The reaction rates are non linear functions of the

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The reaction rates are non-linear functions of the metabolite concentrations (typically from in vitro kinetics). 1. v j is the jth reaction rate, b is the transport rate vector, S ij is the “Stoichiometric matrix” = moles of metabolite i produced in reaction j V syn V deg V trans V use
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9 RBC model integration Reference Glyc- PPP ANM Na + /K + Osmot. Trans- Hb-5 Gpx Shape olysis Pump port ligands Hb Ca Rapoport ’74-6 + - - - - - - - - - Heinrich ’77 + - - - - - - - - - Ataullakhanov’81 + + - - - - - - - - Schauer ’81 + - + - - - - - - - Brumen ’84 + - - + + - - - - - Werner ’85 + - - + + + - - - - Joshi ’90 + + + + + + - - - - Yoshida ’90 - - - - - - + - - - Lee ’92 + + + + + + ( + ) - - - Gimsa ’98 - - - - - - - - - + Destro-Bisol ‘99 - - - - - - - (-) - - Jamshidi ’00 + + + + + + - - - -
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10 Scopes & Assumptions Mechanism of ATP utilization other than nucleotide metabolism and the Na + /K + pump (75%) is not specifically defined Ca 2+ transport not included Guanine nucleotide metabolism neglected little information, minor importance Cl - , HCO 3 - , LAC, etc. are in “pseudo” equilibrium No intracellular concentration gradients Rate constants represent a “typical cell” Surface area of the membrane is constant Environment is treated as a sink
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11 Glycolysis Dynamic Mass Balances DPGM PGK GAPDH TA TKII TKI GAPDH TPI ALD TPI ALD ALD PFK TKII TA PFK PGI PDH G PGI HK v v v DPG dt d v v v v v v P GA dt d v v DHAP dt d v v FDP dt d v v v v P F dt d v v v P G dt d 3 , 1 3 6 6 6 LDH GAPDH LAC LDH LDH PYR PK PK EN EN PGM DPGase PGM PGK v v NADH dt d v v LAC dt d v v v PYR dt d v v PEP dt d v v PG dt d v v v PG dt d ex ex 2 3 ase DPG DPGM v v DPG dt d 3 , 2 i j ij trans use deg syn i b v S V V V V dt dX ) ( ) (
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12 Enzyme Kinetic Expressions Phosphofructokinase 4 6 4 4 4 0 6 6 6 1 1 1 1 1 1 6 1 6 PFK P F PFK AMP PFK Mg PFK ATP free PFK PFK PFK ATP Mg PFK ATP Mg PFK P F PFK P F PFK PFK mx PFK K P F K AMP K Mg K ATP L N K ATP Mg K ATP Mg K P F K P F N v v AMP v F6P
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13 Kinetic Expressions All rate expressions are similar to the previously shown rate expression for phosphofructokinase. Model has 44 rate expressions with ~ 5 constants each ~ 200 parameters What are the assumptions associated with using these expressions?
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14 Kinetic parameter assumptions in vitro values represent the in vivo parameters protein concentration in vitro much lower than in vivo enzyme interactions (enzymes, cytoskeleton, membrane, …) samples used to measure kinetics may contain unknown conc. of effectors (i.e. fructose 2,6-bisphosphate) enzyme catalyzed enzyme modifications all possible concentrations of interacting molecules been considered (interpolating) e.g. glutamine synthase (unusually large # of known effectors) 3 substrates, 3 products, 9 significant effectors 4 15 (~10 9 ) measurements: 4 different conc. of 15 molecules (Savageau, 1976) in vivo probably even more complex, but approximations are effective. have all interacting molecules been discovered?
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