quantifying nitrogen fixation by heterotrophic bacteria in
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Quantifying nitrogen fixation by heterotrophic bacteria in sinking marine particles
Chakraborty, Subhendu; Andersen, Ken H.; Visser, André W.; Inomura, Keisuke ; Follows, Michael J.;Riemann, Lasse
Published in:Nature Communications
Publication date:2021
Document VersionPublisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):Chakraborty, S., Andersen, K. H., Visser, A. W., Inomura, K., Follows, M. J., & Riemann, L. (2021). Quantifyingnitrogen fixation by heterotrophic bacteria in sinking marine particles. Nature Communications, 12, [4085].
1
Quantifying nitrogen fixation by heterotrophic bacteria in sinking marine particles 1
Subhendu Chakraborty1,2,
*, Ken H. Andersen2, André W. Visser
2, Keisuke Inomura
3, Michael J. 2
Follows4, Lasse Riemann
1,* 3
1Department of Biology, Marine Biological Section, University of Copenhagen, Helsingør, 4
Denmark 5
2Centre for Ocean Life, DTU Aqua, Technical University of Denmark, Kemitorvet, Kgs. Lyngby, 6
Denmark 7
3School of Oceanography, University of Washington, Seattle, WA, USA 8
4Department of Earth, Atmosphere and Planetary Sciences, MIT, Cambridge, MA, United States of 9
America 10
11
Running title: Nitrogen fixation in sinking marine particles 12
13
Current address (Subhendu Chakraborty): Systems Ecology Group, Leibniz Centre for Tropical 14
Marine Research (ZMT), Bremen, Germany 15
16
*Corresponding authors: Department of Biology, Marine Biological Section, University of 17
Copenhagen, Helsingør, Denmark. Tel: +4591714664. Email: [email protected]; 18
2
Abstract 20
Nitrogen ( ) fixation by heterotrophic bacteria associated with sinking particles contributes to 21
marine N cycling, but a mechanistic understanding of its regulation and significance are not 22
available. Here we develop a mathematical model for unicellular heterotrophic bacteria growing on 23
sinking marine particles. These bacteria can fix under suitable environmental conditions. We 24
find that the interactive effects of polysaccharide and polypeptide concentrations, sinking speed of 25
particles, and surrounding and concentrations determine the fixation rate inside 26
particles. fixation inside sinking particles is mainly fueled by respiration rather than 27
respiration. Our model suggests that anaerobic processes, including heterotrophic fixation, 28
can take place in anoxic microenvironments inside sinking particles even in fully oxygenated 29
marine waters. The modelled fixation rates are similar to bulk rates measured in the aphotic 30
ocean, and our study consequently suggests that particle-associated heterotrophic fixation 31
contributes significantly to oceanic fixation. 32
Keywords 33
fixation; Sinking marine particles; Heterotrophic bacteria; Anaerobic respiration; Anoxic 34
interior; Trait-based optimization model 35
36
37
38
39
40
3
Introduction 41
Nitrogen (N) is an essential element for all living organisms but its availability often limits the 42
growth and productivity of terrestrial and aquatic ecosystems. Although molecular dinitrogen gas 43
( ) is highly abundant in the marine water column, only specific prokaryotes that can fix 44
(diazotrophs) using the nitrogenase enzyme complex1 assimilate this form of nitrogen. 45
Nevertheless, nitrogen fixation maintains the inventory of biologically available nitrogen in the 46
open oceans, which fuels primary production1,2
, and thereby affects the biogeochemical cycling of 47
both nitrogen and carbon3. 48
fixation was thought to exclusively be carried out by cyanobacteria in the oligotrophic and 49
sunlit upper layers of the tropical and subtropical oceans (reviewed in Zehr4). However, 50
accumulating evidence shows that fixation is surprisingly widespread, for example in the deep 51
sea5, nutrient-rich coastal waters
6, and cold Arctic waters
7. Moreover, analyses of genes (nifH) 52
encoding the enzyme complex used for fixation document that non-cyanobacterial diazotrophs 53
are almost ubiquitous across the world‟s oceans, often dominate nifH gene libraries over 54
cyanobacteria, and occasionally express nitrogenase8–10
. Hence, the emerging picture shows 55
fixation as a global marine process partially carried out by non-cyanobacterial diazotrophs, but their 56
ecology and contribution to total fixation remain enigmatic10
. 57
Nitrogenase is irreversibly inactivated by 11
. Cyanobacteria adopt several strategies to 58
protect nitrogenase from inactivation by 12
. Heterotrophic diazotrophs may under rich culture 59
conditions surround cells with extracellular polymers13
to lower the permeability to extracellular 60
to protect the nitrogenase, but since this is highly energy-demanding14
it is an unlikely strategy in 61
the relatively nutrient-poor marine water column. Recent work, inspired by the pioneering work of 62
Paerl and co-workers15,16
, has suggested that heterotrophic fixation takes place in low-oxygen or 63
4
anaerobic microzones associated with marine particles (reviewed in Riemann et al.17
and in Bombar 64
et al.10
). Indeed, anaerobic microzones are occasionally associated with marine particles18,19
. Recent 65
studies show fixation is stimulated by the presence of particles20,21
and that heterotrophic 66
diazotrophs are associated with plankton specimens22,23
and marine aggregates24,25
. Hence, beyond 67
doubt, marine particles provide, at least ephemeral, conditions suitable for fixation by 68
heterotrophic bacteria. 69
Cellular removal by diazotrophs is considered highly energy-demanding, even more 70
energetically expensive than fixation per se14
. Hence, considerable amounts of labile carbon 71
(e.g. carbohydrate and amino acids) are required to sustain particle-associated microbial respiration 72
beyond the specific energy requirements for diazotrophy. Interestingly, preferential microbial 73
utilization of N-rich organics on particles26
and release of
27 may increase particle C:N ratios 74
over time26
, gradually making N acquisition by fixation increasingly advantageous. 75
While synthesizing ATP during respiration, is used as the most common and favorable 76
form of electron acceptor by prokaryotes. In the absence of , other electron acceptors (e.g.
