The methods below are described in Garcia et al. (2011).

Culture conditions
Stock and experimental cultures of Trichodesmium erythraeum GBRTRL101 (GBR; from the Great Barrier Reef, Pacific Ocean) and IMS101 (IMS; from coastal North Carolina, Atlantic Ocean) were cultured at 24 degrees C (unless otherwise stated) in an artificial seawater medium without fixed N using a modified version of the YBCII recipe of Chen et al. (1996). Phosphate and trace metal solutions were filtered (0.2 um) and added in concentrations equivalent to the AQUIL recipe (Morel et al. 1979) to microwave- (experiment with GBR) or autoclave-sterilized (experiments with IMS) seawater. Irradiance was supplied with cool white fluorescent bulbs on a 12:12 light:dark cycle. For all experiments, cultures were grown in triplicate using a semi-continuous batch culturing method to achieve steady state exponential growth for approximately 7-10 generations prior to sampling, in order to fully acclimatize cells to treatment pCO2 and irradiance conditions. We monitored cell density every 2-3 days using microscopic cell counts. When the biomass reached approximately 100-200 trichomes per mL (~100-200 nmol C per mL), we diluted cultures with fresh medium to 50-100 trichomes per mL (~50-100 nmol C per mL). In this semi-continuous culturing method, the growth rate determines the dilution rate; this culturing technique does not attempt to control the growth rate with the dilution rate, as continuous culturing methods do.

Experimental Design: IMS growth vs. light experiment
This experiment served as a reference for determining the range of irradiance levels used in our CO2 and light experiments. Cultures of IMS were cultured at 27 degrees C in fifteen 800-mL culturing flasks on a 12:12 light:dark cycle at 25, 50, 100, 180 and 300 umol quanta per square meter per second irradiance. Once cells had achieved steady state, we determined cellular growth rates using microscopic cell counts between dilutions.

Analytical Methods: Growth rates
Growth rates were estimated by measuring relative increases in cell number per unit volume between dilutions (2-3 day periods) in steady-state cultures.

Seawater carbonate system estimates
Total dissolved inorganic carbon (DIC) was preserved in whole water samples (5-70 mL; stored at 4 degrees C) with a 5% HgCl2 solution (final concentration diluted to 0.5% HgCl2) as described in Fu et al. (2007), and estimated by acidifying 5 mL and quantifying the CO2 trapped in an acid sparging column (model: CM 5230) with a carbon coulometer (model: CM 140, UIC inc., Joliet, IL, USA). Reference material for the DIC analysis was prepared by Andrew Dickson at Scripps Institute of Oceanography. pH was measured with a pH meter (model: Orion 5 star Thermo Scientific, Beverly, MA, USA) and was monitored to ensure that perturbations of the seawater with the either air or certified pre-mixed air (Gilmore Liquid Air Company 750 ppm) resulted in the desired target pH of either ~8.2 or ~7.95. For the CO2/light manipulation experiment with GBR, samples for total DIC were taken from cultures at the same time CO2 and N2 fixation rates were estimated. For the CO2/light manipulation experiment with IMS, measurements of pH were paired with total DIC samples 5-6 days prior to measuring rates of CO2- and N2 fixation and were used to calculate pCO2 at 24 degrees C using the CO2sys program provided by Lewis and Wallace (1998) with K1 and K2 constants from Mehrbach et al. (1973) refit by Dickson and Millero (1987).

Carbonate system parameters in the experiment:

Strain	pCO2 treatment	DIC (uM)	pH	Calculated pCO2 (ppm)
IMS	Present day	2018 ±27	8.23 ±0.01	435 ± 9
IMS	100-year projected	2116 ±15	8.00 ± 0	771 ± 8
GBR	Present-day	2037 ±9	n.d.	n.d.
GBR	100-year projected	2165 ±9	n.d.	n.d.

References:
Chen, Y. B., Zehr, J. P. & Mellon, M. 1996. Growth and nitrogen fixation of the diazotrophic filamentous nonheterocystous cyanobacterium Trichodesmium sp IMS 101 in defined media: Evidence for a circadian rhythm. J. Phycol. 32:916-923. DOI: 10.1111/j.0022-3646.1996.00916.x
Dickson, A. G., & Millero, F. J. 1987. A comparison of the equilibrium constants for the dissociation of carbonic acid in seawater media. Deep-Sea Res. 34:1733-1743. DOI: 10.1016/0198-0149(87)90021-5
Lewis, E. and D. W. R. Wallace (1998). Program Developed for CO2 System Calculations. ORNL/CDIAC-105. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenessee. Available at: http://cdiac.ornl.gov/oceans/co2rprt.html.
Mehrbach, Y., Culberson, C., Hawley, J. & Pytkovicz, R. 1973. Measurement of the apparent dissociation constants of carbonic acid in seawater at atmospheric pressure. Limnol. Oceanogr. 18:897-907.
Morel, F. M. M., Rueter, J. G., Anderson, D. M. 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