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A mathematical model of glutathione metabolism.

  • Michael C Reed
  • Rachel L Thomas
  • Jovana Pavisic
  • S Jill James
  • Cornelia M Ulrich
  • H Frederik Nijhout
Theor Biol Med Model 2008; 5 : 8
Abstract
BACKGROUND: Glutathione (GSH) plays an important role in anti-oxidant defense and detoxification reactions. It is primarily synthesized in the liver by the transsulfuration pathway and exported to provide precursors for in situ GSH synthesis by other tissues. Deficits in glutathione have been implicated in aging and a host of diseases including Alzheimer's disease, Parkinson's disease, cardiovascular disease, cancer, Down syndrome and autism.
APPROACH: We explore the properties of glutathione metabolism in the liver by experimenting with a mathematical model of one-carbon metabolism, the transsulfuration pathway, and glutathione synthesis, transport, and breakdown. The model is based on known properties of the enzymes and the regulation of those enzymes by oxidative stress. We explore the half-life of glutathione, the regulation of glutathione synthesis, and its sensitivity to fluctuations in amino acid input. We use the model to simulate the metabolic profiles previously observed in Down syndrome and autism and compare the model results to clinical data.
CONCLUSION: We show that the glutathione pools in hepatic cells and in the blood are quite insensitive to fluctuations in amino acid input and offer an explanation based on model predictions. In contrast, we show that hepatic glutathione pools are highly sensitive to the level of oxidative stress. The model shows that overexpression of genes on chromosome 21 and an increase in oxidative stress can explain the metabolic profile of Down syndrome. The model also correctly simulates the metabolic profile of autism when oxidative stress is substantially increased and the adenosine concentration is raised. Finally, we discuss how individual variation arises and its consequences for one-carbon and glutathione metabolism.

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
SAH 19.1432773636787 default_compartment
SAM 81.1684566962769 default_compartment
aic 0.942750394171554 default_compartment
bGSH 12.6996048211362 default_compartment
bGSSG 0.484328542816829 default_compartment
bcys 185.50378543937 default_compartment
bglut 60.4330872702655 default_compartment
bgly 221.101111778807 default_compartment
bmet 30.0 default_compartment
bser 150.0 default_compartment
c10fTHF 3.40907070478307 default_compartment
c5mTHF 4.4965335653401 default_compartment
cCH2THF 0.506278119133034 default_compartment
cCHTHF 0.278602708139276 default_compartment
cDHF 0.0385952337473159 default_compartment
cGSH 6590.56824161192 default_compartment
cGSSG 61.3019611792609 default_compartment
cHCOOH 13.0888186429922 default_compartment
cTHF 4.61991966766058 default_compartment
ccys 194.96740946034 default_compartment
cglc 9.80842470037426 default_compartment
cglut 3219.39793573653 default_compartment
cgly 924.429820216685 default_compartment
cser 562.834377270222 default_compartment
cyt 36.8825861752429 default_compartment
dmg 0.707382712261505 default_compartment
ext 1.0 default_compartment
hcy 1.12248362561721 default_compartment
m10fTHF 15.9087989350187 default_compartment
mCH2THF 1.66610924423152 default_compartment
mCHTHF 1.54929073348709 default_compartment
mHCOOH 55.820116666595 default_compartment
mTHF 20.995801088388 default_compartment
met 49.1868215837869 default_compartment
mgly 2040.43402532595 default_compartment
msarc 9.16245914628594 default_compartment
mser 2114.87119909779 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 v_1 met = SAM

0.4 * (0.23 + 0.8 * exp(-0.0026 * SAM)) * vmMATi * (met / kmMATimet) / (1 + met / kmMATimet) * (kiMATiGSSG + 66.71) / (kiMATiGSSG + cGSSG)
v_10 ccys = ext

0.35/200*ccys^2
v_11 v_11 ccys + cglut = cglc

vmgcl * (cglut * ccys - cglc / keqgcl) / (kmgclccys * kmgclglut + kmgclccys * cglut + ccys * kmgclglut * (1 + cGSH / kmgclgsh + cglut / kmgclglut) + cglc / kmgclglc + cGSH / kmgclgsh) * (kagcl + H2O2) / (kagcl + H2O2ss)
v_12 cglc + cgly = cGSH

vmgs*(cgly*cglc - cGSH/keqgs)/(kmgscglc*kmgscgly + cglc*kmgscgly + cgly*kmgscglc*(1 + cglc/kmgscglc) + cGSH/kpcgsh)
v_13 {2.0}cGSH = cGSSG

vmGPX*((cGSH/(kmGPXgsh + cGSH))^2)* (H2O2/(9*kmGPXH2O2 + H2O2))
v_14 cGSSG = {2.0}cGSH

