Modelsof the

Catalytic Mechanismof

Adenylyl Cyclase

Clayton Fan

December 20, 2004

Cyclic AMP (cAMP) plays a significant role in the intracellular signaling pathways in the striatum.

Greengard, P. Science 2001; 294:1024-1030

This model focuses on the mechanism of cAMP synthesis involving the membrane-bound adenylyl cyclase (AC). We selected AC5 as the isoform of our model.

Sunahara RK, Taussig R. Molecular Interventions 2002 Jun; 2(3):168-184

Our model conforms to the catalytic mechanism of a P-site inhibition study by Dessauer and Gilman, with the inhibition path (E-PPi-I) removed. The objective is to take this catalytic mechanism and reduce it to a simplified model without significantly altering the result. The result is the production of of cAMP as a function of time.

Dessauer, C. W. et al. J. Biol. Chem. 1997;272:27787-27795

The fitted rate constants from the Dessauer-Gilman Model.

k1 2.62 x 10-4 /nMs k7 2060 /s

k2 89.5 /s k8 1.11 x 10-4 /nMs

k3 59 /s k9 0.30 /s

k4 2.6 /s k10 1.42 x 10-7 /nMs

k5 0.8 /s k11 56 /s

k6 2.78 x 10-6 /nMs k12 3.54 x 10-4 /nMs

From Dessauer, C. W. et al. J. Biol. Chem. 1997;272:27787-27795

Procedures and Methods

The Dessauer-Gilman model is simplified by removing the slower E-cAMP path, leaving the E-PPi path. We simulated the progress of the catalysis for both models to verify that the result of the simplified model is not significantly different from that of the original full model. The simplified model is further reduced by removing one or more intermediate steps. The simulated cAMP progress data of the simplified model is used to compute a new set of rate constants.

XPP is used to simulate the catalytic progress of the product, substrate and enzyme complexes. MATLAB is used to plot the simulated result. DynaFit is used to compute rate constants to fit simulated cAMP progress curves for the reduced models.

Original Full Dessauer-Gilman Model (Bifurcated Pathway)

Simplified Dessauer-Gilman Model (E-PPi Pathway)

Result

Result of the simulation shows that there is no significant difference in cAMP progress between the simplified and original versions of the Dessauer-Gilman

Model.

• # ACC.ode• # Adenylyl Cyclase ATP-cAMP pathway, through E-PPi and E-cAMP

complexes• #• # e0 - [E](0), intial enzyme (E) concentration• # ee - [E](t).• # es - [E-ATP](t).• # eqp - [E-cAMP-PPi](t).• # eq - [E-cAMP](t).• # ep - [E-PPi](t).• #• # Enzyme E (Adenylyl Cyclase)• # Products cAMP, PPi• # Substrate ATP.• #• cAMP' = k09*eq - k10*ee*cAMP \• + k07*eqp - k08*ep*cAMP

• PPi' = k11*ep - k12*ee*PPi \• + k05*eqp - k06*eq*PPi

• ATP' = -k01*ee*atp + k02*es• #• # ee(t)• #• ee = e0-es-eqp-eq-ep• aux ee = ee• #ee' = k02*es - k01*ee*ATP + k09*eq + k11*ep - k10*ee*cAMP -

k12*ee*PPi• #• #es(t)• #• es'=k01*ee*ATP + k04*eqp - (k02 + k03)*es• #• # eqp(t)• #• eqp'=k03*es + k06*eq*PPi + k08*ep*cAMP - (k04+k05+k07)*eqp• #• # eq(t)• #• eq'=k05*eqp + k10*ee*cAMP - k06*eq*PPi - k09*eq• #• # ep(t)• #• ep'=k07*eqp + k12*ee*PPi - k08*ep*cAMP - k11*ep

• #• # Initial values• #• # ATP, 10 microMolar to 2.56 mM• # init atp=0.002,amp=0.020,ppi=0.002• #• init ATP=0.002• init cAMP=0• init PPi=0• #• # Rate constants in (1/s) or (1/M)(1/s), Dessauer et al, 1997• #• # • par k01=262000• par k02=89.5• par k03=59• par k04=2.6• par k05=0.8• par k06=2780• par k07=1060• par k08=111000• par k09=0.39• par k10=142• par k11=56• par k12=354000• #• # Initial Free Enzyme concentration, e0 = 2 microMolar• #• #• par e0=2e-6• #• @ Total=500 dt=0.01 xlo=0 xhi=500 ylo=0 yhi=0.0015

maxstor=600000 \• bounds=1000000 nOutput=10 back=white method=Stiff• #• # Data columns: Time cAMP PPi ATP es eqp eq ep ee• #• doneOriginal Full Dessauer-Gilman

ModelXPP Code

http://www.benning.net/neuro/AC/simulate/ACC.ode

• # ACP.ode• # Adenylyl Cyclase ATP-cAMP pathway, through E-PPi

complex only• #• # e0 - [E](0), intial enzyme (E) concentration• # ee - [E](t).• # es - [E-ATP](t).• # eqp - [E-cAMP-PPi](t).• # eq - [E-cAMP](t). <--- NOT used• # ep - [E-PPi](t).• #• # Enzyme E (Adenylyl Cyclase)• # Products cAMP, PPi• # Substrate ATP• #• cAMP' = k07*eqp - k08*ep*cAMP

• PPi' = k11*ep - k12*ee*PPi

• ATP' = -k01*ee*atp + k02*es

• #• # ee(t)• #• ee = e0-es-eqp-ep• aux ee=ee• #ee' = k02*es - k01*ee*ATP + k11*ep - k12*ee*PPi• #• # es(t)• #• es'=k01*ee*ATP + k04*eqp - (k02 + k03)*es• #• # eqp(t)• #• eqp'=k03*es + k08*ep*cAMP - (k04+k07)*eqp• #• # eq(t)• #• #eq'= k10*ee*cAMP - k09*eq• #• # ep(t)• #• ep'=k07*eqp + k12*ee*PPi - k08*ep*cAMP - k11*ep

• #• # Initial values• #• # ATP, 10 microMolar to 2.56 mM• # init atp=0.002,amp=0.020,ppi=0.002• #• init ATP=0.002• init cAMP=0• init PPi=0• #• # Rate constants in (1/s) or (1/M)(1/s), Dessauer

et al, 1997• #• par k01=262000• par k02=89.5• par k03=59• par k04=2.6• #par k05=0.8• #par k06=2780• par k07=1060• par k08=111000• #par k09=0.39• #par k10=142• par k11=56• par k12=354000• #• # Initial Free Enzyme concentration, e0 = 2

microMolar• #• par e0=2e-6• #• @ Total=500 dt=0.01 xlo=0 xhi=500 ylo=0 yhi=0.0015

maxstor=600000 \• bounds=1000000 nOutput=10 back=white method=Stiff• #• # Data columns: Time cAMP PPi ATP es eqp eq qp ee• #• done

Simpified Dessauer-Gilman ModelXPP Code

http://www.benning.net/neuro/AC/simulate/ACP.ode

The simplified model is further simplified into several reduced models by removing one or more intermediate steps. Some or all kinetic constants are computed by fitting them to the cAMP progress curve of the non-reduced simplified model.

Model 0

Model 1

Model 2

Mechanism Rate Constants Link to DynaFit Result

Simplified Model

E + ATP <===> E-ATP : k01 k02

E -ATP <===> E-cAMP-PPi : k03 k04

E-cAMP-PPi <===> E-PPi + cAMP :k07 k08

E-PPi <===> E + PPi : k11 k12

k01 = 2.62 x 10-4 /nMs

k02 = 89.5 /s

k03 = 59 /s

k04 = 2.6 /s

k07 = 1,060 /s

k08 = 1.1 x 10-5 /nMs

k11 = 56 /s

k12 = 3.54x 10-4 /nMs

Initial conditions:

[ATP] = 2 mM

[E] = 2 μM

SimplifiedModel 0

(reduced)

E + ATP <===> ES : k01 k02

ES <===> E + cAMP : k11 k12

Fitted:

k01 = 1.276 x 10-4 /nMs

k02 = 0.2612 /s

k11 = 28.46 /s

k12 = 2.592x 10-4 /nMs

http://www.benning.net/neuro/AC/fit/AC0model/

SimplifiedModel 1

(reduced)

E + ATP <===> ESS : k13 k24

ESS <===> EP + cAMP : k07 k08

EP <===> E + PPi : k11 k12

Fitted:

k13 = 7.3094 x 10-5 /nMs

k24 = 6.141 /s

Fixed:

k07 = 1,060 /s

k08 = 1.1 x 10-5 /nMs

k11 = 56 /s

k12 = 3.54x 10-4 /nMs

http://www.benning.net/neuro/AC/fit/AC1model/

SimplifiedModel 2

(reduced)

E + ATP <===> ES : k01 k02

ES <===> ESS : k03 k04

ESS <===> E + cAMP : k711 k812

Fitted:

k711 = 48.666 /s

k812 = 7.4244 x 10-4

/nMs

Fixed:

k01 = 2.62 x 10-4 /nMs

k02 = 89.5 /s

k03 = 59 /s

k04 = 2.6 /s

http://www.benning.net/neuro/AC/fit/AC2model/

All three reduced models fit very well to the cAMP progress data of the non-reduced model. Model 0 is taken for further analysis on its dependence on initial substrate (ATP) concentration. The result shows that there is no significant dependence.

[ATP] = 2 mM

[AC] = 2 μM

Fitted

[ATP] = 10 μM

[AC] = 2 μM

Simulated from fitted rate constants

Model 0 is taken for analysis on its dependence on initial free enzyme (AC) concentration. The result shows that there is no significant dependence.

[ATP] = 2 mM

[AC] = 20 μM

Simulated from fitted rate constants

[ATP] = 2 mM

[AC] = 2 μM

Fitted

[ATP] = 2 mM

[AC] = 0.2 μM

Simulated from fitted rate constants

• # AC0model.ode• # Adenylyl Cyclase ATP-cAMP pathway;• # Simplified Model 0: reduced from Simplified Model• # Enzyme ee (Adenylyl Cyclase)• # Enzyme-Substrate es• # Products cAMP• # Substrate ATP• #• cAMP' = k11 *es - k12*ee*cAMP• ATP' = -k01*ee*ATP + k02 *es• es' = k01*ee*ATP - (k02 + k11)*es + k12*ee*cAMP• ee' = -k01*ee*ATP + (k02 + k11)*es - k12*ee*cAMP• #• # Initial values• #• # ATP, 10 microMolar to 2.56 mM• # init atp=0.002,ee=2e-6• #• init ATP=0.002• init cAMP=0• init ee=2e-6• #• # Rate constants in (1/s) or (1/M)(1/s)• #• # • par k01=127600• par k02=0.2612• par k11=28.46• par k12=259200• #• @ Total=500 dt=0.01 xlo=0 xhi=500 ylo=0 yhi=0.0015

maxstor=600000 \• bounds=1000000 nOutput=10 back=white method=Stiff• #• # Data columns: Time cAMP PPi ATP ess ep ee• #• done

• # AC1model.ode• # Adenylyl Cyclase ATP-cAMP pathway;• # Simplified Model 1: redued from Simplified Model• #• # Enzyme ee (Adenylyl Cyclase)• # Enzyme-Substrate es• # Products cAMP• # Substrate ATP• #• cAMP' = k11 *es - k12*ee*cAMP• ATP' = -k01*ee*ATP + k02 *es• es' = k01*ee*ATP - (k02 + k11)*es + k12*ee*cAMP• ee' = -k13*ee*ATP + k24*es - k12*ee*cAMP• #• # Initial values• #• # ATP, 10 microMolar to 2.56 mM• # init atp=0.002,ee=2e-6• #• init ATP=0.002• init cAMP=0• init ee=2e-6• #• # Rate constants in (1/s) or (1/M)(1/s)• #• # • par k01=127600• par k02=0.2612• par k11=28.46• par k12=259200• #• @ Total=500 dt=0.01 xlo=0 xhi=500 ylo=0 yhi=0.0015

maxstor=600000 \• bounds=1000000 nOutput=10 back=white method=Stiff• #• # Data columns: Time cAMP PPi ATP ess ep ee• #• done

Reduced ModelsSimplified Model 0 and Model 1

XPP Codehttp://www.benning.net/neuro/AC/simulate/AC0model.odehttp://www.benning.net/neuro/AC/simulate/AC1model.ode

References

• Greengard, P. (2001) The neurobiology of slow synaptic transmission.Science. 294 (5544), 1024-1030.

• Sunahara, R.K. and Taussig, R. (2002) Isoforms of mammalian adenylyl cyclase: multiplicities of Signaling. Mol. Interv. 2(3):168-184

• Dessauer, C.W. and Gilman, A.G. (1997) The Catalytic Mechanism of Mammanlian Adenylyl Cyclase. J. Biol. Chem. 272, 27787-27795

• Kuzmic, P. (1996) Program DYNAFIT for the Analysis of Enzyme Kinetic Data: Application to HIV Proteinase. Anal. Biochem. 237, 260-273.