Biogenic Silica Dissolution in Diatom Aggregates: Insights from Reactive Transport Modelling

Vol. 517: 35–49, 2014 MARINE ECOLOGY PROGRESS SERIES Published December 15 doi: 10.3354/meps11028 Mar Ecol Prog Ser

Biogenic silica dissolution in diatom aggregates: insights from reactive transport modelling

Brivaëla Moriceau1,*, Goulven Gildas Laruelle2,3, Uta Passow4, Philippe Van Cappellen5, Olivier Ragueneau1

1Laboratoire des Sciences de l’Environnement Marin, UMR 6539 CNRS/UBO/IRD, IUEM, Technopôle Brest-Iroise, 4 rue Dumont d’Urville, 29280 Plouzané, France 2Faculty of Geosciences, Department of Earth Sciences — Geochemistry, Utrecht University, PO Box 80021, 3508 TA Utrecht, The Netherlands 3Biogeochemical Modelling of the Earth System, Dépt. des Sciences de la Terre et de l’Environnement, Université Libre de Bruxelles, 1050 Bruxelles, Belgium 4Marine Science Institute, University of California Santa Barbara, CA 93106, USA 5Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, ON N2L 3G1, Canada

ABSTRACT: Diatom aggregates contribute significantly to the vertical sinking flux of particulate matter in the ocean. These fragile structures form a specific microhabitat for the aggregated cells, but their internal chemical and physical characteristics remain largely unknown. Studies on the impact of aggregation on the Si cycle led to apparent inconsistency. Despite a lower biogenic silica (bSiO2) dissolution rate and diffusion of the silicic acid (dSi) being similar in aggregates and in seawater, dSi surprisingly accumulates in aggregates. A reaction−diffusion model helps to clarify this incoherence by reconstructing dSi accumulation measured during batch experiments with aggregated and non-aggregated Skeletonema marinoi and Chaetoceros decipiens. The model calculates the effective bSiO2 dissolution rate as opposed to the experimental apparent bSiO2 dissolution rate, which is the results of the effective dissolution of bSiO2 and transport of dSi out of the aggregate. In the model, dSi transport out of the aggregate is modulated by alternatively considering retention (decrease of the dSi diffusion constant) and adsorption (reversible chemical bonds between dSi and the aggregate matrix) processes. Modelled bSiO2 dissolution is modulated by the impact of dSi concentration inside aggregates and diatom viability, as enhanced persistence of metabolically active diatoms has been observed in aggregates. Adsorption better explains dSi accumulation within and outside aggregates, raising the possible importance of dSi travelling within aggregates to the deep sea (potentially representing 20% of the total silica flux). The model indicates that bSiO2 dissolution is effectively decreased in aggregates mainly due to higher diatom viability but also to other parameters discussed herein.

KEY WORDS: Silicic acid · dSi accumulation · dSi diffusion · dSi adsorption · Transparent exopolymer particles · TEP · Viability · Si cycle

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INTRODUCTION areas (Nelson et al. 1995, Tréguer et al. 1995, Mann 1999, Booth et al. 2002, Tréguer & De La Rocha 2013), Diatoms are an important phytoplankton group for diatoms contribute appreciably to carbon export the study of biogeochemical cycles, linking carbon (Nel son et al. 1995, Tréguer et al. 1995, Buesseler and silica cycles through their particular metabolism. 1998, Ragueneau et al. 2006). This statement is sup- With a share of 40% on average of the global oceanic ported by strong correlations observed at depth be - primary production and up to 75% in nutrient-rich tween silica and organic carbon sinking fluxes (Arm-

*Corresponding author: [email protected] © Inter-Research 2014 · www.int-res.com 36 Mar Ecol Prog Ser 517: 35–49, 2014

strong et al. 2002, 2009, Ragueneau et al. 2006). Con- 2007b). This raises the question of how such high dSi sidering that export results from the equilibrium concentrations can occur inside aggregates while dSi between sedimentation and remineralisation rates, a diffusion extrapolated from oxygen diffusion is similar single cell has almost no chance of escaping dissolu- to diffusion in seawater and bSiO2 dissolution is lower tion and degradation in the euphotic zone (Moriceau in aggregates. In laboratory experiments, dissolution et al. 2007a), except for some large deep-dwelling rates for aggregated diatoms are derived from the ki- diatoms (Kemp et al. 2006). However, as components netics of the dSi concentration increase outside the of aggregates or faecal pellets, diatoms can be ex - aggregates. The net dissolution rates measured from ported to the deep layers of the ocean and to the sed- the build-up of dSi outside the aggregates are appar- iment floor in only few days, as shown by direct ent silica dissolution rates resulting from both the observations of diatomaceous phytodetritus at the effective dissolution rate of frustules inside the ag - sea floor (Billett et al. 1983, Kemp et al. 2000). Aggre- gregates and the transport of the newly generated dSi gates and faecal pellets are indeed the main contri- out of the aggregates. The only way to separate the butors to the sedimentation fluxes (Thornton 2002, effects of dissolution kinetics and intra-aggregate Turner 2002, Guidi et al. 2009, Iversen & Ploug 2010, transport is to use a reaction-transport model to calcu-

Stemmann & Boss 2012). late the effective bSiO2 dissolution rates of aggregated The aggregation process promotes the export of sil- dia toms while reconstructing the accumulation of dSi ica not only through an increase in the sedimentation inside the aggregates. We therefore conducted 2 sets rate, but also through a decrease in biogenic silica of modelling experiments to test the implications of al-

