Table 2.

Description of the major model variables, Ca²⁺-channel/receptor details, and feedback loops present in the ODE systems corresponding to single-cell models yielding GPCR mediated [Ca_c²⁺]-oscillations.

Model	Channels considered	Drug	Cell line/ type	ODE variables	Across plasma membrane		Across endoplasmic reticulum		Across mitochondria		Feedback loops
					Jin	Jout	JIP3 + Jleak + JCICR	JSERCA	Jin	Jout
Kummer et al. (2000) [59]	IP3R, SERCA, Ca2+-ATPase, Ca2+ entry channel on plasma membrane	ATP	Hepatocyte	[Gα], [PLC], [Cac2+], [CaER2+]	k12[PLC] + k13[Gα]	$-\frac{k_{14}\left[C{a}_c^{2+}\right]}{\left[C{a}_c^{2+}\right]+k_{15}}$	$\frac{k_{10}\left[C{a}_c^{2+}\right]\left[\mathit{PLC}\right]\left[C{a}_{\mathit{ER}}^{2+}\right]}{\left[C{a}_{\mathit{ER}}^{2+}\right]+K_{11}}$	$-\frac{k_{16}\left[C{a}_c^{2+}\right]}{\left[C{a}_c^{2+}\right]+k_{17}}$	---	---	–ve feedback of [Cac2+] on IP3R and Gα at high concentrations +ve feedback of [Cac2+] on IP3R
Larsen et al. (2004) [60]	IP3R, SERCA, Ca2+-ATPase, Ca2+ entry channel on plasma membrane, MCU, NCLX	---	---	[Gα], [PLC], [Cac2+], [CaER2+], [Camit2+]	k12[PLC] + k13[Gα]	$-\frac{k_{14}\left[C{a}_c^{2+}\right]}{\left[C{a}_c^{2+}\right]+k_{15}}$	$\frac{k_{10}\left[C{a}_c^{2+}\right]{\left[\mathit{PLC}\right]}^4}{{\left[\mathit{PLC}\right]}^4+k_{11}^4}\left(\left[C{a}_{\mathit{ER}}^{2+}\right]-\left[C{a}_c^{2+}\right]\right)$	$-\frac{k_{16}\left[C{a}_c^{2+}\right]}{k_{17}^8+\left[C{a}_c^{2+}\right]}$	$\frac{k_{20}\left[C{a}_c^{2+}\right]}{\left[C{a}_c^{2+}\right]+k_{21}}\left(\left[{\mathit{Ca}}_{\mathit{mit}}^{2+}\right]-\left[C{a}_c^{2+}\right]\right)$	$-\frac{k_{18}{\left[{\mathit{Ca}}_c^{2+}\right]}^8}{k_{19}^8+{\left[{\mathit{Ca}}_c^{2+}\right]}^8}$	–ve feedback of [Cac2+] on IP3R and Gα at high concentrations +ve feedback of [Cac2+] on IP3R
De Pittà et al. (2009) [61]	IP3R, SERCA, Leak channel on ER	Glutamate	Astrocytes	[Cac2+], [CaER2+], [CaExt2+], [IP3]	---	---	rcm′ ∞ 3n′ ∞ 3h3([CaER2+] − [Cac2+]) +rL([CaER2+] − [Cac2+])	$-\frac{{\nu }_{\mathit{ER}}{\left[C{a}_c^{2+}\right]}^2}{K_{\mathit{ER}}^2+{\left[C{a}_c^{2+}\right]}^2}$	---	---	+ve and –ve feedback of [Cac2+] on IP3R –ve feedback of [IP3] on IP3 production
Giri et al. (2014) [54]	IP3R, SERCA, Ca2+-ATPase	Norepinephrine	HeLa	[Gα], [PLC], [Cac2+], [CaER2+]	k12[PLCβ]	$-\frac{k_7\left[C{a}_c^{2+}\right]}{\left[C{a}_c^{2+}\right]+{\mathit{Km}}_6}$	$k_6\frac{\left[C{a}_{\mathit{ER}}^{2+}\right]}{\left[{\mathit{Km}}_4+\left[C{a}_{\mathit{ER}}^{2+}\right]\right]}\left[\mathit{PLC}-\beta \right]\left[C{a}_c^{2+}\right]$	$-\frac{k_8\left[C{a}_c^{2+}\right]}{\left[C{a}_c^{2+}\right]+{\mathit{Km}}_5}$	---	---	–ve feedback of [Cac2+] on IP3R and Gα at high concentrations +ve feedback of [Cac2+] on IP3R

[G_α]is the concentration of G_αsubunit,[PLC]is the concentration of PLC.

[Ca_c²⁺], [Ca_ER²⁺]and [Ca_mit²⁺]refer to Ca²⁺ concentration in the cytoplasm, endoplasmic reticulum, and mitochondria respectively.