1. Models of the Catalytic Mechanism of Adenylyl Cyclase Clayton Fan December 20, 2004

2. Cyclic AMP (cAMP) plays a significant role in the intracellular signaling pathways in the striatum. Greengard, P. Science 2001; 294:1024-1030

3. 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

4. Our model conforms to the catalytic mechanism of a P-site inhibition study by Dessauer and Gilman, with the inhibition path (E-PP i -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

5. The fitted rate constants from the Dessauer-Gilman Model. k1k1 2.62 x 10 -4 /nM s k7k7 2060/s k2k2 89.5/s k8k8 1.11 x 10 -4 /nM s k3k3 59/s k9k9 0.30/s k4k4 2.6/s k 10 1.42 x 10 -7 /nM s k5k5 0.8/s k 11 56/s k6k6 2.78 x 10 -6 /nM s k 12 3.54 x 10 -4 /nM s From Dessauer, C. W. et al. J. Biol. Chem. 1997;272:27787-27795

6. Procedures and Methods The Dessauer-Gilman model is simplified by removing the slower E-cAMP path, leaving the E-PP i 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.

7. 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.

14. # 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 # done Original Full Dessauer-Gilman Model XPP Code http://www.benning.net/neuro/AC/simulate/ACC.ode

15. # 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 Model XPP Code http://www.benning.net/neuro/AC/simulate/ACP.ode

16. 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

17. MechanismRate ConstantsLink 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 /nM s k02 = 89.5 /s k03 = 59 /s k04 = 2.6 /s k07 = 1,060 /s k08 = 1.1 x 10 -5 /nM s k11 = 56 /s k12 = 3.54x 10 -4 /nM s Initial conditions: [ATP] = 2 mM [E] = 2 μM Simplified Model 0 (reduced) E + ATP ES : k01 k02 ES E + cAMP : k11 k12 Fitted: k01 = 1.276 x 10 -4 /nM s k02 = 0.2612 /s k11 = 28.46 /s k12 = 2.592x 10 -4 /nM s http://www.benning.net/neuro/AC/fit/AC0model/ Simplified Model 1 (reduced) E + ATP ESS : k13 k24 ESS EP + cAMP : k07 k08 EP E + PPi : k11 k12 Fitted: k13 = 7.3094 x 10 -5 /nM s k24 = 6.141 /s Fixed: k07 = 1,060 /s k08 = 1.1 x 10 -5 /nM s k11 = 56 /s k12 = 3.54x 10 -4 /nM s http://www.benning.net/neuro/AC/fit/AC1model/ Simplified Model 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 /nM s Fixed: k01 = 2.62 x 10 -4 /nM s k02 = 89.5 /s k03 = 59 /s k04 = 2.6 /s http://www.benning.net/neuro/AC/fit/AC2model/

18. 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

23. 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

33. # 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 Models Simplified Model 0 and Model 1 XPP Code http://www.benning.net/neuro/AC/simulate/AC0model.ode http://www.benning.net/neuro/AC/simulate/AC1model.ode

34. 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.