The mathematics of tanning

Table 3 Parameters of the model with approximate magnitudes, references, descriptions and units

Parameter	Appr. value	Reference	Description	Unit
γ_s	10^-1	Optimized from data	Signal substance degradation rate	1/h
f _min	10³	Optimized from data	Constitutive melanin production	tau/h
f _ind	10³	Optimized from data	Tanning ability	tau/h
A	10⁰	Optimized from data	Dendrite growth rate	cd/h
γ_M	10^-2	Optimized from data	Melanin degradation rate	1/h
w	10^-1	Derived from [40]	Cell movement rate	cell/h
T _c	25	Derived from [40]	Thickness, corneum	cd
T _g	2	Derived from [40]	Thickness, granulosum	cd
T _s	4	Derived from [40]	Thickness, spinosum	cd
T _b	1	Derived from [40]	Thickness, basale	cd
area	5	Derived from [40, 42, 48]	Area of melanin unit	cd*cd

Unit of volume is number of cells and unit of length is cell diameter (cd). Melanin amount is measured in the arbitrary unit of [42] (tau). Estimated values are related to each other and the rest of the model. Their absolute values are not regarded as predictions.