Constraining growth rates and the ratio of living to nonliving particulate carbon using beam attenuation and adenosine‐5′‐triphosphate at Station ALOHA

Carbon is not only the foundation of all life on our planet, but also an element that persists in detrital material long after living organisms die. Quantifying the relative amount of living and nonliving carbon in suspended particles in the ocean is challenging and rarely done; yet it is key to understanding the fate of organic matter and informing food web models. Here, we use particulate adenosine‐5′‐triphosphate (ATP) and particulate carbon (PC) data collected as a component of the Hawaii Ocean Time‐series program to show that living particles comprise only ~ 26–42% of the total PC pool in the surface waters of the North Pacific Subtropical Gyre, regardless of time of year. Diel‐resolving particulate beam attenuation data are then used in conjunction with PC and ATP data to constrain living particle net growth rates for this system, yielding rates of ~ 0.5–0.7 d−1 year‐round. These estimates are realistic and consistent with previous microscopy and incubation‐based work in the region.

Total organic carbon in the ocean is distributed among three operationally-defined pools: dissolved organic carbon (which includes colloids and particles < 0.2 μm such as viruses), nonliving particulate organic carbon (e.g., detritus), and living carbon or biomass (Karl and Dobbs 1998). The daily cycles of life and death of ocean microbes largely facilitate the exchange of organic carbon between these three reservoirs (Rochna 1963;Karl et al. 1991;Karl and Dobbs 1998). This makes the sheer mass of living organisms "one of the most important master variables in microbial ecology" (Karl and Dobbs 1998). Yet, the proportion of living microbial biomass in the ocean relative to total organic carbon is poorly constrained, as is how such a parameter varies in situ over seasonal to multi-year times scales. Current estimates of the relative percentage of living carbon within the euphotic zone in the global ocean varies widely, ranging from~30% of the total particulate carbon (PC) in the oligotrophic subtropics tõ 80-100% in more eutrophic systems (Holm-Hansen and Booth 1966;Gordon 1971;Gordon et al. 1979;Costa-Pierce et al. 1984;Karl and Dobbs 1998;Graff et al. 2015). While the general consensus is that the fraction of living biomass scales onto ocean productivity (although exceptions have been argued, see Arteaga et al. 2016), how it varies within an ecosystem is not well known. This is the case largely because there is no direct way to separate living from detrital carbon (Eppley 1968;Laws 2013). Prior efforts to do so have relied on single cell analysis and sorting flow-cytometry, which are time-consuming, laborious, and only able to access a fraction of the microbial population (e.g., < 5 μm; Heldal et al. 2003;Graff et al. 2012Graff et al. , 2015. Indirect proxies for the living component of carbon in the ocean also exist. The concentration of the light-harvesting pigment chlorophyll a (Chl a) can be used as a proxy for the autotrophic fraction of living cells (e.g., Sathyendranath et al. 2009). However, the carbon to Chl a ratio is not constant; cells may alter cellular Chl a content as a function of the ambient light and nutrient environment and, hence, Chl a-to-phytoplankton carbon ratios may vary by an order of magnitude (e.g., Marra 1997).
The scattering or attenuation of light in situ or as estimated from ocean color satellites have also been used as optical proxies for carbon concentrations (e.g., Behrenfeld et al. 2005). Specifically, the particulate beam attenuation coefficient (c p ), an optical property generally measured at 660 nm, is considered a reliable proxy for in situ PC concentrations (living + nonliving) in oligotrophic waters where particle sizes are roughly constrained between 0.5 and 20 μm (Siegel et al. 1989;Stramski and Kiefer 1991;Gardner et al. 1993;Bishop 1999) and where the shape of the particle size distribution (PSD) does not change significantly over time (Stramski and Kiefer 1991). High frequency observations of c p have shown that this property oscillates over the diel cycle presenting minimum concentrations around sunrise and maximum concentrations around sunset, reflecting the balance between daytime particle growth due to photosynthesis and nighttime losses such as respiration (Siegel et al. 1989;Cullen et al. 1992;Stramski et al. 1995;Claustre et al. 2008;White et al. 2017). This diel-oscillating portion of the c p signal is often attributed to the dynamics of living particles, such that its daily amplitude has been shown to correlate with the daily rate of 14 C-based carbon fixation in oligotrophic systems (White et al. 2017). This suggests that the amplitude relative to the baseline should also approximate a fraction of the living component of PC but, to our knowledge, this has not been tested.
A more classical approach to measurement of living carbon is via quantification of particulate adenosine-5 0 -triphosphate (ATP); ATP is a ubiquitous molecule present in all living cells, heterotrophs and autotrophs alike (Holm-Hansen 1973;Karl 1980). Since ATP is present in the cytoplasm, it is not retained by particulate material upon cell death and autolysis, and is not readily adsorbed (Holm-Hansen and Booth 1966); it is considered a reliable proxy for total living microbial biomass, provided that the living carbon : ATP ratio can be approximated within reasonable bounds. This is indeed assumed to be the case; the intracellular concentration of ATP is maintained at a basal level proportional to biovolume (1-2 mM; Karl and Dobbs 1998) suggesting that carbon-toparticulate ATP ratios should be fixed. In a recent reanalysis of ATP as a biomass indicator, Bochdansky et al. (2021) found the mean C : ATP ratio measured via five different approaches for the diatom Thallasiosira weissflogii (280) to be "remarkably similar to the 250 ratio in Holm-Hansen (1970)" and concluded that "ATP may be the closest metric we have for determining how alive a parcel of water truly is".
ATP is not routinely sampled in the open ocean. However, the Hawaii Ocean Time-series (HOT) program is a notable exception. Since 1989, the HOT program has made nearmonthly measurements of particulate ATP throughout the euphotic zone along with other carbon and biomass markers such as total PC concentrations, flow cytometric measurements of picoplankton and heterotrophic bacteria (HBact), and pigment concentrations at Station ALOHA,~100 km north of the island of Oahu, Hawaii (see Karl and Church 2017). Since 2015, this program has also obtained high frequency measurements of c p , providing an unprecedented opportunity to compare independent methods for estimation of biomass and growth of living and detrital material. Here we report the first ever comparison of particulate ATP and optical proxies for carbon composition and detail the time-dependent variability in these fractions in the North Pacific Subtropical Gyre (NPSG) over a 15+ year period.

Particulate beam attenuation coefficient
Continuous (< 1 min sampling resolution) measurements of the beam attenuation coefficient at 660 nm using a C-Star instrument in flow-through mode (25 cm pathlength, Sea-Bird Scientific) have been collected during HOT cruises at near-monthly resolution from 2015 to 2020 (n = 37 cruises and a total of 92 d; HOT cruises #272-323). HOT cruises last 4 days and are centered at Station ALOHA (22.75 N; 158 W). Sampling periods including transit to and from station were excluded to avoid convolution of spatial variability to the observed signal; thus, each cruise provides~1-3 days of high-resolution, continuous beam attenuation data. The C-Star instrument is operated using a dark optical tube to avoid light contamination, and setup includes a debubbler and a valve control device used to divert water pumped from~7 m depth to a 0.2 μm membrane filter for the first 10 min of every hour to provide background estimates of beam attenuation due to water and dissolved substances (Slade et al. 2010). These blank values were linearly interpolated throughout the cruise and subtracted from the raw measurements to provide particulate beam attenuation coefficients (c p , m À1 ). Data were subsequently binned to hourly intervals.
Adequate interpretation of c p as a proxy for PC requires that the c p : PC relationship is robust over time. Previous work relying on high-frequency pairs of c p and PC data in this region (up to 6Â per day) showed good correspondence between c p and PC (slope = 749 AE 98 [mean AE SD] mg C m À2 ; r 2 = 0.89), constant c p : PC ratio across samples dominated by blooms vs. non-blooms, and no discernable diurnal oscillations in the ratio of c p : PC (Henderikx-Freitas et al. 2020). Significant changes in the PSD, however, can affect c p : PC slopes, given that attenuation efficiency is a nonlinear function of particle size (Stramski and Kiefer 1991). The PSD is thought to vary little over the seasonal cycle at Station ALOHA White et al. 2015). Particle size data are not readily available to fully test these assumptions on a cruise-to-cruise basis. For these reasons, the analysis relies on the overall patterns of c p without explicit conversions to PC units, while acknowledging the potential for biases in the c p : PC relationships affecting specific cruises.