77
and ) may be used in a stepwise manner according to their free energy yields
28, with a rather 78
small drop-off in the theoretical energy yield for respiration, followed by
respiration 79
with almost tenfold less energy yield per electron donor29
. However, respiration is likely the 80
primary form of anaerobic respiration supporting fixation since reducing diazotrophs 81
have been widely found30,31
, also on marine particles32,33
. 82
Another important factor regulating fixation in sinking marine particles is the particle size, 83
which varies from micrometers to several millimeters34
. The particle size spectrum follows a power 84
law relationship showing a decrease in particle abundance with increasing size35
. Because of 85
smaller surface to volume ratios, large particles are more likely to develop an anoxic interior 86
5
suitable for fixation. Moreover, particles face changing and concentrations while 87
descending in the water column. The rate of change depends on particle sinking speed, but no 88
universal size-sinking speed relationship exists36
. Although all these external factors can have huge 89
influences, the extent by which they affect heterotrophic fixation inside sinking particles is 90
currently unclear. 91
To quantitatively analyze the conditions when heterotrophic fixation occurs on sinking 92
particles, we present a trait-based model of heterotrophic bacteria associated with sinking particles. 93
This effort aims to encapsulate an understanding of the dynamics between (micro)environmental 94
conditions and the requirements and constraints of heterotrophic fixation. Specifically, the 95
model captures basic cellular processes determining growth and fixation in an individual cell 96
and then scales up to the population level to address particle dynamics and the contribution to total 97
fixation in the water column. We also examine how the size of particles, initial concentrations of 98
polysaccharide and polypeptide, and environmental concentration influence heterotrophic 99
fixation inside sinking particles, and the succession of aerobic and anaerobic respiration as support 100
for fixation. In doing so we identify potentially testable hypothetical consequences: (H1) Excess 101
acquired N released by cells and hydrolysis products diffuse away from the particle and contribute 102
to an organic solute trail in the water column as the particle sinks. (H2) fixation by heterotrophic 103
diazotrophs depends on the generation of particle-associated low-oxygen microenvironments. (H3) 104
During the “life span” of a sinking marine particle there is an ephemeral window of opportunity 105
where environmental conditions are conducive for heterotrophic fixation. (H4) reduction 106
is more important for fixation within sinking particles than reduction. (H5) The particle 107
sinking speed and concentrations of and in the water column affects fixation rates. 108
Although the model is developed to investigate fixation, it also provides critical insights on 109
biochemistry and microbial respiratory processes inside sinking particles. 110
6
Results and discussion 111
Overview of the model 112
The overall model consists of a „cell model‟ and a „particle model‟. The cell model describes basic 113
cellular processes, like uptake of resources, respiration, growth, and fixation rate. The cell model 114
is embedded in a dynamic model, called „the particle model‟, that deals with interactions of cells 115
with the available abiotic factors (polysaccharide, polypeptide, , ,
) over time. 116
The cell model describes a population of facultative fixing heterotrophic bacteria growing inside 117
a particle sinking through a water column. A schematic representation of the processes inside a 118
single cell is presented in Figure 1 and the full description of mathematical forms and equations are 119
provided in the Methods section. The cell uses ectoenzymes to degrade polymers (polysaccharides 120
and polypeptides) to oligomers or monomers (glucose and amino acids) that it can efficiently take 121
up to fulfill its C and N requirements. The uptake of glucose and amino acids follows Michaelis-122
Menten kinetics. The model accounts for acquired C and N to ensure that the cell satisfies its needs 123
for both. While glucose uptake provides only C, amino acids provide both C and N (Equations (1) 124
and (2)). 125
C obtained from glucose and amino acids is respired to carry out resource uptake, cellular 126
maintenance (Fig. 1), and standard metabolism (Equation (6)). , , and
are used as 127
electron acceptors in a stepwise manner in order of their free energy yield to perform respiration37
. 128
In the absence of sufficient , the cell uses to continue respiration, although all N necessary 129
for growth comes from organic sources and fixation (whenever possible). The further need of 130
electron acceptor is fulfilled by . 131
7
The cell can carry out fixation to supplement its N requirement. It regulates the rate of 132
fixation to optimize its growth rate. As nitrogenase is irreversibly inhibited by 11
, the cell needs 133
low conditions inside particles or increased respiration to make the cell free and thereby 134
enable fixation. 135
The synthesis of biomass using available C and N from resource uptake and electron 136
acceptors follows Liebig‟s law of the minimum and is constrained by the cellular C:N ratio ( ) 137
(Equation (21)). Any excess assimilated C or N is excreted from the cell. The cell division rate is 138
found from the mass-specific synthesis rate. 139
The particle model consists of a sinking particle that contains polysaccharides and polypeptides and 140
is colonized by facultative nitrogen-fixing bacteria (Supplementary Fig. S1). Only fractions of these 141
polymers are considered labile, i.e. accessible by bacteria. Bacterial enzymatic hydrolysis converts 142
labile polysaccharides and polypeptides into monosaccharides (glucose) and amino acids that are 143
efficiently taken up by bacteria. Excess glucose and amino acids diffuse out of the particle to the 144
surrounding environment, while and diffuse into the particle from the surrounding water. 145
is the second most abundant anion in seawater with an estimated concentration of 28 mM
38 146
(roughly three orders of magnitude higher concentration than ) whereas is also plentiful 147
with an average concentration of 0.4 mM in seawater38
(more than two orders of magnitude higher 148
concentration than ). Due to these high concentrations of
and inside particles, the 149
uptake is assumed to be limited by the cellular maximum uptake capacities and not by the rate of 150
diffusion towards the cell. Depending on the available concentrations of glucose, amino acids, , 151
and inside the particle, bacteria carry out fixation (Equation (23)). Fe, an essential 152
component in the nitrogenase complex, is considered nonlimiting as sinking particles contain high 153
levels of Fe39
. The predation on bacteria is represented by a linear mortality term. The interactions 154
8
between particle, cells, and the surrounding environment are explained in the supplementary Fig. 155
S1, equations are provided in Table 1, and a full description of the particle model is provided in the 156
Methods section. 157
158
Biochemical dynamics inside a particle under static environmental conditions 159
The dynamics inside a particle of radius 0.125 cm with initial polysaccharide and polypeptide 160
concentrations of μg G L-1
and μg A L-1
, with relative lability of 0.238 and 0.5, 161
respectively, are depicted in Fig. 2. We simulate a population of bacterial cells of radius μm 162
( cell-1
) growing inside a particle where the surrounding glucose, amino acids, , , 163
and concentrations are kept fixed at 50 μg G L
-1, 5 μg A L
-1, 50 μmol L
-1, 15 μmol 164
L-1
, and μmol L-1
. Here, concentrations inside the particle are given as per liter of 165
particle and outside as per liter of water. A full description of the included parameters and their 166
values is available in Supplementary Material S1 and Table S1. The bacteria hydrolyze labile 167
polysaccharides and polypeptides into glucose and amino acids using ectoenzymes (Fig. 2a, b). As a 168
result, glucose and amino acid concentrations increase inside particles (Fig. 2c, d), which causes a 169
high growth rate of cells (~3.6 d-1
; Fig. 2j), an increase in bacterial abundance (Fig. 2g), and a 170
decrease in labile polysaccharide and polypeptide concentrations. The occurrence of such a high 171
bacterial abundance is not rare inside natural sinking particles25,42,43
. The growth rates observed in 172
the model are high for the temperature regime but conceivable given that there are some reports of 173
extremely high growth rates in particle-associated bacteria albeit at higher temperatures and in 174
different environments than modeled here40,41
. The increased community respiration (Fig. 2h) 175
decreases concentration and eventually leads to anoxia in the particle interior (Fig. 2e). This is 176
consistent with ephemeral anoxia inside marine aggregates19
and the anoxia observed inside 177
9
suspended cyanobacterial colonies of comparable size18
. The gradual formation of low-oxygen or 178
anoxic conditions and depletion of organic N (amino acids) facilitates fixation (Fig. 2i), 179
supported by aerobic respiration followed by
respiration (Fig. 2e, f). The lesser energetic 180
yield of respiration leads to a reduced growth rate (~0.6 d
-1). Furthermore, when
181
becomes exhausted (Fig. 2f), cells respire (not shown in the figure) and the growth rate 182
becomes very low (~0.2 d-1
). Because of the energetic constraints, fixation during this phase also 183
becomes low. The presence of such and
reducing bacteria is common in sinking 184
particles44
. Eventually, fixation ceases due to increased levels as the exhaustion of labile 185
carbon in the particle decreases cell concentration and influx exceeds consumption (aerobic 186
respiration). 187
We performed a sensitivity analysis, adapted from earlier studies45
, to investigate how 188
different factors affect the fixation rate inside particles (Supplementary Fig. S2). fixation rate 189
was found to increase with increased maximum glucose uptake rate and maximum amino acid 190
uptake rate, and decrease with the cost of amino acids uptake, hydrolysis rate of polysaccharide, and 191
the fraction of diffusivity within particles compared to water. Significant decreases in 192
fixation rate were observed with an increase in hydrolysis rate of polysaccharide and a decrease in 193
maximum glucose uptake rate. Not surprisingly, the sensitivity analysis suggests hydrolysis and 194
uptake as key parameters affecting fixation, pinpointing the importance of particle composition 195
and bioavailability for particle-associated fixation. 196
197
Cellular mechanisms of fixation 198
10
To explore the cellular mechanism of fixation, we examine concentrations and rates over time at 199
a radial distance of 0.027 cm from the particle center (Fig. 3). We identify four phases: (I) C limited 200
phase, (II) high respiration phase, (III) fixing phase, and (IV) fading phase. The different phases 201
are based on limitations of either C or N or electron acceptor where the growth rate is determined 202
by the minimum availability of these three substances (Equations (21) and (22); Fig. 3a). Available 203
C for growth is the C remaining from total C uptake after paying the respiratory costs, whereas the 204
N available for growth comes from uptake and fixation. A stepwise conceptual flow chart of 205
how different factors are responsible for different events inside particles is provided in 206
Supplementary Fig. S3. 207
I. Due to high respiratory cost, cells are limited by C, which is seen by the light blue line 208
coinciding with the magenta line in Fig. 3a. Growth rates are high, up to 3.6 day-1
. Excess N 209
and hydrolysis products not taken up by cells26
will diffuse away from the particle and 210
contribute to an organic solute trail in the water column as the particle sinks46
, supporting 211
our hypothesis H1. 212
II. The large bacterial population causes high community respiration, matching or exceeding 213
the diffusive influx of , and anoxia forms in the particle interior (Fig. 3e). Cells start 214
respiring and even
reduction happens at the end of this phase (not shown in the 215
figure) when is depleted. Now growth is limited by the availability of electron 216
acceptor (the yellow line coincides with the magenta in Fig. 3a). An organic solute trail rich 217
in both C and N is predicted during this phase. The amino acid concentration decreases 218
rapidly during the final part of this phase (Fig. 3c). 219
III. Because of our initial choice of polysaccharide and polypeptide concentrations, amino acids 220
are exhausted. In real life, bacterial preferential degradation of N-rich organics results in 221
similar early exhaustion of amino acids26
. Glucose remains available as C source (Fig. 3c), 222
11
so cells start fixing to maintain growth (Fig. 3d). However, since the available in the 223
particle is insufficient to support respiration, and
also act as electron acceptors 224
during this phase. Cells become co-limited by N from fixation and electron acceptor 225
(green and yellow lines coincide; Fig. 3a) and we predict that the expected solute trail 226
consists only of C during this phase. Because of the lower free energy yield, fixation 227
decreases when using as an additional electron acceptor. Towards the end of this 228
phase, the respiratory cost of glucose uptake decreases with the decrease in glucose 229
concentration to such an extent that there is excess after performing respiration. At that 230
point, cells increase respiration to burn excess to perform fixation for a very short 231
interval of time, resulting in a peak in fixation rate (Fig. 3d) and the respiratory cost for 232
removal (Fig. 3b). 233
IV. Cells have insufficient C to deal with excess and consequently stop fixation. N 234
becomes the limiting factor for cell growth and growth ceases. Later, the growth rate 235
becomes negative as there is no glucose left needed for basal respiration. Throughout this 236
phase, the bacterial concentration decreases (Fig. 3c). 237
The identification of different phases yields insights relevant for several of our hypotheses. As 238
the particle sinks, it will be tailed by an organic matter solute trail. Its composition depends on the 239
internal state of the particle. During the „C limited phase‟ and „High respiration phase‟, the expected 240
trail consists of both C and N, whereas during the „ fixation phase‟, the trail contains only C. The 241
amount of C and N in the trail can be estimated from the outgoing flux of the organic matter from 242
the particle, supporting our hypothesis H1. Comparing different respiratory costs related to 243
fixation in terms of direct respiration, enzyme production, and removal, it becomes evident that 244
when cells use respiratory protection to keep nitrogenase viable and enable fixation, the related 245
cost becomes much higher than the direct cost for fixation (Fig. 3b). A similar high cost of 246
12
management during fixation was previously shown to exceed the costs of fixation per se for 247
the heterotrophic soil bacterium Azotobacter vinelandii14
. We therefore conclude that active 248
management by particle-associated heterotrophic diazotrophs is not prevalent, but that they rather 249
depend on the generation of low-oxygen microenvironments by community respiration, supporting 250
our initial hypothesis H2. 251
The observed fast transitions of glucose and amino acids happen when the exponential growth 252
of bacteria leads to high bacterial abundance and high degradation of polymers (Fig. 2, 3c). Similar 253
fast changes in bacterial abundance and co-occurring resource utilization have been observed in an 254
experiment showing degradation of transparent exopolymer particles derived from cultures of the 255
coccolithophore Emiliania huxleyi47
. However, a very sharp transition has been observed for 256
fixation rate (Fig. 2i, 3d). Because of the cost related to fixation, fixation starts only when 257
there is no N available from amino acid (Fig. 3c). The rate of fixation is determined by the 258
available electron acceptors (Fig. 3a) and results in a sharp transition at the beginning of 259
fixation. fixation stops when the C available from glucose is not sufficient to burn excess to 260
keep the cell free; consequently, fixation terminates abruptly. 261
262
Effects of particle size, , and initial polysaccharide and polypeptide concentrations 263
Marine particles are highly variable in size34
and chemical composition. For example, the C:N ratio 264
(and implied polysaccharide:polypeptide availability) varies considerably, depending on 265
environmental conditions48
. Moreover, while descending in the water column, particles face a range 266
of surrounding concentrations. Therefore, we examined the implications for fixation in 267
particles of different sizes under different polysaccharide, polypeptide, and concentrations (Fig. 268
4). We considered open ocean particles with radius 5 μm to 0.25 cm49
and estimated the total 269
13
amount of fixed per particle by allowing bacteria to grow inside particles for 20 days. As 270
expected, large particles provide a suitable environment for fixation. The minimum size of 271
particles where fixation is possible increases with polysaccharide concentration (Fig. 4a), 272
decreases with environmental concentration (Fig. 4c), and attains a maximum at intermediate 273
polypeptide concentration (Fig. 4b). fixation does not occur in particles with radius below ~0.03 274
cm. The increase in fixation with polysaccharide concentrations is consistent with observations 275
of stimulated fixation in seawater upon the addition of C substrate (e.g. Rahav et al.21
). 276
Interestingly, maximum fixation occurs at intermediate polypeptide concentrations (~ 277
μg L-1
) in large particles (Fig. 4b). Our interpretation is that low polypeptide concentrations do not 278
allow cells to grow to high concentrations and create an anoxic interior, whereas, at high 279
concentrations, cells cover their N demand by amino acid assimilation and, therefore, refrain from 280
fixation. 281
Maximum fixation in large particles occurs under very low (~0.3 μmol L-1
) and 282
intermediate (~80 μmol L-1
) levels (Fig. 4c). Under very low concentrations, cellular 283
respiration is expected to occur using and
as electron acceptors causing low cellular 284
growth rate and a slowly increasing cell concentration. However, fixation occurs for a long time 285
period and makes the total fixation per particle relatively high (Supplementary Fig. S4d). At 286
intermediate levels, cells are not limited by and reach a high growth rate during the initial 287
phase. Therefore a high cell concentration is rapidly obtained (Supplementary Fig. S4c) causing 288
reduced levels suitable for fixation for a relatively shorter time interval (Supplementary Fig. 289
S4d). The combination of high cellular fixation rate and high cell concentration results in high 290
total fixation per particle. At a high level (~200 μmol L-1
), this low period is very short, 291
possibly because of a large diffusion loss of glucose associated with extensive polysaccharide 292
hydrolysis caused by the high cell concentration (Supplementary Fig. S4c). This lowers the total 293
14
amount of fixed per particle. However, the concentrations of , where these two maxima occur, 294
depend on the initial polysaccharide and polypeptide concentrations. With a decrease in these 295
concentrations, the intermediate concentration, where the maximum occurs, decreases 296
(Supplementary Fig. S5) and finally merges with the other maximum at low (not shown). 297
Indeed, empirical results confirm the existence of such optimal concentration for fixation and 298
a level of 6 μmol L-1
has been observed for heterotrophic diazotrophs50
. 299
By simultaneously varying initial labile polysaccharide and polypeptide concentrations in 300
small and large particles at different surrounding concentrations, it appears that fixation is 301
restricted to large particles with high initial polysaccharide and polypeptide concentrations when 302
concentration is high (Fig. 5a). However, under low concentrations, fixation occurs even at 303
lower concentrations of polysaccharides and polypeptides (Fig. 5b). fixation can also occur in 304
relatively smaller particles, however, only when the initial polysaccharide concentration is high and 305
the surrounding concentration is low (Fig. 5c). 306
The amount of POC present in particles can be considered a proxy for polysaccharide and 307
polypeptide concentrations. The presence of high POC in freshly formed particles from dense 308
phytoplankton blooms51
and fecal pellets52
would increase the likelihood of particle-associated 309
fixation. Likewise, the seasonally high POC content of particles during late spring in high latitude 310
areas53
could increase the likelihood of particle-associated fixation at this time. On the other 311
hand, the size of particles, which also has a profound impact on fixation, is closely associated 312
with the species responsible for particle formation. For instance, since particles are larger during 313
diatom blooms compared to cyanobacterial blooms54
, an increased likelihood of fixation during 314
diatom blooms would be expected. The latitudinal variation in particle size spectrum with a 315
dominance of larger particles at higher latitudes compared to smaller particles in the oligotrophic 316
15
subtropical gyres 55
indicates a greater opportunity for particle-associated fixation at high 317
latitudes. Hence, the potential for particle-associated fixation is highly dependent on local 318
dynamics in the size and composition of particles, together with the local conditions. 319
320
fixation in sinking particles 321
To explore the dynamics of fixation in sinking particles of different sizes, we use vertical 322
profiles of and in the upper 500 m of the Mauritanian upwelling zone in the North 323
Atlantic Ocean (NAO; Fig. 6)56
. concentration drops to hypoxic levels (~62.5–157 µmol L-1
) in 324
the water column between 100–600 m (Fig. 6a). fixation coincides mainly with the presence of 325
an anoxic particle interior. The amount of fixed increases with particle size and because of 326
higher sinking rates and more C to fuel respiration the existence of both anoxic interior (regions 327
within magenta lines) and fixation (within white lines) in large particles occur in deeper waters 328
and persist for longer time (Fig. 6b). We presume that fixation stops in deep water when labile 329
material in the particle is exhausted. This shows that the window of opportunity where 330
environmental conditions are conducive for heterotrophic fixation is ephemeral, supporting our 331
hypothesis H3. 332
In the anoxic particle interior, and
function as electron acceptors. The model 333
suggests that the fraction of particle volume where denitrification occurs (maximum 6%) is much 334
smaller than the fraction of volume of occurrence of reduction (maximum 90%) (Fig. 6c, d). 335
The model predicts that despite being energetically profitable, does not play a big role in 336
fixation and reduction appears as the key anaerobic process within sinking particles. This is 337
due to very high cell concentration near the surface of the particle (Fig. 2g) that creates a high 338
respiratory demand for electron acceptors, exhausts close to the particle surface, and prevents 339
16
from reaching the particle interior (Fig. 2f). As a result, fixation in most of the particle 340
interior is supported by respiration, which confirms the importance of
reduction in 341
particle-associated fixation compared to reduction, supporting hypothesis H4. 342
Diazotrophy among reducing bacteria is well established in various marine 343
environments57,58
. 344
Influence of sinking speed on particle-associated fixation. 345
The speed at which particles sink is a critical parameter since it determines the duration of exposure 346
to environmental conditions (e.g. ) that influence fixation inside particles. Sinking speed is 347
affected by a multitude of factors related to particle composition, size, and density59–61
, and no 348
universal size-sinking velocity relationship exists36
. We, therefore, examine scenarios with three 349
types of particles: (1) natural marine snow measured in situ off California62
, (2) laboratory-made 350
diatom aggregates, and (3) coccolithophore aggregates measured in vitro51
. Sinking speed is lowest 351
for natural marine snow followed by diatom aggregates and coccolithophore aggregates (Fig. 7a). 352
For the sake of simplicity, these particles are assumed to vary only in their sinking speeds and not in 353
their initial concentrations and lability of polysaccharides and polypeptides. We again use the 354
vertical profile of and at the NAO but extended to 1,500 m depth with a hypoxic region 355
between 100-600 m depth (Fig. 7b). 356
Three different aspects are evident from the analysis. Firstly, when particles sink at a speed 357
similar to natural marine snow (~15-75 m d-1
), anoxic microenvironments are created (regions 358
within magenta lines) and fixation happens (indicated by color) in particles within the hypoxic 359
zone (Fig. 7e). However, with higher sinking speeds similar to diatom (~2-180 m d-1
) and 360
coccolithophore (~20-375 m d-1
) aggregates, the existence of anoxia and fixation inside particles 361
can extend beyond the hypoxic strata of the water column (Fig. 7d,e); both anoxic interior and 362
17
fixation are predicted even at 1,800 m depth for large coccolithophore aggregates (not in the figure). 363
Secondly, the depth window where fixation occurs increases with particle sinking speed (7c-e). 364