(vmgr*(cGSSG/kmgrGSSG) * (cNADPH/ kmgrNADPH))/(1 + cGSSG/kmgrGSSG + cNADPH/kmgrNADPH + (cGSSG/kmgrGSSG)*(cNADPH/kmgrNADPH))
v_15 cGSSG = bGSSG

(vmGSSGl* cGSSG)/(kmGSSGl + cGSSG)*(kaGSSGl + H2O2)/(kaGSSGl + H2O2ss)
v_16 cGSSG = bGSSG

(vmGSSGh* cGSSG)/(kmGSSGh + cGSSG)*(kaGSSGh + H2O2)/(kaGSSGh + H2O2ss)
v_17 cGSH = ext

0.002*cGSH
v_18 cGSH = bGSH

(vmgshoutl*cGSH*cGSH*cGSH)/((kmgshoutl)^3 + cGSH*cGSH*cGSH)
v_19 cGSH = bGSH

(vmgshouth*cGSH)/(cGSH + kmgshouth)
v_2 v_2 met = SAM

vmMATiii * met^1.21 / (kmMATiiimet + met^1.21) * (1 + 7.2 * SAM^2 / (kmMATiiiSAM + SAM^2)) * (kiMATiiiGSSG + 66.71) / (kiMATiiiGSSG + cGSSG)
v_20 cGSSG = ext

0.1*cGSSG
v_21 bglut = cglut

vmglutin*bglut/(kmbglut + bglut) - kglutin*cglut
v_22 bcys = ccys

vmcysin*bcys/(kcysinbcys + bcys)
v_23 bser = cser

vmserin*bser/(kbser + bser) - krserin*cser
v_24 bgly = cgly

vmglyin*bgly/(kmbgly + bgly) - kcgly*cgly
v_25 {3.0}mgly = cgly

vmfgly*mgly/(3*(kgly+mgly)) - vmrgly*cgly/(kgly+cgly)
v_26 {3.0}mHCOOH = cHCOOH

khcooh*mHCOOH/3 - khcooh*cHCOOH
v_27 {3.0}mser = cser

Vmser*mser/(3*(Kmsermser + mser)) - Vmser*cser/(Kmsermser + cser)
v_28 cser + cTHF = cCH2THF + cgly

VmfcSHMT*(cser/KmcSHMTcser)*(cTHF/KmcSHMTcTHF)/(1 + (cser/KmcSHMTcser) + (cTHF/KmcSHMTcTHF) + (cser/KmcSHMTcser)*(cTHF/KmcSHMTcTHF)) - VmrcSHMT*(cgly/KmcSHMTcgly)*(cCH2THF/KmcSHMTcCH2THF)/(1 + (cgly/KmcSHMTcgly) + (cCH2THF/KmcSHMTcCH2THF) + (cgly/KmcSHMTcgly)*(cCH2THF/KmcSHMTcCH2THF))
v_29 cDHF = cTHF

VmcDHFR*(cDHF/KmcDHFRcDHF)*(cNADPH/KmcDHFRcNADPH)/(1 + (cDHF/KmcDHFRcDHF) + (cNADPH/KmcDHFRcNADPH) + (cDHF/KmcDHFRcDHF)*(cNADPH/KmcDHFRcNADPH))
v_3 SAM = SAH

Vmmeth*SAM/(KmmethSAM*(1 + SAH/KmmethSAH) + SAM)
v_30 cTHF + cHCOOH = c10fTHF

VmcFTS*(cTHF/KmcFTScTHF)*(cHCOOH/KmcFTScHCOOH)/(1 + (cTHF/KmcFTScTHF) + (cHCOOH/KmcFTScHCOOH) + (cTHF/KmcFTScTHF)*(cHCOOH/KmcFTScHCOOH))
v_31 c10fTHF = cTHF

VmcFTD*(c10fTHF/kmcFTDc10fTHF)/(1 + (c10fTHF/kmcFTDc10fTHF))
v_32 c10fTHF = aic + cTHF

VmcPGT*(c10fTHF/KmcPGTc10fTHF)*(GARP/KmcPGTGARP)/(1 + (c10fTHF/KmcPGTc10fTHF) + (GARP/KmcPGTGARP) + (c10fTHF/KmcPGTc10fTHF)*(GARP/KmcPGTGARP))
v_33 c10fTHF + aic = cTHF

