Table 1. Variables and parameters in the model.

Symbols	Implications	Values
L, L1, L2	ligand concentration	Variable (in nM)
R, R1, R2	number of free surface receptors	Variable
Ri, R1i, R2i	number of intracellular free receptors	Variable
LR*, L1R1*, L2R2*	number of active receptor-ligand complex	Variable
LRd, L1R1d, L2R2d	number of desensitized receptor-ligand complex	Variable
LRi, L1R1i, L2R2i	number of internalized receptor-ligand complex	Variable
Rtot	total number of receptors	25,000 [25]
kf	ligand receptor association rate	8.4×107 M−1 s−1 [23], [35]
kr	low-affinity ligand receptor dissociation rate	0.37 s−1 [23], [27]
kdes	desensitization rate	0.065 s−1 for desensitizable receptor[23], [27]; 0 for nondesensitizable receptor
ki	internalization rate	0.0033 s−1 [23], [36]
kup	up-regulation rate	0.004 s−1 [23], [24]
Lmax, L1max, L2max	highest concentration at the gradient center	17.6 nM [25] if no additional caption
L0	basal ligand concentration	0 nM [25]
A	radius of the gradient region	1000 µm [25]
ρ, ρ1, ρ2	distance from the gradient center	Variable (in µm) [25]
n	power of the gradient function	3 [25]

The numerical values for parameters are the same for both ligand-receptor pairs unless stated otherwise.