Supplemental Tables: Parameter Tables

Supplemental Table 1: Molecular numbers and concentrations in the initial condition

ID	Group	Molecular Name	#	Total #	Conc. (mM)	Total Conc.	Notes
A1	mGluR	Glu	0	300	0	250	Glutamate released at the synaptic cleft should be removed within milliseconds because individual EPSC responses can be seen with high-frequency stimuli (100 Hz), for instance, in Takechi et al. (1998) Nature 396:757-760. Thus, we estimated that the decaying time constant of Glu is 5 msec. The initial number of Glu that access mGluRs localized at the edge of PSD was set to 300, because concentration in neurotransmitter at the edge of spine is less than that at the center of spine (Franks et al. (2003) J Neurosci 23:3186-3195). This amount of Glu is sufficient to activate most of the mGluRs. # in the Supplemental Tables indicates the initial number of the molecules in its present state, and the total # indicates the total number of the molecules in any state.
A2	mGluR	mGluR	10	18	8.3333	15	Metabotropic glutamate receptor type 1. Although the characteristic of this receptor was examined in two first cloning papers (Masu et al. (1991) Nature 349:760-765; Houamed et al. (1991) Science 252:1318-1321), we cannot estimate [mGluR] because the receptors were overexpressed by functional expression in Xenopus oocytes. In Bhalla and Iyengar (1999) Scinece 283:381-387, they estimated 0.3 mM mGluR in a cell, and we took this value. Since the volume of the cytosol in the spine is 0.1 mm³ in our model, the number of mGluRs was estimated to be 18. The number is similar to those of AMPARs and VGCCs in a hippocampal dendritic spine (Matsuzaki et al. (2001) Nat Neurosci 4:1086-1092; Sabatini and Svoboda (2000) Nature 408:589-593). We modeled that mGluRs localize at the PSD, which has 1/50-fold volume of the cytosol. We obtained 8.3333 mM mGluR in the PSD.
A3	mGluR	mGluR-Glu	0	18	0	15	mGluRs activated by Glu binding.
A4	mGluR	Gq-GDP	52	60	43.333	50	Trimeric G-protein Gq family. In Bhalla and Iyengar (1999) Science 283:381-387, they estimated 1.0 mM Gq in a cell. Since the cytosolic volume in the spine is 0.1 mm³, the number of Gq was estimated to be 60. We obtained 50 mM Gq in the PSD because the cytosol has 50-fold volume of the PSD.
A5	mGluR	mGluR-Gq	8	18	6.6667	15	mGluRs binding to Gq without Glu. It is not clear whether mGluRs and Gq form complex before ligand stimulation (small K_d), or ligand stimulation on mGluRs leads to the binding of mGluRs and Gq (large K_d). In this model, we assumed half of the mGluRs bind Gq before glutamate release.
A6	mGluR	Glu-mGluR-Gq	0	18	0	15	Intermediated state for Gq activation of Glu-mGluR-Gq complex.
A7	mGluR	Ga-GTP	0	60	0	50	Activated Gqa subunit. Gq-GTP binds PLCb to enhance IP₃ productivity of PLCb.
A8	mGluR	Gbc	0	60	0	50	G-protein bg complex. In this simulation, there are no proteins activated by Gbg.
A9	mGluR	Ga-GDP	0	60	0	50	Inactivated Gqa subunit. Ga-GDP rapidly binds Gbg to form a trimer.
B1	PLC	PIP2	5000	5000	4166.7	4166.7	Phosphatidylinositol-4,5-bisphosphate. Molecular biology of the cell 4^th edition says that 5000000 lipid molecules exist in a 1 mm² area of the plasma membrane. Since PIP₂ is a minor lipid (less than 1%), the number of PIP₂ in the PSD was estimated to be 5000.
B2	PLC	PLC-PIP2	42	50	35	41.667	PLCb subtype 4. We modeled PLCb to bind PIP₂ before PLC activation by Ca²⁺, because PIP₂ concentration is high enough to bind almost all PLC in saturation. Bhalla and Iyengar (1999) Science 283:381-387 estimated 0.8 mM PLCb in a cell. Since the cytosolic volume in the spine is 0.1 mm³, the number of Gq was estimated to be 50. We obtained 42 mM PLCb in the PSD because the cytosol has 50-fold volume of the PSD.
B3	PLC	PLC-PIP2-Ca	7.5	50	6.25	41.667	Without Gq, PLCb activity is very low.
B4	PLC	PLC-PIP2-Gq	0	50	0	41.667	This state has no enzyme activity. PLCb4 requires Ca²⁺ for activation.
B5	PLC	PLC-PIP2-Ca-Gq	0	50	0	41.667	Fully activated form of PLCb4. PLCb hydrolyzes PIP₂ into DAG and IP₃. PLCb4 activation is dependent on Gq, whereas some other PLCb subtypes are not.
B6	PLC	PLC-Ca	0.5	50	0	41.667	The intermediate states of PLCb that do not bind PIP₂. We assumed that PLCb in the basal states bind PIP₂.
