We construct a data-constrained model of the ocean’s coupled macronutrient and micronutrient cycles. The model focuses initially on phosphate and dissolved iron. The nutrient cycling is embedded in a data-assimilated steady ocean circulation. Biological nutrient uptake is parameterized in terms of nutrient and physical limitations on plankton growth, without the need of tracers for the concentration of phytoplankton. The uptake parameterization is formulated using a novel, versatile functional form that is able to capture different plankton classes, both in terms of size and species. A matrix formulation of the discretized partial differential equations allows for very efficient solutions and facilitates the objective optimization of key model parameters by minimizing the mismatch with the observed global nutrient climatology. This approach matches observed phosphate and iron concentration with RMS errors of less than 10%. In the near future, the model will allow us to quantify the timescales and pathways with which perturbations in the iron supply are communicated throughout the world ocean’s ecosystem. Including the ocean’s silicon cycle will elucidate the role of diatoms in the biological pump and the sensitivity of elemental ratios to iron perturbations.