VmcART*(c10fTHF/KmcARTc10fTHF)*(aic/KmcARTaic)/(1 + (c10fTHF/KmcARTc10fTHF) + (aic/KmcARTaic) + (c10fTHF/KmcARTc10fTHF)*(aic/KmcARTaic))
v_34 cTHF = cCH2THF

kfcNE*cTHF*HCHO - krcNE*cCH2THF
v_35 cCHTHF = c10fTHF

VmfcMTCH*(cCHTHF/KmcMTCHcCHTHF)/(1 + cCHTHF/KmcMTCHcCHTHF) - VmrcMTCH*(c10fTHF/KmcMTCHc10fTHF)/(1 + c10fTHF/KmcMTCHc10fTHF)
v_36 cCH2THF = cDHF

VmcTS*(DUMP/KmcTSDUMP)*(cCH2THF/KmcTScCH2THF)/(1 + (DUMP/KmcTSDUMP) + (cCH2THF/KmcTScCH2THF) + (DUMP/KmcTSDUMP)*(cCH2THF/KmcTScCH2THF))
v_37 cCH2THF = cCHTHF

VmfcMTD*(cCH2THF/KmcMTDcCH2THF)/(1 + cCH2THF/KmcMTDcCH2THF) - VmrcMTD*(cCHTHF/KmcMTDcCHTHF)/(1 + cCHTHF/KmcMTDcCHTHF)
v_38 v_38 cCH2THF = c5mTHF

VmcMTHFR * cCH2THF / KmcMTHFRcCH2THF * (cNADPH / KmcMTHFRcNADPH) / (1 + cCH2THF / KmcMTHFRcCH2THF + cNADPH / KmcMTHFRcNADPH + cCH2THF / KmcMTHFRcCH2THF * (cNADPH / KmcMTHFRcNADPH)) * 63.72 / (10 + piecewise(0, lt(SAM, SAH), SAM - SAH))
v_39 mTHF + mser = mgly + mCH2THF

VmfmSHMT*(mser/KmmSHMTmser)*(mTHF/KmmSHMTmTHF)/(1 + (mser/KmmSHMTmser) + (mTHF/KmmSHMTmTHF) + (mser/KmmSHMTmser)*(mTHF/KmmSHMTmTHF)) - VmrmSHMT*(mgly/KmmSHMTmgly)*(mCH2THF/KmmSHMTmCH2THF)/(1 + (mgly/KmmSHMTmgly) + (mCH2THF/KmmSHMTmCH2THF) + (mgly/KmmSHMTmgly)*(mCH2THF/KmmSHMTmCH2THF))
v_4 v_4 SAM + cgly = SAH + msarc

260 * SAM / ((63 + SAM) * (1 + SAH / kmGNMTSAH)) * cgly / (kmGNMTcgly + cgly) * (4.8 / (0.35 + c5mTHF))
v_40 mTHF + mHCOOH = m10fTHF

VmfmFTS*(mTHF/KmmFTSmTHF)*(mHCOOH/KmmFTSmHCOOH)/(1 + (mTHF/KmmFTSmTHF) + (mHCOOH/KmmFTSmHCOOH) + (mTHF/KmmFTSmTHF)*(mHCOOH/KmmFTSmHCOOH)) - VmrmFTS*(m10fTHF/KmmFTSm10fTHF)/(1+(m10fTHF/KmmFTSm10fTHF))
v_41 m10fTHF = mTHF

VmmFTD*(m10fTHF/kmmFTDm10fTHF)/(1 + (m10fTHF/kmmFTDm10fTHF))
v_42 mCHTHF = m10fTHF

VmfmMTCH*(mCHTHF/KmmMTCHmCHTHF)/(1 + mCHTHF/KmmMTCHmCHTHF) - VmrmMTCH*(m10fTHF/KmmMTCHm10fTHF)/(1 + m10fTHF/KmmMTCHm10fTHF)
v_43 mCH2THF = mCHTHF

VmfmMTD*(mCH2THF/KmmMTDmCH2THF)/(1 + mCH2THF/KmmMTDmCH2THF) - VmrmMTD*(mCHTHF/KmmMTDmCHTHF)/(1 + mCHTHF/KmmMTDmCHTHF)
v_44 mTHF + mgly = mCH2THF

