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vanHeerden1

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Model

vanHeerden1

This model reproduces Figure 1B of the paper.

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Manuscript information

Lost in transition: start-up of glycolysis yields subpopulations of nongrowing cells.

  • Johan H van Heerden
  • Meike T Wortel
  • Frank J Bruggeman
  • Joseph J Heijnen
  • Yves J M Bollen
  • Robert Planqué
  • Josephus Hulshof
  • Tom G O'Toole
  • S Aljoscha Wahl
  • Bas Teusink
Science 2014; 343 (6174): 1245114
Abstract
Cells need to adapt to dynamic environments. Yeast that fail to cope with dynamic changes in the abundance of glucose can undergo growth arrest. We show that this failure is caused by imbalanced reactions in glycolysis, the essential pathway in energy metabolism in most organisms. The imbalance arises largely from the fundamental design of glycolysis, making this state of glycolysis a generic risk. Cells with unbalanced glycolysis coexisted with vital cells. Spontaneous, nongenetic metabolic variability among individual cells determines which state is reached and, consequently, which cells survive. Transient ATP (adenosine 5'-triphosphate) hydrolysis through futile cycling reduces the probability of reaching the imbalanced state. Our results reveal dynamic behavior of glycolysis and indicate that cell fate can be determined by heterogeneity purely at the metabolic level.

Unit definitions 0

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

Compartments 1

Id Name Spatial Dimensions Size
compartment compartment 3.0 1.0

Species 24

Id Name Initial Quantity Compartment Fixed
ACE ACE 0.0474837 compartment (compartment) ✘
ATP ATP 2.06497 compartment (compartment) ✘
BPG BPG 0.111 compartment (compartment) ✘
CO2 CO2 1.0 compartment (compartment) ✔
ETOH ETOH 0.0 compartment (compartment) ✔
F16P F16P 0.836 compartment (compartment) ✘
F6P F6P 0.75247 compartment (compartment) ✘
G6P G6P 3.085 compartment (compartment) ✘
GLCi GLCi 0.087 compartment (compartment) ✘
GLCo GLCo 110.0 compartment (compartment) ✔
GLY GLY 0.15 compartment (compartment) ✔
Glyc Glyc 0.0 compartment (compartment) ✔
NAD NAD 0.0 compartment (compartment) ✔
NADH NADH 0.044 compartment (compartment) ✘
P2G P2G 0.13771 compartment (compartment) ✘
P3G P3G 0.825 compartment (compartment) ✘
PEP PEP 0.1404 compartment (compartment) ✘
PHOS PHOS 10.0 compartment (compartment) ✘
PYR PYR 0.884031 compartment (compartment) ✘
Prb Prb 5.0 compartment (compartment) ✘
SUCC SUCC 0.0 compartment (compartment) ✔
TRIO TRIO 0.5177 compartment (compartment) ✘
Trh Trh 0.0 compartment (compartment) ✔
X X 0.0 compartment (compartment) ✔

Initial assignments 0

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
Reactions 18
Id Name Objective Coefficient Reaction Equation And Kinetic Law Flux Bounds
v1 v1 GLCi + Prb = G6P

VMAXHK * (GLCi * (-SUMAXP + (1 - 4 * KEQAK) * Prb + pow(4 * (1 - 4 * KEQAK) * KEQAK * pow(Prb, 2) + pow(SUMAXP - (1 - 4 * KEQAK) * Prb, 2), 0.5)) / (2 * (1 - 4 * KEQAK) * KMHKATP * KMHKGLCi) - G6P * (Prb - (-SUMAXP + (1 - 4 * KEQAK) * Prb + pow(4 * (1 - 4 * KEQAK) * KEQAK * pow(Prb, 2) + pow(SUMAXP - (1 - 4 * KEQAK) * Prb, 2), 0.5)) / (1 - 4 * KEQAK)) / (KEQHK * KMHKATP * KMHKGLCi)) / (compartment * (1 + G6P / KMHKG6P + wt * G6P / KiHKG6P + GLCi / KMHKGLCi) * (1 + (-SUMAXP + (1 - 4 * KEQAK) * Prb + pow(4 * (1 - 4 * KEQAK) * KEQAK * pow(Prb, 2) + pow(SUMAXP - (1 - 4 * KEQAK) * Prb, 2), 0.5)) / (2 * (1 - 4 * KEQAK) * KMHKATP) + (Prb - (-SUMAXP + (1 - 4 * KEQAK) * Prb + pow(4 * (1 - 4 * KEQAK) * KEQAK * pow(Prb, 2) + pow(SUMAXP - (1 - 4 * KEQAK) * Prb, 2), 0.5)) / (1 - 4 * KEQAK)) / KMHKADP))
v10 v10 P2G = PEP

VmENO * (P2G - PEP / KeqENO) / (compartment * KmENOP2G * (1 + P2G / KmENOP2G + PEP / KmENOPEP))
v11 v11 PEP = Prb + PYR

VmPYK * PEP * pow(1 + PEP / KmPYKPEP, -1 + npyk) * (Prb - (-SUMAXP + (1 - 4 * KeqAK) * Prb + pow(4 * (1 - 4 * KeqAK) * KeqAK * pow(Prb, 2) + pow(SUMAXP - (1 - 4 * KeqAK) * Prb, 2), 0.5)) / (1 - 4 * KeqAK)) / (compartment * KmPYKPEP * (KmPYKADP + Prb - (-SUMAXP + (1 - 4 * KeqAK) * Prb + pow(4 * (1 - 4 * KeqAK) * KeqAK * pow(Prb, 2) + pow(SUMAXP - (1 - 4 * KeqAK) * Prb, 2), 0.5)) / (1 - 4 * KeqAK)) * (pow(1 + PEP / KmPYKPEP, npyk) + L0PYK * pow((1 + (-SUMAXP + (1 - 4 * KeqAK) * Prb + pow(4 * (1 - 4 * KeqAK) * KeqAK * pow(Prb, 2) + pow(SUMAXP - (1 - 4 * KeqAK) * Prb, 2), 0.5)) / (2 * (1 - 4 * KeqAK) * KmPYKATP)) / (1 + F16P / KmPYKF16P), npyk)))
v12 v12 PYR = ACE + CO2

VmPDC * pow(PYR, nPDC) / (compartment * pow(KmPDCPYR, nPDC) * (1 + pow(PYR, nPDC) / pow(KmPDCPYR, nPDC)))
v13 v13 {2.0}ACE + {3.0}NAD = SUCC + {3.0}NADH

KSUCC * ACE / compartment
v14 v14 GLCo = GLCi

VmGLT * (GLCo - GLCi / KeqGLT) / (compartment * KmGLTGLCo * (1 + GLCo / KmGLTGLCo + GLCi / KmGLTGLCi + 0.91 * GLCo * GLCi / (KmGLTGLCi * KmGLTGLCo)))
v15 v15 ACE + NADH = ETOH + NAD

-(VmADH * (ETOH * (NADt - NADH) - ACE * NADH / KeqADH) / (compartment * KiADHNAD * KmADHETOH * (1 + ETOH * KmADHNAD / (KiADHNAD * KmADHETOH) + KmADHNADH * ACE / (KiADHNADH * KmADHACE) + (NADt - NADH) / KiADHNAD + ETOH * (NADt - NADH) / (KiADHNAD * KmADHETOH) + ETOH * ACE * (NADt - NADH) / (KiADHACE * KiADHNAD * KmADHETOH) + KmADHNADH * ACE * (NADt - NADH) / (KiADHNAD * KiADHNADH * KmADHACE) + NADH / KiADHNADH + ETOH * KmADHNAD * NADH / (KiADHNAD * KiADHNADH * KmADHETOH) + ACE * NADH / (KiADHNADH * KmADHACE) + ETOH * ACE * NADH / (KiADHETOH * KiADHNADH * KmADHACE))))
v16 v16 NADH + TRIO = PHOS + GLY + NAD

VmG3PDH * (-(GLY * (NADt - NADH) / KeqG3PDH) + NADH * TRIO / (1 + KeqTPI)) / (compartment * KmG3PDHDHAP * KmG3PDHNADH * (1 + (NADt - NADH) / KmG3PDHNAD + NADH / KmG3PDHNADH) * (1 + GLY / KmG3PDHGLY + TRIO / ((1 + KeqTPI) * KmG3PDHDHAP)))
v17 v17 Prb = PHOS

KATPASE * (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / (compartment * (2 - 8 * KeqAK))
v18 v18 X = PHOS

KPHOS * (pT - PHOS) / compartment
v2 v2 G6P = F6P

VmPGI * (-(F6P / KeqPGI) + G6P) / (compartment * KmPGIG6P * (1 + F6P / KmPGIF6P + G6P / KmPGIG6P))
v3 v3 G6P + Prb = Glyc + {2.0}PHOS

KmGLYCOGEN * G6P / compartment
v4 v4 Prb + {2.0}G6P = Trh + {3.0}PHOS

wt * KTREHALOSE * G6P / compartment
v5 v5 F6P + Prb = F16P

gR * VmPFK * F6P * (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) * (1 + F6P / KmPFKF6P + (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / ((2 - 8 * KeqAK) * KmPFKATP) + gR * F6P * (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / ((2 - 8 * KeqAK) * KmPFKATP * KmPFKF6P)) / (compartment * (2 - 8 * KeqAK) * KmPFKATP * KmPFKF6P * (L0 * pow(1 + CPFKF26BP * F26BP / KPFKF26BP + CPFKF16BP * F16P / KPFKF16BP, 2) * pow(1 + 2 * CPFKAMP * KeqAK * pow(SUMAXP - pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5), 2) / ((-1 + 4 * KeqAK) * KPFKAMP * (SUMAXP - Prb + 4 * KeqAK * Prb - pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5))), 2) * pow(1 + CiPFKATP * (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / ((2 - 8 * KeqAK) * KiPFKATP), 2) * pow(1 + CPFKATP * (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / ((2 - 8 * KeqAK) * KmPFKATP), 2) / (pow(1 + F26BP / KPFKF26BP + F16P / KPFKF16BP, 2) * pow(1 + 2 * KeqAK * pow(SUMAXP - pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5), 2) / ((-1 + 4 * KeqAK) * KPFKAMP * (SUMAXP - Prb + 4 * KeqAK * Prb - pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5))), 2) * pow(1 + (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / ((2 - 8 * KeqAK) * KiPFKATP), 2)) + pow(1 + F6P / KmPFKF6P + (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / ((2 - 8 * KeqAK) * KmPFKATP) + gR * F6P * (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / ((2 - 8 * KeqAK) * KmPFKATP * KmPFKF6P), 2)))
v6 v6 F16P = {2.0}TRIO

VmALD * (F16P - KeqTPI * pow(TRIO, 2) / (KeqALD * pow(1 + KeqTPI, 2))) / (compartment * KmALDF16P * (1 + F16P / KmALDF16P + TRIO / ((1 + KeqTPI) * KmALDDHAP) + KeqTPI * TRIO / ((1 + KeqTPI) * KmALDGAP) + KeqTPI * F16P * TRIO / ((1 + KeqTPI) * KmALDF16P * KmALDGAPi) + KeqTPI * pow(TRIO, 2) / (pow(1 + KeqTPI, 2) * KmALDDHAP * KmALDGAP)))
v7 v7 PHOS + TRIO + NAD = BPG + NADH

(-(VmGAPDHr * BPG * NADH / (KmGAPDHBPG * KmGAPDHNADH)) + KeqTPI * VmGAPDHf * (NADt - NADH) * PHOS * TRIO / ((1 + KeqTPI) * KmGAPDHGAP * KmGAPDHNAD)) / (compartment * (1 + (NADt - NADH) / KmGAPDHNAD + NADH / KmGAPDHNADH) * (1 + PHOS) * (1 + BPG / KmGAPDHBPG + KeqTPI * TRIO / ((1 + KeqTPI) * KmGAPDHGAP)))
v8 v8 BPG = P3G + Prb

