Supplemental Table 2: Kinetic rate constants in the reactions

ID

Group

Reaction Name

kf

kb (/sec)

Kd (mM)

Notes

a1

mGluR

Glu_bind_mGluR

11.11

100

9

The dependency of slow EPSCs on glutamate concentrations was measured in the first two cloning papers (Masu et al. (1991) Nature 349:760-765; Houamed et al. (1991) Science 252:1318-1321). We took the Kd value from Masu et al. (1991) Nature 349:760-765.

a2

mGluR

Glu_bind_mGluR-Gq

11.11

100

9

a3

mGluR

mGluR_bind_Gq

2

100

50

The value of Kd influences whether mGluRs can bind Gq in the resting state. Higher Kd tends to allow mGluRs to bind Gq before glutamate release, whereas lower Kd does not. We assumed that half of the mGluRs are bound to Gq at the basal state.

a4

mGluR

mGluR-Glu_bind_Gq

2

100

50

The detailed balance determines the Kd value from the loop, mGluR à Glu-mGluR à Glu-mGluR-Gq à mGluR-Gq à mGluR.

a5

mGluR

Activate_Gq

116

 

 

As far as we know, there is only one paper that measured kcat for Gq activation by G-protein coupled receptors (Fay et al. (1991) Biochemistry 30:5066-5075). Unfortunately, they used muscarinic cholinergic receptors (mAchRs), not mGluRs, as G-protein coupled receptors. Reported kcat value was 0.01 /sec, and taken in two simulation papers (Fiala et al. (1996) J Neurosci 16:3760-3774; Bhalla and Iyengar (1999) Science 283:381-387). This value was too small to yield micromolar IP3 concentrations in our simulation. We neglect the reported parameter value and arbitrarily assumed kcat of 116 /sec.

a6

mGluR

Basal-ActGq

0.0001

 

 

Basal activity of exchange of GDP to GTP in Gq. The reaction is so slow that it can be neglected.

a7

mGluR

Inact_Gq

0.02

 

 

From Berstein et al. (1992) JBC 267:8081-8088, kcat for GTPase activity of Gq itself is only 0.8 /min. Gq inactivation is facilitated by PLC in this simulation.

a8

mGluR

Trimerize_Gq

6

 

 

The parameter value determines the speed of binding Gqa-GDP and Gbg. This reaction is thought to be fast. We used the same value as in Bhalla and Iyengar (1999) Science 283:381-387. Although 6 /sec of kf might seem to be small, trimerization completes within 1 sec after glutamate stimulation.

b1

PLC

PLC-PIP2_bind_Ca

300

100

0.3333

Ca2+-dependency of PLCb4 activity has not been quantitatively measured. We took the Kd value from the parameters in PLCb1 (Smrcka et al. (1991) Science 251:804-807), as well as Bhalla and Iyengar (1999) Science 283:381-387.

b2

PLC

PLC-PIP2-Gq_bind_Ca

900

30

0.03333

Ca2+-dependency of PLCb4 activity has not been quantitatively measured. We took the Kd value from the parameters in PLCb1 (Smrcka et al. (1991) Science 251:804-807), as Bhalla and Iyengar (Science 283:381-387 (1999)) did. Note that the basal [Ca2+]i is enough to activate PLC-PIP2-Gq.

b3

PLC

PLC-PIP2_bind_Gq

800

40

0.05

The detailed balance determines the Kd value from the loop, PLC-PIP2 à PLC-Ca-PIP2 à PLC-Ca-Ga-PIP2 à PLC-Gq-PIP2 à PLC-PIP2.

b4

PLC

PLC-PIP2-Ca_bind_Gq

1200

6

0.005

From Fig. 4 in Lee et al. (1994) JBC 269:25335-25338, affinity for Gaq is 5 nM. Because of this high affinity, most of the activated Ga bind PLCb in our simulation.

b5

PLC

PLC-Ca_bind_Gq

1200

6

0.005

b6

PLC

IP3_prd_without_Gq

2

 

 

PLCb4 has basal activity of IP3 production without Gq. The measurement of this activity is difficult because PLCb4 is inhibited by ribonucleotides (Lee et al. (1994) JBC 269:25335-25338). Therefore, we assumed this parameter to hold basal [IP3] at 0.1 mM.

b7

PLC

IP3_prd_with_Gq

160

 

 

The measurement of this enzyme activity is difficult because PLCb4 is inhibited by ribonucleotides (Lee et al. (1994) JBC 269:25335-25338). We used the activity of PLCb1 in Mishra and Bhalla (2002) Biophys J 83:1298-1316.

b8

PLC

PLC-Ca_bind_PIP2

1

170

170

A biochemical paper reported Km of 100-200 mM for PIP2 in several types of PLCb (James et al. (1995) JBC 270:11872-11881). We took the affinity of PLCb1 (Km = 170 mM).