VmmGDC*(mgly/KmmGDCmgly)*(mTHF/KmmGDCmTHF)/(1 + (mgly/KmmGDCmgly) + (mTHF/KmmGDCmTHF) + (mgly/KmmGDCmgly)*(mTHF/KmmGDCmTHF))
v_45 mTHF + msarc = mgly + mCH2THF

VmmSDH*(msarc/KmmSDHsarc)*(mTHF/KmmSDHmTHF)/(1 + (msarc/KmmSDHsarc) + (mTHF/KmmSDHmTHF) + (msarc/KmmSDHsarc)*(mTHF/KmmSDHmTHF))
v_46 mTHF + dmg = msarc + mCH2THF

VmmDMGD*(dmg/KmmDMGDdmg)*(mTHF/KmmDMGDmTHF)/(1 + (dmg/KmmDMGDdmg) + (mTHF/KmmDMGDmTHF) + (dmg/KmmDMGDdmg)*(mTHF/KmmDMGDmTHF))
v_47 mTHF = mCH2THF

kfmNE*mTHF*HCHO - krmNE*mCH2THF
v_48 bmet = met

vmmetin*bmet/(kmmetinoutmethionine + bmet) - kmetincmethionine*met
v_49 v_49 ext = bcys

vocysb + k0 * bGSSG * bGSH
v_5 SAH = hcy

Vmfah*(SAH/KmahSAH)/(1 + (SAH/KmahSAH)) - (1)*6*Vmrah*(hcy/Kmahhcy)/(1 + (hcy/Kmahhcy))
v_50 v_50 ext = bglut

voglub + k0 * bGSSG * bGSH
v_51 v_51 ext = bgly

voglyb + k0 * bGSSG * bGSH
v_52 cser = ext

1.2*cser
v_53 cglut = ext

0.07*cglut
v_54 bGSH = bgly + bcys + bglut

90*bGSH
v_55 bGSSG = {2.0}bgly + {2.0}bcys + {2.0}bglut

135/2*bGSSG
v_56 bgly = ext

0.1*bgly
v_57 bcys = ext

0.35*bcys
v_58 bglut = ext

0.1*bglut
v_59 bGSH = ext

0.7*bGSH
v_6 v_6 hcy = met + dmg

Vmbhmt * (hcy / Kmbhmthcy) / (1 + hcy / Kmbhmthcy) * BET / (Kmbhmtbet + BET) * exp(-0.0021 * (SAH + SAM)) * exp(0.0021 * 102.59) * (H2O2ss + KibhmtH2O2) / (H2O2 + KibhmtH2O2)
v_60 bGSSG = ext

7.5*bGSSG
v_7 hcy + c5mTHF = met + cTHF

vmMS*(hcy/kmMShcy)/(1 + (hcy/kmMShcy))*(c5mTHF/kmMSmTH4)/(1 + (c5mTHF/kmMSmTH4))*(kiMSH2O2 + H2O2ss)/(kiMSH2O2 + H2O2)
v_8 v_8 hcy + cser = cyt

Vmcbs * cser / (Kmcbsserine + cser) * hcy / Kmcbshcy / (1 + hcy / Kmcbshcy) * 1.2 / ((30 / (SAM + SAH))^2 + 1) * (1.2 / ((30 / 102.59)^2 + 1))^-1 * (kaH2O2 + H2O2) / (kaH2O2 + H2O2ss)
v_9 cyt = ccys

vmctgl*(cyt/kmctglcyt)/(1 + (cyt/kmctglcyt))