B7	PLC	PLC-Ca-Gq	0	50	0	41.667
B8	PLC	DAG	0	0	0	0	Diacylglycerol activates no enzyme in the model because we do not implement DAG-dependent enzymes such as protein kinase C.
B9	PLC	IP3_PSD	0.12	12	0.1	10	IP₃ is produced by PLCb in the PSD and diffuses to the cytosol.
C1	IP3deg	IP3_spine	6	600	0.1	10	We set the basal [IP₃] to 0.1 mM in this simulation. [IP₃] measurement in living cells is difficult. The only report is Luzzi et al. (1998) J Biol Chem 273:28657-28662. They estimated 0.04 mM IP₃ in Xenopus Oocytes by using capillary electrophoresis.
C2	IP3deg	IP3_3-kinase	52	54	0.86667	0.9	IP₃ 3-kinase, which phosphorylates IP₃ to IP₄. In Takazawa et al. (1989) Biochem J 261:483-488, 0.020 mg of protein was purified from 700 g of bovine brain tissue. The yield was 4.4% and the molecular weight was 35000. Thus, 0.020 mg x (100%/4.4%) / (35000 g/mol) / 0.7 liter = 0.019 mM while assuming the specific gravity of the tissue 1 kg/liter. This enzyme is highly localized in Purkinje dendritic spines (Yamada et al. (1993) Brain Res 606:335-340; Go et al. (1993) Neurosci Lett 158:135-138). Therefore, we increased [IP3K] to 0.9 mM.
C3	IP3deg	IP3K-2Ca	2	54	0.033333	0.9	Ca²⁺-bound state of IP3K.
C4	IP3deg	IP3K-2Ca-IP₃	0	54	0	0.9	Ca²⁺- and IP₃-bound state of IP3K.
C5	IP3deg	IP3_5-phos	58.8	60	0.98	1	IP₃ 5-phosphatase, which dephosphorylates IP₃ to IP₂. From Verjans et al. (1992) Eur J Biochem 204:1083-1087, 0.806 mg of IP5P was obtained from 2 kg of brain tissue. The yield was 15% and the molecular weight was 43,000. Thus, 0.806 mg x (100%/15%) / (43000 g/mol) / 2 liter brain = 0.06 mM, while assuming the specific gravity of the tissue 1 kg/liter. A study using antibodies showed that the enzyme was highly expressed in the Purkinje neurons (De Smedt et al. (1996) JBC 271:10419-10424). Thus, we increased it to 1 mM.
C6	IP3deg	IP5P-IP3	1.2	60	0.02	1	Intermediate binding state of IP₃ 5-phosphatase and IP₃.
D1	IP3R	IP3Rec	14.22	16	0.237	0.26667	IP₃R type 1 is highly expressed in Purkinje cells. We counted 16 immunogold spots in the figure of the PF spine slice in Otsu et al. (1990) Cell Struct Function 15:163-173. Since the slice has 1/4 thickness of a spine and IP₃Rs are homotetramers, the number of IP₃Rs in a PF spine was estimated to be 16 (= 16 /(1/4) /4).
D2	IP3R	IP3R-IP3	0.06	16	0.1	0.26667	IP₃-bound state of IP₃Rs. In our IP₃R kinetics model, IP₃ binding to IP₃Rs allows activation of the IP₃Rs by Ca²⁺.
D3	IP3R	IP3R_open	0.01	16	0.00016667	0.26667	Open state of IP₃Rs.
D4	IP3R	IP3R-Ca	1.5	16	0.025	0.26667	Inactivation state of IP₃Rs, bound to one Ca²⁺ ion.
D5	IP3R	IP3R-2Ca	0.18	16	0.003	0.26667	Inactivation state of IP₃Rs, bound to two Ca²⁺ ions.
D6	IP3R	IP3R-3Ca	0.03	16	0.0005	0.26667	Inactivation state of IP₃Rs, bound to three Ca²⁺ ions.
D7	IP3R	IP3R-4Ca	0	16	0	0.26667	Inactivation state of IP₃Rs, bound to four Ca²⁺ ions.
E1	CaReg	CaSpine	3.6	3.6	0.06	0.06	Free cytosolic Ca²⁺ concentration, [Ca²⁺]_i. The basal [Ca²⁺]_i is set to 0.06 mM.
E2	CaReg	Ca2+PSD	0.072	0.072	0.06	0.06	Ca²⁺ concentration in the postsynaptic density. This concentration is used only for Ca²⁺-dependent PLCb activation. It has a slight effect on IP₃ productivity of PLCb in the PSD.
E3	CaReg	SERCA	148	155	2.4667	2.5833	Sacro- and endoplasmic reticulum Ca²⁺-ATPase. SERCA is a dominant protein in the ER, constituting 80% of the ER membrane protein (Stryer Biochemistry 5^th edition). SERCA type 2 is dominant in the Purkinje cells (Takei et al. (1992) J Neurosci 12:489-505). We assumed the number of SERCA so that [Ca²⁺]_ER is 150 mM at the basal state.
E4	CaReg	SERCA-2Ca	7	155	0.11667	2.5833	Ca²⁺-bound state of SERCA.
