dupreez4

mmol

min

L

None

None

mM

From steady-state to synchronized yeast glycolytic oscillations I: model construction.

  • Franco B du Preez
  • David D van Niekerk
  • Bob Kooi
  • Johann M Rohwer
  • Jacky L Snoep
FEBS J. 2012; 279 (16): 2810-2822
Abstract
UNLABELLED: An existing detailed kinetic model for the steady-state behavior of yeast glycolysis was tested for its ability to simulate dynamic behavior. Using a small subset of experimental data, the original model was adapted by adjusting its parameter values in three optimization steps. Only small adaptations to the original model were required for realistic simulation of experimental data for limit-cycle oscillations. The greatest changes were required for parameter values for the phosphofructokinase reaction. The importance of ATP for the oscillatory mechanism and NAD(H) for inter-and intra-cellular communications and synchronization was evident in the optimization steps and simulation experiments. In an accompanying paper [du Preez F et al. (2012) FEBS J279, 2823-2836], we validate the model for a wide variety of experiments on oscillatory yeast cells. The results are important for re-use of detailed kinetic models in modular modeling approaches and for approaches such as that used in the Silicon Cell initiative.
DATABASE: The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/dupreez/index.html.

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
0.001 mole
1.0 litre
0.001 mole litre^(-1.0)
60.0 second
Id Name Spatial dimensions Size
default_compartment 3.0 1.0 L
Id Name Initial quantity Compartment Fixed
ACE 0.0204796335883082 mmol/L default_compartment
ACEo 0.0199832348425703 mmol/L default_compartment
ADP ADP <assignment rule> mmol/L default_compartment
AMP 0.815615549032524 mmol/L default_compartment
ATP 1.60200361393713 mmol/L default_compartment
BPG 8.04607071179563e-05 mmol/L default_compartment
F16P 7.88018175756601 mmol/L default_compartment
F6P 0.494145977137238 mmol/L default_compartment
G3P 0.898510944946246 mmol/L default_compartment
G6P 2.26358698183118 mmol/L default_compartment
GLCi 0.030050982468921 mmol/L default_compartment
NAD NAD <assignment rule> mmol/L default_compartment
NADH 0.390801474565893 mmol/L default_compartment
P2G 0.0132315645673044 mmol/L default_compartment
P3G 0.126790594836765 mmol/L default_compartment
PEP 0.0104013226052447 mmol/L default_compartment
PYR 1.87974762229335 mmol/L default_compartment
TRIO 3.03393493804436 mmol/L 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_ACEt ACE = {0.02}ACEo

optACEt*kACEt*(ACE - ACEo)
v_ADH v_ADH ACE + NADH = ∅

-(VmADH * (ETOH * NAD - ACE * NADH / KeqADH) / (KiADHNAD * KmADHETOH * (1 + ETOH * KmADHNAD / (KiADHNAD * KmADHETOH) + KmADHNADH * ACE / (KiADHNADH * KmADHACE) + NAD / KiADHNAD + ETOH * NAD / (KiADHNAD * KmADHETOH) + ETOH * ACE * NAD / (KiADHACE * KiADHNAD * KmADHETOH) + KmADHNADH * ACE * NAD / (KiADHNAD * KiADHNADH * KmADHACE) + NADH / KiADHNADH + ETOH * KmADHNAD * NADH / (KiADHNAD * KiADHNADH * KmADHETOH) + ACE * NADH / (KiADHNADH * KmADHACE) + ETOH * ACE * NADH / (KiADHETOH * KiADHNADH * KmADHACE))))
v_AK v_AK ∅ = AMP + ATP

133.333 * AKopt * (ADP^2 - AMP * ATP / KeqAK)
v_ALD F16P = {2.0}TRIO

(VmALD*(F16P - (KeqTPI*TRIO^2)/(KeqALD*(1 + KeqTPI)^2)))/(KmALDF16P*(1 + F16P/KmALDF16P + TRIO/((1 + KeqTPI)*KmALDDHAP) + (KeqTPI*TRIO)/((1 + KeqTPI)*KmALDGAP) + (KeqTPI*F16P*TRIO)/((1 + KeqTPI)*KmALDF16P*KmALDGAPi) + (KeqTPI*TRIO^2)/((1 + KeqTPI)^2*KmALDDHAP*KmALDGAP)))
v_ATP ATP = ∅