Global parameters

Id Value
BET 50.0
DUMP 20.0
GARP 10.0
H2O2 0.01
H2O2ss 0.01
HCHO 500.0
KibhmtH2O2 0.01
KmahSAH 6.5
Kmahhcy 150.0
Kmbhmtbet 100.0
Kmbhmthcy 12.0
KmcARTaic 100.0
KmcARTc10fTHF 5.9
KmcDHFRcDHF 0.5
KmcDHFRcNADPH 4.0
KmcFTScHCOOH 43.0
KmcFTScTHF 3.0
KmcMTCHc10fTHF 100.0
KmcMTCHcCHTHF 250.0
KmcMTDcCH2THF 2.0
KmcMTDcCHTHF 10.0
KmcMTHFRcCH2THF 50.0
KmcMTHFRcNADPH 16.0
KmcPGTGARP 520.0
KmcPGTc10fTHF 4.9
KmcSHMTcCH2THF 3200.0
KmcSHMTcTHF 50.0
KmcSHMTcgly 10000.0
KmcSHMTcser 600.0
KmcTSDUMP 6.3
KmcTScCH2THF 14.0
Kmcbshcy 1000.0
Kmcbsserine 2000.0
Kmcdoccys 3100.0
KmmDMGDdmg 50.0
KmmDMGDmTHF 50.0
KmmFTSm10fTHF 22.0
KmmFTSmHCOOH 43.0
KmmFTSmTHF 3.0
KmmGDCmTHF 50.0
KmmGDCmgly 3400.0
KmmMTCHm10fTHF 100.0
KmmMTCHmCHTHF 250.0
KmmMTDmCH2THF 2.0
KmmMTDmCHTHF 10.0
KmmSDHmTHF 50.0
KmmSDHsarc 320.0
KmmSHMTmCH2THF 3200.0
KmmSHMTmTHF 50.0
KmmSHMTmgly 10000.0
KmmSHMTmser 600.0
KmmethSAH 1.4
KmmethSAM 1.4
Kmsermser 5700.0
Vmbhmt 2160.0
VmcART 55000.0
VmcDHFR 2000.0
VmcFTD 500.0
VmcFTS 3900.0
VmcMTHFR 6000.0
VmcPGT 24300.0
VmcTS 5000.0
Vmcbs 420000.0
Vmcdo 1327.15
Vmfah 320.0
VmfcMTCH 500000.0
VmfcMTD 80000.0
VmfcSHMT 5200.0
VmfmFTS 2000.0
VmfmMTCH 790000.0
VmfmMTD 180000.0
VmfmSHMT 11440.0
VmmDMGD 15000.0
VmmFTD 1050.0
VmmGDC 15000.0
VmmSDH 15000.0
Vmmeth 180.0
Vmrah 755.0
VmrcMTCH 20000.0
VmrcMTD 600000.0
VmrcSHMT 15000000.0
VmrmFTS 6300.0
VmrmMTCH 20000.0
VmrmMTD 594000.0
VmrmSHMT 30000000.0
Vmser 10000.0
cNADPH 50.0
k0 0.0
kaGSSGh 0.01
kaGSSGl 0.01
kaH2O2 0.035
kagcl 0.01
kbser 150.0
kcgly 1.0
kcysin 70.0
kcysinbcys 2100.0
keqgcl 5597.0
keqgs 5600.0
kfcNE 0.03
kfmNE 0.03
kglutin 1.0
kgly 5700.0
kglyin 630.0
khcooh 100.0
kiMATiGSSG 2140.0
kiMATiiiGSSG 4030.0
kiMSH2O2 0.01
kmGNMTSAH 18.0
kmGNMTcgly 130.0
kmGPXH2O2 0.01
kmGPXgsh 1330.0
kmGSSGh 1250.0
kmGSSGl 7110.0
kmMATiSAM 50.0
kmMATiiiSAM 129600.0
kmMATiiimet 300.0
kmMATimet 41.0
kmMShcy 1.0
kmMSmTH4 25.0
kmbglut 300.0
kmbgly 150.0
kmcFTDc10fTHF 20.0
kmctglcyt 500.0
kmetin 30.0
kmetincmethionine 1.0
kmgclccys 100.0
kmgclglc 300.0
kmgclglut 1900.0
kmgclgsh 8200.0
kmgrGSSG 107.0
kmgrNADPH 10.4
kmgscglc 22.0
kmgscgly 300.0
kmgshe 3300.0
kmgshout 240.0
kmgshouth 150.0
kmgshoutl 3000.0
kmmFTDm10fTHF 20.0
kmmetinoutmethionine 150.0
kpcgsh 30.0
krcNE 22.0
krmNE 20.0
krserin 1.0
kserin 150.0
vmGPX 4500.0
vmGSSGh 40.0
vmGSSGl 4025.0
vmMATi 650.0
vmMATiii 220.0
vmMS 500.0
vmctgl 1500.0
vmcysin 14950.0
vmfgly 10000.0
vmgcl 3600.0
vmglutin 28000.0
vmglyin 4600.0
vmgr 892.5
vmgs 5400.0
vmgshe 304.0
vmgshout 1000.0
vmgshouth 150.0
vmgshoutl 1100.0
vmmetin 913.4
vmrgly 10000.0
vmserin 2700.0
vocysb 70.0
voglub 273.0
voglyb 630.0

Local parameters

Id Value Reaction

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments