Table 1.

Model initial conditions and parameters

Species/Constant Value Rationale 
R for M1 500 µm−2 From fluorescencea 
R for eP2Y2 1 µm−2 Fig. S7; Fig. 2 A in Dickson et al., 2013  
G (G proteins) 40 µm−2 To fit concentration–response curve of currenta 
P (PLC) 10 µm−2 To fit concentration–response curve of currenta 
(free) PIP2 5,000 µm−2 From distribution of PH domainsb 
Bound PIP2 10,000 µm−2 See Fig. 6 B; generally (fold_PIP2-1) * 5,000 µm−2 
PI(4)P 4,000 µm−2 To allow doubling of PIP2 by PIP 5-kinase 
PI 140,000 µm−2 As previouslyb 
IP3 (cytosol) 0.01 µM Steady state of basal PLC and IP3ase 
DAG 23 µm−2 Steady state of basal PLC and DAGase 
Ca2+ (cytosol) 0.13 µM Steady state of basal IP3R Ca2+ flux and SERCA (bistable equilibrium, also stable at 0.02 µM) 
Ca2+ (ER) 400 µM Jafri and Keizer, 1995; Duman et al., 2008  
0.8 h3 is the fraction of noninactivated IP3Rs 
LIBRAvIII 6 µM As estimated from fluorescencea 
IP3 (pipette) 1–100 µM Used only to simulate calibration experiment 
Fura-4F 1 µM Excessive buffering in the model above 1 µM 
C1 domain 0.5 µM From fluorescence assuming low expressiona; reproduces 1 nM Oxo-M response in relation to 10 µM Oxo-M response 
size_pipette 10,000 µm3 Reproduce steady-state values of Fig. 6 D in Dickson et al., 2013  
Surface (membrane) 1,500 µm2 From cell capacitance 
size_cytosol 2,500 µm3 From surface–volume ratio 
size_ER 462 µm3 18% cytosol, from Jafri and Keizer, 1995, and Duman et al., 2008. 
fold_PIP2 See Fig. 6 B  
k_4K (rest) 0.00078 s−1 KCNQ2/3 current recovery after Oxo-Mb; generally fold_PIP2 * 0.00023 s−1 
k_5K (rest) 0.06 s−1 KCNQ2/3 current recovery after VSPb; generally fold_PIP2 * 0.02 s−1 
k_4K (agonist) & k_5K (agonist) see Fig. 7 (E and F) c Concentration dependence informed by Oxo-M dose–response curveb; transition smoothed by an exponential to avoid transients 
k_4K (recovery) & k_5K (recovery) see Fig. 7 (E and F) c KCNQ2/3 current recoveryb; transition smoothed by an exponential to avoid transients 
k_PLC 0.6 µm2s−1 From KCNQ2/3 inhibitionb; fold_PIP2 * 0.2 µm2s−1 
k_IP3ase 0.08 s−1 Reproduce duration of LIBRAvIII and Fura-4F responses (Figs. 6 and 4 in Dickson et al., 2013); as in Xu et al., 2003  
k_DAGase 0.05 s−1 To fit C1 decay 
KIP3 (IP3R0.1 µM To have maximum activity with 1 nM Oxo-M 
KCa (IP3R0.2 µM Bezprozvanny et al., 1991  
kCa (IP3R0.2 µM Bezprozvanny et al., 1991  
kP (SERCA1.3 µM Duman et al., 2008  
vP (SERCA0.3 Height of plateau in Fura-4F response to Oxo-M; see Fig. S8 B in Dickson et al., 2013  
k_pipette 0.03 s−1 Giving approximately a time constant of 50 s as observed for diffusion of dyes and the onset of Fig. 6 B in Dickson et al., 2013  
KD_LIBRAvIII 0.5 µM Tanimura et al., 2009  
KD_C1 0.3 µM Oxo-M concentration–response of C1/CAAX FRET 
KD_Fura-4F 0.77 µM Invitrogen 
Species/Constant Value Rationale 
R for M1 500 µm−2 From fluorescencea 
R for eP2Y2 1 µm−2 Fig. S7; Fig. 2 A in Dickson et al., 2013  
G (G proteins) 40 µm−2 To fit concentration–response curve of currenta 
P (PLC) 10 µm−2 To fit concentration–response curve of currenta 
(free) PIP2 5,000 µm−2 From distribution of PH domainsb 
Bound PIP2 10,000 µm−2 See Fig. 6 B; generally (fold_PIP2-1) * 5,000 µm−2 
PI(4)P 4,000 µm−2 To allow doubling of PIP2 by PIP 5-kinase 
PI 140,000 µm−2 As previouslyb 
IP3 (cytosol) 0.01 µM Steady state of basal PLC and IP3ase 
DAG 23 µm−2 Steady state of basal PLC and DAGase 
Ca2+ (cytosol) 0.13 µM Steady state of basal IP3R Ca2+ flux and SERCA (bistable equilibrium, also stable at 0.02 µM) 
Ca2+ (ER) 400 µM Jafri and Keizer, 1995; Duman et al., 2008  
0.8 h3 is the fraction of noninactivated IP3Rs 
LIBRAvIII 6 µM As estimated from fluorescencea 
IP3 (pipette) 1–100 µM Used only to simulate calibration experiment 
Fura-4F 1 µM Excessive buffering in the model above 1 µM 
C1 domain 0.5 µM From fluorescence assuming low expressiona; reproduces 1 nM Oxo-M response in relation to 10 µM Oxo-M response 
size_pipette 10,000 µm3 Reproduce steady-state values of Fig. 6 D in Dickson et al., 2013  
Surface (membrane) 1,500 µm2 From cell capacitance 
size_cytosol 2,500 µm3 From surface–volume ratio 
size_ER 462 µm3 18% cytosol, from Jafri and Keizer, 1995, and Duman et al., 2008. 
fold_PIP2 See Fig. 6 B  
k_4K (rest) 0.00078 s−1 KCNQ2/3 current recovery after Oxo-Mb; generally fold_PIP2 * 0.00023 s−1 
k_5K (rest) 0.06 s−1 KCNQ2/3 current recovery after VSPb; generally fold_PIP2 * 0.02 s−1 
k_4K (agonist) & k_5K (agonist) see Fig. 7 (E and F) c Concentration dependence informed by Oxo-M dose–response curveb; transition smoothed by an exponential to avoid transients 
k_4K (recovery) & k_5K (recovery) see Fig. 7 (E and F) c KCNQ2/3 current recoveryb; transition smoothed by an exponential to avoid transients 
k_PLC 0.6 µm2s−1 From KCNQ2/3 inhibitionb; fold_PIP2 * 0.2 µm2s−1 
k_IP3ase 0.08 s−1 Reproduce duration of LIBRAvIII and Fura-4F responses (Figs. 6 and 4 in Dickson et al., 2013); as in Xu et al., 2003  
k_DAGase 0.05 s−1 To fit C1 decay 
KIP3 (IP3R0.1 µM To have maximum activity with 1 nM Oxo-M 
KCa (IP3R0.2 µM Bezprozvanny et al., 1991  
kCa (IP3R0.2 µM Bezprozvanny et al., 1991  
kP (SERCA1.3 µM Duman et al., 2008  
vP (SERCA0.3 Height of plateau in Fura-4F response to Oxo-M; see Fig. S8 B in Dickson et al., 2013  
k_pipette 0.03 s−1 Giving approximately a time constant of 50 s as observed for diffusion of dyes and the onset of Fig. 6 B in Dickson et al., 2013  
KD_LIBRAvIII 0.5 µM Tanimura et al., 2009  
KD_C1 0.3 µM Oxo-M concentration–response of C1/CAAX FRET 
KD_Fura-4F 0.77 µM Invitrogen 
a