(KATPASE*ATP^nATP)/(KmATP^nATP + ATP^nATP)
v_ENO P2G = PEP

(VmENO*(P2G - PEP/KeqENO))/(KmENOP2G*(1 + P2G/KmENOP2G + PEP/KmENOPEP))
v_G3PA G3P = ∅

(VmG3PA*G3P)/(KmG3PAG3P*(1 + Phi/KmG3PAPhi)*(1 + G3P/KmG3PAG3P))
v_G3PDH v_G3PDH NADH + TRIO = G3P

VmG3PDH * (-(G3P * NAD / KeqG3PDH) + NADH * TRIO / (1 + KeqTPI)) / (KmG3PDHDHAP * KmG3PDHNADH * (1 + ADP / KmG3PDHADP + ATP / KmG3PDHATP + F16P / KmG3PDHF16P) * (1 + NAD / KmG3PDHNAD + NADH / KmG3PDHNADH) * (1 + G3P / KmG3PDHG3P + TRIO / ((1 + KeqTPI) * KmG3PDHDHAP)))
v_GAPDH v_GAPDH TRIO = BPG + NADH

(-(VmGAPDHf * BPG * NADH / (KeqGAPDH * KmGAPDHGAP * KmGAPDHNAD)) + KeqTPI * VmGAPDHf * NAD * TRIO / ((1 + KeqTPI) * KmGAPDHGAP * KmGAPDHNAD)) / ((1 + NAD / KmGAPDHNAD + NADH / KmGAPDHNADH) * (1 + BPG / KmGAPDHBPG + KeqTPI * TRIO / ((1 + KeqTPI) * KmGAPDHGAP)))
v_GLK v_GLK ATP + GLCi = G6P

VmGLK * (-(ADP * G6P / KeqGLK) + ATP * GLCi) / (KmGLKATP * KmGLKGLCi * (1 + ADP / KmGLKADP + ATP / KmGLKATP) * (1 + G6P / KmGLKG6P + GLCi / KmGLKGLCi))
v_GLT ∅ = GLCi

(VmGLT*(GLCo - GLCi/KeqGLT))/(KmGLTGLCo*(1 + GLCo/KmGLTGLCo + GLCi/KmGLTGLCi + (alpha*GLCo*GLCi)/(KmGLTGLCi*KmGLTGLCo)))
v_GLYCO ATP + G6P = ∅

KGLYCOGEN*ATP*G6P
v_LACTO ACEo = ∅

optLACTO*CN*kLACTO*ACEo
v_PDC PYR = ACE

(VmPDC*PYR^nPDC)/(KmPDCPYR^nPDC*(1 + PYR^nPDC/KmPDCPYR^nPDC))
v_PFK ATP + F6P = F16P

(gR*VmPFK*ATP*F6P*(1 + ATP/KmPFKATP + F6P/KmPFKF6P + (gR*ATP*F6P)/(KmPFKATP*KmPFKF6P)))/(KmPFKATP*KmPFKF6P*((L0*(1 + (CPFKAMP*AMP)/KPFKAMP)^2*(1 + (CiPFKATP*ATP)/KiPFKATP)^2*(1 + (CPFKATP*ATP)/KmPFKATP)^2*(1 + (CPFKF26BP*F26BP)/KPFKF26BP + (CPFKF16BP*F16P)/KPFKF16BP)^2)/((1 + AMP/KPFKAMP)^2*(1 + ATP/KiPFKATP)^2*(1 + F26BP/KPFKF26BP + F16P/KPFKF16BP)^2) + (1 + ATP/KmPFKATP + F6P/KmPFKF6P + (gR*ATP*F6P)/(KmPFKATP*KmPFKF6P))^2))
v_PGI v_PGI G6P = F6P

VmPGI * (-(F6P / KeqPGI) + G6P) / (KmPGIG6P * (1 + F6P / KmPGIF6P + G6P / KmPGIG6P))
v_PGK v_PGK BPG = ATP + P3G

VmPGK * (KeqPGK * ADP * BPG - ATP * P3G) / (KmPGKATP * KmPGKP3G * (1 + ADP / KmPGKADP + ATP / KmPGKATP) * (1 + BPG / KmPGKBPG + P3G / KmPGKP3G))
v_PGM P3G = P2G

(VmPGM*(-(P2G/KeqPGM) + P3G))/(KmPGMP3G*(1 + P2G/KmPGMP2G + P3G/KmPGMP3G))
v_PYK v_PYK PEP = ATP + PYR

VmPYK * (ADP * PEP - ATP * PYR / KeqPYK) / (KmPYKADP * KmPYKPEP * (1 + ADP / KmPYKADP + ATP / KmPYKATP) * (1 + PEP / KmPYKPEP + PYR / KmPYKPYR))
v_SUC {2.0}ACE + {4.0}ATP = {3.0}NADH

