Dynamics of glucose and insulin concentration connected to the β ‐cell cycle: model development and analysis

Table 1 Model parameters

	Value	Definition
p ₁	$6.0594 × 1 0 − 5 1 min$	transition rate G₁ → S
p ₂	$4.9861 × 1 0 − 3 1 min$	transition rate S → G₂/M
p ₃	$8.9444 × 1 0 − 4 1 min$	transition rate G₂/M → G₁
p ₄	$3.3194 × 1 0 − 4 1 min$	apoptosis rate
p ₅	$0.056 100 ml mg$	influence factor of glucose
p ₆	0.3 $mg 100 ml min$	rate of glucose production
p ₇	0.003 $1 min$	glucose effectiveness
		at zero insulin
p ₈	$360 × 1 0 − 3 100 ml mg min$	insulin sensitivity
p ₉	0.622 $1 min$	secretion rate of insulin
p ₁₀	0.3 $1 min$	decay rate of insulin
p ₁₁	0.0337 $1 min$	rate of provision increase
p ₁₂	1.72×10⁻⁹ mg	average insulin amount per β‐cell
bv	3.33 ml	blood volume of 35g mouse
f	0.5	proportionality factor
h	5	Hill coefficient
P ₀	186.506 $mg 100 ml$	Michaelis constant
$X ̄ max$	1.65×10⁻³ mg	maximal amount of insulin
		per pancreas
k	3.3	Hill coefficient
C	149.78 $mg 100 ml$	Michaelis constant

Parameters of model (9) used for the simulations shown in Figures5 and6 in Section ’Simulation’. The parameter values are based on biological experiments of[4, 20, 31, 32].