}{d time} (ACLAC) = V_ALS - (V_ALDC + V_NEALC)

Component: ACET

\frac{d}{d time} (ACET) = V_ALDC + V_NEALC - (V_ACETDH + V_ACETEFF)

Component: ATP

\frac{d}{d time} (ATP) = V_GLYC + V_ACK - V_ATPase

Component: ADP

Component: NADH

\frac{d}{d time} (NADH) = V_GLYC + V_PDH - (V_LDH + V_ACALDH + V_ADH + V_ACETDH + V_NOX)

Component: NAD

Component: ACCOA

\frac{d}{d time} (ACCOA) = V_PDH - (V_ACALDH + V_PTA)

Component: COA

Component: AC

Component: BUT

Component: ETOH

Component: GLC

Component: LAC

Component: O

Component: P

Component: V_GLYC

V_GLYC = \frac{V_GLYC_max \frac{GLC}{Km_GLC} \frac{NAD}{Km_NAD} \frac{ADP}{Km_ADP}}{(1.0 + \frac{GLC}{Km_GLC} + \frac{PYR}{Km_PYR}) (1.0 + \frac{NAD}{Km_NAD} + \frac{NADH}{Km_NADH}) (1.0 + \frac{ADP}{Km_ADP} + \frac{ATP}{Km_ATP})}

Component: V_LDH

V_LDH = \frac{V_LDH_max \frac{1.0}{Km_PYR Km_NADH} (PYR NADH - (\frac{LAC NAD}{Keq}))}{(1.0 + \frac{PYR}{Km_PYR} + \frac{LAC}{Km_LAC}) (1.0 + \frac{NADH}{Km_NADH} + \frac{NAD}{Km_NAD})}

Component: V_PDH

V_PDH = \frac{V_PDH_max \frac{1.0}{1.0 + Ki \frac{NADH}{NAD}} \frac{PYR}{Km_PYR} \frac{NAD}{Km_NAD} \frac{COA}{Km_COA}}{(1.0 + \frac{PYR}{Km_PYR}) (1.0 + \frac{NAD}{Km_NAD} + \frac{NADH}{Km_NADH}) (1.0 + \frac{COA}{Km_COA} + \frac{ACCOA}{Km_ACCOA})}

Component: V_PTA

V_PTA = \frac{V_PTA_max \frac{1.0}{Ki_ACCOA Km_P} (ACCOA P - (\frac{ACP COA}{Keq}))}{1.0 + \frac{ACCOA}{Ki_ACCOA} + \frac{P}{Ki_P} + \frac{ACP}{Ki_ACP} + \frac{COA}{Ki_COA} + \frac{ACCOA P}{Ki_ACCOA Km_P} + \frac{ACP COA}{Km_ACP Ki_COA}}

Component: V_ACK

V_ACK = \frac{V_ACK_max \frac{1.0}{Km_ADP Km_ACP} (ACP ADP - (\frac{AC ATP}{Keq}))}{(1.0 + \frac{ACP}{Km_ACP} + \frac{AC}{Km_AC}) (1.0 + \frac{ADP}{Km_ADP} + \frac{ATP}{Km_ATP})}

Component: V_ACALDH

V_ACALDH = \frac{V_ACALDH_max \frac{1.0}{Km_ACCOA Km_NADH} (ACCOA NADH - (\frac{NAD COA ACAL}{Keq}))}{(1.0 + \frac{NAD}{Km_NAD} + \frac{NADH}{Km_NADH}) (1.0 + \frac{ACCOA}{Km_ACCOA} + \frac{COA}{Km_COA} + \frac{ACAL}{Km_ACAL} + \frac{ACAL COA}{Km_ACAL Km_COA})}

Component: V_ADH

V_ADH = \frac{V_ADH_max \frac{1.0}{Km_ACAL Km_NADH} (ACAL NADH - (\frac{ETOH NAD}{Keq}))}{(1.0 + \frac{NAD}{Km_NAD} + \frac{NADH}{Km_NADH}) (1.0 + \frac{ACAL}{Km_ACAL} + \frac{ETOH}{Km_ETOH})}

Component: V_ALS

V_ALS = \frac{V_ALS_max \frac{PYR}{Km_PYR} (1.0 - (\frac{ACLAC}{PYR Keq})) {(\frac{PYR}{Km_PYR} + \frac{ACLAC}{Km_ACLAC})}^{N - 1.0}}{1.0 + {(\frac{PYR}{Km_PYR} + \frac{ACLAC}{Km_ACLAC})}^{N}}

Component: V_ALDC

V_ALDC = \frac{V_ALDC_max \frac{ACLAC}{Km_ACLAC}}{1.0 + \frac{ACLAC}{Km_ACLAC} + \frac{ACET}{Km_ACET}}

Component: V_ACETEFF

V_ACETEFF = \frac{V_ACETEFF_max \frac{ACET}{Km_ACET}}{1.0 + \frac{ACET}{Km_ACET}}

Component: V_ACETDH

V_ACETDH = \frac{V_ACETDH_max \frac{1.0}{Km_ACET Km_NADH} (ACET NADH - (\frac{BUT NAD}{Keq}))}{(1.0 + \frac{ACET}{Km_ACET} + \frac{BUT}{Km_BUT}) (1.0 + \frac{NADH}{Km_NADH} + \frac{NAD}{Km_NAD})}

Component: V_ATPase

V_ATPase = \frac{V_ATPase_max {(\frac{ATP}{ADP Km_ATP})}^{N}}{1.0 + {(\frac{ATP}{ADP Km_ATP})}^{N}}

Component: V_NOX

V_NOX = \frac{V_NOX_max \frac{NADH O}{Km_NADH Km_O}}{(1.0 + \frac{NADH}{Km_NADH} + \frac{NAD}{Km_NAD}) (1.0 + \frac{O}{Km_O})}

Component: V_NEALC

V_NEALC = k ACLAC

Source: Derived from workspace Hoefnagel, Starrenburg, Martens, Hugenholtz, Kleerebezem, Vanswam, Bongers, Westerhoff, Snoep, 2002 at changeset 7153ddf5b010.; This exposure was expired. A more up-to-date exposure is available, or view related resources.

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Metabolic engineering of lactic acid bacteria, the combined approach: kinetic modelling, metabolic control and experimental analysis