Finally, our study predicts that the highest fixation rate (1.46 μg N (cm3 particle)
-1 d
-1) is attained 365
in large particles at intermediate sinking velocities, similar to that of diatom aggregates (Fig. 7d). 366
Since the presence of higher concentrations of can stimulate
respiration in a relatively 367
larger volume fraction of particles, and due to the higher energy yield of respiration relative 368
to reduction, we speculate that higher concentrations of
during the time of fixation 369
boosts fixation rate in diatom aggregates. High sinking speed, similar to that of coccolithophore 370
aggregates, transports particles quickly to deep water with high and concentrations (Fig. 371
7e). We expect that high concentration favors relatively high fixation, but high 372
concentration lowers the fixation rate in coccolithophore aggregates. Therefore, the interplay 373
between particle sinking speed and vertical water column profiles of and concentrations 374
determines the fixation rate, supporting our hypothesis H5. 375
376
fixation in contrasting oceanic environments 377
fixation is dependent on the and concentrations in the water column, but those are 378
highly variable around the global ocean. We investigated fixation rates in three contrasting water 379
columns: an minimum zone in the Eastern Tropical South Pacific (ETSP)56
, the Mauritanian 380
upwelling zone in the NAO56
, and an open ocean site (OO; N, W)63,64
. The ETSP has 381
minimum zones with < 5 μmol L-1
at ~150–600 m depth (Fig. 8a), the NAO has reduced 382
levels (~62.5–157 µmol L-1
) at ~100–600 m (Fig. 8d), whereas the open ocean site has high 383
concentration throughout the water column (>157 µmol L-1
; Fig. 8g). concentrations increase 384
gradually up to 800 m depth, with decreasing levels from ETSP to NAO and to the open ocean site. 385
18
We consider particles with sinking speed similar to natural marine snow and examine fixation 386
rates per unit volume of particle (Fig 8c,f,i). To compare with existing measurements, we further 387
calculate fixation rates per unit volume of water (Fig. 8b,e,h) and depth-integrated fixation 388
rates by multiplying the number of particles with fixation per particle (Equation (34))35
. 389
Maximum fixation rates per volume of particle and per volume of water lie within ranges 390
0.31-1.1 μg N (cm3 particle)
-1 d
-1 (Fig. 8c,f,i) and 0.14-0.7 μmol N m
-3 d
-1 (Fig. 8b,e,h). The highest 391
rate of fixation is in the NAO followed by the ETSP. Interestingly, fixation is observed even 392
at the high concentrations of the open ocean, although, the fixation rates and the depth 393
window of fixation are smaller than for the other two scenarios. Since the abundance and size 394
spectrum of particles vary with latitude and seasonally at high latitudes65
, we test the sensitivity of 395
fixation rates by varying the parameter determining the abundance ( ) and the proportion of 396
large and small particles ( ). We find that the fixation rate varies between 0.3-1.7 μmol N m-3
d-1
397
inside sinking particles (Supplementary Fig. S6). Our modelled fixation rates are comparable 398
with bulk fixation rates measured in the aphotic ocean (0-0.89 μmol N m-3
d-1
)9,66
where active 399
autotrophic cyanobacterial diazotrophs are not expected. Our calculated depth-integrated 400
fixation rates lie within the range 7.1-65.1 μmol N m-2
d-1
. Empirical evidence from regions, where 401
fixation is dominated by heterotrophic bacteria, shows similar levels of depth-integrated 402
fixation rates; e.g. 6.27–16.6 μmol N m-2
d-1
in the equatorial and southern Indian Ocean67
and 12.4 403
– 190.9 μmol N m-2
d-1
in the South Pacific Gyre68
. In comparison, depth-integrated fixation 404
rates by cyanobacteria in most regions of the global upper ocean are in the order of 1–100 μmol N 405
m-2
d-1 69
. Hence, taken together, our modelled rates for heterotrophic bacteria on particles are 406
consistent with empirical bulk rates from the deep sea and comparable to areal rates measured for 407
cyanobacteria. This supports empirical studies suggesting that aphotic fixation can account for a 408
19
significant or even predominant fraction of water column fixation66,70
, and substantiates the idea 409
that aphotic fixation may be important to global nitrogen budget considerations5. 410
411
The effects of temperature variation 412
The variation in water temperature has the potential to alter fixation rates through 413
increases in metabolic rates and diffusive processes with temperature. Since sinking particles face a 414
decreasing gradient in temperature as they descend through the water column, especially in the 415
lower latitudes, we examined the effects of temperature on the amount of fixed at an open ocean 416
site in the North Atlantic Ocean (OO; N, W)63,64
. A small increase in the amount of total 417
fixation rate, from 7.1 μmol N m-2
d-1
to 8.4 μmol N m-2
d-1
, and a slight downward shift in the 418
positioning of fixation in the water column was observed (Supplementary Fig. S7). On one 419
hand, elevated temperature increases fixation rate by stimulating metabolic activity. On the other 420
hand, elevated temperature stimulates the influx of via diffusion, which hampers fixation 421
Therefore, the impact of temperature on metabolic rates and diffusion tends to counter one another 422
on sinking particles. Hence, even at a site showing a large decrease in temperature between surface 423
and depth, the effects of temperature on fixation are fairly small. 424
425
Conclusions and broader implications 426
Our model suggests that particle-associated heterotrophic fixation is viable and reasonable based 427
on the known properties and physics of marine particles and reveals a significant contribution to the 428
oceanic biological fixation. The likelihood and rate of fixation associated with any individual 429
particle will depend upon numerous factors. These include the vertical profiles of and 430
20
through which the particle sinks, but in particular also the particle composition and bioavailability, 431
including the initial polysaccharide and polypeptide concentrations, together with the size, sinking 432
speed, and abundance of particles, as suggested by the model sensitivity analysis. We show how 433
low- or anoxic zones generated inside sinking particles by microbial respiration provide 434
conditions suitable for heterotrophic fixation, however, only in particles larger than about 0.03 435
cm in radius. Moreover, we show that these anoxic microenvironments can promote anaerobic 436
respiratory processes that even extend into well-oxygenated deep waters. Interestingly, our 437
simulations suggest that even in particles that favor fixation at a point in their descent, the 438
window of time (depth) where diazotrophy occurs is likely to be short. However, despite the 439
necessity of several coinciding environmental conditions for fixation in particles, the criteria are 440
met in natural particles. Because of the huge number and heterogeneity among particles sinking in 441
the ocean44
, it is highly likely that a large number of individual particles at any given time might 442
meet these criteria and in doing so, confer a fitness advantage on a subset of bacteria that retain the 443
ability to fix nitrogen. This may explain the ubiquity and persistence of the genetic signature for 444
heterotrophic fixation throughout the oceans8. The combined knowledge of the probability 445
density of particle sizes, compositions, and sinking speeds is suggested to predict the average rates 446
of fixation associated with particles. 447
Our model makes several interesting and potentially testable predictions: Firstly, the C:N 448
composition of particle “trails” will reflect the interior state and might be a way to probe the 449
response of different particle types or conditions. Secondly, the model predicts a “preference” for 450
electron acceptor over
in low oxygen particles. Thirdly, heterotrophic diazotrophs 451
mostly use local and ephemeral oxygen conditions and get windows of opportunity for their 452
fixation. Fourthly, fixation can occur on large particles with high concentrations of 453
polysaccharides and polypeptides in fully oxygenated marine waters, but also on older less 454
21
substrate-rich particles if oxygen concentration in the surrounding water is low. These predictions 455
could be promoted as perspectives for future experiments. 456
457
Methods 458
The cell model 459
Growth rate of a cell: 460
The growth rate of a bacteria cell depends on the acquisition of C (from the particle) and N (from 461
the particle and through fixation), as well as on metabolic expenses in terms of C. 462
Uptake of C and N 463
Bacteria get C from glucose and both C and N from amino acids. The total amount of C available 464
for the cell from monomers is (units of C per time) 465
466
and the amount of N available from monomer is (N per time) 467
468
where and are uptake rates of glucose and amino acids, is the fraction of C in glucose, and 469
and are fractions of C and N in amino acids. 470
The rate of obtaining N through fixation is: 471
472
22
where regulates fixation rate and fixation can happen at a maximum rate . 473
fixation is only limited by the maximum fixation rate as dissolved dinitrogen ( ) gas in 474
seawater is assumed to be unlimited71
. 475
The total uptake of C and N from different sources becomes 476
(4) 477
(5) 478
Costs 479
Respiratory costs of cellular processes together with fixation and its associated removal cost 480
depend on the cellular concentration. Two possible scenarios can be observed: 481
Case 1: When concentration is sufficient to maintain aerobic respiration 482
Respiratory costs for bacterial cellular maintenance can be divided into two parts: one dependent on 483
limiting substrates and the other one is independent of substrate concentration72
. Here we consider 484
only the basal respiratory cost , which is independent of the limiting substrates and is assumed 485
as proportional to the mass of the cell (μg C). In order to solubilize particles, particle-attached 486
bacteria produce ectoenzymes that cleave bonds to make molecules small enough to be transported 487
across the bacterial cell membrane. Cleavage is represented by a biomass-specific ectoenzyme 488
production cost 73
. The metabolic costs associated with the uptake of hydrolysis products and 489
intracellular processing are assumed to be proportional to the uptake ( ): and where the 490
‟s are costs per unit of resource uptake. In a similar way, the metabolic cost of fixation is 491
assumed as proportional to the fixation rate:
, where is the bacterial C:N ratio. 492
If we define all the above costs as direct costs, then the total direct respiratory cost becomes 493
23
Indirect costs related to fixation arises from the removal of from the cell and the 494
production/replenishment of nitrogenase as the enzyme is damaged by . The cell can remove 495
either by increasing respiration74
or by increasing the production of nitrogenase enzyme itself 75
. 496
Here we consider only the process of removal by increasing respiration. To calculate this 497
indirect cost, the concentration of present in the cell needs to be estimated. 498
Since the time scale of concentration inside a cell is short, we have assumed a pseudo 499
steady state inside the cell; the diffusion rate inside a cell is always balanced by the respiration 500
rate 14
, which can be expressed as 501
Here is the conversion factor of respiratory to C equivalents and is the actual 502
diffusion rate into a cell from the particle and can be calculated as 503
( )
where is the cell radius, is the local concentration inside the particle, is the cellular 504
concentration, and is the effective diffusion coefficient of over cell membrane layers. 505
The effective diffusion coefficient can be calculated according to Inomura et al.14
in terms of 506
diffusion coefficient inside particles ( ), the diffusivity of cell membrane layers relative to water 507
( ), the radius of cellular cytoplasm ( ), and the thickness of cell membrane layers ( ) as 508
The apparent diffusivity inside particles ( ) is considered as a fraction
of the diffusion 509
coefficient in seawater ( ) 510
. (10) 511
24
Combining (7) and (8) gives the cellular concentration as 512
[
] 513
If there is excess present in the cell after respiration ( , then the indirect cost of 514
removing the excess to be able to perform fixation can be written as 515
where is the Heaviside function: 516
{
Therefore, the total aerobic respiratory cost becomes: 517
Case 2: Anaerobic respiration 518
When available is insufficient to maintain aerobic respiration ( ), cells use 519
and
for respiration. The potential uptake, , is 520
521
where and
are maximum uptake rate and affinity for uptake, respectively. 522
However, the actual rate of uptake,
, is determined by cellular respiration and can be 523
written as 524
( (
))
25
where is the conversion factor of respiratory
to C equivalents and the maximum 525
diffusion rate into a cell can be obtained by making cellular concentration zero in 526
(8) as 527
(17) 528
Further, in the absence of sufficient , the cell uses
as an electron acceptor for 529
respiration. Since the average concentration of in seawater is 29 mmol L
-1 77,
is a non-530
limiting nutrient for cell growth and the potential uptake rate of is mainly governed by the 531
maximum uptake rate as 532
533
where is the maximum uptake rate for
uptake. The actual rate of uptake,
, 534
can be written as 535
( (
))
where is the conversion factor of respiratory
to C equivalents. 536
According to formulations (16) and (19), and
uptake occurs only when the 537
diffusive flux of , and both and are insufficient to maintain respiration Moreover, the 538
uptake rates of and
are regulated according to the cells‟ requirements. 539
Uptakes of and
incur extra metabolic costs
and
, 540
where and
are costs per unit of and
uptake. The total respiratory cost can 541
be written as 542
26
Synthesis and growth rate 543
The assimilated C and N are combined to synthesize new structure. The synthesis rate is constrained 544
by the limiting resource (Liebig‟s law of the minimum) and by available electron acceptors such 545
that the total flux of C available for growth (μg C d-1
) is: 546
[
] 547
Here, the total available C for growth is , the C required to synthesize biomass 548
from N source is , and the C equivalent inflow rate of electron acceptors to the cell is 549
. We assume that excess C or N is released from the cell 550
instantaneously. 551
Synthesis is not explicitly limited by a maximum synthesis capacity; synthesis is constrained 552
by the C and N uptake in the functional responses (Equations (28) and (29)). The division rate of 553
the cell (d-1
) is the total flux of C available for growth divided by the C mass of the cell ( ): 554
555
The resulting division rate, , is a measure of the bacterial fitness and we assume that the cell 556
regulates its fixation rate depending on the environmental conditions to gain additional N while 557
maximizing its growth rate. The optimal value of the parameter regulating fixation 558
( ) then becomes: 559
560
and the corresponding optimal division rate becomes 561
562
563
27
The particle model 564
We consider a sinking particle of radius (cm) and volume (cm3) (Supplementary Fig. S1). The 565
particle contains facultative nitrogen-fixing bacterial population (cells L-1
), polysaccharides 566
(μg G L-1
), and polypeptides (μg A L-1
) at a radial distance (cm) from the center of 567
the particle, where G and A stand for glucose and amino acids. We assume that only fractions 568
and of these polymers are labile ( ), i.e. accessible by bacteria. 569
Bacterial enzymatic hydrolysis converts the labile polysaccharides and polypeptides into 570
monosaccharides (glucose) ( μg G L-1
) and amino acids ( μg A L-1
) that are efficiently taken up 571
by bacteria. Moreover, the particle contains , , and
with concentrations 572
(μmol O2 L-1
), (μmol NO3 L
-1), and
(μmol SO4 L-1
). Glucose and amino acids 573
diffuse out of the particle whereas and diffuse into the particle from the surrounding 574
environment. Due to the high concentration of in ocean waters, we assume that
is not 575
diffusion limited inside particles, its uptake is limited by the maximum uptake capacity due to 576
physical constraint. The interactions between particle, cells, and the surrounding environment are 577
explained in Supplementary Fig. S1 and equations are provided in Table 1 of the main text. 578
We assume that labile polysaccharide ( ) and polypeptide ( ) are hydrolyzed into glucose and 579
amino acids at rates and with the following functional form 580
(26) 581
(27) 582
where and are maximum hydrolysis rates of the carbohydrate and peptide pool, and and 583
are respective affinities. and represent uptake of glucose and amino acids: 584
28
(28) 585
(29) 586
where and are maximum uptake rates of glucose and amino acids, whereas and are 587
corresponding affinities. Hydrolyzed monomers diffuse out of the particle at a rate . 588
is the optimal division rate of cells (Equation (24)) and represents the mortality rate 589
(including predation) of bacteria. and
represent the diffusive flux of and the 590
consumption rate of , respectively, through the bacterial cell membrane.
