the geochemical fingerprint of microbial long-distance …at work, where electrons are passed on...

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Geochimica et Cosmochimica Acta 152 (2015) 122–142

The geochemical fingerprint of microbial long-distanceelectron transport in the seafloor

Filip J.R. Meysman a,c,⇑, Nils Risgaard-Petersen b, Sairah Y. Malkin c,1,Lars Peter Nielsen b

a Department of Ecosystem Studies, The Netherlands Institute of Sea Research (NIOZ), Korringaweg 7, 4401 NT Yerseke, The Netherlandsb Section for Microbiology and Center for Geomicrobiology, Department of Bioscience, Aarhus University, 8000 Aarhus C, Denmark

c Department of Analytical, Environmental and Geo-Chemistry, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium

Received 23 June 2014; accepted in revised form 14 December 2014; Available online 19 December 2014

Abstract

Recently, a novel “electrogenic” type of sulfur oxidation has been documented in marine sediments, whereby long filamen-tous cable bacteria are generating electrical currents over centimeter-scale distances. Here we propose a numerical modeldescription that is capable of quantitatively simulating the solute depth profiles and biogeochemical transformations in suchelectro-active marine sediments. The model is based on a conventional reactive transport description of marine sediments,which is extended with a new model formulation for the long-distance electron transport induced by the cable bacteria.The mechanism of electron hopping is implemented to describe the electron transport along the longitudinal axis of the micro-bial filaments. We demonstrate that this model is capable of reproducing the observed geochemical fingerprint of electrogenicsulfur oxidation, which consists of a characteristic set of O2, pH and H2S depth profiles. Our simulation results suggest thatthe cable bacteria must have a high affinity for both oxygen and sulfide, and that intensive cryptic sulfur cycling takes placewithin the suboxic zone. A sensitivity analysis shows how electrogenic sulfur oxidation strongly impacts the biogeochemicalcycling of sulfur, iron, carbon and calcium in marine sediments.� 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. INTRODUCTION

Recently, an entirely novel type of microbial respirationhas been discovered, whereby long filamentous bacteria arecapable of generating and mediating electrical currents overcentimeter-scale distances (Nielsen et al., 2010; Pfeffer et al.,2012; Risgaard-Petersen et al., 2012). This novel “electro-genic” type of microbial sulfur oxidation was first discov-ered in laboratory experiments (Nielsen et al., 2010), buthas recently also been demonstrated to occur under a rangeof natural conditions, including coastal mud plains, aqua-

http://dx.doi.org/10.1016/j.gca.2014.12.014

0016-7037/� 2014 The Authors. Published by Elsevier Ltd.

This is an open access article under the CC BY-NC-ND license (http://crea

⇑ Corresponding author. Tel.: +31 113 577 450.E-mail address: [email protected] (F.J.R. Meysman).

1 Present address: Department of Marine Sciences, University ofGeorgia, 325 Sanford Dr., Athens GA 30602, USA.

culture areas, salt marshes, and seasonally hypoxic basins(Malkin et al., 2014). The process has potentially a largeimpact on the elemental cycling within the seafloor, as elec-trogenic sulfur oxidation has been shown to dominate theoxygen consumption, and strongly impacts the cycling ofcarbon, sulfur and iron with the sediment (Risgaard-Petersen et al., 2012).

The evidence for long distance electron transport isbased on electrochemical and geochemical observations inmarine sediments. A most remarkable feature of electro-genic sulfur oxidation (e-SOx) is the spatial segregation ofredox half reactions, as inferred from O2, pH and H2Sdepth profiles (Nielsen et al., 2010). These geochemical datasuggest that strong oxidative removal of sulfide takes placein deeper sediment layers, while reductive consumption ofoxygen occurs within the oxic zone just below the sedi-ment–water interface (Nielsen et al., 2010). To make such

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F.J.R. Meysman et al. / Geochimica et Cosmochimica Acta 152 (2015) 122–142 123

a separation of half-reactions possible, there must be a pathby which electrons are transferred from deeper sedimenthorizons (where electrons are harvested from sulfide) tothe surface layer (where electrons are transferred to oxy-gen). Further support for long-distance electron transferof electrons was recently obtained by a new type of electri-cal sediment profiling (Damgaard et al., 2014). When anelectron current is induced in the sediment, a correspondingelectrical field is anticipated, which drives an ionic counter-current in the pore water to maintain charge balance. Fine-scale measurement of the electric potential distribution insediments have revealed this predicted electrical field whenthe geochemical fingerprint of e-SOx is present (Risgaard-Petersen et al., 2014).

Two possible mechanisms were initially proposed toexplain the inferred long-distance electron transfer(Nielsen et al., 2010). One possibility is that the conduc-tance occurs within the mineral matrix, where electronsare passed in grain-to-grain contacts between conductiveminerals, such as pyrite (Kato et al., 2010; Malvankaret al., 2014). A second option is that the electron transportis microbially mediated (Ntarlagiannis et al., 2007). Micro-organisms are known to use diverse strategies such asouter membrane cytochromes, redox shuttles or conduc-tive pili to transport electrons out of the cell and over1–10 lm distances (Reguera et al., 2005; Gorby et al.,2006; Lovley, 2008; Logan and Rabaey, 2012). However,the inferred electron transport takes place over distancesof 10–25 mm (Nielsen et al., 2010; Malkin et al., 2014;Schauer et al., 2014), which exceeds the known lengthscale of microbial electron transport by more than threeorders of magnitude.

Recent investigations provide multiple lines of evidencethat long-distance electron transport is microbially medi-ated. Detailed microscopic investigations have revealed thatelectro-active sediments contain high densities ofunbranched, long filamentous bacteria belonging to thefamily Desulfobulbaceae, which likely extend from the oxiclayer deep into the anoxic zone of the sediment (Pfefferet al., 2012). When e-SOx is induced in laboratory incuba-tions, the depth distribution of these so-called “cable bacte-ria” closely tracks the development of the suboxic zone,suggesting that the filaments are responsible for theobserved sulfur oxidation (Schauer et al., 2014). Targetedmanipulation experiments provide additional support thatthe cable bacteria are crucially implicated in the electrontransport (Pfeffer et al., 2012). A lateral cutting of the fila-ment network (by passing of a thin tungsten wire horizon-tally through sediment) results in an immediate impedimentof the electron transport, as indicated by a sudden and sig-nificant drop in the oxygen consumption (Pfeffer et al.,2012). Furthermore, when filters with defined pore sizeswere inserted into sediment cores, the downward the down-ward expansion of electrogenic sulfur oxidation was onlyobserved when the filter barriers had pore sizes that werelarger than the diameter (�0.5–1 lm) of the filaments(Pfeffer et al., 2012). Finally, when a 5 mm thick layer ofnon-conductive glass microspheres was inserted into a sed-iment core, long-distance electron transport was observedwhen a network of cable bacteria filaments bridged the

non-conductive layer (Pfeffer et al., 2012). These experi-ments challenge the claim by Malvankar et al. (2014) thatcurrents are passing exclusively through conductive miner-als, and instead, support the idea that long-distance elec-tron transfer is mediated by cable bacteria.

Accordingly, the current available observations indicatethat an entirely novel mechanism of electron conduction isat work, where electrons are passed on from cell to cellalong the longitudinal axis of long, filamentous bacteria(Pfeffer et al., 2012). This finding that microbial activitycan facilitate long-distance electron transfer provides anew paradigm for sediment biogeochemistry. The remotespatial coupling of redox half reactions defies conventionalideas of how microbes interact with their environment andhow redox cycling occurs within marine deposits (Nealson,2010). Long-distance electron transfer short-circuits theconventional redox cascade (Froelich et al., 1979) andallows electron acceptors and electron donors to interactwith each other without being in close proximity. More-over, the process substantially reduces the time by whichredox oscillations in the water column (e.g., due to changesin O2 concentrations) are transduced into deeper sedimentlayers (Nielsen et al., 2010).

Given its groundbreaking character, the process ofelectrogenic sulfur oxidation elicits many questions. Arethe microbial filaments truly responsible for the electrontransport? If so, what is the exact mechanism of electrontransfer along a microbial filament? Do we understandthe strong pH excursions and other pore water signalsobserved in electro-active sediments? How strongly doese-SOx affect the elemental cycling in marine sediments?To help answer these questions, a more quantitativeunderpinning of the current conceptual understanding ofe-SOx process is needed. Therefore, the aim of the presentstudy is to develop and apply a biogeochemical model thatquantitatively simulates the elemental cycling associatedwith electrogenic sulfur oxidation. In a first step, wedescribe the conceptual model of electrogenic sulfur oxida-tion that has emerged from recent experimental observa-tions. Subsequently, we construct a reactive transportmodel of an electro-active marine sediment, whichincludes a mechanistic model of how electrons can betransported along the longitudinal axis of the cable bacte-ria that perform electrogenic sulfur oxidation. In a thirdstep, we show that this model is capable of quantitativelyreproducing the typical biogeochemical fingerprint ofe-SOx, as documented by high-resolution O2, pH andH2S microsensor depth profiling. In a final step, we applythe model to quantitatively evaluate the impact of e-SOxon the biogeochemical cycling of sulfur, iron, carbonand calcium in marine sediments.

2. MODEL FORMULATION

2.1. Conceptual model of long-distance electron transport

In order to describe sedimentary biogeochemical cyclingwith mathematical models, one has to make judiciousabstractions. Coastal marine sediments are characterizedby intense organic matter cycling and a complex sulfur

124 F.J.R. Meysman et al. / Geochimica et Cosmochimica Acta 152 (2015) 122–142

cycle (Canfield et al., 2005). Oxygen typically disappearswithin the first few millimeters, due to strong oxygen con-sumption in the top layer of the sediment (Glud, 2008).In deeper anoxic sediment layers, hydrogen sulfide is gener-ated by dissimilatory sulfate reduction (Jorgensen, 1977),and once produced, this sulfide can have a variety of fates.Part of the sulfide can react with various iron compounds toform iron sulfide phases and eventually pyrite. Anotherpart will be reoxidized to sulfur compounds with intermedi-ate oxidation state (such as elemental sulfur, thiosulfate).Eventually, these intermediates can be converted to sulfate,via a complex interplay of strictly abiotic reactions, as wellas microbially catalyzed oxidation and disproportionationreactions (Jorgensen , 1982; Canfield et al., 2005).

For the purpose of this paper, it is useful to consider twoidealized pathways of sulfur oxidation (Fig. 1). These twopathways have in common that oxygen features as the elec-tron acceptor, while sulfate acts as the final oxidation prod-uct. The principal difference concerns the location of thetwo half reactions of sulfide oxidation. In the first pathway,referred to as “canonical sulfur oxidation” (abbreviated“c-SOx”), sulfide oxidation and oxygen reduction occurwithin the same location, i.e., at the oxic–anoxic interfacewhere oxygen (O2) and free sulfide (H2S) are in contact(Fig. 1a). In contrast, the second pathway represents thenewly discovered process of “electrogenic sulfur oxidation”

(abbreviated “e-SOx”). In this case, long filamentous bacte-ria are bridging a wide suboxic zone, which separates theoxic and sulfidic sediment horizons (Fig. 1b). The twohalf-reactions of sulfur oxidation are spatially segregatedand are coupled via long-distance electron transport.

