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**Cost of Active Uptake**

The cost of nitrogen (N) uptake from the soil, for each soil layer, is influenced by two key parameters:

1. The relationship between soil N content and N uptake
2. The relationship between root carbon (C) density and N uptake

For non-mycorrhizal uptake, the cost is calculated as:
$N_{cost,nonmyc,j} = \frac{k_{n,nonmyc}}{N_{smin,j}} + \frac{k_{c,nonmyc}}{c_{root,j}}$

For active uptake, the cost is calculated as:
$N_{cost,active,j} = \frac{k_{n,active}}{N_{smin,j}} + \frac{k_{c,active}}{c_{root,j}}$

The value of $k_{n,active}$ varies depending on whether the uptake is by ecto- or arbuscular-mycorrhizal fungi:
$k_{n,active} = \left\{\begin{array}{lr} k_{n,Eactive}& e = 1\\ k_{n,Aactive}& e = 0 \end{array}\right\}$

where $e=1$ represents the fraction of the plant functional type (PFT) that is ectomycorrhizal, and $e=0$ represents the fraction that is arbuscular-mycorrhizal.