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: CO2/light experiments
Two separate experiments were conducted with two T. erythraeum strains: GBR and IMS. Cultures of Trichodesmium sp. (GBR) were grown in 12 1-L polycarbonate bottles at 35 and 220 umol quanta per square meter per second at two concentrations of CO2 (see below). In the experiment with IMS, cultures were grown in 18 1-L polycarbonate bottles at 38, 100 and 220 umol quanta per square meter per second at two concentrations of CO2. Both experiments were conducted on a 12:12 light:dark cycle at 24 degrees C.

Within each irradiance treatment for both experiments, cultures were bubbled with 0.2 um filtered lab air (for the experiment with IMS) or pre-mixed air (prepared by Gilmore Liquid Air Company, South El Monte, CA, USA) containing present-day (380 ppm certified value for the experiment with GBR) and elevated, 100-year predicted (750 ppm certified value for both CO2 experiments) atmospheric CO2 concentrations. The rate of bubbling was visually monitored daily to ensure that cultures were bubbled with sufficient positive gas flow to keep the pH of the cultures at an appropriate level for respective CO2 treatments. Based on rates of gas utilization from the supply cylinders, estimated gas flow rates were between 30-60 mL per min.

Due to incubator availability constraints in the laboratory, the light manipulation and the CO2/light manipulation experiments were conducted at slightly different temperatures. While we do not have growth and N2 fixation rates in response to temperature for GBR, rates of Trichodesmium isolate IMS are not significantly different from each other at 24 degrees C and 27 degrees C (Breitbarth et al. 2007).

N2 fixation
We estimated N2 fixation rates with two methods: the acetylene reduction method and the 15N2 isotope tracer method. For the acetylene reduction method, described in Capone (1993), two 10-mL samples from each experimental replicate were incubated under treatment-specific conditions of irradiance and temperature in air-tight vials for ~10 hours (starting from the beginning of the light period) with 2 mL acetylene in 16.75 mL of headspace. The amount of ethylene accumulation was then estimated in 200 uL headspace gas with a gas chromatograph (model: GC-8A, Shimadzu Scientific Instruments, Columbia, MD, USA) at the 2nd, 4th, 6th, and 8th hour of the light period yielding 3 two-hour rates of ethylene accumulation. The accumulation of ethylene over 8 hours was used to calculate total gross N2 fixation rates (see explanation below) using a conversion ratio of 3:1 for acetylene to N2 reduction. Maximum gross N2 fixation rates were determined by finding the maximum rate of ethylene accumulation over a ~2-hour period. To calculate the concentration of ethylene in seawater from the concentration in the vial headspace, we used the Bunsen coefficient (0.088; from Breitbarth et al. 2004) for ethylene in seawater at 24 degrees C and a salinity of 35. We also estimated N2 fixation rates with the 15N2 isotope tracer method (Mulholland and Bernhardt 2005) by injecting 160 uL of highly enriched (99%) 15N2 gas into combusted (4 hours, 450 degrees C) 159 mL gas tight bottles filled with culture (without headspace) from a treatment replicate (triplicate samples for each experimental treatment). Culture samples were then incubated for 12 hours under treatment-specific conditions of irradiance and temperature during the light period only and we terminated incubations by filtering samples onto pre-combusted (450 degrees C, 4 hours) Whatman GF/F filters. pH was not determined in culture subsamples that were used to estimate N2 fixation after the incubation period in our experiments. Samples were stored frozen and dried before analysis with a Europa 20/20 isotope ratio mass spectrometer equipped with an automated nitrogen and carbon analyzer (ANCA). Estimates of N2 fixation made with the isotope tracer (15N2) method should represent net N2 fixation rates, because it estimates fixed N that is retained within cells. We assumed that the acetylene reduction method estimates gross N2 fixation rates because this estimate includes N fixed regardless of fate (see Mulholland & Bernhardt 2005; Mulholland et al. 2004). We estimated net 15N2 fixation rates in our experiment with IMS, but not in our experiment with GBR.

Carbon fixation
We inoculated two 30 mL samples from each treatment replicate with 25 or 50 uL of 1 mCurie (mCi) stock solution of sodium bicarbonate (H14CO3-; 0.83-1.7 uCi per mL final concentration). Samples were incubated for 24 hours under treatment-specific conditions of irradiance and temperature and then filtered onto Whatman GF/F filters and rinsed 3 times with ~5 mL filtered seawater to remove extracellular H14CO3-. Non-photosynthetically driven 14C incorporation was determined by incubating replicate culture samples (30 mL) for 24 hours in opaque bottles at the experimental temperature with the same concentration of H14CO3-; these values were subtracted from measured total 14C incorporation to estimate photosynthetic incorporation. The total radioactivity of H14CO3- was determined by stabilizing 25 or 50 uL of the 1 mCi H14CO3- with 100 uL of a basic solution of phenylethylamine (99%) before adding 4 mL of Ultima Gold® XR (PerkinElmer, Shelton CT, USA) Radioactivity of 14C was determined on a Multi-purpose Scintillation Counter (model: LS-6500, Beckman Coulter, Fullerton, CA, USA). Carbon fixation rates (moles of CO2 fixed per unit time) were estimated by calculating the ratio of the radioactivity of photosynthetically-driven 14C incorporation into cells over 24 hours to the total radioactivity of H14CO3- and multiplying that ratio by the total dissolved inorganic carbon concentration (DIC).

Trichome length
In our light/CO2 manipulation experiment with IMS, trichome length was measured in samples collected from treatment-specific acclimated cultures 2 days prior to and on the final sampling day. Length data from the two time points were averaged and the resulting mean value from each experimental replicate was used in our analyses.

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:
Breitbarth, E., Mills, M. M., Friedrichs, G. & LaRoche, J. 2004. The Bunsen gas solubility coefficient of ethylene as a function of temperature and salinity and its importance for nitrogen fixation assays. Limnol. Oceanogr.: Methods 2:282-288. DOI: 10.4319/lom.2004.2.282
Breitbarth, E., Oschlies, A., & LaRoche J. 2007. Physiological constraints on the global distribution of Trichodesmium - effect of temperature on diazotrophy. Biogeosciences. 4:53-61. doi:10.5194/bg-4-53-2007
Capone, D. G. 1993. Determination of nitrogenase activity in aquatic samples using the acetylene reduction procedure. In: Kemp, P. F., J. J. Cole, B. F. Sherr, E. B. Sherr (eds). Handbook of methods in aquatic microbial ecology. Lewis Publishers, Boca Raton, FL, p 621–631.
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
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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
Mulholland, M. R. and Bernhardt, P. W. 2005. The effect of growth rate, phosphorus concentration and temperature on N2-fixation, carbon fixation, and nitrogen release in continuous cultures of Trichodesmium IMS101. Limnol. Oceangr. 50:839-849.

tricho_fixation.csv