Table 2. Parameters.

Parameter	Units	Meaning	Value
t0	[mo]	starting age for numerical integration of slow model, in months	0
tend	[mo]	final age for numerical integration of slow model, in months	1080
Bmax	[Mc]	maximal beta-cell population size (carrying capacity)	4000
B0	[Mc]	baseline value of B at slow initial time (age t0)	1000
νBG	[#]	exponent of the Hill function describing replication stimulation by glycemia	2
GB50	[mM]	glycemia of half-maximal beta-cell replication stimulation	9
η0	[/mo]	baseline value of η at slow initial time (age t0)	0.04
kXηG0	[/mo]	baseline value of kXηG at slow initial time (age t0)	0.02
kηendprop	[#]	Level of kη at the end of life (at tend) as proportion of kη start	0.4
kGG	[/mo]	rate of convergence of fasting glycemia from start-of-day to end-of-day values	0.4
Gf0	[mM]	fasting glycemia at age t0	4.2
kXA	[/mo]	spontaneous elimination rate constant of (glycosylated) Haemoglobin	0.4
A0	[%]	baseline value of A at slow initial time (age t0)	5
VG	[L/kg]	glucose distribution volume	0.19
VI	[L/kg]	insulin distribution volume	0.19
W	[kg]	experimental subject’s body weight	70
kXIstart	[/min]	apparent first-order elimination rate constant for insulin at baseline (at age t0)	0.05
kXIend	[/min]	apparent first-order elimination rate constant for insulin at the end of a normal life (e.g. at age 90 years)	0.045
$k_{XGI0}^{max}$	[/min]	baseline value of $k_{XGI}^{max}$ at slow initial time (age t0)	0.08
$k_{XGI0}^0$	[/min/pM]	baseline value of $k_{XGI}^0$ at slow initial time (age t0)	0.00015
$f_{kXGI}^{min}$	[#]	minimum value possible for $k_{XGI}^{max}$ as proportion of its baseline value at age t0	0.05
tkXGIstart	[mo]	starting time of $k_{XGI}^{max}$ decrease	216
νkXGI	[#]	exponent for $k_{XGI}^{max}$ decrease	3
tkXGI50	[mo]	time of half-maximal $k_{XGI}^{max}$ decrease	800
λGI0	[/pM/mM]	baseline value of λGI at slow initial time (age t0)	0.015
$f_{\lambda GI}^{min}$	[#]	minimum value possible for λGI as proportion of its baseline value at age t0	0.05
tλGIstart	[mo]	starting time of λGI decrease	216
νλGI	[#]	exponent for λGI decrease	8
tλGI50	[mo]	time of half-maximal λGI decrease	550
$k_{IB0}^{max}$	[pmol/min /Mc]	baseline value of $k_{IB}^{max}$ at slow initial time (age t0)	0.5
$f_{kIB}^{min}$	[#]	minimum value possible for $k_{IB}^{max}$ as proportion of its baseline value at age t0	0.25
tkIBstart	[mo]	starting time of $k_{IB}^{max}$ decrease	216
νkIB	[#]	exponent for $k_{IB}^{max}$ decrease	2.5
tkIB50	[mo]	time of half-maximal $k_{IB}^{max}$ decrease	950
kJS0	[/min]	baseline value of kJS at slow initial time (age t0)	0.0235
αLyKxgi	[/mo]	rate of onset of effect of Ly on kXGI	0.1
βLyKxgi	[/mo]	rate of decay of effect of Ly on kXGI	0.009
LyKxgiCurr	[#]	maximal effect of Ly therapy as proportional increase of kXGI above current level.	0
αLyLamgi	[/mo]	rate of onset of effect of Ly on λGI	0.3
βLyLamgi	[/mo]	rate of decay of effect of Ly on λGI	0.01
LyLamgiCurr	[#]	maximal effect of Ly therapy as proportional increase of λGI above current level.	0
αLyKjs	[/mo]	rate of onset of effect of Ly on kJS	0.05
βLyKjs	[/mo]	rate of decay of effect of Ly on kJS	0.002
LyKJS	[#]	Effect of Ly therapy on gastric emptying rate kJS as fraction of current value, when positive accelerates gastric emptying	0
τ0	[min]	starting time for numerical integration of fast model, in minutes after midnight	360
τend	[min]	final time for numerical integration of fast model, in minutes	1800
τ1	[min]	time of breakfast in minutes after midnight	420
$M_1^{\mathtt{\text{gluc}}}$	[mmol]	breakfast contribution to circulating glucose	417
τ2	[min]	time of lunch in minutes after midnight	720
$M_2^{\mathtt{\text{gluc}}}$	[mmol]	lunch contribution to circulating glucose	280
τ3	[min]	time of dinner in minutes after midnight	1080
$M_3^{\mathtt{\text{gluc}}}$	[mmol]	dinner contribution to circulating glucose	280
$k_{Xgbrox}^{max}$	[mmol /kgBW /min]	maximal brain glucose oxidation	0.0059
Gbrox50	[mM]	glycemia of half-maximal brain glucose oxidation	0.5
kGJ	[/min]	transfer rate constant from intestine to plasma, absorption rate	0.025
fGJ	[#]	proportion of absorbed nutrients entering the circulation	0.9
kXG	[/min]	first-order insulin-independent glucose tissue uptake rate	0.001
$k_{GI}^{max}$	[mmol /min]	maximal rate of insulin-dependent hepatic glucose production	0.75
LG50	[pM]	glucagon concentration of half-maximal stimulation of gluconeogenesis or glycogen lysis	0.05
L0	[pM]	fasting Glucagon plasma concentration	15
kXL	[/min]	first-order glucagon elimination rate from plasma	0.04
$f_{LG}^{min}$	[#]	minimum possible value for glucagon secretion rate as proportion of its max value at zero glycemia	0.15
λLG	[/mM]	exponential rate of decay of glucagon secretion with increasing glycemia	0.55
fIJ	[#]	maximum jejunal glucose content additional effect (as proportion of plasma glucose effect) towards insulin secretion by pancreas, max incretin effect	1.15
JG50	[mmol]	jejunal glucose content at which incretin effect is half-maximal	200
νIG	[#]	exponent for increase in β-cell-mass-specific insulin secretion rate with increasing glycemia	3
GI50	[mM]	glycemia of half-maximal β-cell-mass-specific insulin secretion rate	14.4
ClInulin	[L/kgBW /min]	Inulin clearance or glomerular filtration rate	0.0018
Furine	[L/kgBW /min]	Urinary flow	0.00002
Du	[/z2]	tubular glucose diffusion coefficient	0
$k_{GU}^{max}$	[mmol /kgBW /min]	maximal rate of glucose transfer from pre-urine to plasma (glucose reabsorption)	0.027
CGU50	[mM]	tubular glucose concentration of half-maximal transport	19
λVZ	[/z]	Exponent for decay of water or volume flow along tubule	8
λQZ	[/z]	Exponent for decay of glucose reabsorption along tubule	7
If0	[pM]	fasting insulinemia at age t0	19.8
IKXGI50	[pM]	insulinemia of haf-maximal effect on peripheral tissue glucose uptake	333
$k_{GL}^{max}$	[mmol /min]	maximal rate of glucagon-dependent, treatment-insensitive hepatic glucose production	0.0685
$k_{LG}^{max}$	[pM/min]	maximal rate of glucose-dependent glucagon secretion effect on glucagon concentration	2.56
kη start	[/mo2]	spontaneous recovery rate of the pancreas at t0	0.00085
$k_{BB}^{min}$	[/mo]	minimum value of the replication rate kBB	-0.0104
kAG	[%/mo /mM]	rate constant of production of glycosylated haemoglobin from circulating glucose	0.395