Falkenburger et al., 2010a.

b

Falkenburger et al., 2010b.

c

The steady-state Oxo-M concentration dependence of PIP2 synthesis was inferred from the concentration dependence of KCNQ2/3 inhibition (Fig. 9 C in Falkenburger et al., 2010b). Specifically, k_4K values that reproduced the Oxo-M concentration dependence of KCNQ2/3 inhibition (markers in Fig. 7 E) were fitted by a sigmoid and the concentration dependence of k_5K computed with the same midpoint and slope. The extent of PI 4-kinase and PIP 5-kinase acceleration was fine-tuned to reproduce the >90% depletion of PIP2 and 80% depletion of PIP measured biochemically for 10 µM Oxo-M (i.e., 7.5-fold acceleration of the PI 4-kinase 10-fold acceleration of the PIP 5-kinase). In addition, the onset of the acceleration of PIP2 synthesis was smoothed by an exponential to avoid positive PIP2 transients resulting from too fast acceleration (<1-s time constant); the recovery of PIP2 synthesis to resting values was smoothed by an exponential (5-s time constant) to avoid negative PIP2 transients upon Oxo-M wash (Fig. 7 F; see Fig. S9 in Dickson et al., 2013). Thus, k_4K (agonist) = k_4K_rest + stim_4K * (1 − e−t/τ_onset) with stim_4K = 0.0078/(1 + e4.86-278*agonist) and k_5K (agonist) = k_5K_rest + stim_5K * (1 − e−t/τ_onset) with stim_5K = 0.2 /(1 + e4.86-278*agonist); τ_onset = 1 s. k_4K_recovery = k_4K_rest + stim_4K * e(end−t)/τ_recovery, and k_5K_recovery = k_5K_rest + stim_5K * e(end−t)/τ_recovery with τ_recovery = 5 s.

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