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 + 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) = 0.5 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

ADP = A_tot - ATP

Component: NADH

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

Component: NAD

NAD = NAD_tot - NADH

Component: ACCOA

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

Component: COA

COA = C_tot - ACCOA

Component: AC

Component: BUT

Component: ETOH

Component: GLC

Component: LAC

Component: O

Component: P

Component: V_GLYC

V_GLYC = \{\begin{matrix} V_GLYC_temp if V_GLYC_temp \geq 0 \\ V_GLYC_temp otherwise \end{matrix} V_GLYC_temp = \frac{\frac{\frac{\frac{V_GLYC_max GLC}{Km_GLC} NAD}{Km_NAD} ADP}{Km_ADP}}{(1 + \frac{GLC}{Km_GLC} + \frac{PYR}{Km_PYR}) (1 + \frac{NAD}{Km_NAD} + \frac{NADH}{Km_NADH}) (1 + \frac{ADP}{Km_ADP} + \frac{ATP}{Km_ATP})}

Component: V_LDH

V_LDH = \{\begin{matrix} V_LDH_temp if V_LDH_temp \geq 0 \\ V_LDH_temp otherwise \end{matrix} V_LDH_temp = \frac{\frac{V_LDH_max}{Km_PYR Km_NADH} (PYR NADH - (\frac{LAC NAD}{Keq}))}{(1 + \frac{PYR}{Km_PYR} + \frac{LAC}{Km_LAC}) (1 + \frac{NADH}{Km_NADH} + \frac{NAD}{Km_NAD})}

Component: V_PDH

V_PDH = \{\begin{matrix} V_PDH_temp if V_PDH_temp \geq 0 \\ V_PDH_temp otherwise \end{matrix} V_PDH_temp = \frac{\frac{\frac{\frac{\frac{V_PDH_max}{1 + \frac{Ki NADH}{NAD}} PYR}{Km_PYR} NAD}{Km_NAD} COA}{Km_COA}}{(1 + \frac{PYR}{Km_PYR}) (1 + \frac{NAD}{Km_NAD} + \frac{NADH}{Km_NADH}) (1 + \frac{COA}{Km_COA} + \frac{ACCOA}{Km_ACCOA})}

Component: V_PTA

V_PTA = \{\begin{matrix} V_PTA_temp if V_PTA_temp \geq 0 \\ V_PTA_temp otherwise \end{matrix} V_PTA_temp = \frac{\frac{V_PTA_max}{Ki_ACCOA Km_P} (ACCOA P - (\frac{ACP COA}{Keq}))}{1 + \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 = \{\begin{matrix} V_ACK_temp if V_ACK_temp \geq 0 \\ V_ACK_temp otherwise \end{matrix} V_ACK_temp = \frac{\frac{V_ACK_max}{Km_ADP Km_ACP} (ACP ADP - (\frac{AC ATP}{Keq}))}{(1 + \frac{ACP}{Km_ACP} + \frac{AC}{Km_AC}) (1 + \frac{ADP}{Km_ADP} + \frac{ATP}{Km_ATP})}

Component: V_ACALDH

V_ACALDH = \{\begin{matrix} V_ACALDH_temp if V_ACALDH_temp \geq 0 \\ V_ACALDH_temp otherwise \end{matrix} V_ACALDH_temp = \frac{\frac{V_ACALDH_max}{Km_ACCOA Km_NADH} (ACCOA NADH - (\frac{NAD COA ACAL}{Keq}))}{(1 + \frac{NAD}{Km_NAD} + \frac{NADH}{Km_NADH}) (1 + \frac{ACCOA}{Km_ACCOA} + \frac{COA}{Km_COA}) (1 + \frac{ACAL}{Km_ACAL})}

Component: V_ADH

V_ADH = \{\begin{matrix} V_ADH_temp if V_ADH_temp \geq 0 \\ V_ADH_temp otherwise \end{matrix} V_ADH_temp = \frac{\frac{V_ADH_max}{Km_ACAL Km_NADH} (ACAL NADH - (\frac{ETOH NAD}{Keq}))}{(1 + \frac{NAD}{Km_NAD} + \frac{NADH}{Km_NADH}) (1 + \frac{ACAL}{Km_ACAL} + \frac{ETOH}{Km_ETOH})}

Component: V_ALS

V_ALS = \{\begin{matrix} V_ALS_temp if V_ALS_temp \geq 0 \\ V_ALS_temp otherwise \end{matrix} V_ALS_temp = \frac{\frac{V_ALS_max PYR}{Km_PYR} (1 - (\frac{ACLAC}{PYR Keq})) {(\frac{PYR}{Km_PYR} + \frac{ACLAC}{Km_ACLAC})}^{N - 1}}{1 + {(\frac{PYR}{Km_PYR} + \frac{ACLAC}{Km_ACLAC})}^{N}}

Component: V_ALDC

V_ALDC = \{\begin{matrix} V_ALDC_temp if V_ALDC_temp \geq 0 \\ V_ALDC_temp otherwise \end{matrix} V_ALDC_temp = \frac{\frac{V_ALDC_max ACLAC}{Km_ACLAC}}{1 + \frac{ACLAC}{Km_ACLAC} + \frac{ACET}{Km_ACET}}

Component: V_ACETEFF

V_ACETEFF = \{\begin{matrix} V_ACETEFF_temp if V_ACETEFF_temp \geq 0 \\ V_ACETEFF_temp otherwise \end{matrix} V_ACETEFF_temp = \frac{\frac{V_ACETEFF_max ACET}{Km_ACET}}{1 + \frac{ACET}{Km_ACET}}

Component: V_ACETDH

V_ACETDH = \{\begin{matrix} V_ACETDH_temp if V_ACETDH_temp \geq 0 \\ V_ACETDH_temp otherwise \end{matrix} V_ACETDH_temp = \frac{\frac{V_ACETDH_max}{Km_ACET Km_NADH} (ACET NADH - (\frac{BUT NAD}{Keq}))}{(1 + \frac{ACET}{Km_ACET} + \frac{BUT}{Km_BUT}) (1 + \frac{NADH}{Km_NADH} + \frac{NAD}{Km_NAD})}

Component: V_ATPase

V_ATPase = \{\begin{matrix} V_ATPase_temp if V_ATPase_temp \geq 0 \\ V_ATPase_temp otherwise \end{matrix} V_ATPase_temp = \frac{V_ATPase_max {(\frac{ATP}{ADP})}^{N}}{{Km_ATP}^{N} + {(\frac{ATP}{ADP})}^{N}}

Component: V_NOX

V_NOX = \{\begin{matrix} V_NOX_temp if V_NOX_temp \geq 0 \\ V_NOX_temp otherwise \end{matrix} V_NOX_temp = \frac{\frac{V_NOX_max NADH O}{Km_NADH Km_O}}{(1 + \frac{NADH}{Km_NADH} + \frac{NAD}{Km_NAD}) (1 + \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 59cb833f3bb3.

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