ID

Supplemental Table 2: Kinetic rate constants in the reactions

ID	Group	Reaction Name	*k_f*	*k_b* (/sec)	K_d (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 K_d 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 K_d influences whether mGluRs can bind Gq in the resting state. Higher K_d tends to allow mGluRs to bind Gq before glutamate release, whereas lower K_d 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 K_d 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 k_cat 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 k_cat 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 k_cat 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, k_cat 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 k_f 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 K_d 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 K_d 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 K_d 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 K_m 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 (K_m = 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 K_d value from a Ca²⁺ simulation paper (Dunplot and Erneux (1997) Cell Calcium 22:321-331). K_m for Ca²⁺ = 0.3 mM and Hill coefficient = 2.
c2	IP3deg	IP3K-2Ca_bind_IP3	100	80	0.8	We took the K_m value from a Ca²⁺ simulation paper (Dunplot and Erneux (1997) Cell Calcium 22:321-331). Michaelis constant K_m is 1 mM. K_m = (k_b + k_cat) / k_f = (80 + 20) / 100 = 1 mM.
c3	IP3deg	IP3K_deg_IP3	20			Several studies reported very different V_max 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 K_m value from a Ca²⁺ simulation paper (Dunplot and Erneux (1997) Cell Calcium 22:321-331). Michaelis constant K_m = 10 mM. K_m = (k_b + k_cat) / k_f = (72 + 18) / 9 = 10 mM.
c5	IP3deg	IP5P_deg_IP3	18			A purification study reported that V_max = 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 k_cat = 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 (K_d = 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 K_d 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 K_d = 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. K_m = 0.27 mM and the Hill coefficient = 2. K_m² = (k_b + k_cat) / k_f = (1000 + 250) / 17147 = (0.27 mM)².
e3	CaReg	SERCA_uptake	250			In Stryer Biochemistry 5^thedition, one SERCA pumps out less than 100 Ca²⁺ ions per second. Thus, we took k_cat value to be 50 /s at first, but the low k_cat 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 k_cat. 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 k_cat and [SERCA], while keeping V_max (= k_cat x [SERCA]). Thus, we increased k_cat 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. K_m = 0.1 mM and Hill coefficient = 1. K_m = (k_b + k_cat) / k_f = (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 k_cat 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⁺. K_m for Ca²⁺ = 7.3 mM and the Hill coefficient = 2. K_m² = (k_b + k_cat) / k_f = (4000 + 1000) / 93.287 = (7.3 mM)².
e8	CaReg	NCX_uptake	1000			Stryer Biochemistry 5^th 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, k_cat= 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 K_d to be 2 mM, according to Krause and Michalak (1997) Cell 88:439-443.
f1	CaBuf	Ca_bind_MgGreen	1000	19000	19	Apparent K_d 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 K_d = 0.0514 mM and the unbinding rate constant k_b = 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 K_d 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