ATP, Chl a, PC, and HBact
Sampling of ATP, Chl a, PC, and HBact are a routine part of the HOT program core measurement set (https://hahana. soest.hawaii.edu/hot/hot-dogs/). Here, we use all nearmonthly (~10Â per year) ATP (μg L À1 ), Chl a (μg L À1 ), PC (μg L À1 ), and HBact (cells L À1 ) data collected from the top 25 m of the water column via the HOT program from 2003 onwards (HOT cruises #150-307), and processed using standard HOT protocols (see Supporting Information S1). This depth horizon is within the mixed layer depth (MLD) 98% of the time (MLD = 62 AE 26 m for the considered period, and is calculated as the first depth where potential density increases by 0.125 kg m À3 relative to a 10 m offset). Since cruises last several days, not all variables are collected at the same time within each cruise. For instance, ATP and PC are usually collected at the same time of day, but about a day apart. Comparisons among variables were made on a cruise-to-cruise basis, even if they were not obtained at the exact day or time. In order to reduce variability that may arise from potential diel oscillations, only data from the following time windows were selected for each variable: noon-16:00 h local time (for ATP, PC, and HBact, with 91% of data sampled between 14:00 and 15:00 h), and 19:00-midnight (for Chl a, with 92% of data sampled between 20:00 and 21:00 h).
Estimating living C and growth rates from PC, ATP, and c p data Here, we assume that the daily increase in c p or C by proxy reflects a net accumulation factor of living C during carbon components with unknown proportions. C min and C max are the minimum and maximum c p (or C) measured per day, roughly near sunrise and sunset, respectively (see Supporting Information S2). (b) Net C L growth rates (μ d ) calculated using Eq. 2 for a selected range of percent daily increases in c p (e.g., α = 1.1-1.6 [or 10-60%]), and different fractions of C D . Note that daily increases in c p can represent a wide range of percent C L provided that μ d varies accordingly.
daytime (C max /C min ), which is proportional to what Claustre et al. (2008) and White et al. (2017) termed "gross community production." The magnitude of c p reflects the sum of living C (C L , which includes all autotrophic, mixotrophic, and heterotrophic organisms that can be sensed by the transmissometer based on their size and optical properties, and whose interactions result in net C accumulation during the day), and nonliving C (e.g., detritus, C D ), at unknown proportions in the surface ocean (Fig. 1a). Detritus is defined here as the particulate portion of all non-respiratory C losses from all levels of the food web (Wetzel et al. 1972), assuming autochthonous origin. C L is assumed to contain both actively growing particles (at various growth rates) as well as viable particles (i.e., capable of DNA synthesis and division) in dormant or senescent modes (Veldhuis et al. 2001;Kirchman 2016). We additionally assume that (1) c p changes can be linearly related to changes in PC volume over time (White et al. 2017;Henderikx-Freitas et al. 2020); (2) the PSD of living and nonliving pools are similar (no evidence of the contrary is available); (3) the nonliving C pool does not oscillate significantly over the daylight period (e.g., Winn and Karl 1984;Durand and Olson 1996); and (4) the apparent C accumulation during the day is primarily a result of net biological/particle transformation processes (i.e., growth, respiration, grazing, dissolution, aggregation), with sinking, intrusions, and lateral advection assumed to have a negligible role on net changes. Note that an unknown portion of the living C accumulated and lost throughout the daily cycle likely becomes part of the nonliving C pool, and such transformations are implicitly assumed to be contained in the next day's diel cycle amplitude (daily maximum minus daily minimum) and baseline (daily minimum per cruise). Since the C L pool may include particles not actively growing during the photoperiod, it is not possible to directly interpret daily percent increases in c p as increases in percent C L without knowledge of net particulate C L growth rates during the daylight period, μ d (d À1 ), assuming exponential growth: where CmaxÀCD CminÀCD h i is equivalent to the fraction of C L to the total C pool (see Fig. 1a). For simplicity, t is considered to be equal to 1 day to reflect growth rates during the day only, thus assuming near steady state over a 24 h period (White et al. 2017; see overall symmetric cycles in Fig. 2). The ratio of ATP (a proxy for living C) to total PC concentrations provides a more direct estimate of the proportion of C L included in the particulate (> 0.2-202 μm) carbon pool. This requires that ATP concentrations first be converted to C units. Although large variability in C L : ATP values (~100-1000 g g À1 ) can be found in the literature, values for Station ALOHA have been reported to range between 250 and 400 g C : g ATP (Karl 1980;Christian and Karl 1994); thus, ratios using these two conversion factors are presented as lower and upper bounds of percent C L estimates (e.g., % C L = [ATP Â m/ PC] Â 100, where m is either 250 or 400).