KSUCC*ACE
v_Treha v_Treha {2.0}G6P + ATP = ∅

KTREHALOSE * ATP * G6P

Global parameters

Id Value
AKopt 0.538823362397066
AXPsum 4.1
CN 5.0
CPFKAMP 0.0619066304454687
CPFKATP 4.11927102035743
CPFKF16BP 0.508729452985175
CPFKF26BP 0.0166446192764381
CiPFKATP 133.997614964125
ETOH 50.0
EXTERNAL 0.0
F26BP 0.02
GLCo 20.0
KATPASE 38.3151546531701
KGLYCOGEN 0.657952839162031
KPFKAMP 0.0908240053852103
KPFKF16BP 0.0867303342326532
KPFKF26BP 0.000809438316573068
KSUCC 15.5243973118548
KTREHALOSE 0.35532683402403
KeqADH 0.000069
KeqAK 0.45
KeqALD 0.069
KeqENO 6.7
KeqG3PDH 4300.0
KeqGAPDH 0.00562639062770364
KeqGLK 3800.0
KeqGLT 1.0
KeqPGI 0.314
KeqPGK 3200.0
KeqPGM 0.19
KeqPYK 6500.0
KeqTPI 0.045
KiADHACE 1.10269434597499
KiADHETOH 87.5197712783722
KiADHNAD 0.994086925030065
KiADHNADH 0.0266112112630811
KiPFKATP 0.672261990665842
KmADHACE 1.08640493765421
KmADHETOH 17.873472130943
KmADHNAD 0.173151837494663
KmADHNADH 0.106028057123405
KmALDDHAP 2.35279569817395
KmALDF16P 0.289978616714069
KmALDGAP 2.03507983684522
KmALDGAPi 10.1050124140839
KmATP 0.226775365195371
KmENOP2G 0.0384298786845413
KmENOPEP 0.48718115014322
KmG3PAG3P 4.36779649390928
KmG3PAPhi 0.784145076398265
KmG3PDHADP 1.66742704847041
KmG3PDHATP 0.477041600990239
KmG3PDHDHAP 0.434945788250048
KmG3PDHF16P 5.39383791442381
KmG3PDHG3P 0.989904702292856
KmG3PDHNAD 0.864230959749687
KmG3PDHNADH 0.024866434215201
KmGAPDHBPG 0.0105501300482522
KmGAPDHGAP 0.126014064354562
KmGAPDHNAD 0.0877156866078506
KmGAPDHNADH 0.0560916256777303
KmGLKADP 0.263092658044569
KmGLKATP 0.122952862202984
KmGLKG6P 29.9047243861895
KmGLKGLCi 0.070544843764403
KmGLTGLCi 1.2601958510505
KmGLTGLCo 1.14781100891666
KmPDCPYR 2.71686030412305
KmPFKATP 0.639382516791221
KmPFKF6P 0.136442544726107
KmPGIF6P 0.288898425005336
KmPGIG6P 1.31111953478591
KmPGKADP 0.195235190263297
KmPGKATP 0.307178610015771
KmPGKBPG 0.0030168048178011
KmPGKP3G 0.515383408435942
KmPGMP2G 0.0816972711677167
KmPGMP3G 1.1653123960473
KmPYKADP 0.423287756657824
KmPYKATP 1.67932644936778
KmPYKPEP 0.114687461199323
KmPYKPYR 21.2875778903632
L0 0.744428179041052
NADSUM 1.0
Phi 1.20470265921072
VmADH 329.310550256221
VmALD 115.755229155784
VmENO 276.012216851944
VmG3PA 28.7585800442532
VmG3PDH 19.8677206272709
VmGAPDHf 279.717235797774
VmGLK 229.681980633949
VmGLT 43.9573369352783
VmPDC 209.10016696
VmPFK 127.540676183333
VmPGI 274.363965785613
VmPGK 797.96096752776
VmPGM 1591.55726747429
VmPYK 1223.18615050541
alpha 0.91
gR 3.47651271426468
kACEt 1431.0
kLACTO 0.09
nATP 1.0
nPDC 2.3801892387344
optACEt 0.566678504048252
optLACTO 0.566678504048252
yvol 50.0

Local parameters

Id Value Reaction

Assignment rules

Definition
ADP = AXPsum - AMP - ATP
NAD = NADSUM - NADH

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments