vanEunen2

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Testing biochemistry revisited: how in vivo metabolism can be understood from in vitro enzyme kinetics.

  • Karen van Eunen
  • José A L Kiewiet
  • Hans V Westerhoff
  • Barbara M Bakker
PLoS Comput. Biol. 2012; 8 (4):
Abstract
A decade ago, a team of biochemists including two of us, modeled yeast glycolysis and showed that one of the most studied biochemical pathways could not be quite understood in terms of the kinetic properties of the constituent enzymes as measured in cell extract. Moreover, when the same model was later applied to different experimental steady-state conditions, it often exhibited unrestrained metabolite accumulation.Here we resolve this issue by showing that the results of such ab initio modeling are improved substantially by (i) including appropriate allosteric regulation and (ii) measuring the enzyme kinetic parameters under conditions that resemble the intracellular environment. The following modifications proved crucial: (i) implementation of allosteric regulation of hexokinase and pyruvate kinase, (ii) implementation of V(max) values measured under conditions that resembled the yeast cytosol, and (iii) redetermination of the kinetic parameters of glyceraldehyde-3-phosphate dehydrogenase under physiological conditions.Model predictions and experiments were compared under five different conditions of yeast growth and starvation. When either the original model was used (which lacked important allosteric regulation), or the enzyme parameters were measured under conditions that were, as usual, optimal for high enzyme activity, fructose 1,6-bisphosphate and some other glycolytic intermediates tended to accumulate to unrealistically high concentrations. Combining all adjustments yielded an accurate correspondence between model and experiments for all five steady-state and dynamic conditions. This enhances our understanding of in vivo metabolism in terms of in vitro biochemistry.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
default_compartment 3.0 1.0
Id Name Initial quantity Compartment Fixed
ACALD 0.04 default_compartment
BPG 0.00001 default_compartment
F16P 14.63 default_compartment
F6P 0.8 default_compartment
G6P 4.22 default_compartment
GLCi 0.1 default_compartment
NADH 0.29 default_compartment
P2G 0.13 default_compartment
P3G 0.96 default_compartment
PEP 0.12 default_compartment
PYR 3.48 default_compartment
TRIO 1.0 default_compartment

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
v_1 ∅ = GLCi

(VMAXGLT*(GLCo/KMGLTGLCo - GLCi/(KMGLTGLCo*KEQGLT)))/(1 + GLCo/KMGLTGLCo + GLCi/KMGLTGLCi + 0.91*(GLCo*GLCi)/(KMGLTGLCo*KMGLTGLCi))
v_10 BPG = P3G

(VMAXPGK*((KEQPGK*BPG*ADP)/(KMPGKP3G*KMPGKATP) - (P3G*ATP)/(KMPGKP3G*KMPGKATP)))/((1 +BPG/KMPGKBPG + P3G/KMPGKP3G)*(1 + ATP/KMPGKATP + ADP/KMPGKADP))
v_11 P3G = P2G

(VMAXPGM*(P3G/KMPGMP3G - P2G/(KMPGMP3G*KEQPGM)))/(1 + P3G/KMPGMP3G + P2G/KMPGMP2G)
v_12 P2G = PEP

(VMAXENO*(P2G/KMENOP2G - PEP/(KMENOP2G*KEQENO)))/(1 + P2G/KMENOP2G + PEP/KMENOPEP)
v_13 v_13 PEP = PYR

(VMAXPYK*PEP/KMPYKPEP*(1 + PEP/KMPYKPEP)^(n10 - 1))/(L10*((ATP/KMPYKATP + 1)/(F16P/KMPYKF16P +1))^n10 + (1 + PEP/KMPYKPEP)^n10)*ADP/(ADP + KMPYKADP)
v_14 PYR = ACALD

(VMAXPDC*PYR^NHPDC)/(KMPDCPYR^NHPDC*(1 + PYR^NHPDC/KMPDCPYR^NHPDC))
v_15 {2.0}PYR = {3.0}NADH

KSUC
v_16 ACALD + NADH = ∅

-(VMAXADH*(((NADt - NADH)*ETOH)/(KIADHNAD*KMADHETOH) - (NADH*ACALD)/(KIADHNAD*KMADHETOH*KEQADH)))/((1 + (NADt - NADH)/KIADHNAD + (KMADHNAD*ETOH)/(KIADHNAD*KMADHETOH) + (KMADHNADH*ACALD)/(KIADHNADH*KMADHACALD) + NADH/KIADHNADH + ((NADt - NADH)* ETOH)/(KIADHNAD*KMADHETOH) + (KMADHNADH *(NADt - NADH)*ACALD)/(KIADHNAD*KIADHNADH*KMADHACALD) + (KMADHNAD*ETOH*NADH)/(KIADHNAD*KMADHETOH*KIADHNADH) + (NADH*ACALD)/(KIADHNADH*KMADHACALD) + ((NADt - NADH)* ETOH*ACALD)/(KIADHNAD*KMADHETOH*KIADHACALD) + (ETOH*NADH*ACALD)/(KIADHETOH*KIADHNADH*KMADHACALD)))
v_17 ACALD = NADH

KACE*ACALD
v_2 GLCi = G6P

(VMAXHK*(GLCi/KMHKGLCi*ATP/KMHKATP - (G6P*ADP)/(KMHKGLCi*KMHKATP*KEQHK) ))/((1 + GLCi/KMHKGLCi + G6P/KMHKG6P + T6P/KIHKT6P)*(1 + ATP/KMHKATP + ADP/KMHKADP))
v_3 ∅ = {2.0}GLCi

KTRE1
v_4 G6P = F6P

(VMAXPGI*(G6P/KMPGIG6P - F6P/(KMPGIG6P*KEQPGI)))/(1 + G6P/KMPGIG6P + F6P/KMPGIF6P)
v_5 {2.0}G6P = ∅

KTRE2
v_6 F6P = F16P

(VMAXPFK*gR*F6P*ATP*(1 + F6P/KMPFKF6P*ATP/KMPFKATP + (gR*F6P*ATP)/(KMPFKF6P*KMPFKATP)))/(KMPFKF6P*KMPFKATP*((1 + F6P/KMPFKF6P*ATP/KMPFKATP + (gR*F6P*ATP)/(KMPFKF6P*KMPFKATP))^2 + ((L0*(1 + (CiPFKATP*ATP)/KiPFKATP)^2*(1 + (CPFKAMP*AMP)/KPFKAMP)^2*(1 + (CPFKF26BP*F26BP)/KPFKF26BP + (CPFKF16BP*F16P)/KPFKF16BP)^2)/((1 + ATP/KiPFKATP)^2*(1 + AMP/KPFKAMP)^2*(1 + F26BP/KPFKF26BP + F16P/KPFKF16BP)^2))*(1 + (CPFKATP*ATP)/KMPFKATP)^2))
v_7 F16P = {2.0}TRIO

(VMAXALD*(F16P/KMALDF16P - (KEQTPI/(1 + KEQTPI)*TRIO*1/(1 + KEQTPI)*TRIO)/(KMALDF16P*KEQALD)))/(1 + F16P/KMALDF16P + (KEQTPI/(1 + KEQTPI)*TRIO)/KMALDGAP + (1/(1 + KEQTPI)*TRIO)/KMALDDHAP + (KEQTPI/(1 + KEQTPI)*TRIO*1/(1 + KEQTPI)*TRIO)/(KMALDGAP*KMALDDHAP) + (F16P*KEQTPI/(1 + KEQTPI)*TRIO)/( KMALDGAPi*KMALDF16P))
v_8 NADH + TRIO = ∅

KGLY
v_9 TRIO = BPG + NADH

(CGAPDH*((VMAXGAPDHf*KEQTPI/(1 + KEQTPI)*TRIO*(NADt - NADH))/(KMGAPDHGAP*KMGAPDHNAD) -(VMAXGAPDHr*BPG*NADH)/(KMGAPDHBPG*KMGAPDHNADH)))/((1 + (KEQTPI/(1 + KEQTPI)*TRIO)/KMGAPDHGAP + BPG/KMGAPDHBPG)*(1 + (NADt - NADH)/KMGAPDHNAD +NADH/KMGAPDHNADH))

Global parameters

Id Value
ACE 10.0
ADP 0.81
AMP 0.25
ATP 3.92
CGAPDH 1.0
CO2 1.0
CPFKAMP 0.0845
CPFKATP 3.0
CPFKF16BP 0.397
CPFKF26BP 0.0174
CiPFKATP 100.0
ETOH 25.0
EXTERNAL 1.0
F26BP 0.009
GLCo 50.0
GLY 10.0
KACE 0.5
KEQADH 0.000069
KEQALD 0.069
KEQENO 6.7
KEQGLT 1.0
KEQHK 3800.0
KEQPGI 0.314
KEQPGK 3200.0
KEQPGM 0.19
KEQTPI 0.045
KGLY 24.9
KIADHACALD 1.1
KIADHETOH 90.0
KIADHNAD 0.92
KIADHNADH 0.031
KIHKT6P 0.04
KMADHACALD 1.11
KMADHETOH 17.0
KMADHNAD 0.17
KMADHNADH 0.11
KMALDDHAP 2.4
KMALDF16P 0.3
KMALDGAP 2.0
KMALDGAPi 10.0
KMENOP2G 0.04
KMENOPEP 0.5
KMGAPDHBPG 0.51
KMGAPDHGAP 0.39
KMGAPDHNAD 2.85
KMGAPDHNADH 0.007
KMGLTGLCi 11.0
KMGLTGLCo 11.0
KMHKADP 0.23
KMHKATP 0.15
KMHKG6P 30.0
KMHKGLCi 0.08
KMPDCPYR 6.36
KMPFKATP 0.71
KMPFKF6P 0.1
KMPGIF6P 0.3
KMPGIG6P 1.4
KMPGKADP 0.2
KMPGKATP 0.3
KMPGKBPG 0.003
KMPGKP3G 0.53
KMPGMP2G 0.08
KMPGMP3G 1.2
KMPYKADP 0.3
KMPYKATP 9.3
KMPYKF16P 0.2
KMPYKPEP 0.19
KPFKAMP 0.0995
KPFKF16BP 0.111
KPFKF26BP 0.000682
KSUC 0.0
KTRE1 2.2
KTRE2 0.0
KiPFKATP 0.65
L0 0.66
L10 60000.0
NADt 1.59
NHPDC 1.9
T6P 0.36
TREH 2.0
VMAXADH 744.0
VMAXALD 153.0
VMAXENO 285.0
VMAXGAPDHf 1514.0
VMAXGAPDHr 877.0
VMAXGLT 121.0
VMAXHK 223.0
VMAXPDC 297.0
VMAXPFK 165.0
VMAXPGI 852.0
VMAXPGK 3030.0
VMAXPGM 748.0
VMAXPYK 636.0
gR 5.12
n10 4.0

Local parameters

Id Value Reaction

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments