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Co-occurrence of Fe and P stress in natural populations of the marine diazotroph Trichodesmium

. Trichodesmium is a globally important marine microbe that provides fixed nitrogen (N) to otherwise N limited 15 ecosystems. In nature, nitrogen fixation is likely regulated by iron or phosphate availability, but the extent and interaction of these controls are unclear. From metaproteomics analyses using established protein biomarkers for iron and phosphate stress, we found that co-stress is the norm rather than the exception for Trichodesmium colonies in the North Atlantic ocean. Counter-intuitively, the nitrogenase enzyme was more abundant under co-stress as opposed to single nutrient stress. This is consistent with the idea that Trichodesmium has a specific physiological state during nutrient co-stress. Organic nitrogen 20 uptake was observed and occurred simultaneously with nitrogen fixation. Quantification of the phosphate ABC transporter PstA combined with a cellular model of nutrient uptake suggested that Trichodesmium is generally confronted by the biophysical limits of membrane space and diffusion rates for iron and phosphate acquisition in the field. Colony formation may benefit nutrient acquisition from particulate and organic nutrient sources, alleviating these pressures. The results highlight that to predict the behavior of Trichodesmium , both Fe and P stress must


Introduction
The diazotrophic cyanobacterium Trichodesmium plays an important ecological and biogeochemical role in the tropical and subtropical oceans globally. By providing bioavailable nitrogen (N) to otherwise N-limited ecosystems, it supports basin-scale food webs, increasing primary productivity and carbon flux from the surface ocean (Capone, 1997;30 Carpenter and Romans, 1991;Coles et al., 2004;Deutsch et al., 2007;Sohm et al., 2011). Nitrogen fixation is energetically and nutritionally expensive, so it typically occurs when other sources of N are unavailable, i.e. in N-starved environments (Karl et al., 2002). However, nitrogen availability is not the sole control on nitrogen fixation, which must be balanced against F 2 the cell's overall nutritional status. Because it can access a theoretically unlimited supply of atmospheric N 2 , Trichodesmium often becomes phosphorus (P) limited Hynes et al., 2009;Orchard, 2010;Sañudo-Wilhelmy et al., 35 2001;Wu et al., 2000). It also has a tendency to experience iron (Fe) limitation because the nitrogenase enzyme is irondemanding (Bergman et al., 2013;Chappell et al., 2012;Rouco et al., 2018;Sunda, 2012;.
There is uncertainty about when and where Trichodesmium is Fe and P stressed and how this impacts nitrogen fixation in nature. Some reports suggest that Trichodesmium is primarily phosphate stressed in the North Atlantic, and primarily Fe stressed in the Pacific, owing to relative Fe and P availability in these regions (Bergman et al., 2013;Chappell 40 et al., 2012;Frischkorn et al., 2018;Hynes et al., 2009;Orchard, 2010;Sañudo-Wilhelmy et al., 2001). However, others have suggested that Fe and P can be co-limiting to Trichodesmium; one incubation study found two examples of Fe/P colimitation in the field (Mills et al., 2004). Even less clear is how Fe and/or P stress impacts nitrogen fixation. For instance, despite the intuitive suggestion that nitrogen fixation is limited by Fe or P availability, laboratory evidence indicated that Trichodesmium is specifically adapted to co-limited conditions, with higher growth and N 2 -fixation rates under co-limitation 45 than under single nutrient limitation (Garcia et al., 2015;. There are several protein biomarkers for Fe and P stress in Trichodesmium, many of which are periplasmic binding proteins involved in nutrient acquisition. For Fe, this includes the IdiA and IsiB proteins and for phosphorus, specifically phosphate, the PstS and SphX proteins (see Table S1). In Trichodesmium, IsiB, a flavodoxin, and IdiA, an ABC transport protein, are expressed under Fe limiting conditions, and both are conserved across species with high sequence identity 50 (Chappell et al., 2012;Webb et al., 2007). Transcriptomic and proteomic studies have shown that they are more abundant under Fe stress conditions, though there is low-level basal level expression (Chappell et al., 2012;Snow et al., 2015;. In this dataset, IsiB and IdiA were both highly abundant and correlated to one another ( Figure S1).
IdiA is used as the molecular biomarker of Fe stress in the following discussion, but the same conclusions could be drawn from IsiB distributions. Like IdiA and IsiB, SphX and PstS are conserved across diverse Trichodesmium species (Chappell et 55 al., 2012;. SphX is abundant at the transcript and protein level under phosphate limitation (Orchard et al., 2009;Orchard, 2010). PstS, a homologous protein located a few genes downstream of SphX, responds less clearly to phosphate stress. In Trichodesmium, the reason may be that PstS is not preceded by a Pho box, a regulatory DNA sequence which is necessary for P based regulation (Orchard et al., 2009). Thus, in this study we focused on SphX as a measure of phosphate stress and IdiA as a marker of Fe stress. 60 Here, we present evidence based on field metaproteomes that Trichodesmium colonies were simultaneously Fe and P stressed, particularly in the tropical and subtropical Atlantic. While Fe/P stress has been suggested before, this study provides molecular evidence for co-stress in a broad geographical and temporal survey. This co-stress occurred across significant gradients in Fe and P concentration, suggesting nutrient stress was driven not only by biogeochemical gradients but also by Trichodesmium's response to nutrient depletion; we explore possible biophysical and biochemical mechanisms 65 behind this. Fe and P stress were positively associated with nitrogen fixation and organic nitrogen uptake, suggesting that Trichodesmium's Fe, P, and N statuses are linked, perhaps via a regulatory network.

Sample acquisition
A total of 37 samples were examined in this study. Samples were acquired by the authors on various research 70 expeditions and most exist in biological duplicate or triplicate (Table S2). Trichodesmium colonies were hand-picked from 200 μm or 130 μm surface plankton net tows, rinsed thrice in 0.2 μm filtered trace metal clean surface seawater into trace metal clean LDPE bottles, decanted onto 0.2-5 μm filters, and frozen until protein extraction. The samples were of mixed puff and tuff morphology types, depending on the natural diversity present at the sampling location. The majority of samples considered in this study were taken in the early morning pre-dawn hours. Details such as filter size, morphology, location, 75 cruise, date, and time of sampling are provided in Table S2.

Sample acquisition
Proteins were extracted by a detergent based method following Saito et al. (2014) and Lu et al. (2005). To reduce protein loss and contamination, all tubes were ethanol rinsed and dried prior to use and all water and organic solvents used 80 were LC/MS grade. Sample filters were placed in a tube with 1-2 mL 1% sodium dodecyl sulfate (SDS) extraction buffer (1% SDS, 0.1 M Tris/HCL pH 7.5, 10 mM EDTA) and incubated for 10 min at 95°C with shaking, then for one hour at room temperature with shaking. The protein extract was decanted and clarified by centrifugation (14100xg) at room temperature.
The crude protein extracts were quantified with the colormetric BCA protein concentration assay with bovine serum albumin as a standard (Pierce catalog number 23225). Extracts were concentrated by 5 kD membrane centrifugation (Vivaspin spin 85 columns, GE Healthcare). The protein extracts were purified by organic precipitation in 0.5 mM HCl made in 50% methanol and 50% acetone at -20 °C for at least one week, then collected by centrifugation at 14100xg for 30 min at 4 °C, decanted and dried by vacuum concentration for 10min. The protein pellets were re-suspended in a minimum amount of 1% SDS extraction buffer, and re-quantified by BCA protein concentration assay to assess extraction efficiency.
The proteins were embedded in a 500 μL final volume acrylamide gel, which was then cut up into 1 mm pieces to 90 maximize surface area and rinsed in 50:50 acetonitrile: 25 mM ammonium bicarbonate overnight at room temperature. The next morning, the rinse solution was replaced and the rinse repeated for 1 hour. Gels were dehydrated thrice in acetonitrile, dried by vacuum centrifugation, and rehydrated in 10 mM dithiothrietol (DTT) in 25 mM ammonium bicarbonate, then incubated for one hour at 56 °C with shaking. Unabsorbed DTT solution was removed and the volume recorded, allowing for calculation of the total gel volume. Gels were washed in 25 mM ammonium bicarbonate, then incubated in 55 mM 95 iodacetamide for one hour at room temperature in the dark. Gels were again dehydrated thrice in acetonitrile. Trypsin (Promega Gold) was added at a ratio of 1:20 μg total protein in 25 mM ammonium bicarbonate in a volume sufficient to barely cover the gel pieces. Proteins were digested overnight at 37 °C with shaking. Any unabsorbed solution was then removed to a new tube and 50μL of peptide extraction buffer (50% acetonitrile, 5% formic acid in water) was added and incubated for 20 min at room temperature. The supernatant as then decanted and combined with the unabsorbed solution, and 100 F 4 the step then repeated. The resulting peptide mixture was concentrated by vacuum centrifugation to 1 μg μL -1 concentration based on the starting protein concentration. Finally, the peptides were clarified by centrifugation at room temperature, taking the top 90% of the volume to reduce the carry over of gel debris.

Data acquisition 105
The global proteomes were analysed by online comprehensive active-modulation two-dimensional liquid chromatography (LC x LC-MS) using high and low pH reverse phase chromatography with inline PLRP-S (200μm x 150mm, 3μm bead size, 300A pore size, NanoLCMS Solutions) and C18 columns packed in house (100 mm x 150 mm, 3 µm particle size, 120 Å pore size, C18 Reprosil-Gold, Dr. Maisch GmbH packed in a New Objective PicoFrit column). The first dimension utilized an 8 hour pH = 10 gradient (10mM ammonium formate and 10mM ammonium formate in in 90% 110 acetonitrile), and was trapped every 30min on alternating dual traps, then eluted at 500nL/min onto the C18 column with a 30 min gradient (0.1% formic acid and 0.1% formic acid in 99.9% acetonitrile). 10 μg of protein was injected per run directly onto the first column using a Thermo Dionex Ultimate3000 RSLCnano system (Waltham, MA), and an additional RSLCnano pump was used for the second dimension gradient. The samples were then analyzed on a Thermo Orbitrap Fusion mass spectrometer with a Thermo Flex ion source (Waltham, MA). MS1 scans were monitored between 380-1580 115 m/z, with a 1.6 m/z MS2 isolation window (CID mode), 50 millisecond maximum injection time and 5 second dynamic exclusion time.

Relative quantitation of peptides and proteins
Raw spectra were searched with the Sequest algorithm using a custom-built genomic database (Eng, Fischer, 120 Grossmann, and MacCoss, 2008). The genomic database consisted of a publically available Trichodesmium community metagenome available on the JGI IMG platform (IMG ID 2821474806), as well as the entire contents of the CyanoGEBA project genomes (Shih et al., 2013). Protein annotations were derived from the original metagenomes. SequestHT mass tolerances were set at +/-10ppm (parent) and +/-0.8 Dalton (fragment). Cysteine modification of +57.022 and methionine modification of +16 were included. Protein identifications were made with Peptide Prophet in Scaffold (Proteome Software) 125 at the 95% protein and peptide identification levels. Relative abundance was measured by averaging the precursor intensity (area under the MS1 peak) of the top 3 most abundant peptides in each protein, then normalizing this value to total precursor ion intensity. Normalization and global false discovery rate (FDR) calculations, which were 0.1% at the peptide level and 1.2% at the protein level, were performed in Scaffold (Proteome Software). FDR was calculated by Scaffold using the probabilistic method by summing the assigned protein or peptide probabilities and dividing by the maximum probability Statistical tests of relationships between proteins were conducted with the scipy stats package F 5 (https://docs.scipy.org/doc/scipy/reference/stats.html) using linear Pearson tests when the relationship appeared to be linear and a Spearman rank order test when this was not the case. 135

Absolute quantitation of peptides
A small number of peptides were selected for absolute quantitation using a modified heterologous expression system. The peptides were ensured to be specific to Trichodesmium species based on sequence identity compared to over 300 marine bacteria genomes, three metagenomes, and 956 specialized assemblies (see www.metatryp.whoi.edu) (Saito et 140 al., 2015). A custom plasmid was designed that contained the Escherichia coli K12 optimized reverse translation sequences for peptides of interest separated by tryptic spacers (protein sequence = TPELFR). The peptides and transition ions included are provided in Table S7. To avoid repetition of the spacer nucleotide sequence, twelve different codons were utilized to encode the spacer. Six equine apomyoglobin and three peptides from the commercially available Pierce peptide retention time calibration mixture (product number 88320) were also included. The sequence was inserted into a pet(30a)+ plasmid 145 using the BAMH1 5' and XhoI 3' restriction sites.
The plasmid was transformed into competent tuner(DE3)pLys E.coli cells and grown on kanamycin amended LB agar plates to ensure plasmid incorporation. A single colony was used to inoculate a small amount of kanamycin containing 15 N labelled S.O.C. media (Cambridge Isotope Laboratories) as a starter culture. These cells were grown overnight and then used to inoculate 10 mL of 15 N labeled, kanamycin-containing SOC media. Cells were grown to approximately OD600 0.6, 150 then induced with 1 mM isopropyl β-D-1-thiogalactopyranoside (IPTG), incubated in the overexpression phase overnight at room temperature and harvested by centrifugation.
Cells were lysed with BugBuster detergent with added benzonase nuclease. The extracts were centrifuged and a large pellet of insoluble cellular material remained. Because the plasmid protein was large, this pellet contained a large number of inclusion bodies containing nearly pure protein. The inclusion bodies were solubilized in 6 M urea at 4 °C 155 overnight. The protein was reduced, alkylated, and trypsin digested in solution to generate a standard peptide mixture.
The standard mixture was calibrated to establish the exact concentration of the peptides. A known amount (10 fmol μL -1 ) of the commercially available Pierce standard peptide mixture (Catalog number 88320) and an apomyoglobin digest was spiked into the standard. The ratio of Pierce (isotopically labelled according to JPT standards) or apomyoglobin (light) to heavy standard peptide MS2 peak area was calculated and used to establish the final concentration of the standard peptide 160 mixture Milo, 2013). Multiple peptides were used for this calibration and the standard deviation among them was approximately 10%. Finally, the linearity of the peptide standard was tested by generating a dilution curveand ensuring that the concentration of each peptide versus MS2 peak area was linear between 0.001 and 20 fmol μL -1 concentration, using 10uL injections consistent with experimental injection volumes.
The sample was prepared at 0.2 μg μL -1 concentration, with 10 μL injected to give a total of 2 μg total protein 165 analyzed. The heavy labelled standard peptide mixture was spiked into each sample at a concentration of 10 fmol μL -1 . The concentration of the light peptide was calculated as the ratio of the MS2 area of the light:heavy peptide multiplied by 10 μg F 6 μL -1 . A correction was applied for protein recovery before and after purification, and the result was the absolute concentration of the peptide in fmol μg -1 total protein.
The percent of the membrane occupied by the ABC transporter PstA was calculated by converting the absolute 170 protein concentration to molecules per Trichodesmium cell, using average values for Trichodesmium cell volume , carbon content per volume (Strathmann, 1967), protein content per g carbon (Rouwenhorst, et al., 1991), and the cross sectional area of a calcium ATPase (Hudson et al., 1992) (see Table S3).

