Culturing and experimental conditions
Experimental cultures were grown with a semi-continuous culturing method at 28 degrees C in autoclave-sterilized artificial seawater medium with nutrients added in concentrations equivalent to the recipe for the Aquil medium (except for NO3-), as in Garcia et al. (2011) and originally described by Morel et al. (1979).

P-light-CO2 experiment and cellular growth rates
In the P-light-CO2 experiment, triplicate cultures were diluted every two days to 5 x 103 cells per mL with medium that contained treatment concentrations of PO43- ranging from 0.1 - 4.0 umol per L. Cells were counted microscopically in each replicate culture with a hemocytometer at the end of each dilution period, and steady state growth rates were calculated from an increase in culture cell number per unit volume between 2-3 dilution periods (4-6 days) after cultures were acclimated to treatment conditions for 7-10 generations.

A low cell biomass was necessary to control CO2 concentrations in cultures and a consistent dilution period reduced variations in growth rates between dilutions. In the P-light-CO2 experiment cultures were grown in 1 L polycarbonate bottles at 40 or 150 umol quanta per square meter per second and bubbled with 19 Pa or 81 Pa pCO2 pre-mixed air supplied and certified by Gilmore Liquid Air Company. Culture pH was measured with a pH meter using the National Bureau of Standards (NBS) scale for seawater pH measurements (model: Orion 5 star, Thermo Scientific). For the P-light-CO2 experiment seawater was bubbled and pre-equilibrated with treatment concentrations of pCO2 before measuring pH and adding nutrients. This was essential to maintain high pH values in the 19 Pa pCO2 treatments. The investigators excluded data from the high light, 19-Pa pCO2 treatment where the pH was >0.05 units lower than the expected pH range of 8.45-8.49 (specifically, the 0.4, 0.8, 2.0 umol total P per L treatments).

Light was supplied on a 12:12 light:dark cycle with cool white fluorescent bulbs. The investigators terminally sampled each replicate culture 24 hours after the last dilution for N2-fixation rates and CO2-fixation rates, and at this point they also sampled for P-uptake rate measurements and cellular P content from each replicate in the P-light-CO2 experiment. To acclimate cultures to low P conditions in the P-light-CO2 experiment, the investigators consecutively reduced the concentration of P by transferring cultures acclimated to neighboring P concentrations in the experimental matrix. Steady-state growth was not achievable in treatments with the lowest P concentrations because growth rates continuously declined when the concentration of P was reduced to those concentrations. In these cases, the investigators sampled cultures before growth rates became negative, except for the low-light, low-P, low-pCO2 treatment, which did have a negative growth rate.

Phosphorus-uptake rates
Phosphorus-uptake rates were determined with radioactive 33PO43- over 24 h. The investigators inoculated 200 mL culture samples from each treatment replicate with 0.46 KBq 33PO43- mL-1, yielding a final added concentration of 0.33 pmol 33PO43- mL-1. The investigators accounted for 33PO43- that was not incorporated into the cell by inoculating parallel 200 mL culture samples (pooled from 3 experimental replicates) with the same final activity and concentration of 33PO43- just before filtering at the end of the 24 h incubation period.

Cellular P
Near the end of the light period (9th-11th hour), samples were filtered for cellular P content (50 mL) from each replicate onto combusted (450 degrees C, 4 h) Whatman GF/F filters and measured them as in Fu et al. (2005). Filtered samples were rinsed 3 times with 2 mL 0.017 mol L-1 Na2SO4 and placed in 20 mL glass scintillation vials with 2 mL 0.017 MgSO4, which was evaporated at ~80 degrees C over a few days. Filters were combusted at 450 degrees C for 2 h to release P from organic compounds. After cooling, filters were reheated to 80 degrees C along with 5 mL 0.2 mol per liter HCl for 30 minutes and phosphate concentrations were estimated spectrophotometrically with the colorimetric assay described by Lebo and Sharp (1992).

References:
Garcia, N. S., F.-X. Fu, , C. L. Breene, P. W. Bernhardt, M. R. Mulholland, J. A. Sohm, and D. A. Hutchins. 2011. Interactive effects of irradiance and CO2 on CO2- and N2 fixation in the diazotroph Trichodesmium erythraeum (Cyanobacteria). J. Phycol. 47: 1292-1303. DOI: 10.1111/j.1529-8817.2011.01078.x

Lebo, M. E., and J. H. Sharp. 1992. Modeling phosphorus cycling in a well-mixed coastal plain estuary. Estuar. Coastal Shelf Sci. 35: 235-252. doi: 10.1016/S0272-7714(05)80046-0

Morel, F. M. M., J. G. Rueter, D. M. Anderson, and Guillard, R. R. L. 1979. Aquil: Chemically defined phytoplankton culture medium for trace metal studies. J. Phycol. 15:135-141. DOI: 10.1111/j.1529-8817.1979.tb02976.x