E5	CaReg	PMCA	68	108	1.1333	1.8	Plasma membrane Ca²⁺-ATPase. Type 2 of PMCA is abundant in Purkinje cells (de Talamoni et al. (1993) PNAS 90:11949-11953). PMCA has higher affinity and lower capacity than Na⁺/Ca²⁺ exchangers. At the basal [Ca²⁺]_i, PMCA pumps out much more Ca²⁺ ions than Na⁺/Ca²⁺. We chose [PMCA] so that [Ca²⁺]_i is 0.06 mM at the basal state.
E6	CaReg	PMCA-Ca	40	108	0.66667	1.8	Ca²⁺-bound state of PMCA.
E7	CaReg	NCX	32	32	0.53333	0.53333	Na⁺/Ca²⁺ exchangers. They use Na⁺ electrochemical gradient across the plasma membrane as their energy source. Note that we do not model membrane potential. NCXs play a major role in pumping out intracellular Ca²⁺ at micromolar levels of [Ca²⁺]_i,.
E8	CaReg	NCX-2Ca	0	32	0	0.53333	Ca²⁺-bound state of Na⁺/Ca²⁺ exchangers.
E9	CaReg	CaStore	1800	30000	150	2500	Free Ca²⁺ concentration in the ER, [Ca²⁺]_ER, was previously assumed to be more than 1 mM in 1990s (for example, Fiala et al. (1996) J Neurosci 16:3760-3774; Bezprozvanny and Ehrich (1994) J Gen Physiol 104:821-856). Recent studies using low-affinity Ca²⁺ indicators implied [Ca²⁺]_ER at submicromolar levels (e.g. Park et al. (2000) EMBO J 19:5729-5739). Thus, we used 150 mM [Ca²⁺]_ER in the simulation.
E10	CaReg	calreticulin	9.6x10⁵	1.032x10⁶	80000	86000	A well-known Ca²⁺ buffer in the ER. We took the Ca²⁺ biding ratio in the ER to be 5. Bound Ca²⁺ is 5 times free Ca²⁺ in the ER at the basal [Ca²⁺]_ER.
E11	CaReg	calreticulin-Ca	72,000	1.032x10⁶	6000	86000	Ca²⁺-bound state of calreticulin.
E12	CaReg	Ca_ext	1.2x10⁷	1.2x10⁷	2000	2000	Extracellular Ca²⁺ concentration.
F1	CaBuf	MgGreen	14940	15000	249	250	Magnesium Green 1. This low-affinity Ca²⁺ indicator was used at 250-500 mM in Wang et al. (2000) Nat Neurosci 3:1266-1273. To compare our simulation results with the Ca²⁺ imaging directly, we included 250 mM MgGreen in our model.
F2	CaBuf	MgGreen*	60	15000	1	250	Ca²⁺-bound form of MgGreen. MgGreen* (Ca²⁺-bound form) has twice the fluorescence of MgGreen (Ca²⁺-nonbound form). Thus, F_max/F_min = 2.
F3	CaBuf	parvalbumin	1380	3000	23	50	Parvalbumin is highly expressed in GABAergic neurons, including Purkinje cells (de Talamoni et al. (1993) PNAS 90:11949-11953). Considering the high binding ratio at the basal [Ca²⁺]_i (Fierro and Llano (1996) J Physiol 496:617-625), the concentration in parvalbumin should be tens of micromolars.
F4	CaBuf	PV-Ca	1620	3000	27	50	Ca²⁺-bound state of parvalbumin.
F5	CaBuf	Calbindin-D28k	5850	6000	97.5	100	Calbindin-D_28k is highly expressed in Purkinje cells. Ca²⁺ decay in mutant mice with no calbindin-D_28k gene was faster than in wild-type mice (Airaksinen et al. (1997) PNAS 94:1488-1493). Although Maeda et al. (Neuron 24:989-1002 (1999)) studied the effect of Ca²⁺ buffers in cerebellar Purkinje cells and estimated 360 mM [CB], they neglected effects of other high-affinity buffers and Ca²⁺ pumps dependent on [Ca²⁺]_i. [CB] was estimated to be 100 mM in our simulation.
F6	CaBuf	CB-2Ca	150	6000	2.5	100	Ca²⁺-bound state of calbindin-D_28k.
F7	CaBuf	LowAffBuf	5997	6000	99.95	100	Purkinje cells contain low-affinity buffers at high concentrations (Maeda et al. (1999) Neuron 24:989-1002). We fitted the binding ratio in our model to the binding ratio in their Fig. 6 by using two buffers. Low-affinity buffer 1 (LAB) is non-cooperative, and Hill coefficient is 1.
F8	CaBuf	LAB-Ca	3	6000	0.05	100	Ca²⁺-bound state of low-affinity buffer 1.
F9	CaBuf	LowAffBuf2	6000	6000	100	100	Purkinje cells contain low-affinity buffers at high concentration (Maeda et al. (1999) Neuron 24:989-1002). We fitted the biding ratio curve in their Fig. 6 by using two buffers. Low-affinity buffer 2 (LAB2) is cooperative, and the Hill coefficient is 2.
F10	CaBuf	LAB2-2Ca	0	6000	0	100	Ca²⁺-bound state of low-affinity buffer 2.