Self-organizing map analyses 175
Self-organizing maps were used to reduce the dimensionality of the data and explore relationships among covarying proteins of interest. Only Trichodesmium proteins were considered. Analyses were conducted in Python 3.0 and fully reproducible code is available at https://github.com/naheld/self_organizing_map_tricho_metaP.
The input data consisted of a table of protein names (rows) and samples (columns) such that the input vectors contained 2818 features. To eliminate effects of scaling, the data was unit normalized with the Scikit-learn pre-processing 180 algorithm. The input vectors were used to initialize a 100 output node (10x10) self-organizing map using the SOMPY Python library (https://github.com/sevamoo/SOMPY). The output nodes were then clustered using a k-means clustering algorithm (k = 10) implemented in scikit learn. The input nodes (proteins) assigned to each map node were then retrieved and the entire process repeated 10,000 times. Proteins were considered in the same cluster if they appeared in the same cluster of output nodes more than 99.99% of the time. 185

Proteome overview
This study presents 36 field metaproteomes of colonial Trichodesmium populations collected at sixteen locations on four expeditions (Table S2). All but one location were in the subtropical and tropical Atlantic; most samples were collected in the early morning hours to avoid changes occurring on the diel cycle ( Figure 1 and Table S2). The metaproteomes were 190 analyzed with a two-dimensional LC-MS/MS workflow that provided deep coverage of the proteome. This resulted in 4478 protein identifications, of which 2944 were Trichodesmium proteins. The remaining proteins were from colony-associated epibionts, and will be discussed in a future publication. Protein abundance is presented as precursor (MS1) intensity of the three most abundant peptides for each protein, normalized to total protein in the sample. Thus, changes in protein abundance were interpreted as changes in the fraction of the proteome devoted to that protein. The most abundant were GroEL,195 ribosomal, and phycobilisome proteins.
A self-organizing map analysis identified groups of proteins with similar profiles, i.e. proteins whose abundances changed cohesively, suggestive of proteins that may be regulated similarly (Reddy et al., 2016). This revealed the central importance of nitrogen fixation to Trichodesmium. The nitrogenase proteins were among the most abundant in the proteome and were located in clusters 1 and 2 ( Figure 2 and Table S3). Also in these clusters were nitrogen metabolism proteins 200 including glutamine synthetase, glutamine hydrolyzing guanosine monophosphate (GMP) synthase and glutamate racemase. This is consistent with previous reports finding that N assimilation is synchronized with nitrogen fixation (Carpenter et al., 1992).
Nitrogen fixation was closely linked to carbon fixation. Many photosystem proteins clustered with the nitrogenase proteins, including phycobilisome proteins, photosystem proteins, and the citric acid cycle protein 2-oxoglutarate 205 dehydrogenase. This clustering indicated the possibility of direct regulatory links between C and N fixation. The nitrogen regulators P-II and NtcA were also present in this cluster and may mediate this association. In non-nitrogen fixing cyanobacteria, high abundance of the nitrogen regulators NtcA and P-II is suggestive of nitrogen stress (Flores and Herrero, 2005;Saito et al., 2014). In diazotrophs, the role of these regulators is unclear because they do not respond to nitrogen compounds such as ammonia as they do in other cyanobacteria (Forchhammer and De Marsac, 1994). Here, clustering of 210 NtcA and P-II with C and N fixation proteins suggested that they play a role in balancing these processes in field populations, though the details of this role have yet to be elucidated.
In addition to identifying links between C and N fixation, the metaproteomes demonstrated that field populations of Trichodesmium invest heavily in macro-and micro-nutrient acquisition. There were clusters of proteins involved in trace metal acquisition and management, including Fe, zinc, and metal transport proteins, with the latter including proteins likely 215 involved in Ni and Mo uptake (protein IDs TCCM_0270.00000020 and TCCM_0481.00000160). We also noted clusters of proteins involved in phosphate acquisition. Importantly, SphX and PstS appear in separate clusters, highlighting differential regulation of these functionally similar proteins.

