Table 2.

Summary of Hill function parameters used in the present model (Figure 1 and eq. 2; for detailed equations see (Buchwald, 2011)).

Rate	Var.	CHf	n	Rmax	Property and comments
Roxy	coxy	1 μM	1	−0.034 mol/m3/s	Oxygen consumption, basic part. Cut to 0 below critical value, coxy < Ccr,oxy.
Roxy	cgluc	7 mM	2.5	N/A	Oxygen consumption, φo,g metabolic part. Follows increase in metabolic demand; parallels second-phase insulin secretion rate.
Rgluc	cgluc	10 μM	1	−0.028 mol/m3/s	Glucose consumption. Under most conditions, it has no significant influence on insulin secretion.
Rins,ph2	cgluc	7 mM	2.5	H: 1.8×10−5 mol/m3/s M: 3×10−5 mol/m3/s	Insulin secretion rate (second-phase). Total secretion rate is modulated by local oxygen availability (last row). H and M denote values used for human and murine islets, respectively.
Rins,ph1	c′t (∂cgluc/∂t)	0.03 mM/s	2	H: 10×10−5 mol/m3/s M: 21×10−5 mol/m3/s	Insulin secretion rate (first-phase). Modulated to have maximum sensibility around cgluc = 5 mM and be limited at very large or low cgluc. Hill slope of modulating function, σi1,g, changed to 2.5 (previously 4) for a wider range response in phase 1. Release rates kinsL are H: 0.003, M: 0.006 s−1.
Rins, φo,g	coxy	3 μM	3	N/A	Oxygen modulation of insulin secretion rate, φo,g. Limits insulin secretion if coxy becomes critically low.