(bSiO2) dissolution rates (Passow et al. 2003, Moriceau ternative mechanisms of transport and dissolution et al. 2007b). Moreover, while aggregates efficiently within diatom aggregates. export particulate matter, these particles also transport The first set of model simulations sought to under- the dissolved matter trapped within their porewater stand transport of dSi inside an aggregate. The accu- (De La Rocha et al. 2008). Roughly 20% of nitrogen mulation of dSi within aggregates was modelled and carbon fluxes are transported in their soluble alternatively using adsorption and retention pro- forms inside aggregates (Carlson et al. 1994, 1998, cesses to slow down dSi transport within aggregates. Williams 1995, Hansell & Carlson 1998, Engel et al. The goodness of fit to experimental dSi concentra- 2004, Hopkinson & Vallino 2005). To our knowledge, tions measured outside and inside the aggregates similar estimates have not yet been made for silicic was used to choose between these 2 processes. In our acid. Concentrations of silicic acid, dSi, within diatom study, ‘retention’ refers to processes possibly slowing aggregate porewater could be 4 to 50 times higher down dSi transport without involving chemical bind- than the environmental dSi concentrations (Brzezinski ing as in Van der Waals interactions, polarity or size et al. 1997, Moriceau et al. 2007b). On the other hand, of silicic acid molecules, and fractal dimensions of the estimates of dSi diffusion out of aggregates based on aggregates. In contrast, the term ‘adsorption’ in clu- direct determinations of oxygen diffusivity within ag- des all reversible processes involving chemical bind- gregates suggest that diffusion is only slightly ing of dSi to the aggregate matrix. reduced in aggregates, with values approaching 90% The second modelling experiment estimated the of free diffusion in seawater (Ploug & Passow 2007). relative contribution of 2 parameters identified and These 2 results could be easily explained considering measured during an earlier experimental study a very fast bSiO2 dissolution within aggregates to (Moriceau et al. 2007b) to change the effective disso- compensate for the diffusion of dSi out of aggregates lution rates of aggregated diatoms compared to their as hypothesized by Brzezinski et al. (1997). Moreover, free counterparts. The 2 identified processes are (1) this hypothesis would be supported by the bacterial the elevated dSi concentrations inside aggregates community found on marine aggregates (DeLong et that reduce the thermodynamic driving force for al. 1993) together with the high bacterial degradation bSiO2 dissolution and, hence, the effective dissolu- measured in marine aggregates (Smith et al. 1992, tion rate (Van Cappellen & Qiu 1997), and (2) the Iversen & Ploug 2010) that is generally associated diatom cells maintaining a higher ratio of metaboli- with high bSiO2 dissolution rates (Bidle & Azam 1999, cally active cells (hereafter called viability) in the Tamburini et al. 2006). However, direct measurements aggregates than when freely suspended in seawater. of silica dissolution have invalidated this hypothesis, Metabolically active cells tend to inhibit the dissolu- as dissolution rates even lower than in freely sus- tion of their frustules, hence again leading to lower pended diatoms have been measured for aggregated effective silica dissolution rates for aggregated dia - diatom cells (Passow et al. 2003, 2011, Moriceau et al. toms (Nelson et al. 1976, Passow et al. 2011). Moriceau et al.: Biogenic silica dissolution in aggregates 37

The model simulates bSiO2 dissolution of diatom Table 1. Parameters used in the model with the parameteri - frustules within an aggregate. Parameterization is zation and initial conditions chosen from the experiment de - scribed by Moriceau et al. (2007b) and from the literature. dSi: based on data from in vitro dissolution experiments silicic acid; SM: Skeletonema marinoi; CD: Chaetoceros decipi- conducted with Skeletonema marinoi and Chaeto- ens; conc.: concentration; NM: not measurable. Subscript agg: ceros decipiens (Moriceau et al. 2007b). The model aggregate; aq: aqueous calculates effective dissolution rates for the various scenarios con sidered as well as the net flux of Abbreviation Value Units silicic acid out of the aggregates. Using this flux, the Parameter model derived the temporal evolution of internal and −1 Molecular weight MWbSiO2 66 g mol external dSi concentrations. Together with the ave - a 3 −3 Porosity φ 0.95 cm aq cm agg rage internal dSi concentration, the latter can be Diffusion constantb D 0.80 × 10−5 cm2 s−1 compared to the dSi concentrations measured exper- c −1 dSi solubility dSieq 1500 μM (μmol l ) imentally. Final average dSi conc. 3232 −1 in an aggregate dSiagg 80 μM (μmol l ) Viability METHODS SM fviab NM CD 0.50 Model description Aggregate radius SM ragg 0.375 cm CD 0.3 General description Volume of seawater per aggregate SM V 10 cm3 In the model, an aggregate is re pre sented as a CD 12.5 porous sphere of radius ragg composed of biogenic Initial conditions (experimental data) silica (bSiO2) embedded in a gel-like matrix of External dSi conc. −1 transparent exo polymer particles (TEP). Most of the SM dSiext 6 μM (μmol l ) CD 9 aggregate’s volume is occupied by seawater, Internal bSiO2 conc. through which dSi diffuses. The constant porosity φ −1 SM bSiO2 1.41 mmol l agg of 0.95 (Table 1) imposed in the aggregate model CD 3.8 accounts for the volume contributions of diatom aPassow (2002); bRebreanu et al. (2008); cVan Cappellen & cells (1% in Moriceau et al. 2007b) and TEP (4% in Qiu (1997) Passow 2002). Using an equation from a study by Nielsen (1984), and the median value for excess −4 density of marine snow aggregates Δρ = 1.4 × 10 g where Vagg and SAagg are the volume and the surface −3 cm presented by Alldredge & Gotschalk (1988), area of the aggregate, respectively; bSiO2 is the bio- the diffusion layer thickness δ was estimated at genic silica concentration in the aggregate, MWbSiO2 0.01 cm, which is typical for many mass transfer is the molecular weight of the biogenic silica, and problems (Cussler 1984). Ploug & Jørgensen (1999) Radis is the apparent dissolution rate constant of the and Bou dreau & Jørgensen (2001) reported values biogenic silica. between 0.04 and 0.08 cm by measuring oxygen We hypothesized that a diffusive layer of 0.01 cm distributions around an aggregate of similar size as with a dSi concentration of 10−1 μM would not change the diatom aggregates used herein (see Table 1) the results of the model. Consequently, the diffusive sinking freely through seawater at 60 m d−1. At layer was not taken into account in this model. higher flow velocities as generally measured in Spatial and temporal changes in the silicic acid aggregates made in roller tanks (Iversen & Ploug concentration inside the aggregate (dSiagg) are calcu- 2010, Ploug et al. 2010), the relative flow velocity lated assuming spherical symmetry and molecular increases and δ decreases. The concentration dif- diffusion as the only solute transport mechanism: ference of the dSi in the aggregate and its bound- ∂dSiagg 1 ∂ ⎛ ∂dSiagg ⎞ ary layer approximated using Fick’s law should not = ⋅ rD2 ⋅⋅ + R (2) t r 2 r ⎜ eff r ⎟ dSi exceed 10−1 μM. This value was obtained from a ∂ ∂ ⎝ ∂ ⎠ flux of silicic acid across the boundary layer of 1.13 where t is time, r is the radial distance from the × 10−4 nmol cm−2 s−1 calculated with Eq. (1): centre of the aggregate, with a maximum value of

ragg being the radius of the aggregate, Deff is the JV= agg⋅⋅bSiO 2 MW bSiO2 ⋅ Ra dis/ SA agg (1) ()effective diffusion constant, and RdSi is the net rate of 38 Mar Ecol Prog Ser 517: 35–49, 2014

production of dSi in the aggregate or the effective of bSiO2 (Van Cappellen et al. 2002) and will be bSiO2 dissolution rate. used in this study considering the high silicic acid The effective diffusion constant used to model dSi concentrations measured experimentally in aggre- transport inside aggregates, Deff, is calculated using gates (Shanks & Trent 1979, Brzezinski et al. 1997, the molecular diffusion constant of dSi, D. D is pro- Moriceau et al. 2007b). Eq. (5) assumes that diatom portional to the rate at which dSi molecules are trans- cells must be dead in order for their frustules to dis- ported from a more concentrated medium to a less solve (Nelson et al. 1976, Passow et al. 2011). During concentrated one. D has been measured in seawater a model run, the value of fviab remains constant, as no at 15°C by Rebreanu et al. (2008). To adapt the dSi measurable change in the ratio of active diatoms was diffusion constant, D, measured in seawater to the detected for up to 480 h in a study with Thalassiosira aggregate porewater, D is corrected using Eq. (3) for weissflogii aggregates (Garvey et al. 2007). the tortuosity of the aggregate, which is a function of In the ‘adsorption’ version of the model, we hypoth- the aggregate porosity φ (Boudreau 1997): esized that high dSi concentrations inside aggregates are due to adsorption of dSi to the aggregate matrix. D = D /(1 – ln(φ2)) (3) dSi When adsorption occurs, 2 pools of soluble silica Given that aggregate particles are fractal, diatom coexist within the aggregates, i.e. the free dSi, which cells are assumed to be homogeneously distributed is freely diffusing through the aggregate porewater, inside the aggregate. We further assumed that no and the adsorbed dSi, which is reversibly bound to bSiO2 production took place in the aggregates, as the the aggregate matrix. Therefore, the model considers experiments were conducted in the dark (Peters & 3 pools of dSi: (1) the external dSi (dSiext) in the sea- Thomas 1996), hence mimicking aggregates sinking water surrounding the aggregate, (2) the adsorbed rapidly out of the euphotic zone. dSi (dSiads) inside the aggregate and (3) the free dSi (dSifree) in the aggregate. The 3 dSi pools are linked to each other through the adsorption equilibrium

Variations including retention or adsorption between dSifree and dSiads, and through the diffusion of dSifree out of the aggregate: In the retention version, we introduce a retention kads Deff dSiads←→⎯⎯ dSi free ←⎯⎯ → dSiext (6) factor fret equal to or greater than 1: At any point in time and space, the free and D = D /f (4) eff dSi ret adsorbed dSi in the aggregate are assumed to be in

In this version of the model, RdSi of Eq. (2) is equilibrium. We further assume that the 2 concentra- expressed as follows: tions are related by a simple linear isotherm (Berner 1 1980) through the dSi linear adsorption constant kads: RkbSiO MW 10−6 dSi= ⋅⋅ dis22 ⋅() bSiO ⋅ ⋅ φ dSiads= k ads⋅ dSi free (7) m (5) ⎛ ⎞ dSiagg The total concentration of the dSi in aggregate ()1− fviab ⋅−⎜1 ⎟ 333 ⎜ dSi ⎟ (dSiagg ) is calculated by the adsorption version of the ⎝ eq ⎠ 333 model at the end of the dissolution. dSiagg is the sum where kdis is the mass-normalized dissolution rate of the dSifree and dSiads in each slice of the aggregate, 333 constant of bSiO2, MWbSiO2 is the molecular weight of integrated over the whole aggregate. dSiagg is com- bSiO2, fviab is the fraction of metabolically active pared to the internal dSi concentrations measured in diatoms, dSieq is the equilibrium solubility of bSiO2 at laboratory experiments. In the latter, the internal dSi 15°C (Table 1). Note that the dependency of RdSi with is obtained by resuspending aggregates in artificial the undersaturation degree seawater containing no dSi. The fact that the medium is dSi-free causes adsorbed dSi to desorb. The dSi ⎛ ⎞ dSiagg ⎜1− ⎟ analysed in the filtrate after resuspension and break- ⎜ dSi ⎟ ⎝ eq ⎠ age of the sampled aggregate is the total internal dSi 333 concentration of the aggregate dSiagg . can be strongly non-linear at low dSi concentrations In the adsorption version of the model, both the dif- which could be expressed using a value of m > 1, fusion rate of dSifree (Eq. 8), and the dissolution rate where m is the non-linearity parameter. With m = 1, (Eq. 9) are affected by adsorption (Berner 1980): the relation becomes the so-called linear rate law, which is frequently used to describe the dissolution DDeff=+ dSi()1 k ads (8) Moriceau et al.: Biogenic silica dissolution in aggregates 39

tion experiments, 2 with Skeletonema marinoi and 2 1 −6 RkdSi= ⋅⋅ disbSiO22 ⋅ MW bSiO ⋅ 10 ⋅ with Chaetoceros decipiens aggregates. The reac- φ () (9) tion−diffusion model developed here is parameter- ⎛ 1 ⎞ ⎛ dSi ⎞ 1 f 1 free ized using both experimental measurements done ()− viab ⋅⎜ ⎟ ⋅−⎜ ⎟ ⎝ 1+ kads ⎠ ⎝ ddSieq ⎠ during these dissolution experiments and data from the literature (Table 1). Experimental conditions are In contrast, in the retention version, the dissolution described in detail in the study by Moriceau et al. 333 rate depends only on the dSiagg (compare Eqs. 5 & 9). (2007b), and a brief summary is given here. During In both versions, the model-predicted dSiext is the dissolution experiments, aggregated and non- obtained by computing the diffusion flux from the aggregated diatoms were kept in the dark at 13°C. aggregate into the surrounding seawater, using an Continuous sinking was mimicked by using roller average volume of seawater per aggregate consis- tables for diatom aggregates and shaker tables for tent with the experimental conditions (total volume free diatoms. Aggregate concentrations were 100 of the tank divided by the number of aggregates; aggregates l−1 for S. marinoi and 80 aggregates l−1 for Table 1). The surrounding seawater is assumed to be C. decipiens. Aggregate characteristics needed to perfectly mixed, and the boundary condition dSiext = parameterize the model (Table 1) were measured at dSiagg is imposed at the aggregate−medium interface the end of the dissolution experiments. Note that (i.e. at r = ragg, Table 1). After each time step, the these aggregate characteristics were similar to those value of dSiext is updated, taking into account the reported for natural aggregates. mass of dSi that has diffused out of the aggregate Diatom viability was determined by counting the during the time step. The computed temporal evolu- ratio of diatoms stained with fluorescein diacetate tion of dSiext is then compared to the experimental over the total number of diatoms at the beginning of dSiext concentrations versus time measured in the the experiment on C. decipiens (50% of the cells seawater medium surrounding the aggregates. metabolically active in aggregates; unpubl. data). Additionally, the dSi porewater concentration At least 30% of the aggregated S. marinoi were measured at the end of the experiments is compared metabolically active, but the results of Garvey et al. to the integrated concentration of dSi within the (2007) suggest that the rapid fading of the fluores - 333 aggregate (dSiagg ), computed at the end of the model cence of the assay used may invalidate this method run using Eq. (10): for S. marinoi, our second model species.

r Concentrations of dSi in the porewater of 20 aggre- agg 4π dSi (rrrr )⋅⋅⎡ (+ δ )3 − 3 ⎤ gates were determined by isolating each aggregate in ∑ agg agg3 ⎣ agg agg agg ⎦ dSi = r =0 (10) artificial seawater containing no nutrients. dSi concen- agg 4π ⋅⋅r 3 φ tration inside the aggregate was calculated using the 3 agg visible volume (Vagg) of each individual aggregate de- where ragg is the aggregate radius, dSiagg(ragg) is the termined from its width (Wagg) and length (Lagg) as the 2 dSi concentration of the layer between ragg + δragg volume of an equivalent ellipsoid (Vagg = π/6 × W agg × and ragg at t final, and φ is the porosity of the aggre- Lagg). Because the artificial seawater used to isolate gate. each aggregate contained no dSi, the dSi concentration The numerical solution of the model equations uses measured in the aggregate porewater is the total spatial steps of δr = ragg/50 for the retention scenario. dSiagg concentration. Under such conditions, the po- The number of aggregate layers is decreased to 3 in tentially adsorbed dSi would desorb. Internal dSi con- the adsorption scenario, without affecting the results. centration (dSiagg) measured on 20 different aggregates In all model runs, the time steps are 10 h. Parameter for each of the 2 diatom species was 80 μM. values and initial conditions for the simulations are During these 2 experiments, we measured appar- summarized in Table 1. ent dissolution rates by following the temporal evolution of dSi concentrations in the surrounding sea - water of aggregates. Apparent dissolution rates were Input data and model parameterization calculated as the slope of the temporal evolution of

dSi concentrations normalized to the initial bSiO2 Synopsis of the experimental data concentrations. For S. marinoi aggregates, the appar-

ent bSiO2 dissolution rate constant (kdis) was 4.8 nmol −1 −1 The model output was statistically compared to an g bSiO2 s compared to an effective dissolution rate −1 −1 experimental set of data obtained during 4 dissolu- constant of 10.5 nmol g bSiO2 s for freely suspended 40 Mar Ecol Prog Ser 517: 35–49, 2014

S. marinoi. For C. decipiens, an apparent kdis of sents the dSi transport in aggregates. The second −1 −1 4.5 nmol g bSiO2 s was obtained for aggregated modelling experiment evaluated the relative contri- cells and an average effective kdis of 11.4 nmol bution of viability vs. elevated dSiagg to explain the −1 −1 g bSiO2 s for freely suspended cells. observed decrease in the effective bSiO2 dissolution Using the likelihood method described below, the rates of aggregated diatoms compared to freely sus- best model fit to the experimental data was selected pended diatoms. A sensitivity analysis run on the using (1) a large range of kdis determined from the best version of the model investigated its sensitivity dissolution rates measured in the experimental study to specific input parameters, namely viability, poro - −1 −1 (kdis = 1 to 15 nmol g bSiO2 s ), and (2) a large range sity and dSiagg. of retention factors (1 to 300), in order to bracket the estimation of 200 calculated by Brzezinski et al. (1997), or a range of adsorption constants (0 to 10) Expt 1 framing the estimated values of Aller (1983) and Aller & Aller (1998). Retention assumes that diffusion of dSi within an aggregate is slower than in seawater. Consequently, retention processes reduce the net flux of dSi out of

Statistics aggregates but have no direct impact on bSiO2 dissolution (Eqs. 4 & 5). In contrast, adsorption of dSi 333 The dSiagg and dSiext estimated by each model ver- within the aggregate matrix directly impacts the sion for each species were compared to the respec- transport of dSi out of the aggregate and the bSiO2 tive experimental data. The goodness of fit was esti- dissolution rate (Eq. 9). If adsorption processes take mated using the log likelihood (log(L)) method with place in the aggregate, the silicic acid in the aggre- Eq. (11) (Armstrong et al. 2002). This approach gate porewater is divided into 2 pools: the free dSi depends on the amount of data points fitted, and (dSifree), which can diffuse, and the adsorbed dSi allows a direct comparison of the fit obtained by the 2 (dSiads), which is immobile. The ratio of free dSi and model versions using the deviation at each data point adsorbed dSi is constant and equal to the linear between model and data: adsorption constant kads. The calculation of the log ˆ 2 likelihood (Eq. 11) allows us to compare the goodness N ⎛ ∑(log(CCjj)log())− ⎞ (11) log(L )= –⋅ log⎜ ⎟ of fit to the experimental data of each model version. 2 ⎝ N ⎠ Both versions of the model give an effective bSiO2 where N is the number of data points, Cj is the meas- dissolution rate constant that can be directly com- 333 ured concentration (dSiext or dSiagg ) for the data point pared to the dissolution rate constant measured for number j, and the Cˆ j is the corresponding model pre- freely suspended diatoms. In this first experiment diction. As a matter of comparison, note that a 2-point where only dSi transport was investigated, the viabil- difference in the log likelihood is considered to be a ity was set to 0 while the model was otherwise para- sufficient improvement of the fit to justify adding a sup- meterized using the values given in Table 1. plementary parameter to the model. Here our 2 model versions have the same number of parameters; thus, we fixed the threshold at 1 point of log likelihood to decide Expt 2 whether one version gives a better fit than the other. We assessed the relative contribution of the high dSi concentrations and the high diatom viability Model experiments measured in the experimental study to the difference

between the effective bSiO2 dissolution rate constant The 2 model experiments compared reconstructed calculated for aggregated and measured for freely dSi concentrations to an experimental set of data, suspended diatoms. Two extreme scenarios are con- built from 2 dissolution experiments on each species. sidered: (1) kˆdis_agg (dSiagg) is estimated from a model The benefit is to increase the amount of data while run with dSi porewater concentrations set to the taking into account the large heterogeneity of the experimental average of 80 μM and diatom viability aggregates. With the first modelling experiment, we set to 0, implying that no metabolically active assessed which scenario, viz. adsorption or retention, diatoms are aggregated and that all frustules under- yields the best fit to our experimental external and go dissolution; (2) kˆdis_agg (fviab) is calculated from the internal dSi concentrations and most probably repre- model run with dSifree set to a constant minimal value Moriceau et al.: Biogenic silica dissolution in aggregates 41

corresponding to the initial dSiext (6 μM; see Table 1), RESULTS AND DISCUSSION while experimental viability (40%) is used to parameterize the model. For each model setting, the Model Expt 1: Which process best explains dSi model calculates the best effective dissolution rate accumulation in aggregates: retention or adsorbtion? constant kˆ dis_agg (P) needed to reconstruct the ob - served temporal evolution of dSi concentrations out- The large heterogeneity of the aggregates is illus- side the aggregates with these settings. The relative trated by a strong variability of the external dSi contribution of elevated dSi concentrations (Step 1) measurements as shown in Fig. 1a for Skeletonema and diatom viability (Step 2) in explaining the marinoi. Despite the variability of the experimental reduced effective dissolution rates of aggregated data set, both the retention and the adsorption ver- diatoms compared to freely suspended diatoms is sions of the model reproduce reasonably well the then evaluated using the ratio α: measured temporal variation in the dSi concentration

in the seawater surrounding aggregates (dSiext; kPkˆ ()− ˆ Fig. 1a,b) and the final average dSi concentration α (P) = dis_agg dis_agg (12) 333 ˆ inside aggregates (dSiagg ; Fig. 2) for the 2 species. In kkdis_FC− dis_agg 333 the adsorption model, the increase in dSiagg is contin- where kˆ dis_agg is the modelled effective dissolution rate uous over time (Fig. 2a). When the model recon- 333 constant obtained in the first experiment with settings structs the high dSiagg measured inside aggregates from Table 1, while kˆ dis_agg (P) is the effective dissolu- by decreasing the transport of dSi through the matrix tion rate calculated by the model when only the pa- (retention processes), dSiagg first increases rapidly rameter P (i.e. successively dSiagg and fviab) impacts over time to ~90 μM (at the centre of the aggregate) dissolution. k dis_FC is the experimental bSiO2 dissolu- and then more slowly to almost 150 μM (at the centre tion rate coefficient of the freely suspended cells. of the aggregate) with a final average of 80 μM (Fig. 2b). By contrast, the dSi concentrations are homogeneous in the aggregate in the adsorption sce- Sensitivity tests nario (Fig. 2a). Despite a good reconstruction of the internal average and external dSi concentrations, the By running the best model using a range of fixed 2 different processes give a very different description values of fviab from 0 to 1, a porosity ranging from of the physico-chemical conditions possibly existing 0.75 to 0.99 and a range of fixed values of dSiagg from inside aggregates. Unfortunately, neither the gradi- 20 to 140 μM, we assessed the sensitivity of our ent of dSi inside an aggregate nor the evolution of model to parameterization when deriving values of dSi over time in an aggregate can be measured to kads and kdis. help identify the better of the 2 processes.

14 26 a b 13 Modelled using adsorption 24 Modelled using retention 12 Experimental data 22 11 20

(µM) 10

ext 9 16

dSi 8 14

7 12

6 10

5 8 0 50 100 150 200 250 300 0 100 200 300 400 500 600 700 Time (h)

Fig. 1. Temporal evolution of the external silicic acid (dSi) concentrations (dSiext) for (a) Skeletonema marinoi and (b) Chaeto- ceros decipiens from the adsorption (solid line) or the retention (dashed line) model version and experimental data (diamonds). Error bars in (a) are SE 42 Mar Ecol Prog Ser 517: 35–49, 2014

a b 80 200

60 150

(µM) 40 100

agg 20 50 dSi

0 0 300 300300 0.4 0.4 200 0.3 200 0.3 100 0.2 100 0.2 Incubation 0.1 Incubation 0.1 0 0 0 0 time (h) Distance to the centre time (h) Distance to the centre of the aggregate (cm) of the aggregate (cm)

Fig. 2. Temporal and spatial evolution of the internal silicic acid (dSi) concentration of an aggregate (dSiagg) calculated for Skeletonema marinoi using (a) the adsorption and (b) the retention version of the model

The model calculates retention factors of 138 for reconstruction of the external dSi and the internal S. marinoi aggregates and 128 for Chaetoceros decip- dSi for S. marinoi aggregates, the best fit gives a log iens aggregates. As shown by Eq. (4), such retention likelihood of 29.8 with an adsorption coefficient (kads) factors imply a decrease in the effective dSi diffusion of 5.3 and a bSiO2 dissolution rate constant (kdis) of −1 −1 constant by 2 orders of magnitude compared to the 4.7 nmol gbSiO2 s . Best fits of external and internal value of 0.80 × 10−5 cm2 s−1 measured in seawater concentrations of dSi of C. decipiens aggregates at 15°C (Rebreanu et al. 2008) and corrected for yield a log likelihood of 27.6 using a kads of 2.3 and −1 −1 tortuosity (Boudreau 1997). Although the model- kdis of 4.6 nmol gbSiO2 s . These log likelihood val- derived retention factors are in the range of values ues are 2 points above those of the fits obtained with (20−200) postulated from measurements of dSi within the retention model version (Table 2). A 2-point porewater aggregates (Brzezinski et al. 1997), they increase in log likelihood has been considered in are high compared to the value of 1.1 extrapolated other studies (Armstrong et al. 2002, Moriceau et al. from direct measurement of gas diffusion in aggre- 2009) to be good enough to justify an increase in gates (Ploug & Passow 2007). The adsorption version model complexity. In our study, the model versions of the model calculates adsorption coefficients of 2.3 had the same number of parameters. The log likeli- and 5.3. Such adsorption coefficients lead to a de- hood increase establishes the superiority of the crease in diffusion by a factor of 3.3 and 6.3 (see adsorption version of the model over the retention Eq. 8). To our knowledge, the study of Aller (1983) is model. dSi accumulation within aggregates may best the only study that directly measured the dSi diffusion be explained by processes approaching a dSi ‘ad - constant through organic mucus. Despite pro bable sorption’ rather than a ‘retention’ scenario. differences in the chemical composition of the aggre- Adsorption processes in aggregates induce an gate matrix and the mucus-rich micro-environment of accumulation of dSi inside the aggregates. The silicic polychaete and crustacean burrows, the author meas- acid is mainly adsorbed, and only 20% is ‘free’. Free ured a similar decrease in the dSi diffusion constant (factor of 4.3). By con- ˆ Table 2. Model results for the first modelling experiment. k dis_agg: modelled trast, the retention model requires effective dissolution rate constant; fret: retention factor; kads: linear adsorption retention factors that are unrealisti- constant; bSiO2: biogenic silica cally high. ˆ This assessment is consistent with Species Model k dis_agg (nmol fret kads Log −1 −1 the log likelihood calculated for each version g bSiO2 s ) likelihood model run (Table 2). The fit obtained Skeletonema Retention 5.8 138 – 26.6 with the adsorption model is appre- marinoi Adsorption 4.7 – 5.3 29.8 ciably better than with the retention Chaetoceros Retention 4 128 – 24.4 version for both S. marinoi and C. de - decipiens Adsorption 4.6 – 2.3 27.6 cipiens (Table 2). For the temporal Moriceau et al.: Biogenic silica dissolution in aggregates 43

dSi is exchanged with the external environment by Bennett (1991) or the formation of Si-O-C ester- through the diffusion process. Consequently, the bonded complexes or hydrogen-bonded complexes concentration of free dSi is similar to the external (Iler 1977, Bennett 1991, Frampton & Zelisko 2009). concentration as shown by comparison between Such complexes could form in the aggregate matrix, Fig. 3 and Fig. 1b, which concurs with the estimations but also on the diatom cell surfaces, or they could be of Ploug & Passow (2007) of dSi diffusion in aggre- precursors for the silica deposition observed in spe- gates. The first candidates to explain dSi adsorption cific conditions on the bacteria cell surface (Benning are TEP, as they consist of very surface-active sub- et al. 2004). stances and contribute considerably to the aggregate matrix (Passow 2002). The initial volume fraction of TEP (amount of TEP per volume of aggregate) in Model Expt 2 C. decipiens aggregates (879 μg of xanthan equivalent cm−3) is more than 3 times that of S. marinoi Model Expt 1 establishes that the adsorption −3 aggregates (258 μg of xanthan equivalent cm ), version of the model best represents bSiO2 dissolution whereas the kads value is lower for C. decipiens. The in aggregates. Another important result from this fact that dSi adsorption is not directly related to the modelling experiment is that bSiO2 dissolution is not total TEP concentration could invalidate our guess or only apparently but effectively lower in aggregates may also suggest that only some constituents of TEP than in freely suspended diatoms. With this second are involved in the dSi adsorption. Chemical compo- modelling experiment, we aimed to evaluate the con- sition of TEP is complex and varies depending on the tribution of elevated dSi concentrations and longer organisms involved during their formation and mod- diatom viability to this effective decrease. bSiO2 of ification (Passow 2002, Verdugo et al. 2004, Bhaskar aggregated and freely suspended frustules is chemi- et al. 2005, Gogou & Repeta 2010). Adsorption of sil- cally and structurally identical, as diatoms were ver ions on exopolysaccharides (EPS), known to be grown in the exact same conditions. As a conse- precursors and constituents of the TEP, varies with quence, differences in the effective dissolution rate the chemical composition of the EPS (Deschatre et al. between aggregated and freely suspended cells 2014). Other substance classes may also play the role result from differences in the biological state or in the of dSi sorbent. Chemical adsorption may include the local environment surrounding aggregated and freely formation of organo-silicon complexes as observed suspended frustules. Mathematically, for each param-

eter added to Eq. (9) that effectively impacts the bSiO2 25 dissolution in aggregates, the effective dissolution rate constant kˆ dis_agg estimated by the model should get closer to the effective dissolution rate constant measured for freely suspended cells. With Eq. (9), the 20 model considers the contribution of 2 parameters: the internal dSi concentration and the percentage of

metabolically active diatoms (fviab). The relative contribution of each parameter is estimated using the α

(µM) 15 ratio (Eq. 12). When α = 0, the parameter has no effect free on bSiO2 dissolution, whereas when α = 1, the para-

diS meter fully explains the decrease in the bSiO2 dissolution rate measured when diatoms are in aggregates 10 compared to when they are freely suspended. To assess the relative contribution of the dSiagg, the model first calculates the dissolution rate constant by

setting dSifree equal to the experimental final average value of 80 μM (see Eq. 9 and Table 1) and by setting 0 0 100 200 300 400 500 600 700 the viability (fviab) to 0. In this scenario, only dSiagg Time (h) concentrations in aggregates and kads affect the frustule dissolution. The model fits yield kˆ dis_agg (dSiagg) Fig. 3. Temporal evolution of the free silicic acid (dSi) con- equal to the effective dissolution rate constants centrations (dSi ) inside a Chaetoceros decipiens aggre- free ˆ −1 −1 gate predicted by the adsorption model version using k dis_agg calculated in Expt 1 (4.6 nmol gbSiO2 s for parameters detailed in Table 2 C. decipiens, respectively; Table 3). This dissolution 44 Mar Ecol Prog Ser 517: 35–49, 2014

333 rate deviates significantly from the dissolution rate that measurements of dSiagg can be highly variable. constant of freely suspended diatom cells, k dis_FC Viability was not very variable between aggregates (Table 3), that the model was supposed to calculate if but may be very different from in situ viability, as dSiagg were responsible for the total decrease in the marine aggregates are often made up of detritus. The apparent bSiO2 dissolution rates measured in aggre- other tested parameter was porosity, as this parame- gates. The relative contribution given by α is 0. The ter was determined using TEP contribution to the decrease in the bSiO2 dissolution rates measured for aggregate volume measured in another study on dif- aggregated diatoms compared to freely suspended ferent aggregates. We ran the model many times 333 diatoms is not due to dSi accumulation inside the with different settings of fviab, φ and dSiagg to evalu- aggregates. ate the impact of these parameters on the modelled The relative contribution of diatom viability is esti- adsorption and dissolution constants. In the range of mated by calculating kˆ dis_agg (fviab) using the follow- porosities tested, dissolution rate constants estimated ing setting: dSifree equals dSiext, and fviab equals the by the model varied by a maximum of 0.3 nmol −1 −1 experimental value of 0.5. In this scenario, kˆ dis_agg gbSiO2 s , while the modelled adsorption constants −1 −1 (fviab) is 7.2 nmol g bSiO2 s for C. decipiens. This varied by a maximum of 0.2. Thus the model is not modelled dissolution rate constant is bracketed by sensitive to the porosity parameterization in the the effective dissolution rate constant of aggregated range tested. The results for the 2 other parameters −1 −1 cells (kˆ dis_agg = 4.5 nmol gbSiO2 s ) and the experi- are summarized in Fig. 4. mental dissolution rate constant of free cells (k dis_FC = Model-derived values of kads are not sensitive to −1 −1 11.5 nmol gbSiO2 s ). The relative contribution esti- viability (Fig. 4a), in contrast to dissolution rate con- mated with α suggests that viability explains 39% of stants (kˆ dis_agg). When less than 50% of the diatoms the reduction of the bSiO2 dissolution rate constant show respiratory activity (fviab < 0.5), the dissolution when diatom frustules are in aggregates. constant is less variable, but for higher values, mo -

del-derived kˆ dis_agg increases exponentially (Fig. 4b). The degree of uncertainty in the experimental deter- Sensitivity analysis of the adsorption model minations of the viability of ag gregated cells was around 10% for the same species. The sensitivity of

The modelling dissolution can be very much de - kˆ dis_agg to viability could explain the small decoupling pendent on the parameterization used. Paramete - between modelled and experimental dSiext after rization described Table 1 has been fixed using 480 h (Fig. 1b). While experimental tests on the experimental measurements. While laboratory-made impact of aggregation on cell viability show that via- ag gregates are less variable than in situ aggregates, bility can be maintained in aggregates for up to results described by Moriceau et al. (2007b) showed 480 h, there are indications that cell viability drops off at longer time scales (Garvey et al. 2007). Thus,

Table 3. Summary of the bSiO2 dissolution rate constants with the proper experimental data, the model could used in the second modelling experiment to evaluate the be improved by including a time-dependent viability relative contributions, α(dSi ) and α(f ), of the internal agg viab fraction, but such parameters would be difficult to dSi concentration (dSiagg) and of the fraction of metabolically constrain for a general model and at in situ viabilities, active diatoms (fviab), respectively, to slow down the bSiO2 dissolution in Chaetoceros decipiens aggregates. All kdis the model is not so sensitive that the accuracy of the values are in nmol g −1 s−1 bSiO2 kdis calculation would warrant an increase in the model’s complexity. Abbrev. Value Experimental measurements of the averaged internal dSi concentrations (dSi333) in aggregates varied Experimental constants for: agg between 20 and 100 μM. For this range of dSi333, the free diatoms kdis_FC 11.5 agg aggregates kdis_agg 4.5 sensitivity analysis revealed that kdis is only slightly Modelled effective kˆ 4.6 affected (Fig. 4d). To a large degree this is because dis_agg 333 constant for aggregate over the range of dSiagg considered (20−100 μM), the Modelled constant considering only the impact of: aggregate pore solution remains highly undersatu- dSi kˆ (dSi ) 4.6 agg dis_agg agg rated with respect to bSiO2 and, therefore, the Rdis is ˆ fviab kdis_agg(fviab) 7.2 insensitive to dSi concentrations. In contrast, the lin- Relative contribution of: α ear dependence between model-derived kads values dSiagg (dSiagg)0 333 and dSiagg (Fig. 4c) implies an uncertainty of up to fviab α(fviab) 0.39 50% for the kads values reported here. Moriceau et al.: Biogenic silica dissolution in aggregates 45

10 50 a b )

8 –1 10 10 6 bSiO2 g ads 8 k –1 dis_agg ˆ 4 k 6 4

2 (nmol s 2 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 fviab fviab 10 10 c d

8 8 ) –1

6 6 bSiO2 ads g k –1 dis_agg 4 4 ˆ k

2 2 (nmol s

0 0 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140

dSiagg (µM) dSiagg (µM)

Fig. 4. Sensitivity analysis on the adsorption version of the model to reconstruct the dissolution. (a) Sensitivity of the linear adsorption constant kads estimation to diatom viability, fviab. (b) Sensitivity of the modelled effective dissolution rate constant kˆ dis_agg to fviab. (c) Sensitivity of the kads estimation to internal silicic acid (dSi) concentration, dSiagg. (d) Sensitivity of the kˆ dis_agg to dSiagg

In summary, viability parameterization for C. de - gate. All parameters possibly changing bSiO2 disso- cipiens was reliable enough to suggest that diatom lution in an aggregate were not represented in the viability explains 39% of the decrease in apparent model built for this study. Moreover, the parameteri- bSiO2 dissolution rates observed in aggregates com- zation sometimes had to be approximated due to pared to freely suspended cells. Regarding the measurement uncertainty or even to the impossibility adsorption process, the kads parameter is dependent to directly measure some parameters in a single on the parameterization of the internal dSi, which is aggregate. technically difficult to measure. kads evolved from In the model, aggregates are described as porous 1 to 10 when dSiagg varied from 20 to 100 μM. spheres in which bSiO2 is homogeneously distributed. In the 2 experiments, the dissolution rate constants As fractal particles, a homogeneous distribution of calculated by the model to reproduce the dSi the bSiO2 in aggregates seems to be a reasonable as- dynamic in and out of an aggregate were systemati- sumption. We chose to represent only the impact of cally lower than the bSiO2 dissolution rate constants dSi concentrations, adsorption processes and diatom experimentally measured for free suspended cells. viability on bSiO2 dissolution, but our results showed With a perfect representation of the Si cycling in an that they are not the only parameters impacting aggregate and a perfect parameterization of all bSiO2 dissolution in diatom aggregates. At least 60% parameters influencing the bSiO2 dissolution and the of the decrease in the bSiO2 dissolution rate constants dSi transport, the effective bSiO2 dissolution rate cal- measured in aggregates remain unexplained by the culated by the model should be exactly the experi- model. Other explanations may be suggested from mental measurement of the bSiO2 dissolution rate in the literature to elucidate the slowdown of the bSiO2 freely suspended diatoms. However, while realistic, dissolution inside aggregates. First, the aggregate the model is a simplification of an aggregate leading matrix is only considered in the model through poro - to partial representation of the Si cycle in an aggre- sity, which does not change bSiO2 dissolution. This 46 Mar Ecol Prog Ser 517: 35–49, 2014

matrix, often identified as TEP, consists of a complex ral aggregates that could be largely composed of de- pool of organic ligands. TEP composition varies detritus may be lower than in our laboratory-made ag- pending on their origin (bacterial or phytoplankton gregates. In an extreme case where aggregated di- species) as described in the studies by Bhaskar et al. atoms would all be dead, our results suggest that the

