Trichodesmium IMS101 stock culture was grown in nitrogen-free YBCII medium (Chen et al., 1996) containing 5 μM methylphosphonate (MPn, Aladdin, CAS 993-13-5, ≥98%). The stock culture was kept at 27°C, and the light intensity was set at 110 μmol photons m⁻² s⁻¹ with a light–dark cycle of 12:12 h (light source: white LED tubes; light period: 08:00 to 20:00 local time). The cultures were run at five different temperatures (16, 20, 23, 27, 31°C), with all other environmental conditions maintained identical to those of the stock cultures. No other P source or dissolved inorganic phosphorus (DIP) was intentionally added to the cultures. The experimental cultures were kept in the exponential growth phase through regular dilutions performed every 3–15 days depending on the temperatures and growth rates. The semi-continuous cultures ensured that chlorophyll-a (Chl-a) concentrations consistently fell within the range of 0.005–0.05 μg mL⁻¹. The experimental cultures were acclimated to their respective temperatures for more than 6 months prior to measuring physiological and biochemical parameters.

Chl-a concentration was determined using the spectrophotometric method. The cells were filtered onto GF/F filters and subsequently extracted in pure methanol overnight at 4°C in the dark. After extraction, the samples were centrifuged at 12,000 g for 4 min. The resulting supernatant was then scanned for absorbance across the wavelength range of 250–800 nm using a spectrophotometer (Cary 60, Agilent, CA, United States). Chl-a concentration was calculated using the following formula (Ritchie, 2006):

where OD₆₆₅ and OD₇₅₀ were absorbance at wavelengths 665 nm and 750 nm, respectively. The following equation was used to calculate the specific growth rate  μ  based on the Chl-a concentration:

where m₂ and m₁ are the Chl-a values at time t₂ and t₁, respectively.

The following equation modified by Norberg (2004) was utilized to fit the thermal growth curve of Trichodesmium:

where the specific growth rate (μ) is a function of temperature (T). In this equation, the coefficient w represents the thermal niche width, whereas the explicit biological significance of coefficients a, b, and z remain unspecific. Collectively, these four coefficients can be used to derive both the maximum growth rate and the optimum growth temperature (T_opt):

The effective photosynthetic quantum yield of photosystem II (Φ_II) and relative electron transport rate (rETR) were measured by Multi-color PAM (Multi-color PAM, Walz). Samples were acclimated to white actinic light with photon flux intensities similar to the growth conditions for 2 min to measure F_s, and then F_m′ was measured using a saturating pulse (8,000 μmol photons m⁻² s⁻¹, 0.8 s) to obtain the effective quantum yield (Φ_II) as follows (Genty et al., 1989):

Subsequently, rapid light curves (RLC) were measured at 11 actinic light levels [E], from 5 to 2,904 μmol photons m⁻² s⁻¹ with each light exposure lasting for 30 s. Relative electron transport rates (rETR) were calculated as follows (Ralph and Gademann, 2005):

The RLC was fitted by the following equation (Supplementary Figure S1) (Eilers and Peeters, 1988),

where a, b, and c are the fitting coefficients. These three coefficients were used to derive the photosynthetic light-harvesting efficiency (α), maximum relative electron transport rate (rETR_max):

A Cavity Ring-Down Spectroscopy gas analyzer (Picarro Model G2308, CA, United States) was used to measure methane concentrations. A 350 mL sample (V_l) was placed within a polycarbonate (PC) bottle, leaving a 270 mL headspace (V_g). The PC bottle was sealed using a silicone stopper to ensure an airtight condition. The silicone stopper was equipped with two three-way valves for sampling. During the incubation of the samples at each of the temperatures (16, 20, 23, 27, 31°C) for methane measurement, 200 mL of gas in the bottle was replaced with sterile air every 12 h. The methane content in the headspace gas was shaken to equilibrate the dissolved gas with the headspace before subsequent measurement using the Picarro analyzer according to Lenhart et al. (2016). The total methane production rates ( b C H 4 ) were calculated based on the modified formula (Johnson et al., 1990):

where C_g indicates the methane concentration in the headspace (nmol L⁻¹), C_M represents the methane concentration in the headspace after replacing with the sterile air, C_air denotes the methane concentration of the sterile air, and C_g1 and C_g2 signify the methane concentrations at two time points, t₁ and t₂. Additionally, β is the Benson coefficient. V_g represents the headspace volume, while V_l corresponds to the volume of the culture medium. Methane production rates specific to Trichodesmium were determined based on the rates obtained from samples extracted from fractions containing heterotrophic bacteria. Several control experiments were conducted to assess the potential influence of heterotrophic bacteria and to account for systematic errors. To test the bacterial contribution to methane production we filtered YBCII media through a 1.2 μm polycarbonate membrane, which lacked Trichodesmium but retained the heterotrophic bacteria in the cultures. It should be noted that the bacteria attached to the filaments of Trichodesmium might not be filtered off into the medium.

In this study carbon and nitrogen assimilation rates were determined by assessing changes over time for particulate organic carbon (POC) and particulate organic nitrogen (PON) respectively. Briefly, samples for POC and PON measurements were taken at 0, 12, and 24 h after the start of the light period. The changes in particulate organic nitrogen (PON) and particulate organic carbon (POC) were then analyzed to determine the assimilation rate of carbon and nitrogen. Upon sampling, cells were filtered onto pre-combusted (450°C, 4 h) GF/F filters and rinsed with 100 mL fresh nitrogen-free YBCII. Subsequently, the filters were acidified for 24 h in HCl fumes and then dried for 24 h to remove unassimilated inorganic carbon. An elemental analyzer (Vario EL cube, Elementary, Germany) was used to quantify POC and PON. Changes in POC or PON between samples taken at 12 h and 0 h represented the assimilation during the light period, and changes between samples taken at 24 h and 0 h represented the daily assimilation. The results were comparable to the POC and PON production rates, which were calculated as POC or PON content (nmol Chl a⁻¹) × specific growth rate μ (d⁻¹, Supplementary Figure S2) (Tong et al., 2019).

We acknowledge that the POC changes effectively represent integrated assimilation of inorganic carbon and recycling of organic carbon leaked into the media by Trichodesmium. Similarly, the nitrogen assimilation rates, as determined in this study, are indicative of the sum of both N₂-fixation and the recycling of biogenic nitrogen leaked into the media by Trichodesmium.

To determine dissolved inorganic phosphorus (DIP), the samples were filtered through a 0.22 μm cellulose acetate membrane and were then analyzed using an auto-analyzer (AA3, Seal, Germany) at room temperature. For the measurement of particulate phosphorus (PP), we followed the Solórzano method (Solórzano and Sharp, 1980). In brief, the samples were filtered on pre-combusted (450°C, 4 h) GF/F filters (25 mm, Whatman, United States), and rinsed with 100 mL phosphorus-free YBCII artificial seawater. Subsequently, the filters were soaked with 0.017 M MgSO₄, dried at 95°C, and then baked for 2 h at 450°C. Before measurement, the samples were hydrolyzed with acid (0.2 M HCl) at 80°C for 30 min. These procedures convert PP to DIP, which was subsequently quantified with an auto-analyzer (see above). The assimilation rates of phosphorus during a daily cycle were calculated using the PP contents at 0 h, 12 h, and 24 h.

The thermal dependence of methane production and the related assimilation of carbon, nitrogen and phosphorus was analyzed using the Boltzmann-Arrhenius equation (Padfield et al., 2016):

where b(T) represents the metabolic rate at temperature T (Kelvin, K), k Boltzmann’s constant (8.62 × 10⁻⁵ eV K⁻¹), b(T_c) the rate of metabolism normalized to an arbitrary reference temperature, T_c = 25°C, and E_a is the activation energy (in electron volts, eV) for the metabolic process. Supra-optimal temperatures could deviate the metabolic rate from the Boltzmann-Arrhenius equation. Therefore, corresponding values, usually those observed at 31°C, were excluded from this analysis.

The sensitivity of methane production and assimilation of carbon, nitrogen and phosphorus to temperature changes (Q₁₀) from 16°C to 27°C was assessed by the following model (Van't Hoff and Lehfeldt, 1899):

where Rate₁ and Rate₂ indicate metabolic rates at 16°C (T₁) and 27°C (T₂), respectively.

The data were provided as the means of three replicates (independent cultures) with standard deviation (SD) (n = 3). To examine the statistical differences between treatments, one-way ANOVA and Tukey’s test were used. The Brown-Forsythe test and Shapiro–Wilk test were used to check data homoscedasticity and normality, respectively.

The specific growth rate of Trichodesmium increased with temperature (Figure 1; one-way ANOVA, p < 0.001) and was sensitive to temperature changes, with a Q₁₀ value (the rate increase fold for every 10-degree rise in the temperature) of growth rate for temperatures ranged from 16°C to 27°C reaching 8.6 ± 2.3. As the culture temperature increased from 16°C to 27°C, the specific growth rate exhibited a tenfold increase from 0.03 ± 0.01 d⁻¹ to 0.34 ± 0.02 d⁻¹ (Figure 1, Tukey’s test, p = 0.0001). Increasing the growth temperature to 31°C did not significantly change the specific growth rate (0.32 ± 0.05 d⁻¹, Figure 1, Tukey’s test, p = 0.999). According to the Norberg equation, the optimal growth temperature (T_opt) was 29.2°C, corresponding to a maximum growth rate of 0.38 d⁻¹.

The ratio of Chl-a to POC increased with the rise in temperatures (one-way ANOVA, p < 0.0001). The Chl a: POC was 68 ± 1 ng Chl a μmol POC⁻¹ at the lowest growth temperature of 16°C, and increased by 100% to 136 ± 3 ng Chl a μmol POC⁻¹ at 31°C (Table 1; Tukey’s test, p < 0.0001).

In contrast, the ratios of POC to PON were negatively correlated with temperatures (Table 1; one-way ANOVA, p = 0.0004). When the growth temperature increased from 16°C to 31°C, the ratios of POC to PON decreased by 15% from 6.60 ± 0.24 to 5.64 ± 0.26 (Table 1; Tukey’s test, p = 0.004).

The effective quantum yield (Φ_II), a measure indicative of the photosynthetic efficiency of Trichodesmium, increased with rising temperature (one-way ANOVA, p < 0.0001). The value of Φ_II was 0.17 ± 0.02 at the lowest temperature of 16°C and increased by 188% to 0.49 ± 0.01 (Table 1; Tukey’s test, p < 0.0001) at 31°C. The relative maximum electron transport rate (rETR_max) and photosynthetic light-use efficiency (α) showed a similar pattern to Φ_II. Specifically, rETR_max increased by 207% from 73 ± 7 to 224 ± 4 μmol e m⁻² s⁻¹ (Table 1, one-way ANOVA, p < 0.0001), while the value of α increased by 177% from 0.22 ± 0.02 to 0.61 ± 0.01 (Table 1, one-way ANOVA, p < 0.0001) with the temperature increasing from 16 to 31°C.

Methane was produced during both the day and the night, exhibiting a typical temperature response curve (Figure 2, one-way ANOVA, p < 0.0001) and demonstrated sensitivity to temperature changes, with a Q₁₀ value for temperature ranged from 16°C to 27°C, reaching 4.6 ± 0.7. At 16°C, the methane production rates during the light period and daily cycle were 0.120 ± 0.050 nmol CH₄ μm POC⁻¹ day⁻¹ and 0.198 ± 0.042 nmol CH₄ μmol POC⁻¹ day⁻¹, respectively (Figure 2). When the growth temperature increased to 27°C, the rate of methane production reached the maximum, with light-period and daily-cycle values increasing by 407% to 0.608 ± 0.018 nmol CH₄ μmol POC⁻¹ day⁻¹ (Tukey’s test, p < 0.0001) and by 419% to 1.028 ± 0.040 nmol CH₄ μmol POC⁻¹ day⁻¹ (Tukey’s test, p < 0.0001), respectively (Figure 2). The activation energy (E_a) for methane production was 1.09 ± 0.13 eV for light period and 1.08 ± 0.08 eV for daily-cycle. Notably, the amount of methane production in each treatment increased with incubation time (Supplementary Figure S3A) and showed a positive correlation with biomass (Supplementary Figure S4). Methane production was also observed in bacterial controls, and the production rate increased with rising temperature (Supplementary Figure S3B). Trichodesmium dominated the methane production, with heterotrophic bacterial contribution to the total production being 19.7% at 16°C, 1.5% at 20°C, 3.8% at 23°C, 1.9% at 27°C, and 11.4% at 31°C, respectively (Supplementary Figure S3A). Methane production by Trichodesmium was derived by subtracting the bacterial production from the total production, with the possible contribution of the attached heterotrophic bacteria to the filaments of Trichodesmium being ignored.

Carbon, nitrogen, and phosphorus assimilation rates increased with higher growth temperatures (Figure 3, one-way ANOVA, p < 0.0001, p < 0.0001, and p < 0.0001), demonstrating a high sensitivity to temperature changes. The Q₁₀ values for temperature ranged from 16°C to 27°C for POC, PON and POP production were 4.9 ± 0.7, 2.6 ± 0.5, and 2.6 ± 0.3, respectively. When the temperature was raised from 16°C to 31°C, the light-period and daily rates of carbon assimilation increased by 577% from 81 ± 34 to 548 ± 128 nmol C nmol POC⁻¹ day⁻¹ (Tukey’s test, p < 0.0001) and by 650% from 56 ± 11 to 420 ± 103 nmol C μmol POC⁻¹ day⁻¹ (Tukey’s test, p = 0.0002), respectively (Figure 3A). The activation energy (E_a) for carbon assimilation was 1.26 ± 0.15 eV for light period and 1.19 ± 0.19 eV for daily-cycle. As the growth temperature increased from 16°C to 31°C, the nitrogen assimilation rate increased by 475% from 16 ± 2 to 92 ± 12 nmol N μmol POC⁻¹ day⁻¹ (Tukey’s test, p < 0.0001) during the light period, and increased by 250% from 26 ± 6 to 91 ± 14 nmol N μmol POC⁻¹ day⁻¹ (Tukey’s test, p < 0.0001) (Figure 3B). The activation energy (Ea) for nitrogen assimilation was 1.19 ± 019 eV for light period and 0.78 ± 0.25 eV for daily-cycle. The phosphorous assimilation rate was 0.7 ± 0.2 nmol P μmol POC⁻¹ day⁻¹ for the light–dark period at 16°C, and increased by 228% from to 2.3 ± 0.5 nmol P μmol POC⁻¹ day⁻¹ at 31°C (Figure 3C; Tukey’s test, p < 0.0001).

The methane production correlated positively with rates of C, N, and P assimilation, specific growth and relative electron transfer (Figures 4, 5). The daily methane production increased with higher carbon, nitrogen, and phosphorus assimilation (Figure 4). The correlation coefficients between the daily methane production and the assimilation of carbon, nitrogen and phosphorus were 0.83, 0.74, and 0.77, respectively (Figure 4, p < 0.0001, p < 0.0001, p < 0.0001). The methane production quotients (MPQ), ratio of the carbon, nitrogen or phosphorus assimilation rates to the methane production rates, were 253–494 for carbon, 40–128 for nitrogen, and 1.3–3.4 for phosphorus, respectively (Table 2).

The relationship between metabolic activity and growth rates to methane production rates, which was established based on the positive correlations of methane production with the specific growth rate (μ) and relative electron transport rate (rETR), provided the correlation coefficients (R-square) of 0.91 and 0.87, respectively (Figure 5, p < 0.0001, p < 0.0001). Under different growth temperatures, the ratio of specific growth rate to methane production rate ranged from 0.17 to 0.41 and that of rETR to methane production rate ranged from 118 to 215 (Table 2).