As illustrated in Fig. 1, these two sulfur oxidation path-ways will each impose a specific “geochemical fingerprint”on the pore water, that is, a characteristic set O2, pH, andH2S profiles which can be determined by microsensor pro-filing. In canonical sulfur oxidation, the hydrogen sulfide

20

O2

Water column

Canonical sulphide oxida�on

Sediment

21 12 2 42 2H S O SO H− ++ → +

H2S

electrans

pH

[a]

Fig. 1. Conceptual representation of two idealized modes of sulfide oxidhalf reactions occur conjointly at the oxic–anoxic interface. Proton releasezone. (b) Electrogenic sulfur oxidation as proposed by Nielsen et al. (2electron transport. Strong proton consumption within the oxic zone genproduced due to the oxidation of sulfide, thus creating a pH minimum d

produced by sulfate reduction diffuses upwards, and is oxi-dized to sulfate when it comes into contact with O2

(Jorgensen and Revsbech, 1983). This reaction is mediatedby sulfur oxidizing bacteria, which are positioned at theoxic–anoxic interface. The associated metabolism can berepresented by the overall redox reaction:

1

2H2SþO2 !

1

2SO2�

4 þHþ ð1Þ

Electrons are locally transferred between electrondonors and acceptors, i.e., across nanometer distanceswithin the membrane-bound enzymes of the electron trans-port chain (Gray and Winkler, 2005). As a result, nomacro-scale electron transport takes place. The associatedgeochemical fingerprint of canonical sulfur oxidation ischaracterized by (1) the absence of a suboxic zone, i.e.,no separation between the depth at which O2 disappearsand the depth where H2S appears, and (2) a decrease ofthe pH in the oxic zone down to the oxic–anoxic interface,where the oxidation of sulfide releases protons (H+). In dee-per anoxic layers, the pH tends to become constant withdepth (sulfate reduction releases dissolved inorganic carbonand alkalinity in equal proportions).

Electrogenic sulfur oxidation generates a set of pH, O2

and H2S depth profiles that strongly differs from the geo-chemical fingerprint of canonical sulfur oxidation (Nielsenet al., 2010). The pH depth profile has a clear maximumat the oxic–anoxic transition and a pronounced pH mini-mum much deeper in the anoxic zone (Fig. 1b). In addition,there is a prominent suboxic zone, separating the depthwhere O2 disappears and the depth where H2S appears.Laboratory incubations (Nielsen et al., 2010; Pfeffer et al.,2012; Schauer et al., 2014) as well as field observations(Malkin et al., 2014) indicate that this suboxic zone istypically 10–30 mm wide. Nielsen et al. (2010) argued thatthe only way to explain this specific geochemical fingerprint

O2

H2S

mme-

Electrogenicsulphide oxida�on

pH

22 4 4 2O e H H O− ++ + →

12 222142

2

4 5

H S H O

SO e H− − +

+ →

+ +

tronport

[b]

ation in marine sediments. (a) Canonical sulfur oxidation. The twoat the oxic–anoxic interface generates a pH decrease within the oxic010). The half-reactions are spatially separated and are linked byerates a pH maximum. Deeper down in the sediment, protons areeeper in the sediment.


is to assume that the two half reactions of sulfide re-oxida-tion are separated in space. In this conceptual model(Fig. 1b), a cathodic half reaction that involves the O2

reduction, occurs at the oxic–anoxic interface

O2 þ 4e� þ 4Hþ ! 2H2O ð2Þ

The associated consumption of protons generates theobserved pH maximum within the oxic zone. At the sametime, the anodic half reaction, which involves the H2S oxida-tion, occurs much deeper in the anoxic zone of the sediment

1

2H2Sþ 2H2O! 1

2SO2�

4 þ 4e� þ 5Hþ ð3Þ

The associated production of protons generates theobserved pH minimum deeper in the sediment. The spatialseparation of redox half-reactions implies electrical currentsrunning across centimeter scale distances: this electrontransport is needed to couple the anodic (i.e., electron pro-ducing) half-reaction in the deep anoxic layer with thecathodic (i.e., electron consuming) half-reaction at theoxic–anoxic interface (Fig. 1b).

A full understanding of the geochemical fingerprintsassociated with the various pathways of sulfur oxidationis crucial for their detection and identification in naturalhabitats. It was the characterization and interpretation ofthe distinctive geochemical fingerprint of e-SOx that hasled to the original discovery of long-distance electron trans-port (Nielsen et al., 2010). Similarly, the subsequent obser-vation of this distinct biogeochemical signature in variousnatural sediments has led to the conclusion that electro-genic sulfur oxidation is a dominant component of the sed-imentary sulfur cycle in many marine environmentsworldwide (Malkin et al., 2014). In the following sections,we will develop a mechanistic model of electrogenic sulfuroxidation, where we translate the conceptual modeldepicted in Fig. 1 into a reactive transport formulation.This will allow us to compare the geochemical fingerprintsof canonical and electrogenic sulfur oxidation.

2.2. Reactive transport model

The aim of the biogeochemical model is to simulate thedepth profiles of the main pore water solutes and solid sed-iment constituents in electro-active sediments. In these sim-ulations, we pay special attention to a satisfactoryreproduction of the geochemical fingerprint, i.e., the combi-nation of pH, O2 and H2S profiles as determined by micro-sensor profiling. The biogeochemical model has thestructure of a conventional early diagenetic model, whichis the standard approach to describe reactive transport inmarine sediments (Boudreau, 1997; Berg et al., 2003;Meysman et al., 2003). The key innovation is the incorpo-ration of a formulation for the long-distance electron trans-port associated with electrogenic sulfur oxidation, asdescribed in detail below. The core of the reactive transportmodel consists of a set of mass balance equations of theform (Boudreau, 1997; Meysman et al., 2005):

/F@Ci

@t¼ @

@x/F Di

@Ci

@x

� �þX

k

mi;kRk ð4Þ

The quantity Ci represents the concentration of a dissolvedcompound in the pore water, while /F denotes the porosity(the liquid volume fraction), which is assumed to be con-stant with depth. For solid components, the mass balanceEq. (4) has an identical form, but the porosity is replacedby the solid volume fraction (/S ¼ 1� /F ), while Ci

becomes as the concentration of a solid compound,expressed per unit volume of solid phase.

The transport processes included in the model are tai-lored to the experimental conditions in which e-SOx devel-ops (Nielsen et al., 2010; Risgaard-Petersen et al., 2012;Schauer et al., 2014) as well as the natural conditions underwhich the process has been found (Malkin et al., 2014), thatis, organic rich coastal sediments, with minimal physicaldisturbance or bioturbation. The model does not includeadvective pore water flow, as the sediment is consideredcohesive. Bioturbation and bio-irrigation are likewise notincluded, as macrofaunal reworking of the sedimentappears to disrupt the network of filamentous cable bacte-ria involved in e-SOx (Malkin et al., 2014). Furthermore,the process develops quickly, over a period of days to weeks(Schauer et al., 2014; Malkin et al., 2014), and over thistime scale, the influence of sediment deposition and burialcan be ignored. As a result, molecular diffusion is the soledominant transport process for pore water solutes. Themolecular diffusion coefficient Dmol

i is first calculated as afunction of temperature and salinity using the R packagemarelac (Soetaert et al., 2010) and corrected for tortuosityaccording to the modified Wiessberg relation of Boudreau(1996b), i.e., Di ¼ Dmol

i =ð1� 2 ln /F Þ. No diffusive transportis incorporated for solid phase constituents (i.e., Di ¼ 0 forsolids).

The quantities Rk in Eq. (4) represent the rates of thebiogeochemical reactions, where mi;k is the stoichiometriccoefficient of the i-th species in the k-th reaction. The reac-tion set included in the model is listed in Table 1 and pro-vides a parsimonious description of biogeochemical cyclingin organic-rich coastal sediments. The associated kineticrate expressions are listed in Table 2. The set of kineticand equilibrium reactions is adopted from existing modelsof sediment biogeochemistry (Boudreau, 1996a; VanCappellen and Wang, 1996; Berg et al., 2003; Meysmanet al., 2003), to which we have added a new set of reactionsto simulate electrogenic sulfur oxidation. Organic matter inthe sediment is microbially degraded via aerobic respirationand sulfate reduction (reactions K1 and K2 in Table 1). Sul-fate reduction is suppressed under oxic conditions, which isimplemented via a conventional limitation-inhibition for-mulation (Table 2; Soetaert et al., 1996). The free sulfidereleased by sulfate reduction can be re-oxidized in two dif-ferent ways, as illustrated in Fig. 1: either via canonical sul-fur oxidation (reaction K3 in Table 1) or electrogenic sulfuroxidation (reactions E1 and E2 in Table 1). The rate expres-sion for canonical sulfide re-oxidation follows a standardsecond-order rate law (Boudreau, 1997; Table 2). Thekinetic formulation of electrogenic sulfur oxidation isnovel, and is discussed in a separate section below. It isimportant to note that the relative importance of the twosulfur oxidation pathways is not fixed a priori, but formsan emergent property of the model. The rate of each

Table 1List of biogeochemical reactions included in the sediment model. K-type reactions denotes “Kinetic reactions”, E-type reactions stand for“Electrogenic reactions”, while AB-type reactions correspond to “Acid-base dissociation reactions”.

Kinetic reactions

K1 Aerobic respiration CH2OþO2 ! HCO�3 þHþ

K2 Sulfate reduction CH2Oþ 12 SO2�

4 ! HCO�3 þ 12 HS� þ 1

2 Hþ

K3 Canonical sulfur oxidation 12 HS� þO2 ! 1

2 SO2�4 þ 1

2 Hþ

K4 Ferrous iron oxidation Fe2þ þ 14 O2 þ 3

2 H2O! FeOOHþ 2Hþ

K5 Carbonate precipitation Ca2þ þHCO�3 ! CaCO3 þHþ

K6 Carbonate dissolution CaCO3 þHþ ! Ca2þ þHCO�3K7 Iron sulfide precipitation Fe2þ þHS� ! FeSþHþ

K8 Iron sulfide dissolution FeSþHþ ! Fe2þ þHS�

Electrogenic reactions

E1 Cathodic oxygen reduction O2 þ 4e� þ 4Hþ ! 2H2OE2 Anodic sulfide oxidation 1

2 HS� þ 2H2O! 12 SO2�

4 þ 4e� þ 4:5Hþ

Acid-base reactions

AB1 Carbon dioxide dissociation CO2 þH2O! HCO�3 þHþ

AB2 Bicarbonate dissociation HCO�3 ! CO2�3 þHþ

AB3 Borate dissociation BðOHÞ3 þH2O! BðOHÞ�4 þHþ

AB4 Sulfide dissociation H2S! HS� þHþ

AB5 Water dissociation H2O! OH� þHþ

Table 2List of kinetic rate expressions for the reactions included in the model. The rate expressions for kinetic reactions K1–K8 are standardformulations used in sediment biogeochemical models (Soetaert et al., 1996; Van Cappellen and Wang, 1996; Boudreau, 1996a,b; Meysmanet al., 2003). The rate expressions for electrochemical half-reactions E1 and E2 are newly introduced here (see text for details).

Reaction Kinetic rate expression

K1 Aerobic respiration R ¼ ð1� /Þkmin½CH2O� ½O2 �½O2 �þKO2

K2 Sulfate reduction R ¼ ð1� /Þkmin½CH2O� ½SO2�4 �

½SO2�4 �þK

SO2�4

KO2

½O2�þKO2

K3 Canonical sulfur oxidation R ¼ /kCSO½O2�½HS��

K4 Ferrous iron oxidation R ¼ /kFIO½Fe2þ�½O2�

K5 Carbonate precipitation R ¼ ð1� /ÞkCP½Ca2þ�½CO2�

3 �KSP

CaCO3

� 1

� �nCP

K6 Carbonate dissolution R ¼ ð1� /ÞkCD½CaCO3� 1� ½Ca2þ�½CO2�3 �

KSPCaCO3

� �nCD

K7 Iron sulfide precipitation R ¼ ð1� /ÞkISP½Fe2þ�½HS��½Hþ�KSP

FeS

� 1� �nISP

K8 Iron sulfide dissolution R ¼ ð1� /ÞkISD½FeS� 1� ½Fe2þ�½HS��½Hþ�KSP

FeS

� �nISD

E1 Cathodic oxygen reduction R ¼ /kCOR½O2�X T ðf CÞnCOR

E2 Anodic sulfide oxidation R ¼ /kASO½HS��X T ðf F ÞnASO


pathway is effectively determined by the availability andspatial distribution of their reagents (e.g., if both H2S andO2 are present at a given location, canonical sulfur oxida-tion will take place).