The fraction of C L (or the complementary fraction of detrital C, f ) obtained from the ATP analysis can be used in a modification of Eq. 1 to help constrain the net growth rates of C L implied by the daily accumulation of total C measured via c p (see Fig. 1b). Given that C max can be expressed as αC min , where α is a value larger than 1, and C D = fC min , Eq. 1 can be rewritten as: Reliability of the proportions of living and nonliving particles obtained from the ATP and PC data was assessed by checking if realistic values of heterotrophic bacteria carbon quotas, phytoplankton carbon concentrations (PhytoC), and C : Chl a ratios can be implied from the relationships between ATP, PC, HBact, and Chl a, using the inversion approach of Christian and Karl (1994) (see Supporting Information S3). Additionally, traditional estimates of growth rates based on 14 C assimilation per Chl a and phosphorus uptake rates were obtained to aid interpretation of μ d (see Supporting Information S3).

Results and discussion
High frequency c p data revealed repeatable diurnal cycles (Figs. 2, 3a) with a 2-fold change in baseline values (Fig. 3b), 3-fold change in amplitudes (Fig. 3c), and no clear seasonality (see Supporting Information S4). Consistent with the c p dataset, ATP data are illustrative of what Venrick (1993) called the "endless summer" of the North Pacific Subtropical Gyre, where seasonality of the surface ocean biomass is muted (Fig. 4a,b). PC and HBact tend to peak in late summer (Fig. 4c-f), and Chl a signals are consistent with phytoplankton photoadaptation processes (Fig. 4g-h), illustrating how Chl a is not a reliable proxy for surface biomass in this region. The daily percent increase in c p (Fig. 5a) averaged 32 AE 10%, consistent with previous diel-based observations of c p and PC in the region (White et al. 2017;Henderikx-Freitas et al. 2020). ATP : PC ratios show that between 26 AE 8% (for C L : ATP = 250) and 42 AE 12% (for C L : ATP = 400) of particles are living (Fig. 5b). This implies that, on average, the remaining~58-74% are detrital. Percent living C estimates showed little month-to-month variability (coefficient of variation = 7%; Fig. 5b).
Validity of the proportions presented in Fig. 5b was assessed via the inversion approach of Christian and Karl (1994). Assuming a C L : ATP value of 250 yielded average surface C : Chl a ratios of 75 AE 21 g g À1 , C : HBact values of 13 AE 3 fg cell À1 , and estimated PhytoC concentrations of 4 AE 2 mg C m À3 for the May-October period (excluding months of June and September for which coefficients were negative or near zero due to the reduced number of months where ATP, PC, Chl a, and HBact data were available simultaneously). Assuming C L : ATP of 400 yielded average C : Chl a ratios of 119 AE 34 g g À1 , C : HBact of~18 AE 4 fg cell À1 , and PhytoC of~6 AE 4 mg C m À3 . Although variability is large, these values are all within the reported C : Chl a ratios for the surface ocean at Station ALOHA (Christian and Karl 1994), fg cell À1 of C in HBact from various laboratory studies using local NPSG cultures (Casey et al. 2019;White et al. 2019), and PhytoC estimated from fieldand satellitebased studies in the NPSG (Graff et al. 2015;Arteaga et al. 2016), suggesting that the proportion of living particles to the total particulate pool ranging between~26-42% is reasonable. Indeed, percentages are consistent with estimates indicating that living, viable organisms make up~30% of living C in oligotrophic regions (e.g., Winn and Karl 1984;Christian and Karl 1994;Graff et al. 2015), and is in agreement with previous descriptions of the PC pool in the open ocean as consisting of "living carbon in a soup of nonliving organic matter" (Karl and Dobbs 1998).
Together, the daily percent increase in total C (or c p ) of 30% (Fig. 5a) and detrital C fractions averaging 58-74% (Fig. 5b) imply that net growth rates of the living particle pool (μ d ) are constrained between 0.54 and 0.75 d À1 (from Eq. 2; Fig. 1b), where a value of 0.69 d À1 indicates doubling of biomass over the light cycle. Fully validating the magnitudes of the bulk living particle growth rates and quantifying their variability in situ is impractical, since that would require measuring growth rates for all living populations over relevant time scales. Lab-based estimates of phytoplankton growth rates at Station ALOHA alone have been reported to range anywhere between 0.5 and 2 d À1 Jones et al. 1996;Laws 2013). Flow cytometry-based studies have also observed a wide range in growth rates of specific nanoplankton (0.6-1.6 d À1 ; including both autotrophic and heterotrophic organisms > 4-100 μm in diameter; Dugenne et al. 2020), although Prochlorococcus and Synechococcus (the two most abundant picophytoplankton in the oligotrophic gyres) generally exhibit growth rates of~0.5-0.9 d À1 year-round (Liu et al. 1997;Ribalet et al. 2015). Growth rates of heterotrophic bacteria in the oligotrophic ocean have recently been reported to range between 0.5 and 1.1 d À1 (White et al. 2019;Popendorf et al. 2020), but it is not clear to what extent their dynamics are synchronous to that of light-driven organisms. Estimates of net living particle growth rates such as the ones presented here (0.54-0.75 d À1 ), which represent food-web interactions, should be on the lower end of the phytoplankton-specific growth rates calculated for the region. Furthermore, our estimates reconcile well with incubation-based 14 C assimilation per Chl a of~80 AE 25 g C g À1 Chl a d À1 at Station ALOHA which, along with average C : Chl a ratios from above suggest average phytoplankton growth rates between 0.47 and 0.74 d À1 . Likewise, mean phosphate uptake rates of 4 AE 1 nmol P L À1 d À1 for surface waters of Station ALOHA, along with particulate phosphate (P-PO 4 ) pools averaging 12 AE 4 nmol L À1 (Björkman et al. 2018), and assuming that the living P-PO 4 pool makes up~50% of the total P-PO 4 pool (D. Karl, personal communication), suggest similar living particle growth rates of 0.52 AE 0.26 d À1 .
Living particle growth rates that are comparable to specific growth rates of phytoplankton, along with the likelihood that HBact biomass makes up only a small portion of the particulate ATP and c p signals due to their low scattering efficiency (in the case of c p ; Stramski and Kiefer 1991) and small size (~0.1-0.5 μm) compared to filter size (in the case of ATP), suggests that the % daily increase in c p reflects, to first order, the dynamics of living plankton. If these conclusions are correct, one would also expect a diel cycle in ATP concentrations to exist in situ. Understanding to which extent different components of the microbial food web are represented by the bulk growth rates, however, is not straightforward since particles may affect the signals in direct and indirect ways. For instance, HBact convert dissolved organic carbon to PC, and also degrade PC (Azam and Hodson 1977), and such transformations are represented in the bulk c p and ATP signals (White et al. 2017). Similarly, whereas the indirect influence of zooplankton is included in the c p formulations presented here via daytime grazing dynamics, their direct contribution to total biomass changes may be misrepresented if zooplankton biomass is a large portion of total biomass that consistently peaks at nighttime (White et al. 2017). Contemporaneous tracking of these diverse particle pools would be needed to understand how they affect the net growth rates suggested here. Nonetheless, these results may prove relevant in informing biogeochemical models aiming to characterize particle transformation processes associated with conversions between living and nonliving C pools as particles leave the surface mixed-layer.