and are 591
diffusion coefficients of and inside the particle. 592
At the center of the particle ( ) the gradient of all quantities vanishes: 593
|
|
|
|
(30) 594
At the surface of the particle ( ) concentrations are determined by the surrounding 595
environment: 596
| |
|
|
, (31) 597
where and are concentrations of glucose, amino acids, , and in the 598
environment. 599
Calculation of total fixation rate 600
The total amount of fixed in a specific size class of particle, ( g N particle-1), is calculated 601
as 602
29
∫∫
where (cm) is the particle radius and z (m) represents the water column depth. 603
fixation rate per unit volume of water, ( N m-3
d-1
), is calculated as 604
∫∫
Here (cm) represents the size range (radius) of particles, is the fraction of diazotrophs of 605
the total heterotrophic bacteria, and (number of particles per unit volume of water per size 606
increment) is the size spectrum of particles that is most commonly approximated by a power law 607
distribution of the form 608
, (34) 609
where is a constant that controls total particle abundance and the slope represents the relative 610
concentration of small to large particles: the steeper the slope, the greater the proportion of smaller 611
particles and the flatter the slope, and the greater the proportion of larger particles35
. 612
Depth-integrated fixation rate, ( N m-2
d-1
), can be obtained by 613
∫
Assumptions and simplification in the modelling approach 614
According to our current model formulation, the particle size remains constant while sinking. 615
However, in nature, particle size is dynamic due to processes like bacterial remineralization, 616
aggregation, and disaggregation. We neglect these complications to keep the model simple and to 617
30
focus on revealing the coupling between particle-associated environmental conditions and 618
fixation by heterotrophic bacteria. These factors can, however, possibly be incorporated by using in 619
situ data or by using the relationship between carbon content and the diameter of particles49
and 620
including terms for aggregation and disaggregation56
. 621
Our model represents a population of facultative heterotrophic diazotrophs that grow at a rate 622
similar to other heterotrophic bacteria but the whole community initiates fixation when 623
conditions become suitable. However, under natural conditions, diazotrophs may only constitute a 624
fraction of the bacterial community, and their proliferation may be gradual20
, presumably affected 625
by multiple factors. In such case, our approach will overestimate diazotroph cell concentration and 626
consequently the fixation rate. 627
For simplicity, our approach includes only aerobic respiration, and
respiration, 628
although many additional aerobic and anaerobic processes likely occur on particles (e.g Klawonn et 629
al.18
). To our knowledge, a complete picture of such processes, their interactions and effects on 630
particle biochemistry is unavailable. For example, we have assumed that when and are 631
insufficient to maintain respiration, heterotrophic bacteria start reducing . However,
632
reduction has been detected only with a significant lag after the occurrence of anaerobic conditions, 633
suggesting it as a slow adapted process78
, whereas we assume it to be instantaneous. On the other 634
hand, the lag may not be real but due to a „cryptic sulfur cycle‟, where reduction is 635
accompanied by concurrent sulfide oxidation effectively masking sulfide production79
. Hopefully, 636
future insights into interactions between diverse aerobic and anaerobic microbial processes can 637
refine our modelling approach and fine-tune predictions of biochemistry in marine particles. 638
Procedure of numerically obtaining optimal fixation rate 639
31
To avoid making the optimization in Eq. (23) at every time step during the simulation, a lookup 640
table of (Eq. (24)) over realistic ranges of the four resources (glucose, amino acids, , and 641
) and the parameter determining fixation rate ( ) was created at the beginning of the 642
simulation. 643
The effects of temperature on fixation rate 644
To examine the role of temperature variation on fixation rate in sinking particles, we consider 645
hydrolysis of polysaccharide and polypeptide, uptake of glucose and amino acids, uptake of , 646
respiration, and diffusion dependent on temperature. Apart from diffusion, all other processes are 647
multiplied by a factor that represents the factorial increase in rates with C temperature 648
increase. The rate at a given temperature is then 649
(36) 650
Here the reference rate is defined as the rate at the reference temperature We set the 651
reference temperature at room temperature of C. The effect of temperature on the diffusion 652
coefficient D for glucose, amino acids, , and is described by Walden's rule: 653
, (37) 654
where is the viscosity of water at the given temperature , and and are diffusion 655
coefficient and viscosity at . 656
values for different enzyme classes responsible for hydrolysis ( ) lie within the range 1.1-657
2.980
. Here, we have chosen for hydrolysis from the middle of the prescribed range. The 658
values for uptake affinities ( ) are taken as 1.581
. is chosen for all parameters 659
related to respiration ( , , , , ,
, )
82. and are the values of ‟s and 660
32
‟s provided in Table S1. The reference viscosity ( ) and viscosities ( ) at different temperatures 661
are taken from Jumars et al.82
. 662
663
Data Availability 664
The authors declare that the sources of all data supporting the findings of this study are available 665
within the article. 666
Code Availability 667
Matlab codes for Figures 2 and 3 are available at DOI: https://doi.org/10.17894/ucph.da390b38-13d1-668
40a3-a287-9f8742494d65 (https://erda.ku.dk/archives/1e3ce4f581c38fb00bb4311126a9b513/published-669
archive.html). 670
671
672
673
674
675
676
677
678
33
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3731–3739 (1998). 866
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transport of key sulfur oxidizing bacteria. Nat. Commun. 9, 1–11 (2018). 868
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determines temperature response of unicellular plankton communities. Limnol. Oceanogr. 872
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83. Alldredge, A. L., Passow, U. & Haddock, S. H. D. The characteristics and transparent 876
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884
43
Acknowledgments 885
SC and LR were supported by grant 6108-00013 from the Danish Council for Independent Research 886
to LR. The Centre for Ocean Life was supported by the Villum Foundation. KI was supported by 887
the Simons Foundation (Simons Postdoctoral Fellowship in Marine Microbial Ecology, Award 888
544338). MJF was supported by the Simons Collaboration on Computational Biogeochemical 889
Modeling of Marine Ecosystems (CBIOMES; Simons Foundation grant no. 549931). We wish to 890
thank Helle Ploug for her helpful comments on an earlier version of the manuscript. 891
Author contributions 892
S. C., L. R., K. A., and A. V. developed the model. S. C. performed all numerical simulations and 893
analyses with input from K. A. and A. V.. S. C. and L. R. wrote the manuscript. All authors 894
provided critical feedback and helped shape the manuscript. 895
Competing interests 896
The authors declare no competing interests. 897
898
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903
44
Figure Legends: 904
Fig. 1 Schematic representation of the cellular processes. It shows how fluxes of carbon (C), 905
(solid lines), fluxes of nitrogen (N), (dotted lines), and electron acceptors ( , , and
; 906
red dashed line) are combined (blue ellipse) to determine growth rate after paying the cost of 907
respiration (brown explosion). Triangle symbols represent the functional responses for the uptake 908
mechanisms and diffusive inflow of , , and
. represents respiration that includes 909
costs of uptake and mobilization of resources for synthesis, construction/maintenance of structure, 910
and ectoenzyme production. The ellipse represents the synthesis of biomass from the available C, N 911
and electron acceptors following Liebig‟s law of the minimum. Any excess assimilated C or N is 912
excreted from the cell. µ represents the division rate. The black dashed-dotted line represents the 913
regulation of fixation to optimize growth rate and the red dashed-dot line represents the 914
regulation of respiration by electron acceptors. 915
Fig. 2 Dynamics inside a particle of radius 0.125 cm with time. (a) Labile carbohydrate, (b) labile 916
polypeptide, (c) glucose, (d) amino acid, (e) in particle, (f) in particle, (g) bacterial 917
abundance, (h) respiration rate, (i) fixation rate, and (j) growth rate are shown along the particle 918
radius over time. Parameters and concentrations of surrounding factors are taken from Table 2. 919
Fig. 3 Cellular rates and resource concentrations at a radial distance of 0.027 cm from the center of 920
a particle of radius 0.125 cm. (a) Size-specific rates of C uptake (dark blue), total respiration 921
(orange), available C for growth (light blue), available N for growth (green), available EA (electron 922
acceptor , , and
; yellow), and growth rate of a cell (dashed magenta). Regions I, II, 923
III, and IV represent situations when a cell is limited by C, EA, co-limited by N and EA, N, and 924
showing negative growth rate (see text). (b) Respiratory costs related to fixation in terms of 925
direct respiration, enzyme production, and removal. (c) Glucose, amino acid, and bacterial 926
45
concentrations in the particle. (d) Cellular fixation rate. (e) and concentrations in the 927
particle. The grey area represents the time interval of fixation. 928
Fig. 4 The total amount of fixed per particle as a function of particle radius and initial labile 929
polysaccharide (a), initial labile polypeptide (b), and surrounding concentration (c). The white 930
dashed line separates regions of occurrence and non-occurrence of fixation ( μg N 931
particle-1
). The horizontal magenta dashed lines indicate the base value for other plots, e.g., in (a), 932
magenta dashed line represents the level of polysaccharide concentration in panels b and c. The 933
chosen concentration ranges corresponds to those in natural particles 61,83
. 934
Fig. 5 The total amount of fixed at different initial labile polysaccharide and polypeptide 935
concentrations. fixation is observed in a large particle of radius 0.125 cm and surrounding 936
concentrations (a) 50 μmol O2 L-1
and (b) 0.5 μmol O2 L-1
, and (c) in a relatively smaller particle of 937
radius 0.05 cm and surrounding concentrations 0.5 μmol O2 L-1
. Line types are similar as in Fig. 938
4. Note the different ranges of the scale of fixation. 939
Fig. 6 Dynamics inside sinking particles of different sizes in the upper 500 m of the Mauritanian 940
upwelling zone in the North Atlantic Ocean (NAO)56
. and profile in the water column
56 941
(a), total amount of fixed per particle (b), fraction of particle volume where respiration is fueled 942
by denitrification (c), and fraction of particle volume where respiration is fueled by reduction 943
(d). Areas enclosed by white and magenta dashed lines represent the occurrence of fixation 944
(> μg N day-1
particle-1
) and anoxia ( < μmol O2 L-1
), respectively, at the center of 945
particles. 946
Fig. 7 fixation rates in different types of sinking particles with different sinking speeds. (a) 947
Particle radius (cm) versus sinking speeds (m d-1
) of natural marine snow (continuous line) 948
measured in situ off California ( 0.26
; 62
) and of laboratory-made diatom (dashed 949
46
line) and coccolithophore (dotted line) aggregates measured in vitro ( 0.72
and 950
0.47
, respectively51
). (b) and profiles of the Mauritanian upwelling zone 951
in the North Atlantic Ocean (NAO)56
,. (c-e) fixation rates per unit volume of particles of 952
different sizes and types. White and magenta dashed lines are same as in Fig. 6. The area enclosed 953
within the horizontal green lines represents the low- zone. 954
Fig. 8 Comparison of predicted fixation rates in natural marine snow at three contrasting sites in 955
terms of vertical distributions of and
in the ocean: (a-c) minimum zone in the Eastern 956
Tropical South Pacific (ETSP)56
, (d-f) the Mauritanian upwelling zone in the North Atlantic Ocean 957
(NAO)56
, and (g-i) open ocean (OO; N, W)63,64
. (a,d,g) and concentrations in 958
the upper 1000 m vertical water column. (b,e,h) fixation rates per unit volume of water. (c,f,i) 959
fixation rates per unit volume of particle of different size classes. 960
961
962
963
964
965
966
967
968
969
47
Table 1. Equations for the particle model. All quantities vary with time and with distance from 970
the center . The operator in the brackets represents diffusion in spherical coordinates. Definitions, 971
units, and values of each of the parameters are provided in Supplementary Table S1. 972
Variables Equations
Bacteria (cells L-1
)
25(a)
Labile polysaccharides (μg G L-1
)
25(b)
Labile polypeptides (μg A L-1
)
25(c)
Glucose (μg G L-1
)
(
)
25(d)
Amino acids (μg A L-1
)
(
)
25(e)
Oxygen (μmol O2 L-1
)
(
)
25(f)
Nitrate (μmol NO3 L-1
)
(
)
25(g)
973
974