The model reaction set does not account for organicmatter mineralization via the reduction of iron and manga-nese (hydr)oxides. Reduction of metal (hydr)oxides isimportant in marine sediments only when strong metalcycling is sustained by continuous solid phase transport(Aller and Rude, 1988; Canfield et al., 1993; Aller, 2014).For example, in the case of iron cycling, solid iron (hydr)o-xides need to be transported downwards, reduced and con-verted to iron sulfides. To complete the iron cycle, theseiron sulfides need to be transported upwards and reoxidizedback to iron (hydr)oxides upon contact with oxygen. Asnoted above, strong reworking of the sediment apparently

disrupts the cable bacteria network (Malkin et al., 2014),and is therefore excluded from the model. In the absenceof solid phase transport, dissimilatory iron and manganesereduction will not be important as mineralization pathways.

When electrogenic sulfur oxidation is active, the spatialseparation of proton-producing and proton-consumingreactions induces strong pH anomalies in the pore water(Nielsen et al., 2010). This in turn promotes the mobiliza-tion of solid mineral phases like iron sulfides (FeS) and car-bonates (Risgaard-Petersen et al., 2012). The dissolution ofmetal sulfides and carbonates acts as a buffer against pHexcursions, and so, these reactions are included in the reac-tion set to be able to simulate the pH depth profile accu-rately (reactions K6 and K8 in Table 1). Ferrous iron(Fe2+) liberated by FeS dissolution moves upwards, whereit is oxidized to iron hydroxide (FeOOH) upon contact with


O2 (reaction K4 in Table 1), and also diffuses downwards,where it precipitates as FeS (reaction K7 in Table 1). Disso-lution and precipitation reactions follow standard kineticrate laws, where the reaction rate scales with the saturationstate of the pore water (Boudreau, 1996a,b; Van Cappellenand Wang, 1996; Meysman et al., 2003).

To describe the pH dynamics in the pore water, the bio-geochemical model was equipped with a pH calculationprocedure. The modelled set of acid-base dissociation reac-tions includes the carbonate, borate, sulfide and water equi-libria (reactions AB1–AB5, Table 1). The associated totalalkalinity is hence defined as:

AT¼½HCO�3 �þ2½CO2�3 �þ½BðOHÞ�4 �þ½HS��þ½OH��½Hþ�

ð5Þ

The equilibrium constants for the acid-base reactions werecalculated as a function of temperature and salinity usingAquaEnv, a dedicated R-package for acid-base and CO2

system calculations (Hofmann et al., 2010). Specifically,for the carbonate equilibria, we used the relationships pro-vided by Millero et al. (2006).

For all pore water constituents, a fixed concentrationwas imposed as a boundary condition at the sediment–water interface. The concentration values were obtainedfrom measured bottom water conditions at the field site(see below). At the lower boundary, a no flux conditionwas imposed for all pore water solutes. For the solid phaseconstituents, a similar no flux boundary condition wasimposed at both the upper and lower boundaries of themodel domain.

2.3. Electron transport model

To simulate the impact of electrogenic sulfur oxidationon sediment geochemistry, we need to embed the associatedlong-distance transport of electrons into the reactive trans-port formulation. Perturbation experiments suggest that theelectron transport occurs along the longitudinal axis of thecable bacteria (Pfeffer et al., 2012). Microscopy reveals thateach bacterial filament consists of a long chain of cells,which can exceed 30 mm in length and can contain up to20,000 individual cells (Pfeffer et al., 2012; Fig. 2a). Thisserial connection of cells implies that electrons must some-how be passed on from cell to cell. The actual mechanism ofthis intercellular electron transport is as yet unclear, butPfeffer et al. (2012) noticed a remarkable ultrastructurewithin the outer cell wall of the filaments, with fiber-likestructures running along the entire length of the filaments(Fig. 2b). Transmission electron microscopy (TEM) showsthat these fibers are embedded within in the continuousperiplasmic space and electrically insulated from the exter-nal medium by a collective outer membrane (Pfeffer et al.,2012). The hypothesis has been put forward is that thesefiber structures acts as “conductive wires” enabling theobserved electron transfer (Pfeffer et al., 2012).

Here, we follow the hypothesis that these periplasmicfiber structures are indeed conductive, and we propose apossible mechanism for the electron transport throughthese fiber structures. Our description of electron transport

is based on the mechanism of multistep electron hopping,which was originally developed to describe electrical con-ductivity in abiotic polymers containing discrete redoxgroups (Andrieux and Saveant, 1980; Dalton et al., 1990).In this model, electrons are transferred in a bucket-brigademanner along a one-dimensional array of redox sites.Recently, this electron hopping model has been imple-mented to describe the charge transport within so-called“microbial nanowires” (Strycharz-Glaven et al., 2011;Polizzi et al., 2012). These nanowires are hair-like, nanome-ter-wide protein structures, which extend as pili from thecell-wall of dissimilatory metal-reducing bacteria likeShewanella and Geobacter spp. (Reguera et al., 2005). Thesenanowires have been shown to be electrically conductive(El-Naggar et al., 2010), and are thought to be implicatedin the electron transfer from metal-reducing bacteria tosolid electron acceptors, such as metal oxide minerals innatural soils and sediments, and electrode surfaces inmicrobial fuel cells.

Fig. 2c shows a conceptual model scheme of how elec-trons could be transported along the longitudinal axis ofa cable bacterium. Each filament is surrounded by an outerring of conductive fibers, which are each considered to be asequential structure of redox-active enzyme complexes,capable of exchanging electrons with their nearest neigh-bors (these redox molecules are further referred to as elec-tron carriers). The internal structure of the conductivefibers is currently unknown. However, TEM images byPfeffer et al. (2012) shows that the diameter d of a conduc-tive fiber (�50 nm) is considerably larger than those ofnanowires (�5 nm), and much larger than the typicaldiameter of known electron carrying enzyme complexes(e.g., < 0.7 nm in the multi-heme cytochrome MtrC ofShewanella). This suggests that a conductive fiber consistsof multiple electron carriers in each cross-sectional plane,rather than constituting a single longitudinal chain of elec-tron carriers. Here, we assume that each filament containsNF conductive fibers, while each fiber is considered a longcylinder, fully stacked with electron carriers that arearranged on a rectangular grid separated by a distance d.Hence, a conductive fiber will contain NC = AF/d2 electroncarriers in each cross-section, where AF is the cross-sectional area (Fig. 2c). Such a three-dimensionalcylindrical packing of redox sites has the same electrontransport behavior as NC parallel electron carrier chains,as recently demonstrated by the model simulations ofPolizzi et al. (2012) for electron transport in nanowire pili.

Each electron carrier chain is idealized as a one-dimen-sional sequence of electron carriers (Fig. 2c), which eachcan bind one electron and which are separated by the dis-tance d. A given electron carrier at the i-th site along thechain can be in two states: free (carrying no electron,denoted as X i) or charged (carrying an electron, denotedas X �i ).

X i þ e�¢ X �i ð6Þ

If we introduce nCBðxÞ as the density of cable bacteria fila-ments at a given depth x in the sediment (i.e., the numberof filaments that crosses a horizontal plane at depth x, inunits per m2), then X T ¼ nCBðxÞN F AF =d

3 becomes the

cable bacterium

filament

i+1

electron carrier chain

conductivefiber

i-1

i

H2S

O2

SO42-

H2O

electron uploading

electron hopping

electron downloading

[c]

[b][a]

Fig. 2. (a) Microscopic image of a fragment of an cable bacteria filament obtained from the MLG field site and stained by Fluorescent In SituHybridisation (see Malkin et al. (2014), for details). The filament consists of a single, unbranched sequence of cells. (b) Scanning ElectronMicroscopy reveals ridge-like structures running in parallel along the outside of the filaments. These ridges remain continuous across thejunction of neighbouring cells and are hypothesized to house the conductive fibers, which are considered the biopolymeric conduits forelectron transport. (c) Conceptual model of electron transport in a cable bacterium filament. A single filament is surrounded by conductivefibers in the periplasmic space (NF conductive fibers per filament). A single conductive fiber consists out of multiple parallel chains of electroncarriers (NC chains per fiber). Within each electron carrier chain, electrons are transferred in a bucket-brigade manner along a one-dimensional chain of redox sites.


concentration of electron carriers per unit volume of sedi-ment. The total concentration of charge carriers can bedecomposed as X T ¼ ½X �� þ ½X �, where ½X �� is the concen-tration of charged electron carriers at a given depth and½X � is the concentration of free electron carriers. The quan-tities f C ¼ ½X ��=X T and f F ¼ ½X �=X T can be introduced asthe fractions charged and free electron carriers respectively.

The “uploading” of electrons to the electron transportchain is caused by the oxidation of sulfide within the deeperpart of the sediment (Fig. 2c). This can be represented bythe reaction equation for anodic sulfide oxidation (ASO):

1

2HS� þ 4X þ 2H2O! 1

2SO2�

4 þ 4X � þ 9

2Hþ ð7Þ

The associated reaction rate is controlled by the availabil-ity of free sulfide, the availability of electron carriers, andthe level to which these electron carriers are charged, asreflected by the rate expression:

RASO ¼ /kASO½HS��X T ð1� f CÞnASO ð8Þ

When all electron carriers are fully charged with electrons(f C ! 1), the reaction rate vanishes. Similarly, the removalof electrons from the chain occurs via the reduction of oxy-gen within the oxic zone of the sediment. This is representedby the reaction equation for cathodic oxygen reduction(COR):

O2 þ 4X � þ 4Hþ ! 2H2Oþ 4X ð9Þ

The associated kinetic rate expression is given by:

RCOR ¼ /kCOR½O2�X T ðf CÞnCOR ð10Þ

Similarly as for anodic sulfide oxidation, this reaction rateis promoted by the availability of the reactants, i.e., oxygenand charged electron carriers. The reaction rate vanisheswhen charged electron carriers are no longer available(f C ! 0), and so, electrons cannot be “downloaded” fromthe electron transport chain.

Next we need to consider the electron transport along-side the electron carrier chains. Electrons will propagatefrom the anodic part of the electron carrier chain to thecathodic part. By analogy to electron conduction in organicpolymers, we assume that electrons can jump from one elec-tron carrier to the next via “electron hopping” (Strycharz-Glaven et al., 2011; Polizzi et al., 2012). This process isdescribed by the bimolecular electron transfer reaction

X �i þ X iþ1 �k

X i þ X �iþ1 ð11Þ

The hopping frequency k (units: s�1) is the rate constant ofbimolecular electron transfer reaction. Because chargecarriers are all identical the forward and backward rateconstants are identical. At the macroscale, the hopping ofelectrons through the carrier network gives rise to an appar-


ent diffusive transport of free and charged electron carriers(Andrieux and Saveant, 1980; Dalton et al., 1990;Strycharz-Glaven et al., 2011; see full derivation in Appen-dix). The corresponding diffusive fluxes are represented as

JC ¼ �DEX Trf C ð12ÞJF ¼ �DEX Trf F ð13Þ

The diffusion coefficient is given by the Dahms–Ruff expres-sion, DE ¼ kd2, where k is hopping frequency and d the dis-tance between charge carriers, as introduced above. Thisdiffusion coefficient DE reflects the inherent mobility of elec-trons through the carrier network. Because the fraction ofcharged and free carriers must add to unity, i.e.,f F þ f C ¼ 1, the diffusive fluxes of charged and free carriersare exactly opposite. This is indeed a necessary consequenceof electron hopping: if one charge move upwards, an“empty hole” will move downwards (analogous to thetransport of electrons and holes in a semi-conductor).

The flux expressions (12) and (13) for the electron trans-port within the carrier network, together with the kineticrate expressions (8) and (10) for the supply and removalof electron on the carrier network, can be implemented ina mass balance equation for the free and charged electroncarriers.

/@½X �@t¼ @

@x/DEX T

@f F

@x

� �� RASO þ RCOR ð14Þ

/@½X ��@t¼ @

@x/DEX T

@f C

@x

� �þ RASO � RCOR ð15Þ

This new submodel for electrogenic sulfur oxidation henceextends the traditional model of sediment biogeochemistrywith two new mass balances: one for the free electroncarriers ½X � and one for the charged electron carriers ½X ��. Notethat these balance equations are of the diffusion–reaction type,and have the same form as Eq. (4), which is the standardmass balance equation used in sediment biogeochemistry.This implies that we are capable of describing long-distanceelectron transport within the conventional reactivetransport model framework of sediment biogeochemistry.Consequently, the model can be solved with the samenumerical methods and techniques that are availablefor conventional models of sediment biogeochemistry(Boudreau, 1997).

2.4. Numerical solution

Altogether, the model includes 13 state variables: theconcentration of organic matter [CH2O], oxygen [O2], sul-fate [SO4

2�], ferrous iron [Fe2+], iron sulfides [FeS], total freesulfide RH2S = [H2S] + [HS�], total carbonate RCO2 =[CO2] + [HCO3

�] + [CO32�], total borate RB(OH)3 = [B(OH)3]

+ [B(OH)4�], alkalinity AT, calcium [Ca2+], calcium carbon-

ate [CaCO3], free electron carriers [X] and charged electroncarriers [X*]. A numerical solution procedure for the result-ing partial differential equations was implemented in theopen-source programming language R, following the proce-dures of Hofmann et al. (2008) and Soetaert and Meysman(2012). The combination of the mass balance Eq. (4) foreach compound together with the mass action laws of the

acid-base equilibria leads to a differential–algebraic system,which was solved using an operator splitting approach(Solution method [3b] as explained in Hofmann et al.,2008). Following the method-of-lines, we used the R-pack-age ReacTran to expand the spatial derivatives of the partialdifferential equations over the sediment grid using finite dif-ferences (see Soetaert and Meysman, 2012 for details). Thisfinite difference grid was obtained by dividing the sedimentdomain (thickness L = 5 cm) into a grid of 100 sedimentlayers. After finite differencing, the resulting set of ordinarydifferential equations was integrated using the stiff equationsolver vode from the R-package deSolve (Soetaert et al.,2010).

The calculation of the pH equilibrium at each time stepof the numerical simulation was performed via the operatorsplitting approach as detailed in Hofmann et al. (2008).Numerical integration of the ODE system provides the val-ues of the reaction invariants (AT, RCO2, RH2S, RB(OH)3)at each time step. Subsequently, the non-linear system ofalgebraic acid-base expressions was solved for the unknownproton concentration [H+] using the iterative method ofMunhoven (2013). Using this proton concentration (orequally pH value), the full speciation could be calculatedfor all chemical species involved in the acid-base dissocia-tion reactions. The resulting concentrations of the equilib-rium species could then be employed in kinetic rateexpressions. Specifically, the pore water carbonate ion con-centration [CO3

2�] was used in the rate expression for cal-cium carbonate dissolution. The pH values (both dataand simulations) are reported on the total pH scale. Furtherdetails on this pH model procedure are given in Hofmannet al. (2008).

The electrons within the electron carrier pool have ahigh turnover rate (i.e., time scale of seconds), due to smallsize of electron carrier pool and the high rates of electron“uploading” and “downloading” reactions. This fast turn-over introduces so-called stiffness into the resulting partialdifferential equations, which is known to be a challengingproblem for numerical integration (Boudreau, 1997). Simu-lations with a linear dependency (nCOR ¼ nASO ¼ 1) in thekinetic expressions (8) and (10) resulted in a poor conver-gence of the numerical integration routine. Hence, for rea-sons of numerical stability, we used a quadratic dependency(nCOR ¼ nASO ¼ 2) in all further simulations. To test thesensitivity of the model, we performed simulations with ahigher order exponent (nCOR ¼ nASO ¼ 3). This producedvery similar simulation results as a quadratic dependency(differences not distinguishable on graph; results notshown), confirming that the model is not sensitive to theparameters nCOR and nASO.

The objective of the model simulations here is to emu-late the characteristic biogeochemical fingerprint of e-SOxas observed in laboratory sediment incubations (e.g.,Nielsen et al., 2010; Schauer et al., 2014) and field studies(Malkin et al., 2014). One complicating factor in thisrespect is the apparent transient nature of the phenomenon.In laboratory experiments, whereby e-SOx is induced inhomogenized mixtures of natural sediment, the characteris-tic biogeochemical fingerprint typically emerges after�1 week (Schauer et al., 2014; Malkin et al., 2014). The


sediment subsequently displays a period of intense e-SOxactivity, but after �3–4 weeks, the density and activity ofthe cable bacteria starts to decline (Schauer et al., 2014).The initial lag period is attributed to biomass build-upwithin the cable filament network (Schauer et al., 2014),but the details of this development are unclear at present.Similarly, the reasons for the demise of the e-SOx activityafter a few weeks are not fully understood, but depletionof the iron sulfide (FeS) pool has been proposed as thelikely cause (Schauer et al., 2014). At present, it is unknownwhether this successional pattern observed under labora-tory conditions is also representative for natural conditions.Currently, field observations of e-SOx activity are onlyavailable at isolated time points (Malkin et al., 2014).

The model here does not attempt to fully describe theobserved temporal evolution of e-SOx activity. The fielddataset used here for model validation (Malkin et al.,2014) shows a similar fingerprint as observed in laboratoryincubations after �3 weeks, when e-SOx rates are highest(Schauer et al., 2014). The primary objective of our modelsimulations is to reproduce this biogeochemical fingerprintof e-SOx at “peak activity”. To achieve this, we were able toconveniently simplify the model simulation approach.

Table 3List of parameters included in the model. Solid phase concentrations archarge carriers ET is expressed per bulk volume of sediment. “Method”

A = Measurements, B = Literature values, C = Sensitivity analysis, D =(2014); [2] Unpublished data from MLG field site; [3] Soetaert et al. (1996and Wang (1996); [7] Rickard (2006).

Symbol Value

Environmental parameters

Temperature T 10Salinity S 32Pressure P 3.3Porosity / 0.8Concentration organic matter ½CH2O� 550Concentration iron sulfide ½FeS� 100Concentration carbonate ½CaCO3� 1300Depth of sediment domain L 5

Biogeochemical parameters

Mineralization constant kmin 1Canonical sulfur oxidation kCSO 1e+07Ferrous iron oxidation kFIO 1e+07CaCO3 precipitation rate constant kCP 0CaCO3 precipitation exponent nCP 1CaCO3 dissolution rate constant kCD 10CaCO3 dissolution exponent nCD 4FeS precipitation rate constant kISP 1e+4FeS precipitation exponent nISP 1FeS dissolution rate constant kISD 3FeS dissolution exponent nISD 1Oxygen saturation constant KO2

0.00Sulfate saturation constant KSO2�

40.9

Solubility CaCO3 KSPCaCO3

0.39

Solubility FeS KSPFeS 3.16

Electrogenic parameters

Cathodic oxygen reduction kCOR 1.4eAnodic sulfide oxidation kASO 1.4eConcentration charge carriers XT 0.02Diffusion coefficient charges DE 8.4e

Firstly, we do not attempt to reproduce the initial lag per-iod, and so, the model does not resolve the biomass dynam-ics and growth of the filament network. In effect, we assumethat at time zero of the simulations, a given filament net-work is already established. This is done by imposing agiven total electron carrier concentration ET throughoutthe sediment. The goal of the simulations is to examinewhether and how such a filament network can generatethe characteristic geochemical fingerprint.

Secondly, we do not attempt to simulate the observeddecline in activity over a time scale of months, and there-fore, the model ignores any depletion or accumulation ofsolid phase constituents. Instead, the concentrations ofthe three solid phase constituents in the model (organicmatter, calcium carbonate, iron sulfides) are kept constanttime, which is a reasonable assumption during the shortperiod of peak activity. Large stocks of organic matter, cal-cium carbonate and iron sulfides are available in the sedi-ment (Table 3), which will only deplete over a time scaleof months to years. In addition, no depth gradients wereimposed for the solid phase constituents, which mimicsthe homogenized sediment that is typically used as startingmaterial in laboratory experiments (Nielsen et al., 2010;

e expressed per unit volume of solid phase. The concentration ofrefers to the procedure by which parameter values are constrained:Microscopy data, E = Model Fitting. References: [1] Malkin et al.); [4] Boudreau (1997); [5] Meysman et al. (2003); [6] Van Cappellen

Units Method References

�C A [1]– A [1]bar A [1]– A [1]mol m�3 A [2]mol m�3 A [2]mol m�3 A [2]cm –

yr�1 B [3], [4]mol�1 m3 yr�1 B [5], [6]mol�1 m3 yr�1 B [5], [6]mol m�3 yr�1

– B [5]yr�1 B [5]– B [5]mol m�3 yr�1 B [5]– B [5]yr�1 B [5]– B [5]

1 mol m�3 B [5]mol m�3 B [5]

(mol m�3)2 B [5]

mol m�3 B [7]

+8 mol�1 m3 yr�1 C This work+8 mol�1 m3 yr�1 C This work9 mol m�3 D This work+4 cm2 yr�1 E This work

Fig. 3. (a) Electrogenic sulfur oxidation. Comparison between the steady state model simulation (solid lines) and the microsensor field datafrom Marine Lake Grevelingen (dots). Field data were obtained by microsensor profiles (O2, pH, H2S) on sediment cores immediately uponretrieval from the field. The baseline simulation provides the best fit of the model to the data (parameters values listed in Table 3). (b) Steadystate model simulation of canonical sulfur oxidation. The model parameter values are exactly the same as in the electrogenic simulation, butfor the kinetic rate parameters of the anodic and cathodic half-reactions, which were set to zero (kASO = kCOR = 0). (c) Transient modelsimulation over 25 days showing the transition from canonical sulfur oxidation (initial conditions) to electrogenic sulfur oxidation (finalconditions). The depth profiles did not further change after 25 days.


Risgaard-Petersen et al., 2012). The imposed concentrationvalues of the solid phase constituents were derived fromsolid phase analysis on sediment from the field site(Table 3).

The simulations were dynamically run over a suffi-ciently long time period (1000 days) so that all pore waterconcentration profiles attained steady state. Unless statedotherwise, the concentrations of the pore water solutesat all depths were initially set equal to the correspondingvalues in the overlying bottom water at all depths, apartfrom oxygen, for which the initial concentration depthprofile was set to zero. Again, these initial conditionsapproximate the starting conditions typically used in thelaboratory sediment incubations, i.e., sediment homoge-nized under an N2 atmosphere (Risgaard-Petersen et al.,2012). Dynamic simulations starting from different initialconditions arrived at the same steady state (no multiple

stable equilibria). Although the simulated time periodwas 1000 days in total, we noted that after about 25 days,the solute depth profiles achieved all the main characteris-tics of the electrogenic fingerprint, and they did notchange appreciably any further (Fig. 3c). This time scaleclosely matches the period of “peak activity” in laboratoryincubations, and so, we concur that the simulated steadystate concentration profiles are representative for theobserved biogeochemical fingerprint of e-SOx at the timeof “peak activity”.