VmPGK * (KeqPGK * BPG * (SUMAXP - pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / (1 - 4 * KeqAK) - P3G * (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / (2 - 8 * KeqAK)) / (compartment * KmPGKATP * KmPGKP3G * (1 + BPG / KmPGKBPG + P3G / KmPGKP3G) * (1 + (SUMAXP - pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / ((1 - 4 * KeqAK) * KmPGKADP) + (-SUMAXP + Prb - 4 * KeqAK * Prb + pow(pow(SUMAXP, 2) - 2 * SUMAXP * Prb + 8 * KeqAK * SUMAXP * Prb + pow(Prb, 2) - 4 * KeqAK * pow(Prb, 2), 0.5)) / ((2 - 8 * KeqAK) * KmPGKATP)))
v9 v9 P3G = P2G

VmPGM * (-(P2G / KeqPGM) + P3G) / (compartment * KmPGMP3G * (1 + P2G / KmPGMP2G + P3G / KmPGMP3G))

Parameters 0   96

Global parameters

Id Value
CPFKAMP 0.0845
CPFKATP 3.0
CPFKF16BP 0.397
CPFKF26BP 0.0174
CPFKF6P 0.0
CiPFKATP 100.0
F26BP 0.02
KATPASE 39.5
KEQAK 0.45
KEQHK 3800.0
KMHKADP 0.23
KMHKATP 0.15
KMHKG6P 30.0
KMHKGLCi 0.08
KPFKAMP 0.0995
KPFKF16BP 0.111
KPFKF26BP 0.000682
KPHOS 0.1
KSUCC 21.4
KTREHALOSE 2.32
KeqADH 6.9e-05
KeqAK 0.45
KeqALD 0.069
KeqENO 6.7
KeqG3PDH 4300.0
KeqGLT 1.0
KeqPGI 0.314
KeqPGK 3200.0
KeqPGM 0.19
KeqPYK 6500.0
KeqTPI 0.045
KiADHACE 1.1
KiADHETOH 90.0
KiADHNAD 0.92
KiADHNADH 0.031
KiHKG6P 0.07
KiPFKATP 0.65
KmADHACE 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
KmG3PDHDHAP 0.4
KmG3PDHGLY 1.0
KmG3PDHNAD 0.93
KmG3PDHNADH 0.023
KmGAPDHBPG 0.0098
KmGAPDHGAP 0.21
KmGAPDHNAD 0.09
KmGAPDHNADH 0.06
KmGLTGLCi 1.1918
KmGLTGLCo 1.1918
KmGLYCOGEN 5.8
KmPDCPYR 4.33
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
L0 0.66
L0PYK 60000.0
NADt 1.59
SUMAXP 3.1
VMAXHK 226.452
VmADH 810.0
VmALD 322.258
VmENO 365.806
VmG3PDH 70.15
VmGAPDHf 1184.52
VmGAPDHr 6549.68
VmGLT 198.0
VmPDC 1062.58
VmPFK 182.903
VmPGI 339.677
VmPGK 1306.45
VmPGM 2525.81
VmPYK 1088.71
gR 5.12
nPDC 1.9
npyk 4.0
pT 10.0
wt 1.0

Local parameters

Id Value Reaction

Rules 0   0   1

Assignment rules

Definition
ATP = (-SUMAXP + (1.0 - 4.0 * KEQAK) * Prb + pow(4.0 * (1.0 - 4.0 * KEQAK) * KEQAK * pow(Prb, 2.0) + pow(SUMAXP - (1.0 - 4.0 * KEQAK) * Prb, 2.0), 0.5)) / (2.0 * (1.0 - 4.0 * KEQAK))

Rate rules

Definition

Algebraic rules

Definition

Events 0

Trigger Assignments