b9

PLC

PLC-Ca-Gq_bind_PIP2

1

170

170

b10

PLC

inact_Gq_by_PLC-PIP2

8

 

 

PLCb4 has GAP (G-protein activation protein) activity, which enhances the GTPase efficiency of Gq to thousands times. In the review of Montel (2000) Nat Cell Biol 2:E82-E83, the half-time of Gq inactivation is estimated to be 25-75 msec in the existence of PLC. We used the same activity among different PLCb4 states.

b11

PLC

inact_Gq_by_PLC-PIP2-Ca

8

 

 

b12

PLC

inact_Gq_by_PLC-Ca

8

 

 

c1

IP3deg

IP3K_bind_2Ca

1111.1

100

0.3

We took the Kd value from a Ca2+ simulation paper (Dunplot and Erneux (1997) Cell Calcium 22:321-331). Km for Ca2+ = 0.3 mM and Hill coefficient = 2.

c2

IP3deg

IP3K-2Ca_bind_IP3

100

80

0.8

We took the Km value from a Ca2+ simulation paper (Dunplot and Erneux (1997) Cell Calcium 22:321-331). Michaelis constant Km is 1 mM. Km = (kb + kcat) / kf = (80 + 20) / 100 = 1 mM.

c3

IP3deg

IP3K_deg_IP3

20

 

 

Several studies reported very different Vmax values (Irvine et al. (1986) Nature 320:631-634; Takazawa et al. (1989) Biochem J 261:483-488; Choi et al. (1990) Science 248:64-66). Thus, we did not take any reported value from these studies.

c4

IP3deg

IP5P_bind_IP3

9

72

8

We took the Km value from a Ca2+ simulation paper (Dunplot and Erneux (1997) Cell Calcium 22:321-331). Michaelis constant Km = 10 mM. Km = (kb + kcat) / kf = (72 + 18) / 9 = 10 mM.

c5

IP3deg

IP5P_deg_IP3

18

 

 

A purification study reported that Vmax = 20-35 mmol/min/mg protein (Verjans et al. (1992) Eur J Biochem 204:1083-1087). IP3 5-phosphatase is a 43kDa enzyme, and we obtained kcat = 20-35 x 43000/60000 = 18 #/sec/# protein. This unit conversion method was described in De Schutter (2000) Computational Neuroscience, CRC Press, Boca Raton, pp. 31.

d1

IP3R

IP3R_bind_IP3

1000

25800

25.8

From measurement of Ca2+ depletion of the ER stores, the affinity of IP3Rs for IP3 in Purkinje cells is much lower (Kd = 25.8 mM) than in vitro (Fujiwara et al. (2001) Neuroreport 12:2647-2651). The low affinity is consistent with the fact that Ca2+ response to IP3 uncaging in Purkinje cells require strong photostimulus ([IP3] > 10 mM) for (Khodakhah and Ogden (1993) PNAS 90:4976-4980; Finch and Augustine (1998) Nature 396:753-756). Thus, we used Kd of 25.8 mM in the simulation.

d2

IP3R

IP3R-IP3_bind_Ca

8000

2000

0.25

Ca2+ directly binds to IP3Rs for activation. From a bell-shaped Ca2+-dependency of IP3Rs (Bezprozvanny and Ehric (1994) J Gen Physiol 104:821-856; Fujiwara et al. (2001) Neuroreport 12:2647-2651), we obtained Kd = 0.25 mM. The reaction must be faster than Ca2+-dependent IP3R inactivation for Ca2+ positive feedback.

d3

IP3R

IP3R_bind_Ca

8.889

5

0.56249

IP3Rs are completely inactivated at high concentrations of [Ca2+]i (< 10 mM). In our kinetic model, an IP3R has four Ca2+ inactivation sites. This sequential Ca2+ binding reaction was assumed to be positively cooperative. In other words, Ca2+ ions bind a subunit easier as more Ca2+ binds to IP3Rs. How to estimate these parameters is written in Ca2+-dependent IP3R inactivation in the Material and Methods.

d4

IP3R

IP3R-Ca_bind_Ca

20

10

0.5

d5

IP3R

IP3R-2Ca_bind_Ca

40

15

0.375

d6

IP3R

IP3R-3Ca_bind_Ca

60

20

0.33333

e1

CaReg

IP3R_Ca_channel

450

450

(perm)

In Bezprozvanny and Ehrich (1994) J Gen Physiol 104:821-856, they estimated that 5400 Ca2+ ions go through an open IP3R per second at 2500 mM [Ca2+]ER. The unit of permability is not described in GENESIS/kinetikit, but we found that the parameter value of 450 matches the estimation.

e2

CaReg

SERCA_bind_2Ca

17147

1000

0.24149

We took the kinetics parameter of SERCA subtype 2b from Lytton et al. (1992) JBC 267:14483-14489. Km = 0.27 mM and the Hill coefficient = 2. Km2 = (kb + kcat) / kf = (1000 + 250) / 17147 = (0.27 mM)2.

e3

CaReg

SERCA_uptake

250

 

 

In Stryer Biochemistry 5th edition, one SERCA pumps out less than 100 Ca2+ ions per second. Thus, we took kcat value to be 50 /s at first, but the low kcat value caused a problem. The speed of Ca2+ clearance does not increase in proportion to the number of Ca2+ pumps because free Ca2+ concentration becomes low and the Ca2+ binding to the pump decreases in the large presence of Ca2+ pumps with low kcat. We failed to reproduce Ca2+ time course showed in Wang et al. (2000) Nat Neurosci 3:1266-1273 even if we increased the number of pumps. Following the fact that most of the other Ca2+ simulation neglect the binding effect of Ca2+ pumps, we decided to reduce the buffing effect by adjusting kcat and [SERCA], while keeping Vmax (= kcat x [SERCA]). Thus, we increased kcat 5-fold and decreased [SERCA] 1/5-fold.

e4

CaReg

Ca_Leak_from_ER

15

15

(perm)

This leak parameter was dependent on other parameters of Ca2+ regulation.

e5

CaReg

PMCA_bind_Ca

25000

2000

0.08

We took the kinetic parameters of PMCA subtype 2 from Stauffer et al. (1995) JBC 270:12184-12190. Km = 0.1 mM and Hill coefficient = 1. Km = (kb + kcat) / kf = (500 + 2000) / 25000 = 0.1 mM.

e6

CaReg

PMCA_uptake

500

 

 

The capacity of PMCA was increased to 10 times (50 to 500) for the same reason as the increase in kcat for SERCA.

e7

CaReg

NCX_bind_2Ca

93.827

4000

6.5293

Since this model does not include voltage, the efficacy of Na+/Ca2+ uptake should be dependent only on Ca2+ concentration, not on the membrane potential. In Fujioka et al. (2000) J Physiol 529:611-623, they measured Ca2+-dependent current of Na+/Ca2+. Km for Ca2+ = 7.3 mM and the Hill coefficient = 2. Km2 = (kb + kcat) / kf = (4000 + 1000) / 93.287 = (7.3 mM)2.

e8

CaReg

NCX_uptake

1000

 

 

Stryer Biochemistry 5th edition says that a Na+/Ca2+ can extrude 2,000 Ca2+ ions per second. Since the Hill coefficient is 2, a Na+/Ca2+ transports 2 Ca2+ ions at one reaction cycle. Thus, kcat = 2000/2 = 1000 /s.

e9

CaReg

Ca_Leak_from_ext

10

10

(perm)

This leak parameter was dependent on other parameters of Ca2+ regulation.

e10

CaReg

Ca_bind_calreticulin

0.1

200

2000

Calreticulin is a high-concentration and uncooperative buffer. We took Kd to be 2 mM, according to Krause and Michalak (1997) Cell 88:439-443.

f1

CaBuf

Ca_bind_MgGreen

1000

19000

19

Apparent Kd of Magnesium Green 1 for Ca2+ is 19 mM in the presence of endogenous Mg2+, from Wang et al. (2000) Nat Neurosci 3:1266-1273.

f2

CaBuf

PV_bind_Ca

18.5

0.95

0.05315

Parvalbumin is a slow and high-affinity buffer. Most of the parvalbumin binds endogenous Mg2+ at the basal Ca2+ concentration,. In Lee et al. (2000) J Physiol 525:419-431, they measured the apparent dissociation constant Kd = 0.0514 mM and the unbinding rate constant kb = 0.95 /sec in the presence of Mg2+, and we used the parameter values.

f3

CaBuf

CB_bind_2Ca

87

11.275

0.36

Calbindin is a cooperative and high-affinity buffer. We took the Kd value and the Hill coefficient to be 0.36 mM and 2, from Maeda et al. (1999) Neuron 24:989-1002. These values were consistent with (2:2) ratio in Table 1 in Nagerl et al. (2000) Biophys J 79:3009-3018.

f4

CaBuf

LAB_bind_Ca

10

1000

100

We included low-affinity buffers based on Fig. 6 in Maeda et al. (1999) Neuron 24:989-1002. The Hill coefficients of low-affinity buffer 1 (LAB) and low-affinity buffer 2 (LAB2) were taken 1 and 2, respectively.

f5

CaBuf

LAB2_bind_2Ca

1

4000

20