2.5. Model simulations

The model simulation procedure consisted out of twoseparate steps. In a first step, a set of the simulations wasperformed to optimally reproduce the geochemicalfingerprint of e-SOx as observed under field conditions.


To this end the steady state model output was compared toa previously published dataset including O2, pH and H2Smicrosensor profiles obtained from field measurements inMarine Lake Grevelingen (MLG), a seasonal hypoxiccoastal water body in the Dutch Delta area, The Nether-lands (see Malkin et al., 2014 for details on sampling siteand data collection). The resulting model simulation, whichprovides the best fit to the given field dataset, is referred toas the “baseline simulation”.

In a second step, we performed a sensitivity analysis, toexamine the impact of certain parameters and processes onthe biogeochemical cycling within the sediment. To thisend, we changed the baseline simulation in three specificways: (1) inhibition of long-distance electron transport bysetting kCOR ¼ kASO ¼ 0 (“No electron transport” simula-tion), (2) inhibition of iron sulfide dissolution and precipita-tion by setting kISD ¼ kISP ¼ 0 (“No FeS cycling”

simulation), and (3) reduction of carbonate buffering byreducing the dissolution rate kCD by a factor of 4 comparedto the baseline simulation (“Reduced CaCO3” simulation).

3. RESULTS

3.1. Simulation of the e-SOx biogeochemical fingerprint

Electrogenic sulfur oxidation induces a specific biogeo-chemical fingerprint upon the pore water, which consistsof (1) a shallow oxygen penetration depth, indicative ofintense oxygen consumption, (2) a wide suboxic zone thatseparates the oxic and sulfidic sediment horizons, and (3)strong, characteristic pH excursions (Nielsen et al., 2010;Risgaard-Petersen et al., 2012). Fig. 3a shows a set of O2,pH and H2S microsensor profiles obtained from field mea-surements that exhibit this specific biogeochemical finger-print. At the time of sampling, abundant cable bacteriafilaments were detected in these sediments by FluorescenceIn Situ Hybridisation (Fig. 2a; Malkin et al., 2014). Fig. 3aadditionally shows the simulated O2, pH and H2S depthprofiles from the “baseline simulation”, i.e., the best fit ofthe model to the dataset. This baseline simulation success-fully reproduces the three principal features of the biogeo-chemical fingerprint: (1) a shallow oxygen penetration, (2)a wide suboxic zone, and (3) the same strong pH excursionsas observed in the field data. The fitting procedure andresulting parameter values are discussed in more detailbelow.

The model simulation shows a similar increase in sul-fide concentrations at depth as observed in the field data,and the width of the suboxic zone (operationally definedas difference between the first depth where RH2S > 5 lMand the first depth where [O2] < 1 lM) is similar in bothfield data and model simulation (12 mm). Closer examina-tion reveals that the oxygen penetration depth (operation-ally defined as the depth where [O2] < 1 lM) is slightlyhigher in the baseline simulation (1.7 mm) as comparedto the field data (1.2 mm). This suggests that the modelslightly underestimates the sedimentary oxygen demand,which is not unexpected, as the model incorporates onlya selection of the reoxidation reactions that occur underfield conditions (e.g., nitrification is not incorporated).

Yet overall, the baseline simulation reproduces the biogeo-chemical fingerprint very well. Most importantly, the base-line model is capable of generating very similar pHexcursions as seen in the data. Electrogenic sulfur oxida-tion generates a distinct pH depth profile, which consistsof a narrow pH maximum near the oxygen penetrationdepth (indicative of proton consumption by the cathodichalf reaction) followed by a broadly peaked pH minimumin deeper sediment layers (indicative of proton productionby the anodic half reaction). This characteristic pH pat-tern is satisfactorily reproduced by the model. In bothmodel simulation and data, the pH maximum occurs rightat the oxygen penetration depth, and is marginally higherin the model (pHmax = 8.27) than in the field data(pHmax = 8.12). A similar broad zone with low pH valuesstretches across the suboxic zone, where the model slightlyoverestimates the acidification at depth by 0.22 pH units(pHmin = 6.03 in baseline simulation; pHmin = 6.25 inthe field data), indicating that the model presumably lacksa pH buffering mechanism that is present under fieldconditions.

For comparison, Fig. 3b depicts the output of a modelsimulation where electrogenic sulfur oxidation has beenpurposely excluded. To this end, the rate constants of theanodic and cathodic half reactions kASO and kCOR were setto zero, while all other parameter values were kept the sameas in the electrogenic simulation. The corresponding simu-lation output shows that e-SOx has a significant impacton the simulated depth profiles. In the absence of e-SOx,no suboxic zone develops (the O2 and H2S profiles showa small overlap), while the oxygen penetration depth is alsosubstantially deeper (2.6 mm). Furthermore, unlike theelectrogenic profile in Fig. 3a, the pH depth profile doesnot does not generate a subsurface maximum, nor does itshow strong acidic conditions at depth (pH decreases withinthe first 3 mm, and then remains constant around a value of7). These model simulations with and without e-SOx clearlydemonstrate that the typical characteristics of the “electro-genic” fingerprint (shallow O2 penetration, wide suboxiczone, characteristic pH excursions) are generated by theinclusion of the anodic and cathodic half reactions (E1and E2 in Table 1).

3.2. The creation of a suboxic zone

The most discriminating features of the “electrogenic”

fingerprint are the wide suboxic zone in combination withstrong, characteristic pH excursions (Nielsen et al., 2010;Risgaard-Petersen et al., 2012). Note that different interpre-tations of the term “suboxic zone” are encountered in theliterature. In the classical view of sequential redox zonation(Froelich et al., 1979), the suboxic zone is defined as thehorizon between the zones of oxygen reduction and sulfatereduction, where other mineralization pathways (nitratereduction, Mn and Fe reduction) are active. Here, we donot define the suboxic in terms of mineralization pathways,but in terms of pore water concentrations. The suboxiczone is the depth layer where both oxygen and sulfide areundetectably low. As discussed in Section 4.4, sulfate reduc-tion does take place within the suboxic zone, although free


sulfide appears to be absent, thus given rise to cryptic sulfurcycling.

The model presented here provides a mechanistic expla-nation of how long-distance electron transport can generatethe observed suboxic zone. The model simulations revealhow the emergence of the suboxic zone is tightly linked tothe dynamics of the electrons within the electron transportnetwork of the cable bacteria. Fig. 4a shows the depth pro-files of O2 and H2S in the baseline simulation, alongside thesimulated distribution of the charged electron carrier sitesf C within the sediment. The depth profile of charged carriersites shows three clear zones: (1) within the oxic zone, elec-tron carriers are not charged (f C � 0), (2) within the subox-ic zone, electron carriers are partly charged (0 < f C < 1),and (3) within sulfidic zone, electron carriers are completelycharged with electrons (f C � 1). So at the top of the subox-ic zone, O2 will diffusive downwards until it meets chargedelectron carriers (so electrons can be “downloaded” fromthe electron transport network). Conversely, at the bottomof the suboxic zone, H2S will start to accumulate as soon asthe electron transport network is saturated (all electron car-riers are charged and so electrons can no longer be“uploaded” to the electron transport network).

Fig. 4b additionally illustrates this mechanism furtherby displaying the depth distribution of the reaction ratesof cathodic oxygen reduction (COR) and anodic sulfide oxi-dation (ASO). COR is localized within the oxic zone, andsharply peaks around the oxygen penetration depth(Fig. 4b). In contrast, the ASO is widely distributed acrossthe suboxic zone, and shows a moderate subsurface peak ata depth of 12 mm where H2S first appears. This subsurfacemaximum in ASO is due to the consumption of sulfide dif-fusing from below, which is generated by sulfate reductionin deeper sediment horizons. Although there is no discern-able sulfide within the suboxic zone, the model still showsconsiderable ASO (Fig. 4b), thus revealing that a strongcryptic sulfur cycle takes place. The sulfide that fuels this

Fig. 4. (a) Simulated depth profiles of O2 (red line) and RH2S (blue line)carriers (black solid line). This represents the baseline simulation at steaprofiles of the reaction rate of the anodic sulfide consumption and coxidation. The reaction rates are expressed per unit volume of pore waterthe reader is referred to the web version of this article.)

cryptic sulfur cycle is provided by both sulfate reductionas well as FeS dissolution (as further discussed below).Intriguingly, the baseline simulation also indicates thatASO occurs within the oxic zone. As sulfate reduction isprohibited within the oxic zone (Eq. (K2) in Table 2), thesulfide that fuels anodic sulfide oxidation within the oxiczone must be released by FeS dissolution.

3.3. Model parameterization

The good correspondence between model simulationand data (Fig. 3a) is encouraging, but one may rightfullyquestion whether this is not the result of a fortuitous choiceof model parameters. Hence, a critical issue is to examinehow tightly constrained the model is. Stated otherwise, weneed to verify whether only one unique set of parametersmatches the data, or whether multiple sets of parameter val-ues may provide an equally good fit to the data. To examinethis, we devoted substantial effort to a systematic and care-ful parameterization of the model. This exercise showedthat the model parameter set is tightly constrained. Table 3provides an overview of all parameters, which are classifiedinto three categories, depending on the way that parametersvalues were constrained. The first category, referred to as“Environmental parameters”, were directly constrainedbased on the available field data (e.g., temperature, salinityand composition of the overlying bottom water at the fieldsite; porosity, organic carbon, carbonate and iron sulfidecomposition of the sediment solid phase). The second cate-gory, denoted “Biogeochemical parameters”, includesparameters that also feature in conventional models of sed-iment geochemistry. This includes the parameters in thekinetic rate expressions of organic matter mineralizationand subsequent re-oxidation reactions, as well as theparameters describing the dissolution and precipitation ofiron sulfide and calcium carbonate. The values of thesebiogeochemical parameters were constrained based on

, together with the simulated depth distribution of charged electrondy state (parameters values listed in Table 3) (b) Simulated depth

athodic oxygen consumption half-reactions of electrogenic sulfur. (For interpretation of the references to colour in this figure legend,


previous early diagenetic model studies (Table 3 providesthe values and references). By including only Environmen-tal and Biogeochemical parameters, one obtains the simula-tion of canonical sulfur oxidation (as shown in Fig. 3b).The resulting geochemical fingerprint never displays a sub-oxic zone.

The large difference between the simulation output ofcanonical sulfur oxidation (Fig. 3b) versus electrogenic sul-fur oxidation (Fig. 3a) reveals the strong geochemicaleffects of e-SOx on sediment biogeochemistry. The e-SOxsubmodel includes four parameters in total: (1) the densityof charge carrier sites ET within the electrogenic filamentnetwork, (2) the kinetic rate constants kASO and kCOR ofthe anodic and cathodic half reactions, and (3) the chargediffusion coefficient DE, which reflects the mobility ofcharges within the electrogenic filament network. Theseelectrogenic parameters were constrained in a systematicway. In a first step, the value of the charge carrier densityET was determined from known information about themorphology of the cable bacteria. Subsequently, the kineticrate constants kASO and kCOR were constrained by a sensitiv-ity analysis. As a result, only one free model parameterremained: the charge diffusion coefficient DE. In a final step,the parameter value of DE was manually tuned to obtainthe best fit to the O2, H2S and pH data from the MLG fieldsite. We discuss now this parameterization procedure inmore detail.

As already noted above, the density of charge carriersites ET within the filament network can be estimated viathe expression X T ¼ nCBNF AF =d

3, and so its value dependson (1) the density nCB of cable bacteria filaments (expressedper unit of sediment area), (2) the average number of con-ductive fibers NF within the periplasmatic space of singlebacterial filament , (3) the cross-sectional area AF of a singleconductive fiber, and (4) the electron carrier interspacing dwithin the conductive fiber. Although little is known aboutthe structure and geometry of the cable filaments, we triedto constrain each of these four parameters based on avail-able knowledge. At present, there is no direct informationon the interspacing d of the electron carriers within the con-ductive fibers of the filaments. As a first order approach, wehypothesized that the mechanism of electron conduction inconductive fibers could similar to that in bacterial nanowirepili. Recently, Strycharz-Glaven et al. (2011) estimated acarrier interspacing of �1 nm in bacterial nanowires, based

Fig. 5. Sensitivity analysis for the kinetic rate constants of the anodicrepresented here as k). Steady state depth profiles are plotted. Starting froconstants were gradually increased, while keeping all other parameters fielectrogenic sulfur oxidation, and an corresponding expansion of the subk = 108 mol�1 m3 yr�1 the width of the suboxic zone and the associated

on the current–voltage data published by El-Naggar et al.(2010). Such an interspacing of d = 1 nm is consistent withthe heme interspacing in multi-heme cytochromes of Geob-

acter (Pokkuluri et al., 2011) and Shewanella (Clarke et al.,2011), and we assumed a similar value here.

Recently, Pfeffer et al.(2012) have reported a filamentdensity nCB = 1.2 � 108 m�2 for experimental incubations,while Malkin et al. (2014) reported a similar range0.8–1.2 � 108 m�2 from field observations. There is no spe-cific information on filament density at the MLG field siteexamined here, but we assume densities are similar, andso we used a filament density nCB = 1.2 � 108 m�2 in allsimulations. Furthermore, based on scanning electronmicroscopy, Pfeffer et al. (2012) documented that thenumber of fibers per filament was NF = 15–17. Malkinet al. (2014) however reported a broader range ofNF = 16–58 in their field study, presumably reflecting thegreater variability in morphology encountered in the differ-ent habitats investigated. Here we used the median of thereported range, NF = 36. Pfeffer et al. (2012) showed vari-ous imagery from transmission electron microscopy, reveal-ing that conductive fibers are approximately 100 nm wideand 40 nm thick, thus providing a value of AF = 4000nm2. By combining the above estimates for all fourgeometrical parameters, we obtain an electron carrierconcentration of XT = 0.029 mol m�3 (expressed pervolume of bulk sediment). This was the value for XT thatwe used in all simulations (Table 3).

To determine the values of kinetic rate constants kASO

and kCOR, we performed a series of auxiliary simulations,starting from the canonical simulation (kASO ¼ kCOR ¼ 0),and subsequently, gradually increasing the value of thesetwo kinetic rate constants in tandem, while keeping allother parameters fixed (Fig. 3). Increasing kASO and kCOR

resulted in a switch from canonical sulfur oxidation to elec-trogenic sulfur oxidation, and an corresponding expansionof the suboxic zone. However, beyond a given thresholdvalue (1.4 � 107 m3 mol�1 yr�1), a further increase of kASO

and kCOR did no longer change the width of the suboxiczone and the pore water profiles. At this point, free chargecarriers are virtually absent from the sulfidic zone, due tothe high affinity of the anodic half reaction for free chargecarriers (Eq. (8)). Adversely, charged electron carriersimmediately vanish whenever O2 is present, due to the highaffinity of the cathodic half reaction. The kinetic rate

and cathodic half-reactions (kASO = kCOR were varied in tandem,m the canonical simulation (k = 0), the value of the two kinetic ratexed. This results in a transition from canonical sulfur oxidation tooxic zone. However, for an increase beyond the threshold value ofthe pore water profiles do no longer change.

Fig. 6. Comparison of the microsensor fingerprint of different simulations. “Baseline” = Baseline simulation with best fitting parameter set tothe field data. “No electron transport” = Simulation with inhibition of long-distance electron transport. “No FeS cycling” = Simulation withinhibition of iron sulfide precipitation and dissolution. “Reduced carbonate” = Simulation with reduced CaCO3 dissolution. The symbol Xdenotes the saturation state of the pore water.

Table 4Comparison of biogeochemical rates in different model simulations. “Baseline” = baseline simulation. “No e-SOx” = no electrogenic sulfuroxidation. “No FeS” = no iron sulfide precipitation and dissolution. “#CaCO3” = reduced calcium carbonate dissolution.

Process Unit Baseline No e-SOx No FeS #CaCO3

Mineralization mmol C m�2 d�1 13.3 13.2 13.3 13.3Aerobic respiration mmol C m�2 d�1 0.4 0.7 0.7 0.4Sulfate reduction mmol C m�2 d�1 12.9 12.5 12.6 12.9Total oxygen uptake mmol C m�2 d�1 22.7 13.2 13.3 23.6Cathodic oxygen consumption mmol O2 m�2 d�1 21.2 0.0 12.6 22.0Classical sulfide oxidation mmol O2 m�2 d�1 0.1 12.5 0.0 0.1Ferrous iron oxidation mmol Fe m�2 d�1 4.2 0.0 0.0 4.6CaCO3 dissolution mmol C m�2 d�1 40.9 3.7 28.8 32.0Net FeS dissolution mmol S m�2 d�1 4.2 0.0 0.0 4.6



constants kASO and kCOR were fixed at these high thresholdvalues (Table 3), reflecting a high affinity of the cable fila-ments for both O2 and H2S. A biological justification forthis could be that natural selection would drive enzymaticefficiencies towards such high affinities. As the auxiliarysimulations show, such high affinities are critical for the cre-ation of a suboxic zone, suitably removing O2 in the upperlayers, and depleting H2S in deeper layers.

Once the values of kASO and kCOR are fixed, the sole freeparameter in the model is the diffusion coefficient DE ,which represents the mobility of charges within the filamentnetwork. The best model fit to the MLG field data providedDE = 3.5 � 10�7 m2 s�1. Implementing the Dahms–Ruffexpression with an electron carrier interspacing d = 1 nm,this provides a hopping frequency k = 3.7 � 1012 s�1. Thiswould make that the electron hopping frequency lies withinthe picosecond range, which is at the high end of theobserved range for electron transport between redox centersin enzymes (Gray and Winkler, 2005).

3.4. Sensitivity analysis

Recently, it has been shown that e-SOx can have a largeimpact on the geochemical cycling within coastal sediments(Risgaard-Petersen et al., 2012). Starting from the baselinesimulation, we performed a sensitivity analysis to quantita-tively assess how strongly e-SOx affects oxygen consump-tion, iron sulfide cycling and carbonate dissolution(Simulated depth profiles in Fig. 6; Simulated fluxes inTable 4).

4. DISCUSSION

4.1. The biogeochemical fingerprint of electrogenic sulfur

oxidation

Electrogenic sulfur oxidation provides a novel mecha-nism to create a suboxic zone in coastal sediments. How-ever, other processes exist in marine sediments that canalso create suboxic zones. Large sulfur oxidizing bacteria,like the genus Beggiatoa, are able to transport intracellularaccumulations of nitrate downward from the sediment sur-face, and use this nitrate in deeper sediment layers to oxi-dize H2S (Sayama et al., 2005). Upon migration upwardto the oxic zone, these motile bacteria can utilize oxygento re-oxidize the elemental sulfur that has accumulatedintracellularly. A second way to create a suboxic zoneinvolves sulfide removal through shuttling of iron and man-ganese (hydr)oxides (Aller and Rude, 1988; Canfield et al.,1993). In this process, metal oxides are transported down-wards into the sediment by bioturbation and/or physicalmixing, and interact with free sulfide at depth to form metalsulfides (mostly iron sulfides and pyrite). These metal sul-fides are then transported upwards again, where they areregenerated near the sediment–water interface upon contactwith oxygen.

Neither large sulfur bacteria, nor indications of biotur-bation were observed at the MLG field site at the time ofsampling (Malkin et al., 2014). Moreover, the presence ofthe characteristic “electrogenic” pH profile (Fig. 3a)

indicates that e-SOx is responsible for the creation of thesuboxic zone at the MLG field site. The defining featureof e-SOx is the spatial separation of redox half reactions,which hence results in a spatial separation of electronproduction and consumption, thus inducing long-rangeelectrical currents. However, spatial segregation of redoxhalf reactions also implies a spatial separation of protonconsumption and proton production, which hence explainsthe strong pH excursions in the pore water that areobserved. The pH maximum near the depth of oxygen pen-etration is linked to strong proton consumption by cathodicoxygen reduction (Eq. (9)), while the deeper pH minimum iscaused by strong proton production due to anodic sulfideoxidation (Eq. (7)).

If the suboxic zone would be created by either largemotile bacteria or the shuttling of iron and manganese(hydr)oxides, one would expect to see a very different pHsignature. The pH depth profile associated with sulfur oxi-dation by Beggiatoa is characterized by a subsurface pHminimum followed by deeper pH maximum (Sayamaet al., 2005). Similarly, when a suboxic zone is created bystrong metal cycling, the resulting pH profile also shows apH minimum at the oxygen penetration depth followedby deeper pH maximum (Jourabchi et al., 2005). Accord-ingly, these pH profiles show an opposite depth transition(pH min followed by pH max, rather than pH max followedby pH min). Hence, our model simulation results suggestthat the observation of the “electrogenic” pH signaturecan be used as a reliable identifier of electrogenic sulfuroxidation.

As protons are involved in almost any geochemical reac-tion pathway (Table 1), the pH in natural sediments is influ-enced by a multitude of biogeochemical processes. As aconsequence, an adequate simulation of pH depth profilesin marine sediments is difficult, as models need to selectthe proper reactions as well as to accurately constrain therate of these reactions (Meysman et al., 2003; Jourabchiet al., 2005; Soetaert et al., 2007; Hofmann et al., 2008).The fact that we are able to accurately simulate the pH pro-files in electro-active sediment of the Grevelingen providesconfidence that our baseline simulation captures the princi-pal features of the process of electrogenic sulfur oxidation.As noted above, the reactive transport model forms a directimplementation of the conceptual model of electrogenic sul-fur oxidation as displayed in Fig. 1b. Hence, the excellentcorrespondence between data and simulations quantita-tively corroborates the conceptual mechanism of electro-genic sulfur oxidation that has been forwarded (Nielsenet al., 2010; Pfeffer et al., 2012).

4.2. Impact on oxygen consumption

Laboratory incubations suggest that electrogenic sulfuroxidation can be a dominant component in the oxygenuptake of coastal sediments (Nielsen et al., 2010; Schaueret al., 2014). Our simulations demonstrate this quantita-tively. In the baseline simulation, electrogenic sulfide dom-inates the overall O2 consumption: the cathodic oxygenconsumption amounts to 21.2 mmol m�2 d�1 and is respon-sible for the majority (93%) of the total oxygen uptake


(TOU) in the sediment. Canonical sulfur oxidation is negli-gible as a mode of oxygen consumption (0.1 mmol m�2 d�1

or 0.3%) in the baseline simulation. It is important toemphasize that this absence of canonical sulfur oxidationis not hard-coded into the model, but results from compet-itive exclusion. Canonical sulfur oxidation requires thepresence of both oxygen and free sulfide in the pore water.These conditions are inhibited by electrogenic sulfur oxida-tion, as long-distance electron transport causes the develop-ment of a suboxic zone, which spatially segregates theoxygen and free sulfide horizons. Only when electrogenicsulfur oxidation is purposely excluded (“No electron” sim-ulation, Fig. 6), canonical sulfur oxidation fills in the openniche, and takes over the removal of the free sulfide pro-duced by sulfate reduction.

The TOU in the baseline simulation (22.7 mmol m�2 d�1)strongly exceeds the mineralization rate of the sediment(13.3 mmol m�2 d�1 in all simulations). This discrepancyis explained by the dissolution of iron sulfides, whichliberates H2S and Fe2+, and hence creates an additionaloxygen demand. In the “reduced carbonate” simulation,where more FeS is dissolved (see discussion below), thiseffect is even more pronounced (TOU = 23.6 mmol m�2 d�1).When the dissolution of the FeS is inactivated (Table 4), theTOU drops and exactly matches the mineralization rate.Since our model implements a 1:1 carbon to O2 stoichiom-etry in organic matter respiration (see reactions K1 and K2in Table 1), this is also the expected result.

Aerobic mineralization of organic matter only amountsto 0.5 mmol m�2 d�1 in the baseline simulation, and hence,it is only responsible for a small part of the TOU in all sim-ulations. The oxygen penetration depth is very small(1.2 mm), and so heterotrophic micro-organisms can onlyperform aerobic respiration in a thin surface layer, explain-ing the limited contribution of aerobic mineralization to theTOU. In the baseline simulation, another 4.5% of the TOUis taken up by the oxidation of ferrous iron (1.0 mmol m�2

d�1). This ferrous iron is liberated from iron sulfide dissolu-tion as the model does not include dissimilatory iron reduc-tion in the reaction set.

At steady state, the sulfide production will match thesulfide consumption. In turn, the sulfide consumption mustmatch the electron transport, and the electron transport willmatch the cathodic oxygen consumption. This implies thatif the total depth-integrated mineralization rate is fixed, thesulfate reduction will be fixed, and hence, the cathodic oxy-gen consumption and electron flux will be fixed. As everymole of O2 consumed corresponds to the transport of4 mol of electron, the electrical current densities throughthe charge carrier network can be calculated as 4 timesthe cathodic oxygen reduction rate (21.2 mmol m�2 d�1).This provides the current density of 85 mmol electronsm�2 d�1 in the baseline simulation.

4.3. Iron sulfide dissolution: a respiratory turbo boost

Electrogenic sulfur oxidation requires a source of freesulfide, which acts as the electron donor in deeper anoxiclayers. This free sulfide can be supplied in two principalways (Risgaard-Petersen et al., 2012): either via sulfate

reduction (reaction K2) or via the dissolution of iron sul-fides (reaction K8). In the baseline simulation, both path-ways are active. Sulfate reduction supplies 60% of thesulfide (6.4 mmol S m�2 d�1) while iron sulfide dissolutionprovides the remaining 40% (4.2 mmol m�2 d�1). Hence,cable bacteria performing electrogenic sulfur oxidationobtain a substantial part (40%) of their electron donor sup-ply from previously accumulated FeS minerals. Intrigu-ingly, this dissolution of iron sulfide results from apositive feedback process: electrogenic sulfur oxidationgenerates acidic conditions within the suboxic zone, whichstimulates the dissolution of iron sulfide, which releases freesulfide, which then again stimulates electrogenic sulfuroxidation.

The dissolution of iron sulfide is strongly promoted atlower pH values. In effect, when the pH drops belowpKs = 6.8 (where Ks is the first dissociation constant ofH2S), the saturation state XFeS with respect to iron sulfidesdecreases in a quadratic fashion with the proton concentra-tion (Davison et al., 1999; Rickard, 2006)

XFeS ¼½Fe2þ�½HS��

KSPFeS½Hþ�

¼ ½Fe2þ�½H2S�KSKSP

FeS½Hþ�2� ½Fe2þ�RH2S

KSKSPFeS½Hþ�

2ð16Þ

In this expression, Ks denotes the first dissociation constantof H2S and KSP

FeS is the solubility constant of FeS. At pHvalues lower than pKs = 6.8, most sulfide is present asH2S, thus justifying the approximation in Eq. (16). Theimpact of the pH on iron sulfide dissolution is readilyapparent from Fig. 6i, which plots the logarithm of XFeS

for the baseline simulation. In the suboxic zone, the porewater is acidic and strongly undersaturated, thus drivingintense dissolution of FeS. This dissolution leads to astrong accumulation of ferrous iron (Fe2+) in the porewater (Fig. 6). Below the suboxic zone, the pore waterbecomes oversaturated again, due to a rapid increase in sul-fide concentrations with depth. This induces a re-precipita-tion of iron sulfide at depth, which removes the Fe2+ thatdiffuses downwards.

Hence, the protons liberated by electrogenic sulfur oxi-dation acidify the pore water of the suboxic zone, whichstimulates the mobilization of sulfide from FeS, and thisin turn stimulates electrogenic sulfur oxidation. The posi-tive feedback on FeS dissolution is even more pronouncedin the “reduced carbonate” simulation. Due to an absenceof pH buffering by carbonates, the acidification of the sub-oxic zone is more intense (pH minimum = 5.1). This leadsto increased FeS dissolution (4.6 mmol m�2 d�1 versus to4.2 mmol m�2 d�1 in the baseline simulation) and strongerFe2+ accumulation in the pore water (0.8 mM versus0.5 mM in the baseline). In the “reduced carbonate” simu-lation, iron sulfide dissolution supplies 43% of the electrondonors by electrogenic sulfur oxidation.

This positive feedback process is to some extent analo-gous to the turbocharger principle, which make combustionengines more efficient and enables them to produce morepower. This metabolic “turbo” effect is clearly seen whencomparing the cathodic oxygen consumption of the base-line simulation (20.8 mmol m�2 d�1) to the simulation wereFeS dissolution is purposely inhibited (12.5 mmol m�2 d�1).The metabolic dissolution of iron sulfides almost doubles


the respiration activity of the cable bacteria. It should benoted that this process is not sustainable in a steady stateregime, as it depletes the sedimentary FeS pool. Recent lab-oratory sediment incubations have revealed that cable bac-teria populations typically collapse after a period of weeksto months, and this population decline has been linked tothe exhaustion of the sedimentary FeS pool (Schaueret al., 2014). Iron sulfide dissolution has been estimatedto supply 94% of the sulfide for electrogenic sulfur oxida-tion (Risgaard-Petersen et al., 2012), and hence, the deple-tion of the sedimentary FeS pool would substantiallyreduce the electron donor supply of the cable bacteria.

Finally it should be noted that the shape of the biogeo-chemical fingerprint is insensitive to the sulfide source.Fig. 6 shows that even without FeS dissolution, one obtainsan “electrogenic” type fingerprint that is similar in shape aswhen strong FeS dissolution takes place. This suggests thatthe shape of the geochemical fingerprint will also be robustagainst time-variable or non-homogeneous distributions ofFeS, as could be expected under field conditions. As illus-trated in Fig. 6, the emergence of an “electrogenic” type fin-gerprint is uniquely determined by the absence/presence ofelectrogenic sulfur oxidation. The geochemical depth pro-files in the second column of Fig. 6 (no e-SOx simulation)differ markedly from those in the other columns. This pro-vides further support the conclusion above that the obser-vation of an “electrogenic” pH signature can be used asconclusive evidence for the presence of electrogenic sulfuroxidation.

4.4. Cryptic sulfur cycling

Simulated sulfide concentrations are well below 1 lmolL�1 within the suboxic zone, and hence, sulfide would notbe detectable by H2S micro-sensors. Still, the model revealsa strong anodic consumption of sulfide throughout thesuboxic zone (Fig. 4b), which subsequently vanishes indeeper sediment layers, where sulfide first appears in thepore water. This simulation result may seem puzzling:high H2S consumption occurs where there is no H2S in thepore water, while no H2S consumption occurs whenthere is ample H2S in the pore water. However, thiscounterintuitive effect is suitably explained by the crypticsulfur cycling that is intrinsically embedded within themodel formulation.

Our sensitivity analysis shows that the cable bacteriamust have a high affinity for sulfide: only for high kASO

and kCOR values (Table 1), the model is capable of repro-ducing the development of a suboxic zone (Fig. 5). Dueto the high affinity for sulfide, any sulfide liberated by bothsulfate reduction and FeS dissolution is immediately scav-enged. As a result, there is no detectable sulfide presentwithin pore water of the suboxic zone. This cryptic sulfurcycling is further illustrated by the concave shape of theSO4

2� profile within the suboxic zone, indicating that thereis a net production of sulfate, and hence, sulfide must beoxidized within the suboxic zone. A similar concave sulfateprofile has been demonstrated in sediment incubations withcable bacteria where FeS was the major source for electro-genic sulfide oxidation (Risgaard-Petersen et al., 2012).

Anodic sulfide consumption stops beneath the suboxiczone, as soon as sulfide starts to appear in the pore water.This observation can be explained by electron saturationof the electron chain carriers. The deeper in the sediment,the more electrons are uploaded onto the redox chain car-riers by anodic sulfide consumption, and the more saturatedthese electron chains become (Fig. 4a). As a consequence,anodic sulfide consumption eventually becomes limited bythe absence of free electron carriers (see kinetic rate expres-sion Eq. (8)), and the sulfide which is produced by sulfatereduction starts to accumulate in the pore water, giving riseto a sharp increase of the sulfide profile at depth (Fig. 4a).

The model prediction that anodic sulfide consumptionoccurs throughout suboxic zone implies that cells, which arelocated in the suboxic zone, must be metabolically active. Thissuggests that cable bacteria are gaining energy and growingover the entire filament length, and not just the terminal endsthat are in contact with either O2 or H2S. This has recently beenconfirmed by Schauer et al. (2014), who performed detailedmicroscopic observations on the temporal development of thefilament network, and demonstrated that cell division and fila-ment elongation takes place throughout the suboxic zone.

4.5. Carbonate dissolution

Recent studies suggest that coastal sediments could bean important source of alkalinity to the overlying water,favoring the role of the coastal ocean as a potential sinkfor atmospheric CO2 (Thomas et al., 2009; Faber et al.,2012). In the North Sea, it has been estimated that as muchas one-quarter of the overall CO2 uptake may be driven byalkalinity production in the intertidal flat sediments of thesouthern North Sea (Thomas et al., 2009). In these samesediments in the North Sea, it has recently been shown thate-SOx occurs under in situ conditions in a variety of habi-tats, and locally exerts a large impact on the sedimentarygeochemical cycling (Malkin et al., 2014). Hence, it is cru-cial to quantify how strongly e-SOx affects alkalinity releaseand calcium carbonate dissolution in coastal sediments.

Because of the spatial segregation of proton productionand consumption, electrogenic sulfur oxidation generates astrong acidification at depth, while at the same time, itinduces high pH values within the oxic zone. As a conse-quence, electrogenic sulfur oxidation strongly acceleratesthe dissolution of carbonates in the suboxic zone and pro-motes carbonate precipitation in the oxic zone (Risgaard-Petersen et al., 2012). The acidification of the suboxic zoneand associated carbonate dissolution is suitably reproducedin the current model simulations. The dissolution of car-bonates in the baseline simulation (40.9 mmol C m�2 d�1)is substantially higher than the release of dissolved inor-ganic carbon (DIC) resulting from organic matter mineral-ization (13.3 mmol C m�2 d�1). This implies that 75% ofthe DIC efflux out of the sediment is due to carbonate dis-solution. As a result, one obtains a very high respiratoryquotient (i.e., the ratio of DIC efflux/O2 consumption) ofQ = 4.1 in the baseline simulation, compared to Q = 1.3in the “No e-SOx” situation. It should be noted howeverthat the current model simulations do not account forcarbonate re-precipitation within the narrow oxic zone,


which would decrease the net carbonate dissolution in thesediment and reduce the DIC efflux across the sediment–water interface.

In natural sediments, carbonate re-precipitation at thesurface will most likely not fully compensate for carbonatedissolution at depth. The pH maximum occurs close to thesediment water, which promotes the escape of alkalinity tothe overlying water. Moreover, the pH peak within oxic zoneis small (�2 mm), leading to a short transit time for solutediffusion (�30 min). As a result, Ca2+ and carbonate specieshave only a short time window in which they can react to pre-cipitate, before escaping to the overlying water. Recent fluxmeasurements from laboratory experiments, in which elec-trogenic sulfur oxidation developed in de-faunated sedimentcore incubations, support this idea (Rao et al., 2014). A sub-stantial efflux of alkalinity was observed, while the DIC fluxexceeded the estimated carbon mineralization rate by 25%,which hence indicates a net dissolution of carbonate in thesediment (albeit less intense than in the simulations here).