Trichodesmium is simultaneously iron and phosphate stressed throughout the North Atlantic
A surprising emergent observation from the Trichodesmium metaproteomes was the co-occurrence of the iron 220 (IdiA) and phosphate (SphX) stress biomarkers across the samples. The ubiquitous and highly abundant presence of these proteins relative to total protein implied that co-stress may be the norm rather than the exception for Trichodesmium colonies in the field, particularly in the North Atlantic. Even though low-level basal expression of IdiA and SphX has been observed, it was clear that the colonies were devoting a large fraction of their cellular resources to Fe and P uptake, respectively (see Tables S8 and S9) (Webb et al., 2001, Webb et al., 2007, Chappell et al., 2010, Orchard et al., 2010, Snow et al., 2015, 225 Walworth et al., 2016, Frischkorn et al., 2019. This, combined with the responsiveness of IdiA and SphX to nutrient availability in Trichodesmium filaments in the laboratory, indicated that co-stress was occurring. Interestingly, biomarker abundance was not necessarily associated with nutrient concentrations in the surface ocean, suggesting that the colonies were experiencing stress despite variation in nutrient availability (Figure 3 C-D). SphX abundance varied up to 7.5 fold and was negatively associated with dissolved phosphate concentrations, though analytical 230 differences across the field expeditions may have forced this relationship ( Figure S2). Oceanographically, SphX was most abundant in the P-deplete, summer-stratified North Atlantic gyre (JC150 expedition) compared with winter waters near the Amazon river plume (Tricolim expedition) or at station ALOHA, where phosphate concentrations were greater (Hynes et al., F 8 2009;Sañudo-Wilhelmy et al., 2001;Wu et al., 2000). IdiA varied up to 8 fold but there was no observable relationship with dFe concentrations at the surface. Instead, IdiA may be responsive to other factors such as the varying iron requirements of 235 the populations/species examined. It should be highlighted that in this study only Trichodesmium colonies were considered, so factors such as colony size may have affected iron availability and biomarker expression. Additionally, because the surface ocean iron inventory was low, transient inputs such as from the Sahara desert could dramatically impact iron availability on short time scales, and the time scale of these inputs relative to changes in biomarker abundance is not well understood (Kunde et al., 2019). Carefully calibrated datasets relating IdiA and SphX abundance to nutrient-limited growth 240 rates of Trichodesmium in both the filamentous and colonial forms would facilitate quantitative interpretation of this data.

The intersection of Fe, P and N stress
The metaproteomes enabled the relationship between Fe and P stress and overall cellular metabolism to be explored. Nitrogenase protein abundance was positively correlated with both IdiA and SphX, and was in fact highest at the intersection of high Fe and P stress (Figure 4). This observation contrasts with the current paradigm that Trichodesmium 245 down regulates nitrogen fixation when it is Fe or P stressed , Ruoco, et al., 2018, Bergmann et al., 2012, Shi et al., 2007. Instead, it is consistent with the idea that the nutritional demands of nitrogen fixation could drive the organism to Fe and P stress, thereby initiating an increase in Fe and P acquisition proteins including IdiA and SphX. This indicates that the cell's N, P and Fe statuses are linked, perhaps involving one or more regulatory networks, which are particularly common in marine bacteria ( Figure 5) (Held et al., 2019). This network may regulate a specific physiological 250 adaptation to nutrient co-stress. For instance, Fe and P co-limited Trichodesmium cells may reduce their cell size to optimize their surface area: volume quotient for nutrient uptake. However, a putative cell size biomarker Tery_1090, while abundant in co-limited cells in culture, was not identified in these metaproteomes despite bioinformatic efforts to target it, likely because it is a low abundance protein .
Nitrogen fixation is not the only way that Trichodesmium can acquire fixed N (Dyhrman et al., 2006;Küpper et al., 255 2008;Mills et al., 2004;Sañudo-Wilhelmy et al., 2001). In culture, Trichodesmium can be grown on multiple nitrogen sources including urea; in fact, it has been reported that nitrogen fixation provides less than 20% of the fixed N demand of cells, and a revised nitrogen fixation model suggests that Trichodesmium takes up fixed nitrogen in the field (McGillicuddy , 2014;Mulholland and Capone, 1999). In this dataset, a urea ABC transporter was abundant, indicating that urea could be an important source of fixed nitrogen to colonies (Figure 6a). The transporter is unambiguously attributed to Trichodesmium 260 rather than a member of the epibiont community. Of course, this does not rule out the possibility that urea or other organic nitrogen sources such as trimethylamine (TMA) are also utilized by epibionts, although no such epibiont transporters were identified in the metaproteomes.
However, in laboratory studies urea exposure must be unrealistically high (often over 20 μM) for this to occur, compared 265 with natural concentrations which are much lower (Ohki et al., 1991;Wang et al., 2000). In the field, urea utilization and F 9 nitrogen fixation seem to occur simultaneously, with a urea uptake protein positively correlated to nitrogenase abundance ( Figure 6b). Urea and other organic nitrogen sources such as trimethylamine (TMA) could be sources of nitrogen for Trichodesmium, and the relationship to nitrogenase abundance may indicate a general N stress signature driving both organic nitrogen uptake and nitrogen fixation (Walworth et al., 2018). Alternatively, urea uptake could be a colony-specific 270 behavior, since colonies were sampled here as opposed to laboratory cultures that typically grow as single filaments. For instance, urea could be used for recycling of fixed N within the colony, or there could be heterogeneity in nitrogen fixation, with some cells taking up organic nitrogen and others fixing it. These unexpected observations of co-occurring nitrogen fixation and organic nitrogen transport show the value of exploratory metaproteomics, which does not require targeting of a specific protein based on a prior hypothesis. 275

Mechanisms of simultaneous iron and phosphate stress -membrane crowding
ABC transporters are multi-unit, trans-membrane protein complexes that use ATP to shuttle substrates across membranes. Specific ABC transporters are required for both iron versus phosphate uptake (Chappell et al., 2012;Orchard et al., 2009). Nutrient transport rates can be modulated by changing the number of uptake proteins installed on the cell membrane or the efficiency of the uptake proteins through expression of assisting proteins such as IdiA and SphX, which 280 bind Fe or P respectively in the periplasm and shuttle the elements to their respective membrane transport complexes (Hudson and Morel, 1992). The high abundance of proteins involved in ABC transport suggested that nutrient transport rates could limit the amount of Fe and P Trichodesmium can acquire. Thus, we explored whether membrane crowding, i.e. lack of membrane space, can constrain nutrient acquisition by Trichodesmium.
To investigate this, we quantified the absolute concentration of the phosphate ABC transporter PstA, which 285 interacts with the phosphate stress biomarkers SphX and PstS. This analysis is distinct from the above global metaproteomes, which allowed patterns to be identified but did not allow for absolute quantitation of the proteins. The analysis was performed similar to an isotope dilution experiment where labelled peptide standards are used to control for analytical biases. The analysis was performed for three Tricolim and six JC150 stations. Briefly, 15 N labelled peptide standards were prepared and spiked into the samples prior to PRM LC-MS/MS analysis. The concentration of the peptide in 290 fmol μg -1 total protein was calculated using the ratio of product ion intensities for the heavy (spike) and light (sample) peptide and converted to PstA molecules per cell (Table 1 and see also Table S4). The peptide used for quantitation of PstA was specific to Trichodesmium species. Based on these calculations, on average up to 19 to 36% of the membrane was occupied by the PstA transporter. In one population (JC150 expedition, Station 7), up to 83% of the membrane was occupied by PstA alone. While these are first estimates, it is clear that the majority of Trichodesmium cells devoted a large fraction of 295 their membrane surface area to phosphate uptake.
To examine whether membrane crowding can indeed cause nutrient stress or limitation, we developed a model of cellular nutrient uptake in Trichodesmium. The model identifies the concentration at which free Fe or phosphate limits the growth of Trichodesmium cells. This is distinct from nutrient stress, which changes the cell's physiological state but does not necessarily impact growth. In the model, nutrient limitation occurs when the daily cellular requirement is greater than the 300 uptake rate, a function of the cell's growth rate and elemental quota. Following the example of Hudson and Morel (1992), the model assumes that intake of nutrients once bound to the ABC transporter protein is instantaneous, i.e. that nutrient uptake is limited by formation of the metal-transporter complex at the cell surface. This is an idealized scenario, because if intake is the slow step, for instance in a high affinity transport system, the uptake rate would be slower and nutrient limitation exacerbated (discussed below). 305 We considered two types of nutrient limitation in the model (Table S5). First, we considered a diffusion-limited case, in which the rate of uptake is determined by diffusion of the nutrient to the cell's boundary layer (μ*Q = 2 / 3 k D [nutrient], where μ = the cell growth rate, Q = the cell nutrient quota, and k D = the diffusion rate constant, dependent on the surface area and diffusion coefficient of the nutrient in seawater). Based on empirical evidence provided by Hudson and Morel (1992), limitation occurs when the cell quota is greater than 2 / 3 the diffusive-limited flux because beyond this, depletion of the 310 nutrient in the boundary layer occurs. In the second case, membrane crowding limitation, the rate of uptake is determined by the rate of transporter-metal complex formation (μ*Q = k f [transport protein] [nutrient], where k f = the rate of ligand-nutrient complex formation). Here, up to 50% of the membrane can be occupied by the transport protein following the example of and Morel (1992). This is within the range of the above estimates of membrane occupation by phosphate transporter PstA.
The model uses conservative estimates for diffusion coefficients, cell quotas, growth rates, and membrane space occupation 315 to identify the lowest concentration threshold for nutrient limitation; as a result it is likely that Trichodesmium becomes limited at higher nutrient concentrations than the model suggests. At this time, the model can only consider labile dissolved Fe and inorganic phosphate, though Trichodesmium can also acquire particulate iron, organic phosphorus, phosphite, and phosphonates (Dyhrman et al., 2006;Frischkorn et al., 2018;Polyviou et al., 2015;Poorvin et al., 2004;Rubin et al., 2011).
We first considered a spherical cell, where the surface area: volume quotient decreases as cell radius increases 320 ( Figure 7). As the cell grows in size, higher nutrient concentrations are required to sustain growth. This is consistent with the general understanding that larger microbial cells with lower surface area: volume quotient are less competitive in nutrient uptake (Chisholm, 1992;Hudson and Morel, 1992). For a given surface area: volume quotient, the mechanism driving nutrient limitation is whichever model (diffusion or membrane crowding) results in a higher minimum nutrient concentration below which limitation occurs. For a spherical cell, Fe limitation is driven by diffusion when the cell is large and the surface 325 area: volume quotient is low (Figure 7a). However, when cells are smaller and the surface area: volume quotient is high, membrane crowding drives nutrient limitation, meaning that the number of ligands, and not diffusion from the surrounding environment, is the primary control on nutrient uptake. For phosphate, diffusion is almost always the driver of nutrient limitation owing to the higher rate of transporter-nutrient complex formation (k f ) for phosphate, which causes very fast membrane transport rates and relieves membrane-crowding pressures across all cell sizes (Figure 7b) (Froelich et al., 1982). 330 While this model may be directly applicable to some N 2 -fixing cyanobacteria such as Groups B and C, which have roughly spherical cells, Trichodesmium cells are not spheres but rather roughly cylindrical . Thus, we repeated the model calculations for cylinders with varying radii (r) and heights (2r or 10r) based on previous estimates of F 11 Trichodesmium cell sizes (Bergman et al., 2013;Hynes et al., 2012). Cylinders have lower surface area: volume quotient than spheres of similar sizes. In addition, the rate constant (k D ) for diffusion, which is a function of cell geometry, is greater. 335 This increases the slope of the diffusion limitation line such that membrane crowding is important across a greater range of cell sizes (Figure 7c-d). Trichodesmium cell sizes vary in nature, for instance the cylinder height can be elongated, improving the surface area: volume quotient. However, the impact of cell elongation to radius r and height 10r on both diffusion limitation and membrane crowding is subtle (Figure 7e-f). Furthermore, though not explicitly considered here, cylindrical cells living in filaments would have reduced surface area available for nutrient uptake. Thus, we conclude that in 340 certain scenarios, lack of membrane space could hypothetically limit Fe and perhaps P acquisition by Trichodesmium, particularly when the cells live in filaments or colonies as occurs in nature.
A key assumption of the model is that uptake rates are instantaneous. In the above calculations, we use the dissociation kinetics of Fe from water and phosphorus with common seawater cations as the best case (i.e. fastest possible) kinetic scenario for nutrient acquisition. The model does not account for delays caused by internalization kinetics, which 345 would exacerbate nutrient limitation. For instance it does not consider nutrient speciation, which could affect internalization rates, particularly for Fe (Hudson and Morel, 1992). Furthermore, the involvement of the periplasmic binding proteins IdiA and SphX suggest that uptake is not simultaneous; their participation is likely associated with a kinetic rate of binding and dissociation from the periplasmic proteins in addition to any rate of ABC transport.
Membrane crowding could produce real cellular challenges, leading to the observation of Fe and P co-stress across 350 the field populations examined. The above model explicitly allows 50% of the cell surface area to be occupied by any one type of transporter, consistent with our estimate of cell surface area occupied by the PstA transporter. If 50% of the membrane is occupied by phosphate transporters, and another 50% for Fe transporters, this would leave no room for other essential membrane proteins and even the membrane lipids themselves. The problem is further exacerbated if the cell installs transporters for nitrogen compounds such as urea, as the metaproteomes suggest. Thus, installation of transporters for any 355 one nutrient must be balanced against transporters for other nutrients. This interpretation is inconsistent with Liebig's law of nutrient limitation, which assumes that nutrients are independent (Liebig, 1855;Saito et al., 2008). In an oligotrophic environment, membrane crowding could explicitly link cellular Fe, P, and N uptake status, driving the cell to be co-stressed for multiple nutrients.

Advantages of the colonial form 360
Living in a colony has specific advantages and disadvantages for a Trichodesmium cell. Colonies may be able to access nutrient sources that would be infeasible for use by single cells or filaments. For instance, Trichodesmium colonies have a remarkable ability to entrain dust particles and can move these particles into the center of said colony (Basu et al., 2019;Basu and Shaked, 2018;Poorvin et al., 2004;Rubin et al., 2011). In this study, which focused on Trichodesmium colonies, the chemotaxis response regulator CheY was very abundant, particularly in populations sampled near the Amazon 365 and Orinoco river plumes. CheY was positively correlated with Fe stress biomarker IdiA, but not with phosphate stress biomarker SphX, suggesting that chemotactic movement is involved in entrainment of trace metals including from particulate sources (Figure 8).
The metaproteomes and nutrient uptake model presented in this paper support the growing understanding that Trichodesmium must be able to access particulate and organic matter. Living in a colony can be advantageous because such 370 substrates can be concentrated, improving the viability of extracellular nutrient uptake systems. Trichodesmium's epibiont community produces siderophores, which assist in Fe uptake, particularly from particulate organic matter (Chappell and Webb, 2010;Lee et al., 2018). Siderophore production is energetically and nutritionally expensive, so it is most advantageous when resource concentrations are high and loss is low, as would occur in the center of a colony (Leventhal et al., 2019). Colonies may similarly enjoy advantages for phosphate acquisition, particularly when the excreted enzyme 375 alkaline phosphatase is utilized to access organic sources Elizabeth Duncan Orchard, 2010;Orcutt et al., 2013;Yamaguchi et al., 2016;Yentsch et al., 1970). Additionally, the concentration of cells in a colony means that the products of nitrogen fixation, including urea, can be recycled and are less likely to be lost to the environment. By increasing effective size and concentrating deterrent toxins, colony formation may also protect against grazing (Hawser et al., 1992).
A key hallmark of Trichodesmium colony formation is production of mucus, which can capture particulate matter 380 and concentrate it within the colony (Eichner et al., 2019). In addition to particle entrainment, the mucus layer can benefit cells by inhibiting oxygen diffusion, facilitating epibiont associations, regulating buoyancy, defending against grazers and helping to "stick" trichomes together (Eichner et al., 2019;Lee et al., 2017;Sheridan, 2002). However, these benefits come at a cost because the mucus layer hinders diffusion to the cell surface (Figure 9), reducing contact with the surrounding seawater. Despite this, the benefits of colony formation seem to outweigh the costs, since Trichodesmium forms colonies in 385 the field, particularly under stress (Bergman et al., 2013;Capone et al., 1997;Hynes et al., 2012).

Conclusions
Trichodesmium's colonial lifestyle likely produces challenges for dissolved Fe and P acquisition, which must be compensated for by production of multiple nutrient transport systems, such as for particulate iron and organic phosphorous, at a considerable cost. While laboratory studies have largely focused on single nutrient stresses in free filaments, these 390 metaproteomic observations and accompanying nutrient uptake model demonstrate that Fe and P co-stress may be norm rather than the exception fo colonies in the North Atlantic ocean. This means that the emphasis on single limiting nutrients in culture studies and biological models may not capture the complexities of Trichodesmium's physiology in situ. Thus, biogeochemical models should consider incorporating Fe and P co-stress conditions. Specifically, in this study and in others there is evidence that nitrogen fixation is optimal under co-limited or co-stressed conditions, implying that an input of either 395 Fe or P could counter-intuitively decrease N 2 driven new production (Garcia et al., 2015;.
These data demonstrate that Trichodesmium cells are confronted by the biophysical limits of membrane space and diffusion rates for their Fe, P, and possibly urea, acquisition systems. This means that there is little room available for systems that interact with other resources such as light, CO 2 , Ni, and other trace metals, providing a mechanism by which F 13 nutrient stress could compromise acquisition of other supplies. The cell membrane could be a key link allowing 400 Trichodesmium to optimize its physiology in response to multiple environmental stimuli. This is particularly important in an ocean where nutrient availability is sporadic and unpredictable. Future studies should aim to characterize the specific regulatory systems, chemical species and phases (i.e. dissolved versus particulate nutrient sources), and symbiotic interactions that underlie Trichodesmium's unique behavior and lifestyle.

Data Availability
All new data is provided in the supplementary material. The mass spectrometry proteomics data have been deposited to the ProteomeXchange Consortium via the PRIDE partner repository with the dataset identifier PXD016225 and 10.6019/PXD016225 (Perez-Riverol et al., 2019).

Supplement
Supplementary information is provided in a separate file ( Figure S1, Table S1, Table S2, Table S6), with Tables S3,   S4, and S5 provided separately due to their large sizes. helped with proteomics analyses. N.A. prepared the manuscript with contributions from all co-authors.

Competing Interests 420
The authors declare no competing interests. Most samples exist in duplicate or triplicate; see Table S2 for detailed information.    [Fe] env [PO 4 3-] env ? Cell P Regulation (Including PhoRB system) Cell Fe Regulation (Including Fur system) Cell size/growth rate (Including Tery_1090) Cell N Regulation