## 2.18.5. Carbon expenditure on fixation and active uptake.[¶](#carbon-expenditure-on-fixation-and-active-uptake "Permalink to this headline")
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At each model timestep, the overall cost of N uptake is calculated (see below) in terms of C:N ratios. The available carbon (\\(C\_{avail}\\), g m\-2 s\-1) is then allocated to two alternative outcomes, payment for N uptake, or conservation for growth. For each carbon conserved for growth, a corresponding quantity of N must be made available. In the case where the plant target C:N ratio is fixed, the partitioning between carbon for growth (\\(C\_{growth}\\)) and carbon for N uptake (\\(C\_{nuptake}\\)) is calculated by solving a system of simultaneous equations. First, the carbon available must equal the carbon spent on N uptake plus that saved for growth.

> \\\[C\_{growth}+C\_{nuptake}=C\_{avail}\\\]

Second, the nitrogen acquired from expenditure of N (left hand side of term below) must equal the N that is required to match the growth carbon (right hand side of term below).

> \\\[C\_{nuptake}/N\_{cost} =C\_{growth}/CN\_{target}\\\]

The solution to these two equated terms can be used to estimate the ideal \\(C\_{nuptake}\\) as follows,

> \\\[C\_{nuptake} =C\_{tospend}/ ( (1.0+f\_{gr}\*(CN\_{target} / N\_{cost}) + 1) .\\\]

and the other C and N fluxes can be determined following the logic above.

