We construct a mechanistic inverse model of the ocean’s coupled phosphorus, silicon, and iron cycles and analyze the response of the biological pump to perturbations in the iron supply. The nutrient cycles are embedded in a data-assimilated steady global ocean circulation. Biological nutrient uptake is parameterized in terms of nutrient, light, and temperature limitations on growth for three functional classes of phytoplankton. A matrix formulation of the discretized nutrient equations permits efficient numerical solutions that allow optimization of key biogeochemical parameters by minimizing the misfit between modelled and observed concentrations. We perturb the iron supply for a variety of scenarios and systematically quantify the teleconnections in nutrient utilization across the global ocean ecosystem. Specifically, Green-function techniques are used to quantify the transport pathways and timescales with which the perturbations in the nutrient fields are propagated, thus mediating the teleconnections. We find that carbon and opal export can have opposite responses to changes in the iron supply. For example, a globally uniform reduction in the aeolian iron input increases opal export outside of the Southern Ocean but decreases carbon export there. A path-density transport diagnostic applied to the nutrients shows that enhanced iron limitation can untrap silicon from the Southern Ocean and increase opal export outside of the Southern Ocean. However, enhanced iron limitation also leads to non-diatom phytoplankton exporting less carbon in the tropics and to an increase in the biomass fraction of diatoms, which increases the Si:C export ratio. In addition, we investigate the amplitudes of the iron perturbations necessary to eliminate iron limitation and the resulting changes in the patterns of macronutrient limitation.