Dissolution of CaCO3 in marine sediments is principallycontrolled by two main mechanisms: undersaturation-drivendissolution and respiration-driven dissolution (Archer,1996). Undersaturation-driven dissolution occurs at greaterwater depths (i.e., beneath the so-called carbonate saturationhorizon), where the CaCO3 saturation state becomes lowerthan one, due to the combined effects of the biological pumpand the pressure dependence of the CaCO3 solubility(Boudreau et al., 2010). In contrast, respiration-driven disso-lution may occur at shallower depths where the bottom wateris oversaturated with respect to calcite and aragonite. Respi-ration-driven dissolution is caused by the acidification ofinterstitial pore water by due to the respiratory activityof the benthic community, and may account for up to 50%of CaCO3 dissolution in marine sediments (Archer, 1996).Until now, respiration-driven dissolution has been primarilyattributed to the release of CO2 during organic matter degra-dation (e.g., Hales and Emerson, 1996; Jahnke et al., 1997).

CH2OþO2 ! CO2 þH2O

CaCO3 ! Ca2þ þ CO2�3

CH2OþO2 þ CaCO3 ! Ca2þ þ 2HCO�3ð17Þ

The acidifying effect of CO2 may occur either directly, as inaerobic respiration (represented by CH2OþO2 !CO2 þH2O in (17)), or indirectly, as in anoxic respirationfollowed by the oxidation of reduced metabolites (the over-all reaction equation would be identical to CH2OþO2 !CO2 þH2O).

Electrogenic sulfur oxidation induces a very differentmechanism of respiration-driven carbonate dissolution,which is not dependent on organic matter mineralization,but on the proton production during the oxidation of ironsulfides. The overall effect of this form of metabolic dissolu-tion, which is entirely independent from metabolic CO2

release, can be represented by the reaction equations:

FeSþ5

4O2þ

3

2H2O!FeOOHþSO2�

4 þ2Hþ

2CaCO3! 2Ca2þ þ2CO2�3

FeSþ 54O2þ 3

2H2Oþ2CaCO3!FeOOHþSO2�

4 þ2Ca2þ þ2HCO�3

ð18Þ

Electrogenic sulfur oxidation could be a potentially strongdriver of respiration-driven carbonate dissolution in marinesediments, thus reducing the sequestration of carbon in theform of carbonates.

5. CONCLUSIONS

Electrogenic sulfur oxidation (e-SOx) is a recently dis-covered biogeochemical process, which induces electricalcurrents in marine sediments, whereby electrons are trans-ported over centimeter-scale distances from deeper anoxicsediment horizons to the sediment surface (Nielsen et al.,2010). The spatial separation of the oxidation and reduc-tion half reactions induces strong macro-scale concentra-tion and pH gradients in the pore water. This results inthe establishment of a characteristic geochemical finger-print (pH profile with strong excursions, wide suboxiczone), which can be accurately quantified by microsensordepth profiling. In this regard, long-distance electron trans-port is different from extracellular electron transportbetween metal-reducing bacteria and solid phase electronacceptors, where electron transport occurs at the muchsmaller micro-meter scale (Lovley, 2008).

Here we have developed a model description that iscapable of simulating the characteristic geochemical finger-print of e-SOx. The model is based on a conventional reac-tive transport description of marine sediments, which isextended with a new model formulation for long-distanceelectron transport. This model quantitatively supports sev-eral hypotheses about the nature of e-SOx. Firstly, ourmodel simulations fully support the conceptual model orig-inally proposed by Nielsen et al. (2010), in which the redoxhalf reactions of aerobic sulfide oxidation are spatially seg-regated and are linked by long-distance transport. Sec-ondly, our simulations show that electron conductioninside filamentous cable bacteria is a physically realisticmechanism to explain the observed geochemical data. Thishence provides support to the proposition given by Pfefferet al. (2012) that cable bacteria are mediating long distanceelectron transport in marine sediments.

Our model analysis demonstrates that the characteristicpH profile can be used as a reliable identifier of e-SOx activ-ity in both laboratory experiments and field studies. Sensi-tivity analysis showed that the characteristic geochemicalfingerprint was only present when e-SOx was turned on inthe model simulations. Model analysis also showed thate-SOx can strongly impact the biogeochemical cycling ofC, Fe and S in marine sediments, confirming previousresults from sediment incubation studies (Risgaard-Petersen et al., 2012). Due to strong acidification of thepore water, the metabolic dissolution of carbonate andmetal sulfides is strongly promoted, which will ultimatelyreduce the burial of pyrite and carbonate in sediment envi-ronments, if these stocks are not re-supplied at some othermoment in time, when the cable bacteria are not active.Finally, our model simulations suggest that cable bacteriamust have a high affinity for both free sulfide and oxygenin order to create the wide suboxic zone that is observedin electro-active sediments.


The mechanistic model of long distance electron trans-port that is presented here envisions that the electron trans-port by the cable bacteria occurs by means of multistepelectron hopping. Although the resulting model simulationsclosely reproduce the microsensor data from electro-activesediments, this does not exclude alternative mechanismsof electron transport. Future studies may investigate ifthere are any alternatives to multistep electron hopping thatcould equally well explain the presently available data.Recently, a strong debate has ignited about the nature ofelectron transport in nanowire pili of metal-reducing bacte-ria (Malvankar et al., 2012; Strycharz-Glaven and Tender,2012). Two alternative mechanisms, multi-step electronhopping and metal-like electron transport, were put for-ward by different proponents, but the debate is presentlyunresolved. Direct measurements of the electron transport,such as current/voltage measurements on individual fila-ments or fiber structures of cable bacteria, would providethe most straightforward answer to the question of whichconduction mechanism is underlying long-distance electrontransport. However, such direct transport measurementsare challenging and have not been successful so far(Pfeffer et al., 2012). Therefore, it could be worthwhile toexamine as to what extent the strong imprint of electrogenicsulfur oxidation on pore water geochemistry contains anyinformation on the physical properties of the electron con-duction process.

ACKNOWLEDGEMENTS

The research leading to these results has received funding fromthe European Research Council under the European Union’s Sev-enth Framework Programme (FP/2007-2013) through ERC Grants306933 (FJRM) and 291650 (LPN). Furthermore, this research wasfinancially supported by Research Foundation Flanders (Odysseusgrant G.0929.08 to FJRM), Netherlands Organisation for ScientificResearch (VIDI grant 864.08.004 to FJRM) the Danish NationalResearch Foundation (DNRF104 to NR-P), and the Danish Coun-cil for Independent Research|Natural Sciences (LPN). We kindlythank the three anonymous reviewers, whose valuable suggestionsand comments greatly improved this manuscript.

APPENDIX A.

Accordingly, the electron carriers can be in two states:uncharged (carrying no electron, denoted as X j) or charged(carrying an electron, denoted as X �j ).

X j þ e�¢ X �j ð19Þ

Electrons can jump from one carrier to the next via bimo-lecular electron transfer reactions between adjacent electroncarrier. This can be schematically represented by the reac-tion equation

X �j þ X jþ1 ¢ X j þ X �jþ1 ð20Þ

where the index j denotes the position along the sequence ofelectron carriers separated over a distance d. In the contextof redox polymers, this reaction mechanism is commonlyreferred to as “electron hopping”. The number of electronshopping per unit of time is given by:

r ¼ kðPðX �j ÞPðX jþ1Þ �1

Keq

PðX jÞP ðX �jþ1ÞÞ ð21Þ

where P ðX �j Þdenotes the probability that j-th redox site isloaded with an electron. The quantity k is the kinetic rateconstant of the forward reaction or hopping frequency[units: s�1], while Keq is the thermodynamic equilibriumconstant. If the charge carriers are all identical, as weassume here, then transition state theory requires thatKeq ¼ 1.

A bacterial filament capable of long-distance electrontransport hence can be idealized as a set of parallelsequences of electron carriers. If nCBðxÞ represents the cablebacteria filament density at a given depth x in the sediment,i.e., the number of filaments that crosses a horizontal planeat that depth, and NF denotes the number of electron con-ductive fibers per filament, the local density of fiber carriersbecomes NðxÞ ¼ nCBðxÞN F [units: number of fibers m�2]. Ifd is the mean spacing between electron carriers in a conduc-tive fiber, and AF the cross-sectional area of a fiber, then aconductive fiber can be modelled as a set of AF =d

2 parallelelectron carrier chains. The concentration of charge carriersat a given depth can be expressed as

X T ¼ nCBðxÞNF AF =d3 ð22Þ

The total concentration of charge carriers can be decom-posed as X T ¼ ½X � þ ½X ��, where ½X �� is the concentrationof charged electron carriers and ½X � is the concentrationof free electron carriers. The total flux of electrons througha given depth horizon simply amounts to the electron trans-port within a electron carrier chain, multiplied by the num-ber of electron carrier chains within a single fiber,multiplied with the fiber density. Thus, using Eq. (21), thisflux of electrons can be calculated as

JðxÞ ¼ nCBNFAF

d2kðf CðxÞf F ðxþ dÞ � f F ðxÞf Cðxþ dÞÞ

ð23Þ

The quantity f C ¼ ½X ��=X T represents the fraction ofcharged electron carriers, and similarly, f F ¼ ½X �=X T repre-sents the corresponding fraction of free electron carriers,with

f CðxÞ þ f F ðxÞ ¼ 1 ð24Þ

The continuum approximation and the law of large num-bers allows the probabilities in Eq. (21) to be substitutedin Eq. (23) with the concentration fractions. If we substituteEq. (24) into the flux expression (23), the latter can be re-arranged to (See Eq. (17) in Strycharz-Glaven et al., 2011)

JðxÞ ¼ nCBN FAF

d2k d�f Cðxþ dÞ þ f CðxÞ

d

� �

� � nCBN FAF

d3

� �ð k d2ÞdfC

dx¼ �DEX T

dfC

dxð25Þ

Accordingly, we find that the electron transport in the par-allel network of charge carriers obeys Fick’s first law of dif-fusion. In other words, electrons tend to migrate downhill aconcentration gradient of charged electron carriers. The dif-fusion coefficient DE reflects the mobility of the electronsthrough the network and is related to the kinetic properties


of the electron hopping process (21) via the Dahms–Ruffexpression

DE ¼ k d2 ð26Þ

The above analysis assumes that the carrier network is sta-tic. If the electron carriers are also mobile and redistributed,the flux expression (25) can be generalized to:

JC ¼ �DEX Trð½X ��=X T Þ � ð½X ��=X T ÞDTrX T ð27ÞJF ¼ �DEX Trð½X �=X T Þ � ð½X �=X T ÞDTrX T ð28Þ

The movement of electrons through the carrier networkhence results in apparent diffusion of free (flux J F) andcharged (flux J C) electron carriers. The first term on theright hand side expresses the internal transport of chargeswithin the conducting network, while the second termreflects the bulk transport of electron carriers (where DT

is the diffusion coefficient of the electron carriers). Theinternal transport of charged and uncharged carriers isexactly opposite: if one charge move upwards, an “emptyhole” must move downwards (analogous to the transportof electron and holes in a semi-conductor). The total fluxof charged and uncharged carriers is given by

JT ¼ JF þ JC ¼ �DTrX T ð29Þ

The diffusion coefficient DT reflects the intensity with whichthe charge carriers are potentially redistributed within thesediment matrix, for example due to physical or biologicalreworking of the sediment. In the model simulation pre-sented here, we do not consider such charge carrier redistri-bution. We assume that a network of charge carriers hasbeen established within the sediment, which does notchange with time (i.e., a fixed depth profile of X T ðxÞ isimposed).

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