dupreez3

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 0.020961620573545 mmol/L default_compartment
ADP ADP <assignment rule> mmol/L default_compartment
AMP 0.735086409252821 mmol/L default_compartment
ATP 1.71151931449073 mmol/L default_compartment
BPG 8.59865417775755e-05 mmol/L default_compartment
F16P 8.44097120440662 mmol/L default_compartment
F6P 0.578946953777943 mmol/L default_compartment
G3P 0.85406872398333 mmol/L default_compartment
G6P 2.83285776994039 mmol/L default_compartment
GLCi 0.0363872606459786 mmol/L default_compartment
NAD NAD <assignment rule> mmol/L default_compartment
NADH 0.298484471521169 mmol/L default_compartment
P2G 0.0145743573339282 mmol/L default_compartment
P3G 0.134803835263793 mmol/L default_compartment
PEP 0.0170684820602329 mmol/L default_compartment
PYR 4.00163453632936 mmol/L default_compartment
TRIO 3.13659774869995 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_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_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 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 ATP + {2.0}G6P = ∅

KTREHALOSE*ATP*G6P

Global parameters

Id Value
AKopt 0.669027384631504
AXPsum 4.1
CPFKAMP 0.0703733354872318
CPFKATP 3.92007230818607
CPFKF16BP 0.497287747227918
CPFKF26BP 0.0169045870014536
CiPFKATP 129.944855330581
ETOH 50.0
EXTERNAL 0.0
F26BP 0.02
GLCo 20.0
KATPASE 42.0705769854329
KGLYCOGEN 0.977472520682727
KPFKAMP 0.0953464313885568
KPFKF16BP 0.0910578202022938
KPFKF26BP 0.000788204396870689
KSUCC 16.68508899926
KTREHALOSE 0.500616814711998
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 1.06069180458452
KiADHETOH 86.6964879095848
KiADHNAD 0.929334305364439
KiADHNADH 0.0281954142935579
KiPFKATP 0.629349743346242
KmADHACE 1.07248685047976
KmADHETOH 17.2456286627476
KmADHNAD 0.166769639219937
KmADHNADH 0.105656811657223
KmALDDHAP 2.31373624578339
KmALDF16P 0.290710055001503
KmALDGAP 1.92661390756668
KmALDGAPi 9.63179022883364
KmATP 0.235555853813508
KmENOP2G 0.0366500838590152
KmENOPEP 0.485374038512661
KmG3PAG3P 4.19774181864929
KmG3PAPhi 0.752086905478373
KmG3PDHADP 1.45931578303823
KmG3PDHATP 0.520892324585364
KmG3PDHDHAP 0.417843988956108
KmG3PDHF16P 4.42804700123956
KmG3PDHG3P 1.014284409772
KmG3PDHNAD 0.855229911902209
KmG3PDHNADH 0.0244080593501774
KmGAPDHBPG 0.0103571131911046
KmGAPDHGAP 0.169036456827137
KmGAPDHNAD 0.0836010430272397
KmGAPDHNADH 0.060976295368858
KmGLKADP 0.253545174984255
KmGLKATP 0.123817018291608
KmGLKG6P 29.0056944225839
KmGLKGLCi 0.0697345487083755
KmGLTGLCi 1.25861629411934
KmGLTGLCo 1.11844371774078
KmPDCPYR 4.24956584535036
KmPFKATP 0.66667696421218
KmPFKF6P 0.128662486563679
KmPGIF6P 0.2794876594961
KmPGIG6P 1.35840250049127
KmPGKADP 0.193439959393382
KmPGKATP 0.28803020122741
KmPGKBPG 0.00290885157187471
KmPGKP3G 0.495134254954938
KmPGMP2G 0.0779767804899997
KmPGMP3G 1.11080591289804
KmPYKADP 0.475697546620804
KmPYKATP 1.51813362449153
KmPYKPEP 0.127016742234385
KmPYKPYR 20.4730221085492
L0 0.739254244885314
NADSUM 1.0
Phi 1.20470265921072
VmADH 479.951176287046
VmALD 150.282822785562
VmENO 350.467207519718
VmG3PA 36.0054380978204
VmG3PDH 25.2034727708702
VmGAPDHf 324.941804213337
VmGLK 286.092955831363
VmGLT 63.4244580249427
VmPDC 169.130966780205
VmPFK 136.836946410547
VmPGI 315.470814576513
VmPGK 1030.09847797527
VmPGM 2007.9381605905
VmPYK 1329.62417575784
alpha 0.91
biomassFac 0.720903608283592
gR 3.5972036851668
nATP 1.0
nPDC 1.88297482037065

Local parameters

Id Value Reaction

Assignment rules

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

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments