Team:UChile-OpenBio/Experiments

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\begin{matrix} \frac{d V_{c1}}{d t} & = & V_{c1} + \frac{0.8 \cdot 5}{7 \cdot 3600} \cdot \frac{[Lactate{default}]}{[Lactate{default}] + 9.8e-3} \cdot (1 - \frac{"[Lactic acid]"}{0.448}) \\ \frac{d V_{c2}}{d t} & = & V_{c2} + \frac{0.8 \cdot 5}{7 \cdot 3600} \cdot \frac{[Lactate{default}]}{[Lactate{default}] + 9.8e-3} \cdot (1 - \frac{"[Lactic acid]"}{0.448}) \\ \frac{d ([TetR] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot ({k1}_{(K1)} \cdot [mTetR]) \\ - V_{c1} \cdot (({k1}_{(K2,1)} \cdot [TetR] \cdot ["Gen 1"] - {k2}_{(K2,1)} \cdot ["complex 2"])) \\ - (\frac{V_{(d1)} \cdot [TetR]}{{Km}_{(d1)} + [TetR]}) \\ \frac{d (["Gen 1"] \cdot V_{c1})}{d t} & = & - V_{c1} \cdot (({k1}_{(K2,1)} \cdot [TetR] \cdot ["Gen 1"] - {k2}_{(K2,1)} \cdot ["complex 2"])) \\ - V_{c1} \cdot ({k1}_{(K2,2)} \cdot ["Gen 1"]) \\ - V_{c1} \cdot ({k1}_{(K2,3)} \cdot ["Gen 1"]) \\ \frac{d (["complex 1"] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot (({Vo}_{(K1,1)} + {V1}_{(K1,1)} \cdot (1 - \tanh ([TetRg] \cdot (- (\ln ["H+{c1}"]) - 5.5)))) \cdot {GR}_{(K1,1)} - ["complex 1"] \cdot ({dm}_{(K1,1)} + {umax}_{(K1,1)} \cdot \frac{[Lactate{default}]}{[Lactate{default}] + {Ks}_{(K1,1)}} \cdot (1 - \frac{["Lactic acid"]}{{Kla}_{(K1,1)}}))) \\ - V_{c1} \cdot ({k1}_{(K1,2)} \cdot ["complex 1"]) \\ \frac{d (["complex 2"] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot (({k1}_{(K2,1)} \cdot [TetR] \cdot ["Gen 1"] - {k2}_{(K2,1)} \cdot ["complex 2"])) \\ \frac{d (["D-LDH"] \cdot V_{c1})}{d t} & = & - V_{c1} \cdot (\frac{V_{(d2)} \cdot ["D-LDH"]}{{Km}_{(d2)} + ["D-LDH"]}) \\ + V_{c1} \cdot ({k1}_{(K2)} \cdot ["mD-LDH"]) \\ \frac{d (["NAD+"] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot (\frac{V_{(K4)} \cdot ["D-LDH"] \cdot \frac{1}{{Kmb}_{(K4)} \cdot {Kmd}_{(K4)}} \cdot ([Pyruvate] \cdot [NADH] - \frac{[Lactate{c1}] \cdot ["NAD+"]}{{Keq}_{(K4)}})}{(1 + \frac{[Pyruvate]}{{Kmb}_{(K4)}} + \frac{[Lactate{c1}]}{{Kmd}_{(K4)}}) \cdot (1 + \frac{[NADH]}{{Kma}_{(K4)}} + \frac{["NAD+"]}{{Kmc}_{(K4)}})}) \\ \frac{d ([Pyruvate] \cdot V_{c1})}{d t} & = & V_{c1} \cdot 6e-6 \cdot (0.00550965 - [Pyruvate]) \\ \frac{d ([NADH] \cdot V_{c1})}{d t} & = & V_{c1} \cdot 6e-6 \cdot (0.00550965 - [Pyruvate]) \\ \frac{d ([LuxI] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot ({k1}_{(K3)} \cdot [mLuxI]) \\ - V_{c1} \cdot (\frac{V_{(d3)} \cdot [LuxI]}{{Km}_{(d3)} + [LuxI]}) \\ \frac{d (["S-adenosyl-L-methionine"] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot ({k1}_{(G2)} \cdot ["5'-methylthioadenosine"]) \\ - V_{c1} \cdot (\frac{{Vf}_{(K13)} \cdot [LuxI] \cdot (["S-adenosyl-L-methionine"] \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] - \frac{[HSL{c1}] \cdot ["5'-methylthioadenosine"] \cdot ["[acyl-carrier protein]"]}{{Keq}_{(K13)}})}{["S-adenosyl-L-methionine"] \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] \cdot (1 + \frac{[HSL{c1}]}{{Ki3}_{(K13)}}) + {Km1}_{(K13)} \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] + {Km2}_{(K13)} \cdot ["S-adenosyl-L-methionine"] + \frac{{Vf}_{(K13)}}{{Vr}_{(K13)} \cdot {Keq}_{(K13)}} \cdot ({Km4}_{(K13)} \cdot [HSL{c1}] \cdot (1 + \frac{["S-adenosyl-L-methionine"]}{{Ki1}_{(K13)}}) + ["5'-methylthioadenosine"] \cdot ({Km3}_{(K13)} \cdot (1 + \frac{{Km1}_{(K13)} \cdot ["3-oxohexanoyl-[acyl-carrier protein]"]}{{Ki1}_{(K13)} \cdot {Km2}_{(K13)}}) + [HSL{c1}] \cdot (1 + \frac{["3-oxohexanoyl-[acyl-carrier protein]"]}{{Ki2}_{(K13)}})))}) \\ \frac{d (["3-oxohexanoyl-[acyl-carrier protein]"] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot ({k1}_{(G3)} \cdot ["[acyl-carrier protein]"]) \\ - V_{c1} \cdot (\frac{{Vf}_{(K13)} \cdot [LuxI] \cdot (["S-adenosyl-L-methionine"] \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] - \frac{[HSL{c1}] \cdot ["5'-methylthioadenosine"] \cdot ["[acyl-carrier protein]"]}{{Keq}_{(K13)}})}{["S-adenosyl-L-methionine"] \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] \cdot (1 + \frac{[HSL{c1}]}{{Ki3}_{(K13)}}) + {Km1}_{(K13)} \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] + {Km2}_{(K13)} \cdot ["S-adenosyl-L-methionine"] + \frac{{Vf}_{(K13)}}{{Vr}_{(K13)} \cdot {Keq}_{(K13)}} \cdot ({Km4}_{(K13)} \cdot [HSL{c1}] \cdot (1 + \frac{["S-adenosyl-L-methionine"]}{{Ki1}_{(K13)}}) + ["5'-methylthioadenosine"] \cdot ({Km3}_{(K13)} \cdot (1 + \frac{{Km1}_{(K13)} \cdot ["3-oxohexanoyl-[acyl-carrier protein]"]}{{Ki1}_{(K13)} \cdot {Km2}_{(K13)}}) + [HSL{c1}] \cdot (1 + \frac{["3-oxohexanoyl-[acyl-carrier protein]"]}{{Ki2}_{(K13)}})))}) \\ \frac{d (["5'-methylthioadenosine"] \cdot V_{c1})}{d t} & = & - V_{c1} \cdot ({k1}_{(G2)} \cdot ["5'-methylthioadenosine"]) \\ + V_{c1} \cdot (\frac{{Vf}_{(K13)} \cdot [LuxI] \cdot (["S-adenosyl-L-methionine"] \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] - \frac{[HSL{c1}] \cdot ["5'-methylthioadenosine"] \cdot ["[acyl-carrier protein]"]}{{Keq}_{(K13)}})}{["S-adenosyl-L-methionine"] \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] \cdot (1 + \frac{[HSL{c1}]}{{Ki3}_{(K13)}}) + {Km1}_{(K13)} \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] + {Km2}_{(K13)} \cdot ["S-adenosyl-L-methionine"] + \frac{{Vf}_{(K13)}}{{Vr}_{(K13)} \cdot {Keq}_{(K13)}} \cdot ({Km4}_{(K13)} \cdot [HSL{c1}] \cdot (1 + \frac{["S-adenosyl-L-methionine"]}{{Ki1}_{(K13)}}) + ["5'-methylthioadenosine"] \cdot ({Km3}_{(K13)} \cdot (1 + \frac{{Km1}_{(K13)} \cdot ["3-oxohexanoyl-[acyl-carrier protein]"]}{{Ki1}_{(K13)} \cdot {Km2}_{(K13)}}) + [HSL{c1}] \cdot (1 + \frac{["3-oxohexanoyl-[acyl-carrier protein]"]}{{Ki2}_{(K13)}})))}) \\ \frac{d (["[acyl-carrier protein]"] \cdot V_{c1})}{d t} & = & - V_{c1} \cdot ({k1}_{(G3)} \cdot ["[acyl-carrier protein]"]) \\ + V_{c1} \cdot (\frac{{Vf}_{(K13)} \cdot [LuxI] \cdot (["S-adenosyl-L-methionine"] \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] - \frac{[HSL{c1}] \cdot ["5'-methylthioadenosine"] \cdot ["[acyl-carrier protein]"]}{{Keq}_{(K13)}})}{["S-adenosyl-L-methionine"] \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] \cdot (1 + \frac{[HSL{c1}]}{{Ki3}_{(K13)}}) + {Km1}_{(K13)} \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] + {Km2}_{(K13)} \cdot ["S-adenosyl-L-methionine"] + \frac{{Vf}_{(K13)}}{{Vr}_{(K13)} \cdot {Keq}_{(K13)}} \cdot ({Km4}_{(K13)} \cdot [HSL{c1}] \cdot (1 + \frac{["S-adenosyl-L-methionine"]}{{Ki1}_{(K13)}}) + ["5'-methylthioadenosine"] \cdot ({Km3}_{(K13)} \cdot (1 + \frac{{Km1}_{(K13)} \cdot ["3-oxohexanoyl-[acyl-carrier protein]"]}{{Ki1}_{(K13)} \cdot {Km2}_{(K13)}}) + [HSL{c1}] \cdot (1 + \frac{["3-oxohexanoyl-[acyl-carrier protein]"]}{{Ki2}_{(K13)}})))}) \\ \frac{d ([Lactate{c1}] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot (\frac{V_{(K4)} \cdot ["D-LDH"] \cdot \frac{1}{{Kmb}_{(K4)} \cdot {Kmd}_{(K4)}} \cdot ([Pyruvate] \cdot [NADH] - \frac{[Lactate{c1}] \cdot ["NAD+"]}{{Keq}_{(K4)}})}{(1 + \frac{[Pyruvate]}{{Kmb}_{(K4)}} + \frac{[Lactate{c1}]}{{Kmd}_{(K4)}}) \cdot (1 + \frac{[NADH]}{{Kma}_{(K4)}} + \frac{["NAD+"]}{{Kmc}_{(K4)}})}) \\ - (\frac{\frac{{Vf}_{(S1)} \cdot [Lactate{c1}]}{{Kms}_{(S1)}} - \frac{{Vr}_{(S1)} \cdot [Lactate{default}]}{{Kmp}_{(S1)}}}{1 + \frac{[Lactate{c1}]}{{Kms}_{(S1)}} + \frac{[Lactate{default}]}{{Kmp}_{(S1)}}}) \\ \frac{d ([HSL{c1}] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot (\frac{{Vf}_{(K13)} \cdot [LuxI] \cdot (["S-adenosyl-L-methionine"] \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] - \frac{[HSL{c1}] \cdot ["5'-methylthioadenosine"] \cdot ["[acyl-carrier protein]"]}{{Keq}_{(K13)}})}{["S-adenosyl-L-methionine"] \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] \cdot (1 + \frac{[HSL{c1}]}{{Ki3}_{(K13)}}) + {Km1}_{(K13)} \cdot ["3-oxohexanoyl-[acyl-carrier protein]"] + {Km2}_{(K13)} \cdot ["S-adenosyl-L-methionine"] + \frac{{Vf}_{(K13)}}{{Vr}_{(K13)} \cdot {Keq}_{(K13)}} \cdot ({Km4}_{(K13)} \cdot [HSL{c1}] \cdot (1 + \frac{["S-adenosyl-L-methionine"]}{{Ki1}_{(K13)}}) + ["5'-methylthioadenosine"] \cdot ({Km3}_{(K13)} \cdot (1 + \frac{{Km1}_{(K13)} \cdot ["3-oxohexanoyl-[acyl-carrier protein]"]}{{Ki1}_{(K13)} \cdot {Km2}_{(K13)}}) + [HSL{c1}] \cdot (1 + \frac{["3-oxohexanoyl-[acyl-carrier protein]"]}{{Ki2}_{(K13)}})))}) \\ - (D_{(S2)} \cdot ([HSL{c1}] - [HSL{default}]) + {k1}_{(S2)} \cdot {fl}_{(S2)} - {k2}_{(S2)} \cdot [HSL{c1}]) \\ \frac{d (["H+{c1}"] \cdot V_{c1})}{d t} & = & + (\frac{\frac{{Vf}_{(E4)} \cdot ["H+{default}"]}{{Kms}_{(E4)}} - \frac{{Vr}_{(E4)} \cdot ["H+{c1}"]}{{Kmp}_{(E4)}}}{1 + \frac{["H+{default}"]}{{Kms}_{(E4)}} + \frac{["H+{c1}"]}{{Kmp}_{(E4)}}}) \\ - V_{c1} \cdot (({Vo}_{(K1,1)} + {V1}_{(K1,1)} \cdot (1 - \tanh ([TetRg] \cdot (- (\ln ["H+{c1}"]) - 5.5)))) \cdot {GR}_{(K1,1)} - ["complex 1"] \cdot ({dm}_{(K1,1)} + {umax}_{(K1,1)} \cdot \frac{[Lactate{default}]}{[Lactate{default}] + {Ks}_{(K1,1)}} \cdot (1 - \frac{["Lactic acid"]}{{Kla}_{(K1,1)}}))) \\ \frac{d ([TetRg] \cdot V_{c1})}{d t} & = & - V_{c1} \cdot (({Vo}_{(K1,1)} + {V1}_{(K1,1)} \cdot (1 - \tanh ([TetRg] \cdot (- (\ln ["H+{c1}"]) - 5.5)))) \cdot {GR}_{(K1,1)} - ["complex 1"] \cdot ({dm}_{(K1,1)} + {umax}_{(K1,1)} \cdot \frac{[Lactate{default}]}{[Lactate{default}] + {Ks}_{(K1,1)}} \cdot (1 - \frac{["Lactic acid"]}{{Kla}_{(K1,1)}}))) \\ \frac{d ([mTetR] \cdot V_{c1})}{d t} & = & - V_{c1} \cdot ({k1}_{(K1)} \cdot [mTetR]) \\ + V_{c1} \cdot ({k1}_{(K1,2)} \cdot ["complex 1"]) \\ - V_{c1} \cdot (\frac{V_{(d1,2)} \cdot [mTetR]}{{Km}_{(d1,2)} + [mTetR]}) \\ \frac{d ([dmLuxI] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot (\frac{V_{(d2,3)} \cdot [mLuxI]}{{Km}_{(d2,3)} + [mLuxI]}) \\ \frac{d ([dLuxI] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot (\frac{V_{(d3)} \cdot [LuxI]}{{Km}_{(d3)} + [LuxI]}) \\ \frac{d ([dmTetR] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot (\frac{V_{(d1,2)} \cdot [mTetR]}{{Km}_{(d1,2)} + [mTetR]}) \\ \frac{d (["dmD-LDH"] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot (\frac{V_{(d2,2)} \cdot ["mD-LDH"]}{{Km}_{(d2,2)} + ["mD-LDH"]}) \\ \frac{d ([mLuxI] \cdot V_{c1})}{d t} & = & - V_{c1} \cdot ({k1}_{(K3)} \cdot [mLuxI]) \\ - V_{c1} \cdot (\frac{V_{(d2,3)} \cdot [mLuxI]}{{Km}_{(d2,3)} + [mLuxI]}) \\ + V_{c1} \cdot ({k1}_{(K2,3)} \cdot ["Gen 1"]) \\ \frac{d (["dD-LDH"] \cdot V_{c1})}{d t} & = & + V_{c1} \cdot (\frac{V_{(d2)} \cdot ["D-LDH"]}{{Km}_{(d2)} + ["D-LDH"]}) \\ \frac{d (["mD-LDH"] \cdot V_{c1})}{d t} & = & - V_{c1} \cdot ({k1}_{(K2)} \cdot ["mD-LDH"]) \\ + V_{c1} \cdot ({k1}_{(K2,2)} \cdot ["Gen 1"]) \\ - V_{c1} \cdot (\frac{V_{(d2,2)} \cdot ["mD-LDH"]}{{Km}_{(d2,2)} + ["mD-LDH"]}) \\ \frac{d (["H+{default}"] \cdot V_{default})}{d t} & = & - (\frac{\frac{{Vf}_{(E4)} \cdot ["H+{default}"]}{{Kms}_{(E4)}} - \frac{{Vr}_{(E4)} \cdot ["H+{c1}"]}{{Kmp}_{(E4)}}}{1 + \frac{["H+{default}"]}{{Kms}_{(E4)}} + \frac{["H+{c1}"]}{{Kmp}_{(E4)}}}) \\ - V_{default} \cdot (({k1}_{(Ka)} \cdot ["H+{default}"] \cdot [Lactate{default}] - {k2}_{(Ka)} \cdot ["Lactic acid"])) \\ \frac{d ([Lactate{default}] \cdot V_{default})}{d t} & = & - V_{default} \cdot (({k1}_{(Ka)} \cdot ["H+{default}"] \cdot [Lactate{default}] - {k2}_{(Ka)} \cdot ["Lactic acid"])) \\ + (\frac{\frac{{Vf}_{(S1)} \cdot [Lactate{c1}]}{{Kms}_{(S1)}} - \frac{{Vr}_{(S1)} \cdot [Lactate{default}]}{{Kmp}_{(S1)}}}{1 + \frac{[Lactate{c1}]}{{Kms}_{(S1)}} + \frac{[Lactate{default}]}{{Kmp}_{(S1)}}}) \\ - (\frac{\frac{{Vf}_{(E1)} \cdot [Lactate{default}]}{{Kms}_{(E1)}} - \frac{{Vr}_{(E1)} \cdot [Lactate{c2}]}{{Kmp}_{(E1)}}}{1 + \frac{[Lactate{default}]}{{Kms}_{(E1)}} + \frac{[Lactate{c2}]}{{Kmp}_{(E1)}}}) \\ \frac{d (["Lactic acid"] \cdot V_{default})}{d t} & = & + V_{default} \cdot (({k1}_{(Ka)} \cdot ["H+{default}"] \cdot [Lactate{default}] - {k2}_{(Ka)} \cdot ["Lactic acid"])) \\ \frac{d ([HSL{default}] \cdot V_{default})}{d t} & = & - (D_{(E2)} \cdot ([HSL{default}] - [HSL{c2}]) + {k1}_{(E2)} \cdot {fl}_{(E2)} - {k2}_{(E2)} \cdot [HSL{default}]) \\ + (D_{(S2)} \cdot ([HSL{c1}] - [HSL{default}]) + {k1}_{(S2)} \cdot {fl}_{(S2)} - {k2}_{(S2)} \cdot [HSL{c1}]) \\ \frac{d (["PLA-Phasin-Hly{default}"] \cdot V_{default})}{d t} & = & + ({k1}_{(S3)} \cdot ["PLA-Phasin-Hly{c2}"]) \\ \frac{d ([dTetR] \cdot V_{default})}{d t} & = & + (\frac{V_{(d1)} \cdot [TetR]}{{Km}_{(d1)} + [TetR]}) \\ \frac{d ([HSL{c2}] \cdot V_{c2})}{d t} & = & + (D_{(E2)} \cdot ([HSL{default}] - [HSL{c2}]) + {k1}_{(E2)} \cdot {fl}_{(E2)} - {k2}_{(E2)} \cdot [HSL{default}]) \\ - V_{c2} \cdot (\frac{0.5}{3600e-9} \cdot ([LuxR] + \frac{K_{(K5)}}{4 \cdot {[HSL{c2}]}^{2}} - {([LuxR] + \frac{K_{(K5)}}{4 \cdot {[HSL{c2}]}^{2}} - {[LuxR]}^{2})}^{0.5})) \\ \frac{d ([PLA] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{{Vf}_{(K7)} \cdot [phaC] \cdot (["Lactyl-CoA"] - \frac{[PLA]}{{Keq}_{(K7)}})}{["Lactyl-CoA"] + {Kms}_{(K7)} \cdot (1 + \frac{[PLA]}{{Kmp}_{(K7)}})}) \\ - V_{c2} \cdot (({k1}_{(K12)} \cdot ["Phasin-Hly"] \cdot [PLA] - {k2}_{(K12)} \cdot ["PLA-Phasin-Hly{c2}"])) \\ \frac{d (["PLA-Phasin-Hly{c2}"] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (({k1}_{(K12)} \cdot ["Phasin-Hly"] \cdot [PLA] - {k2}_{(K12)} \cdot ["PLA-Phasin-Hly{c2}"])) \\ - ({k1}_{(S3)} \cdot ["PLA-Phasin-Hly{c2}"]) \\ \frac{d ([Acetate] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{{por}_{(K6)} \cdot ["P-CoA-T"] \cdot (\frac{{Vf}_{(K6)} \cdot [Lactate{c2}] \cdot ["acetyl-CoA"]}{{Kms}_{(K6)}} - \frac{{Vr}_{(K6)} \cdot ["Lactyl-CoA"] \cdot [Acetate]}{{Kmp}_{(K6)}})}{1 + \frac{[Lactate{c2}] \cdot ["acetyl-CoA"]}{{Kms}_{(K6)}} + \frac{["Lactyl-CoA"] \cdot [Acetate]}{{Kmp}_{(K6)}}}) \\ \frac{d ([Lactate{c2}] \cdot V_{c2})}{d t} & = & + (\frac{\frac{{Vf}_{(E1)} \cdot [Lactate{default}]}{{Kms}_{(E1)}} - \frac{{Vr}_{(E1)} \cdot [Lactate{c2}]}{{Kmp}_{(E1)}}}{1 + \frac{[Lactate{default}]}{{Kms}_{(E1)}} + \frac{[Lactate{c2}]}{{Kmp}_{(E1)}}}) \\ - V_{c2} \cdot (\frac{{por}_{(K6)} \cdot ["P-CoA-T"] \cdot (\frac{{Vf}_{(K6)} \cdot [Lactate{c2}] \cdot ["acetyl-CoA"]}{{Kms}_{(K6)}} - \frac{{Vr}_{(K6)} \cdot ["Lactyl-CoA"] \cdot [Acetate]}{{Kmp}_{(K6)}})}{1 + \frac{[Lactate{c2}] \cdot ["acetyl-CoA"]}{{Kms}_{(K6)}} + \frac{["Lactyl-CoA"] \cdot [Acetate]}{{Kmp}_{(K6)}}}) \\ \frac{d (["Lactyl-CoA"] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{{por}_{(K6)} \cdot ["P-CoA-T"] \cdot (\frac{{Vf}_{(K6)} \cdot [Lactate{c2}] \cdot ["acetyl-CoA"]}{{Kms}_{(K6)}} - \frac{{Vr}_{(K6)} \cdot ["Lactyl-CoA"] \cdot [Acetate]}{{Kmp}_{(K6)}})}{1 + \frac{[Lactate{c2}] \cdot ["acetyl-CoA"]}{{Kms}_{(K6)}} + \frac{["Lactyl-CoA"] \cdot [Acetate]}{{Kmp}_{(K6)}}}) \\ - V_{c2} \cdot (\frac{{Vf}_{(K7)} \cdot [phaC] \cdot (["Lactyl-CoA"] - \frac{[PLA]}{{Keq}_{(K7)}})}{["Lactyl-CoA"] + {Kms}_{(K7)} \cdot (1 + \frac{[PLA]}{{Kmp}_{(K7)}})}) \\ \frac{d (["acetyl-CoA"] \cdot V_{c2})}{d t} & = & - V_{c2} \cdot (\frac{{por}_{(K6)} \cdot ["P-CoA-T"] \cdot (\frac{{Vf}_{(K6)} \cdot [Lactate{c2}] \cdot ["acetyl-CoA"]}{{Kms}_{(K6)}} - \frac{{Vr}_{(K6)} \cdot ["Lactyl-CoA"] \cdot [Acetate]}{{Kmp}_{(K6)}})}{1 + \frac{[Lactate{c2}] \cdot ["acetyl-CoA"]}{{Kms}_{(K6)}} + \frac{["Lactyl-CoA"] \cdot [Acetate]}{{Kmp}_{(K6)}}}) \\ \frac{d ([dphaC] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{V_{(d10)} \cdot [phaC]}{{Km}_{(d10)} + [phaC]}) \\ \frac{d ([phaC] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot ({k1}_{(K10)} \cdot [mphaC]) \\ - V_{c2} \cdot (\frac{V_{(d10)} \cdot [phaC]}{{Km}_{(d10)} + [phaC]}) \\ \frac{d (["Phasin-Hly"] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot ({k1}_{(K11)} \cdot ["mPhasin-Hly"]) \\ - V_{c2} \cdot (\frac{V_{(d11)} \cdot ["Phasin-Hly"]}{{Km}_{(d11)} + ["Phasin-Hly"]}) \\ - V_{c2} \cdot (({k1}_{(K12)} \cdot ["Phasin-Hly"] \cdot [PLA] - {k2}_{(K12)} \cdot ["PLA-Phasin-Hly{c2}"])) \\ \frac{d (["dPhasin-Hly"] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{V_{(d11)} \cdot ["Phasin-Hly"]}{{Km}_{(d11)} + ["Phasin-Hly"]}) \\ \frac{d (["dmPhasin-Hly"] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{V_{(d11,2)} \cdot ["mPhasin-Hly"]}{{Km}_{(d11,2)} + ["mPhasin-Hly"]}) \\ \frac{d (["mPhasin-Hly"] \cdot V_{c2})}{d t} & = & - V_{c2} \cdot ({k1}_{(K11)} \cdot ["mPhasin-Hly"]) \\ + V_{c2} \cdot ({k1}_{(K11,2)} \cdot ["complex 4"]) \\ - V_{c2} \cdot (\frac{V_{(d11,2)} \cdot ["mPhasin-Hly"]}{{Km}_{(d11,2)} + ["mPhasin-Hly"]}) \\ \frac{d ([LuxR] \cdot V_{c2})}{d t} & = & - V_{c2} \cdot (\frac{0.5}{3600e-9} \cdot ([LuxR] + \frac{K_{(K5)}}{4 \cdot {[HSL{c2}]}^{2}} - {([LuxR] + \frac{K_{(K5)}}{4 \cdot {[HSL{c2}]}^{2}} - {[LuxR]}^{2})}^{0.5})) \\ + V_{c2} \cdot ({k1}_{(K8)} \cdot [mLuxR]) \\ - V_{c2} \cdot (\frac{V_{(d8)} \cdot [LuxR]}{{Km}_{(d8)} + [LuxR]}) \\ \frac{d ([dLuxR] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{V_{(d8)} \cdot [LuxR]}{{Km}_{(d8)} + [LuxR]}) \\ \frac{d ([dmLuxR] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{V_{(d8,1)} \cdot [mLuxR]}{{Km}_{(d8,1)} + [mLuxR]}) \\ \frac{d ([mLuxR] \cdot V_{c2})}{d t} & = & - V_{c2} \cdot ({k1}_{(K8)} \cdot [mLuxR]) \\ + V_{c2} \cdot ({k1}_{(K8,1)} \cdot [LuxRg]) \\ - V_{c2} \cdot (\frac{V_{(d8,1)} \cdot [mLuxR]}{{Km}_{(d8,1)} + [mLuxR]}) \\ \frac{d (["P-CoA-T"] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot ({k1}_{(K9)} \cdot ["mP-CoA-T"]) \\ - V_{c2} \cdot (\frac{V_{(d9)} \cdot ["P-CoA-T"]}{{Km}_{(d9)} + ["P-CoA-T"]}) \\ \frac{d (["dP-CoA-T"] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{V_{(d9)} \cdot ["P-CoA-T"]}{{Km}_{(d9)} + ["P-CoA-T"]}) \\ \frac{d (["dmP-CoA-T"] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{V_{(d9,2)} \cdot ["mP-CoA-T"]}{{Km}_{(d9,2)} + ["mP-CoA-T"]}) \\ \frac{d (["mP-CoA-T"] \cdot V_{c2})}{d t} & = & - V_{c2} \cdot ({k1}_{(K9)} \cdot ["mP-CoA-T"]) \\ + V_{c2} \cdot ({k1}_{(K9,2)} \cdot ["complex 3"]) \\ - V_{c2} \cdot (\frac{V_{(d9,2)} \cdot ["mP-CoA-T"]}{{Km}_{(d9,2)} + ["mP-CoA-T"]}) \\ \frac{d ([dmphaC] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{V_{(d9,3)} \cdot [mphaC]}{{Km}_{(d9,3)} + [mphaC]}) \\ \frac{d ([mphaC] \cdot V_{c2})}{d t} & = & - V_{c2} \cdot ({k1}_{(K10)} \cdot [mphaC]) \\ + V_{c2} \cdot ({k1}_{(K9,3)} \cdot ["complex 3"]) \\ - V_{c2} \cdot (\frac{V_{(d9,3)} \cdot [mphaC]}{{Km}_{(d9,3)} + [mphaC]}) \\ \frac{d (["Phasin-Hlyg"] \cdot V_{c2})}{d t} & = & - V_{c2} \cdot (\frac{{c0}_{(K11,1)} + {c1}_{(K11,1)} \cdot [HSL/LuxR]}{1 + {c0}_{(K11,1)} + {c1}_{(K11,1)} \cdot [HSL/LuxR] + {c2}_{(K11,1)} \cdot ["Phasin-Hlyg"] + {c1}_{(K11,1)} \cdot {c2}_{(K11,1)} \cdot [HSL/LuxR] \cdot ["Phasin-Hlyg"]}) \\ \frac{d ([LuxRg] \cdot V_{c2})}{d t} & = & - V_{c2} \cdot ({k1}_{(K8,1)} \cdot [LuxRg]) \\ \frac{d ([HSL/LuxR] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{0.5}{3600e-9} \cdot ([LuxR] + \frac{K_{(K5)}}{4 \cdot {[HSL{c2}]}^{2}} - {([LuxR] + \frac{K_{(K5)}}{4 \cdot {[HSL{c2}]}^{2}} - {[LuxR]}^{2})}^{0.5})) \\ - V_{c2} \cdot (\frac{{c0}_{(K9,1)} + {c1}_{(K9,1)} \cdot [HSL/LuxR]}{1 + {c0}_{(K9,1)} + {c1}_{(K9,1)} \cdot [HSL/LuxR] + {c2}_{(K9,1)} \cdot ["Gen 2"] + {c1}_{(K9,1)} \cdot {c2}_{(K9,1)} \cdot [HSL/LuxR] \cdot ["Gen 2"]}) \\ - V_{c2} \cdot (\frac{{c0}_{(K11,1)} + {c1}_{(K11,1)} \cdot [HSL/LuxR]}{1 + {c0}_{(K11,1)} + {c1}_{(K11,1)} \cdot [HSL/LuxR] + {c2}_{(K11,1)} \cdot ["Phasin-Hlyg"] + {c1}_{(K11,1)} \cdot {c2}_{(K11,1)} \cdot [HSL/LuxR] \cdot ["Phasin-Hlyg"]}) \\ \frac{d (["complex 4"] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{{c0}_{(K11,1)} + {c1}_{(K11,1)} \cdot [HSL/LuxR]}{1 + {c0}_{(K11,1)} + {c1}_{(K11,1)} \cdot [HSL/LuxR] + {c2}_{(K11,1)} \cdot ["Phasin-Hlyg"] + {c1}_{(K11,1)} \cdot {c2}_{(K11,1)} \cdot [HSL/LuxR] \cdot ["Phasin-Hlyg"]}) \\ - V_{c2} \cdot ({k1}_{(K11,2)} \cdot ["complex 4"]) \\ \frac{d (["complex 3"] \cdot V_{c2})}{d t} & = & + V_{c2} \cdot (\frac{{c0}_{(K9,1)} + {c1}_{(K9,1)} \cdot [HSL/LuxR]}{1 + {c0}_{(K9,1)} + {c1}_{(K9,1)} \cdot [HSL/LuxR] + {c2}_{(K9,1)} \cdot ["Gen 2"] + {c1}_{(K9,1)} \cdot {c2}_{(K9,1)} \cdot [HSL/LuxR] \cdot ["Gen 2"]}) \\ - V_{c2} \cdot ({k1}_{(K9,2)} \cdot ["complex 3"]) \\ - V_{c2} \cdot ({k1}_{(K9,3)} \cdot ["complex 3"]) \\ \frac{d (["Gen 2"] \cdot V_{c2})}{d t} & = & - V_{c2} \cdot (\frac{{c0}_{(K9,1)} + {c1}_{(K9,1)} \cdot [HSL/LuxR]}{1 + {c0}_{(K9,1)} + {c1}_{(K9,1)} \cdot [HSL/LuxR] + {c2}_{(K9,1)} \cdot ["Gen 2"] + {c1}_{(K9,1)} \cdot {c2}_{(K9,1)} \cdot [HSL/LuxR] \cdot ["Gen 2"]}) \end{matrix}