(2005) and Xu et al. (2011). Among the molecules bSiO2 dissolution in aggregates could still be lowered identified in these studies, uronic acids (Welch & by 60% compared to freely suspended cells. Aggre- Vandevivere 1994) or some exopolymeric saccharides gates in natural environments have a more complex known to be TEP precursors (Penna et al. 2003) di- composition than our monospecific aggregates. They rectly impacted bSiO2 dissolution, sometimes favour- may include faecal pellets, algae of many species, ing dissolution and sometimes protecting the bSiO2 bacteria, microzooplankton or larvacean houses. against dissolution. The direct impact of the aggre- Most of this biological complexity has no impact on gate matrix of the Si cycling remains to be identified bSiO2 dissolution or dSi transport. However, bSiO2 in- before being integrated in the model. The aggregate side faecal pellets tends to dissolve even more slowly matrix also contains living organisms, in particular (Jansen 2002), and conversely, the impact of micro- bacteria, which are known to change bSiO2 dissolu- zooplankton grazing, though largely unknown, seems tion. The interaction between organic carbon and to increase recycling (Ragueneau et al. 2006, Schultes bSiO2 at the surface and in the diatom frustule et al. 2010). Among the other biological processes implies that bacterial activity directly im pacts bSiO2 possibly impacting the Si cycle in aggregates, resting dissolution (Patrick & Holding 1985, Bidle & Azam spore formation could occur in the dSi-rich microen- 1999, Moriceau et al. 2009). The bacterial community vironment formed by the aggregates (Alldredge et al. could be both different in aggregates versus free cells 1995). Their dSi consumption vs. a highly silicified (DeLong et al. 1993) and more active in aggregates cell wall could contribute to lower the apparent disso- than in freely suspended cells (Simon et al. 1990). In lution rate of natural aggregates even more compared our experiments, bacteria were highly concentrated to our laboratory-made aggregates that contain no compared to most in situ conditions, and bacterial spores. Overall, it appears that in situ, bSiO2 incorpo- concentrations were typical from non-growing batch rated in aggregates may dissolve slower than bSiO2 cultures. Bacteria were slightly less abundant on ag- freely suspended in the ocean. gregates than in freely suspended cells as found for freshly formed diatom aggregates in a study by Simon et al. (1990), which is in accordance with the Implications for the global Si cycle slow bSiO2 dissolution. However, measurements of activity are needed to resolve this matter. The model predicts that a large fraction of dSi The chemical and biological composition of the within aggregates (on the order of 80%) is adsorbed particles forming the aggregate matrix may change to the aggregate matrix, rather than present as free bSiO2 dissolution. The chemistry of the seawater dSi in the pore solution (using parameters described ‘trapped’ in the aggregate porewater changes con- in Table 2). Adsorption is a reversible process. The ra- siderably compared to the surrounding seawater. Not tio between adsorbed and free dSi is constant and only are nutrient concentrations different, but also equal to the adsorption constant. The adsorbed dSi is oxygen concentrations (Ploug 2001) and pH (e.g. All- continuously desorbed or adsorbed as free dSi con- dredge & Cohen 1987). The high bacterial activity in centrations decrease or increase to maintain the equi- aggregates (Smith et al. 1992, Ziervogel & Arnosti librium represented by the adsorption coefficient. 2008) and in general the high respiration rates Diffusion rate depends on the dSi gradient between (Iversen & Ploug 2010) may provoke a decrease in the outside and the inside of the aggregate. In other the intra-aggregate pH. Indeed, pH values around 7 words, when dSi is less concentrated outside the ag- have been measured inside aggregates. A drop in pH gregate, dSiagg is progressively leaking out of the ag- from 8 to 7 could explain a decrease in the dissolution gregate. Conversely, the external dSi diffuses from rate by a factor of 2 (measured for Cyclotella cryptica the outside to the centre of the aggregate when the by Greenwood et al. 2001). gradient is inverted. In the water column, dSi concen- Before placing our results in a more general con - tration generally increases with depth. During sink- text, we also need to discuss the differences between ing, the aggregate encounters water layers richer in laboratory-made and in situ aggregates. While ag - dSi. Considering only diffusion processes, the aggre- gre gates could provide a microhabitat favouring the gate internal dSi concentration will in crease during survival of diatoms in the dark, their viability in natu- its journey through the water column. Moreover, the Moriceau et al.: Biogenic silica dissolution in aggregates 47

model estimates an adsorption constant between 2 stated by the model, then we could explain the previ- and 5 that can even be up to 10 from the sensitivity ous 3 statements. The presence of a pool of adsorbed analysis. Diffusion processes will en sure that the ad- dSi in the aggregate matrix decreases the pool of sili- sorbed dSi concentration of the aggregate is 2 to 5 cic acid available to diffuse out of aggregates, which times higher than the outside concentrations (Eq. 7). explains why the diffusion coefficient is not de - A rough estimate of the share of dSi to the total silica creased. However, adsorption processes would not exported at depth can be forecast from the adsorption contribute to lower the biogenic silica dissolution of coefficient calculated by our model. We used these the frustules embedded in aggregates. Aggregates model-derived values together with average dSi con- form a microhabitat promoting the survival of dia - centrations of the different oceanic layers based on a toms, which can explain one-third of the effective global box model for the silica cycle (Laruelle et al. decrease in the bSiO2 dissolution rate in aggregates. 2009). This model represents the water column con- Other factors that still need to be identified may addi- sidering 3 boxes. The surface water from 0 to 100 m tionally impact dissolution rates within aggregates, has an average dSi concentration of 5 μM. The meso- in cluding diminished internal pH, bacterial concen- pelagic layer from 100 to 1000 m has a global dSi con- tration or exopolymeric substances. centration of 25 μM, while deep waters below 1000 m If the adsorption constant calculated here is extrap- contain an average of 100 μM of dSi. Using the range olated to the global ocean, the dissolved component of adsorption constants estimated by the model of the Si export could reach up to 20% of the total Si. (2.3−5.3), dSi concentrations inside aggregates in Aggregates have been known to play an essential such a theoretical water column would be 12 to 27 μM role for the vertical transport of particulate silica in in surface waters, 58 to 132 μM in mesopelagic waters the oceans and thus for the cycling of silica. If adsorp- and 230 to 530 μM in deep waters. If we consider an tion processes are indeed occurring inside aggre- average aggregate volume as given in Table 1, the gates, this raises the possibility that aggregation also predicted downward dSi flux would make up 0.5 to plays a role in transporting dissolved silica, which

1.3%, 2.5 to 6.6% and 9.9 to 26.9% of the bSiO2 flux could be important to the oceanic Si cycle. in the surface, mesopelagic and deep layers, respectively. For the integrated water column, the fraction of Acknowledgements. We thank S. Ni Longphuirt and M. silicic acid flux to total silica flux sinking in Gar vey, who kindly read earlier versions of this manuscript, aggregates can be up to 21%, which is similar to esti- and J. Thebault for his help with the figures. We are since- mates for the fluxes of dissolved carbon and nitrogen cerely grateful to the reviewers and the editor for their (Carlson et al. 1994, Hansell & Carlson 1998, Engel et insightful comments that helped to considerably improve al. 2004, Hopkinson & Vallino 2005). Our crude calcu- this manuscript. We acknowledge funding to B.M. from the EU, partly through the ORFOIS (EVK2-CT2001-00100) pro- lations reveal that, overall, the export of dSi to the sea ject and partly through the Si-WEBS (HPRN-CT-2002- floor via sinking aggregates could account for up to 00218) Research Training network of the Marie Curie pro- 4.3 Tmol of Si yr−1. Obviously this is a very rough esti- gramme, and funding to U.P. from the National Science mate, which ig nores disaggregation and grazing and Foundation (NSF). This research was also partly funded by assumes that the flux consists of diatom aggregates King Abdullah University of Science and Technology (KAUST) Center-in-Development Award to Utrecht Univer- only, but it does show that this is a potentially signifi- sity (project No. KUK-C1-017-12). cant component of the marine silica cycle that merits further investigation. LITERATURE CITED

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Editorial responsibility: Katherine Richardson, Submitted: October 17, 2011; Accepted: September 1, 2014 Copenhagen, Denmark Proofs received from author(s): November 24, 2014