Bioelectrochemistry 106 (2015) 194–206

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Bioelectrochemistry

j ourna l homepage: www.e lsev ie r .com/ locate /b ioe lechem

A framework for modeling electroactive microbial biofilms performingdirect electron transfer

Benjamin Korth a, Luis F.M. Rosa a, Falk Harnisch a,⁎, Cristian Picioreanu b

a UFZ — Helmholtz-Centre for Environmental Research, Department of Environmental Microbiology, Permoserstrasse 15, 04318 Leipzig, Germanyb Department of Biotechnology, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands

⁎ Corresponding author.E-mail address: falk.harnisch@ufz.de (F. Harnisch).

http://dx.doi.org/10.1016/j.bioelechem.2015.03.0101567-5394/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 17 November 2014Received in revised form 24 March 2015Accepted 30 March 2015Available online 2 April 2015

Keywords:ModelBioelectrochemical systemsElectrochemically active microbial biofilmsExtracellular electron transferMicrobial electrochemical technologies

A modeling platform for microbial electrodes based on electroactive microbial biofilms performing directelectron transfer (DET) is presented. Microbial catabolism and anabolism were coupled with intracellular andextracellular electron transfer, leading to biofilm growth and current generation. The model includes homoge-neous electron transfer from cells to a conductive biofilm component, biofilm matrix conduction, and heteroge-neous electron transfer to the electrode. Model results for Geobacter based anodes, both at constant electrodepotential and in voltammetric (dynamic electrode potential) conditions, were compared to experimental datafrom different sources. Themodel can satisfactorily describe microscale (concentration, pH and redox gradients)and macroscale (electric currents, biofilm thickness) properties of Geobacter biofilms. The concentration of elec-trochemically accessible redox centers, here denominated as cytochromes, involved in the extracellular electrontransfer, plays the key role andmay differ between constant potential (300mM) and dynamic potential (3 mM)conditions. Model results also indicate that the homogeneous and heterogeneous electron transfer rates have tobe within the same order of magnitude (1.2 s−1) for reversible extracellular electron transfer.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Microbial extracellular electron transfer (EET) describes the abilityof microorganisms to connect their cellular metabolism with the flowof electrons in their surroundings [1–3]. EET is now believed to play akey role for natural redox-cycles [3,4], but it has also attracted everincreasing attention for its technical exploitation [5]. This interest andthe associated progress in research and development during the lastdecade led to the foundation of the emerging field of microbial electro-chemical technologies (MET) [6]. MET now cover different concepts ofapplications ranging from its archetype the microbial fuel cells (MFCs)[7,8] via bioelectrochemical resource recovery [9,10] and microbialelectrosynthesis [11] to biocomputing [12].

In line with the technological advancement, the discovery of theunderlying fundamentals of EET hasmade significant progress, resultingin detailed knowledge on different hierarchical levels from biofilmsvia cells to organelles and molecules [2]. However, there are stilllargely untapped areas and one future key to success will be the con-tinuing standardization, cross-validation and benchmarking of theindividual results [13]. This also holds true for the central elementsof all bioelectrochemical systems (BESs), the microbial electrodes.These electrodes are comprised of electroactive microorganisms (alsoreferred to as electricigens [14] on anodes and electrotrophs on cathodes

[15]) able to perform EET and thereby creating the link between micro-bial physiology and the flow of electric current. Different modes of EETare known including most prominently the direct electron transfer(DET) [16,17]. DET requires a physical contact between the microorgan-ismand the electrode, usually in a biofilmon the electrode surface. DET isnot only restricted to microorganisms at the electrode surface trans-ferring electrons with trans-membrane cytochrome complexes [18,19], as “long-range” DET can also be performed from more distantlocations of the biofilm. One possible mode of long-range DEToccurs via so-called nanowires or conductive pili [20–22] or othercellular appendages [23]. The most common model system for DET-based microbial electrocatalysis is the anodic oxidation of acetateby Geobacter. Even for this model system, comprising pure culturestudies (e.g. [24–26]) as well as Geobacter dominated mixed culturesgenerated by electrochemically driven selection [27,28], differentand sometimes contradictory EET results ([29–33]) have beenshown, leading to the proposal of different mechanisms of electrontransfer.

So far, different numerical models have been proposed for micro-bial fuel cells (e.g. [34–36]) or for electroactive microbial biofilms(e.g. [37–39]). For the latter, the existing models represent eitherthe electron transfer at the electrode by voltammetry (i.e. voltage–current polarization experiments, [25,40,41]) or during biofilm growth[34].

We propose here a unifying modeling framework for DET-basedelectrodes possessing a metal-like conductive matrix: i) connecting

195B. Korth et al. / Bioelectrochemistry 106 (2015) 194–206

electrochemistry withmicrobialmetabolism, ii) allowingmodeling bio-film growth and current production as well as the voltammetricresponse, and iii) representing processes at different hierarchical(i.e.microscopic and macroscopic) levels in a biofilm. Model applica-tions in different conditions on experimental results from studiesobtained by various research groups are presented. Macroscopic per-formance and properties of the biofilm (current density, coulombicefficiency, biofilm thickness development) in response to differentexperimental conditions are described. Furthermore, microscopiceffects such as formation of concentration, pH and redox gradientsare evaluated in order to get principle insights into the thermodynamicsand kinetics of electroactive microorganisms.

2. Model description

2.1. Biological, electrochemical and chemical reactions

2.1.1. Substrate conversionFormodelingpurposes, themetabolismof electroactivemicroorgan-

isms can be separated into several steps: the energy-yielding catabolicreaction, the biomass-producing anabolism and the electron transferfrom the intracellular reduction equivalent NADH to c-type outer sur-face cytochromes, which deliver the electrons to a biofilm conductivematrix and finally to the anode [42–44] (Scheme 1A). For example,acetate, Ac−, is considered here both the microbial carbon and electronsource. If the redox couple NAD+/NADH is the intracellular electronacceptor [45], then the overall catabolic reaction of acetate oxidation(Eq. (1)) can be assumed to occur with a double Michaelis–Mentenreaction rate, rbio (mol Ac− m−3 s−1) (Eq. (2)):

Ac− þ 4H2Oþ 4NADþ→4NADHþ 2HCO−3 þ 5Hþ ð1Þ

Scheme 1. (A) Biochemical reactions and electron transfer of a single cell embedded in the biolism), partly used in the electron transfer via NAD+/NADH and the fixed redox centers (c-typetransfer within the biofilm and the electrochemical boundary conditions. There are no molecu(biofilm/liquid interface) the conductive biofilmmatrix is insulated (dEM/dx=0), the liquid poThe electrons transferred to the biofilmmatrix are collected at the anode surface and result in thperformingmetal-like conductivity. (C) Bulk liquid in the anode compartment. The anolyte is idea membrane (ion flux, JM,y). There is exchange of ions and neutral molecules between biofilm

rbio ¼ qAc−C F;X ¼ qmaxAc−

CAc−

CAc− þ KAc−

CNADþ

CNADþ þ KNADþC F;X ð2Þ

KAc− and KNAD+ are the half-rate coefficients for acetate and NAD+, qmaxAc−

is the maximum biomass specific substrate uptake rate(mol Ac− C-mol X−1 s−1) and the biomass concentration in thebiofilm is CF,X. Further, qAc− (mol Ac− C-mol X−1 s−1) is the ac-etate uptake rate per biomass.

2.1.2. Intracellular electron transferFollowing the catabolic reduction of NAD+ to NADH (Eq. (1)) the

electrons are transferred via multiple redox carriers, like cytochromesand the quinone pool, to the terminal immobile redox centers that areas c-type outer surface cytochromes. Here this entire redox chain ismodeled as cytochromes possessing two oxidation states, R and RH[37] (Eq. (3) and Scheme 1A). The redox centers are assumed to betransmembrane cytochromes and therefore using a 1H+/1e− transfermechanism [46,47].

NADHþ Hþ þ 2R ⇄k f ;m

kr;mNADþ þ 2RH rm ð3Þ

The reversible reaction rate rm is here simply expressed as functionof concentrations of involved chemical species and rate coefficientskf,m and kr,m:

rm ¼ k f ;mCNADHCHþC2R−kr;mCNADþC2

RH: ð4Þ

In this model, tuned for anodic biofilms, the forward reaction ratehas been assumed to be much faster than the reverse one.

film. The energy gained from acetate oxidation is partly used to build up biomass (anabo-outer surface cytochromes) to the conductive matrix, and partly dissipated. (B) Electronlar fluxes at the electrode and the electrode potential is fixed to EA. At the biofilm surfacetential EL takes a zero reference value and the biofilm exchanges ions with the bulk liquid.e current density JA. The red line represents the conductive extrapolymeric biofilmmatrixallymixed and cations are exchanged between anode and cathode compartments throughand anode compartment (fluxes JF,y).

:

196 B. Korth et al. / Bioelectrochemistry 106 (2015) 194–206

2.1.3. Extracellular electron transfer to the conductive matrixThe cytochromes can change redox states by electron transfer with

the biofilm conductive matrix (Scheme 1A, B):

R þ e− þHþ ⇄k f ;e

kr;eRH re ð5Þ

The Butler–Volmer equation is assumed for re (mol R m−3 s−1) andderived as a single electron transfer process between the two redoxstates of the cytochromes:

re ¼ k f ;eCRCHþ−kr;eCRH ð6Þ

The rate coefficients are a function of the electrical potential in theconductive matrix, EM, such that :

k f ;e ¼ k0e exp −αFRT

EM−Eθ0

R

� �� �

kr;e ¼ k0e exp 1−αð Þ FRT

EM−Eθ0

R

� �� � ð7Þ

where k0e is a standard rate for the electron transfer from the cyto-

chromes to the biofilm matrix [48], α is the transfer coefficient and Eθ0

Ris the standard redox potential of the redox centers. The equation wasdeveloped similarly to [50]. This model assumes the cytochromes arein full contact with the conductive matrix, i.e. there is no resistance inthis electron transfer.

So far, twomain approaches exist for modeling the electron transferrate of electroactive microbial anodes: Nernst–Monod (N–M) equation(e.g. [39,50]) and Butler–Volmer (B–V) equation (e.g. [37,49]). Due tothe advantage of a more general approach, in the present model wechose to use B–V equation for modeling electron transfer. In contrast,N–M can be considered as a limiting case of B–V and it is useful if theterminal (heterogeneous) electron transfer is not rate limiting [51]. Adetailed discussion on this can be found in SI 1.4.

2.1.4. Electrical conduction in the biofilmIt was assumed that the microbial cells transfer electrons via cyto-

chromes to a conductive biofilm matrix. The “wires” of the conductivematrix conducting electrons from cells to the electrode (here ananode, Scheme 1B) are insulated from the electrolyte contained in thebiofilm, so that the electrolyte potential EL and the conductive matrixpotential EM are not influencing each other. Electrical conduction is rep-resented by the Ohm's law, which defines the electric current density Jproportional with the gradient of potential EM by the conductivity σM,[49] while maintaining electroneutrality (see SI 2.1):

J ¼ −σMdEMdx

: ð8Þ

Transfer of electrons by microbial redox centers to the conductivematrix with rate re (Scheme 1B) provides the current over the biofilmlength, dJ=dx ¼ re F . With the current source defined by the Butler–Volmer Eqs. (6) and (7) the electron balance in the conductive matrixtakes the form of Eq. (9):

σMd2EMdx2

þ re F ¼ 0: ð9Þ

The conductive matrix is electrically insulated (dEM/dx = 0) at thebiofilm surface (biofilm/liquid interface, x = LF).

Finally, the conductive matrix transfers electrons to the electrodewith a rate rc (mol-e m−2 s−1) being a function of the electrode/matrix

overpotential (EA− EM) and an standard electron transfer ratek0c, differ-

ent from the cell-matrix transfer rate coefficient k0e . The homogeneous

electron transport between cell and biofilm matrix and within thebiofilm is achieved by similar redox species — in contrast to the het-erogeneous electron transfer occurring between the redox centers andthe anode [48]:

rc ¼ k0cLh CR exp −αFRT

EA−EMð Þ� �

−CRH exp 1−αð Þ FRT

EA−EMð Þ� �� �

:

ð10Þ

The current continuity condition at the electrode (x=0) is thereforerc F ¼ −σMdEM=dx and the anodic current density is calculated as JA =rcF = J.

2.1.5. Anabolism and microbial growthThe microbial growth stoichiometry was derived using the thermo-

dynamic principles described byHeijnen andKleerebezem [52]. The en-ergy released by the catabolic reaction (Eq. (1)) is utilized by themicrobial anabolism (Scheme 1A, Eq. (12)):

Ac− þ 4H2Oþ 4NADþ→2HCO−3 þ 5Hþ þ 4NADH ΔGθ0

catð1Þ

0:525Ac− þ 0:2NHþ4 þ 0:275þ→CH1:8O0:5N0:2 þ 0:05HCO−

3 þ 0:4H2O ΔGθ0

an:

ð12Þ

TheGibbs energiesΔGθ0cat andΔG

θ0an at pH 7 and 298 Kwere calculated

with values of ΔGθ0f from Heijnen and Kleerebezem [52], then corrected

for the local reaction conditions (e.g. concentration, temperature)(see Supplementary information 1.2), while the Gibbs energy ofNAD+/NADH couple was estimated from the respective standard poten-

tial (SI 1.1). ΔGθ0cat is positive for standard conditions but after correc-

tion for local reaction conditions it becomes negative, therefore makingbiomass growth possible. To produce biomass, part of the gained cata-bolic energyΔGcat is used in anabolism asΔGan, while another part is dis-

sipated as ΔGmaxdiss ¼ −432 kJ C‐mol X−1 (for an acetate-oxidizing

system [52]). A multiplication factor fcat can be calculated to describethe number of substrate oxidation reactions needed to deliver sufficientenergy for the anabolic reaction and dissipation:

f cat ¼ΔGmax

diss −ΔGan�

ΔGcat: ð13Þ

The overall growth stoichiometry then becomes:

− f cat þ 0:525ð ÞAc−−0:2NHþ4−4 f catNAD

þ− 4 f cat−0:4ð ÞH2O

þ CH1:8O0:5N0:2 þ 2 f cat þ 0:05ð ÞHCO−3 þ 4 f catNADHþ 5 f cat−0:275ð ÞHþ ¼ 0

ð14Þ

The maximum specific biomass growth rate μmax (h−1) and themaintenance coefficient on acetate, mAc− (mol Ac− C-mol X−1 h−1),can also be estimated [52]:

μmax ¼ 3ΔGcat=8þ 4:5ΔGmax

dissexp −

69000R

1T−

1298

�� �ð15Þ

mAc− ¼ 4:5ΔGcat

exp −69000

R1T−

1298

�� �: ð16Þ

Using a Herbert–Pirt relationship and the growth stoichiometry(Eq. (14)), the qmax

Ac− takes the form of Eq. (17), which can be furtherused in Eq. (2):

qmaxAc− ¼ − f cat þ 0:525ð Þμmax þmAc− ð17Þ

197B. Korth et al. / Bioelectrochemistry 106 (2015) 194–206

Finally, the biomass specific conversion rate in any point in the bio-film follows:

μ ¼ 1− f cat þ 0:525ð Þ qAc−−mAc−ð Þ: ð18Þ

The biological conversion rates of compounds y ¼ NADH;NADþ;HCO−

3 ;Hþ are rbio;y ¼ qyC F;X , with qNADH ¼ 4 f catμ−4mAc− ¼ −qNADþ ,qHCO−

3¼ 2 f cat þ 0:05ð Þμ−2mAc− , and qHþ ¼ 5 f cat−0:275ð Þμ−5mAc− .

2.1.6. Chemical reactionsSeveral acid–base equilibria (water, acetate, phosphate and carbon-

ate) were accounted for within the biofilm and bulk electrolyte withmost importantly allowing to estimate pH-values. These fast equilibriawere mathematically described by using rate expressions, as describedin Supplementary information, SI 2.1.

2.2. Mass balances

2.2.1. Biomass (biofilm growth)The biofilm thickness increases in time due to biomass production or

decreases as a result of endogenous metabolism or maintenance. Thenet biomass generation is described by the rate rbio;X ¼ μ C F;X and trans-port within the biofilm is dominated by convection (velocity uF), sothat the biomass conservation in a one-dimensional biofilm domainbecomes [53]:

∂C F;X

∂t¼ −

∂ uFC F;X

� �∂x

þ rbio;X: ð19Þ

By assuming a constant biomass density in the biofilm, CF,X, and azero-velocity condition at the electrode surface (uF = 0 at x = 0),Eq. (19) can be integrated to obtain the speed of the biofilm surfaceadvancement due to net biomass generation (uF = uLF at x = LF,Scheme 1B):

uL F ¼ZL F

0

rbio;XC F;X

dx: ð20Þ

WithuLF calculated at each time step, the change of biofilm thicknessresults from integrating Eq. (21) from an initial thickness LF;0:

dLF

dt¼ uL F: ð21Þ

If desired, rates of biomass detachment from and attachment to thebiofilm can be added to the right-hand-side of Eq. (21) in the future[53].

2.2.2. Electron mediators and fixed redox centersThe balance equations for cytochromes (CF,R and CF,RH) and

NAD+/NADH (C F;NADþ and CF,NADH) in each point x in the biofilmare similar to the biomass balances and consider the relevant rates r F;R ¼−2rm;R−re;R , r F;RH ¼ 2rm;RH þ re;RH , r F;NADþ ¼ rbio;NADþ þ rm;NADþ andr F;NADH ¼ rbio;NADH−rm;NADH. Thus, effective rates change within the bio-film depending on the environmental variables, like electric potentialand cytochrome concentration.

2.2.3. Solutes in biofilmDissolved chemical species in the biofilm, each with a local concen-

tration C F;y x; tð Þ, are characterized by spatial concentration gradients.The Nernst–Planck equations with diffusion and ion migration, coupledwith the electroneutrality condition (see Supplementary information2.1), were used for transport and reaction of ions and neutral molecules

in the biofilm, as detailed in Supplementary information, SI 2.2. At thebiofilm surface all concentrations are equal with those in bulk liquid,while at the electrode surface zero-flux is set.

2.2.4. Solutes in bulk electrolyteConcentrations of solutes in the bulk liquid, CB;y tð Þ, change in time.

The balance equations in the bulk volume (VB) include contributionsfrom acid–base reactions in the bulk liquid, ion flux exchanged withthe biofilm (JF,y) through the area exposed to the bulk (AA), the fluxthrough the membrane (JM,y) with the membrane surface area (AM)and, possibly, new medium additions or substitutions, all detailed in SI2.3.

3. Results and discussion

The presented modeling framework has been applied on experi-mental data from various studies by different research groups. Thereby,for each study case specific input parameters were considered, such aselectrode size, buffer composition, and acetate concentration. Theseparameters are listed in the respective supplementary informationsections.

3.1. Macroscopic level: biofilm growth and current production

This first model application demonstrates how the modeling frame-work allows describing two of themost important performance param-eters of microbial anodes: current density (J) and coulombic efficiency(CE). Fig. 1A shows the current production in time measured for aGeobacter biofilm by Bond and Lovely [54] as well as the best fit modelresults (details on fitting see below). The measured and modeled cur-rent curves are very similar and, in terms of maximum current density,almost identical (36 μA cm−2). When considering a complete digestionof the initially provided substrate (acetate) as well as the two substrateadditions at day 4 and day 5, the achieved coulombic efficiency (CE) canbe calculated. The experimental values (CE=86.6% and CE=90.3% forthe first and second cycle, respectively) are also very close to themodeled ones (CE= 90.4% and CE= 89.8%).

Furthermore, the biofilm thickness is calculated, a parameter usuallynot easy to measure in vivo and in real time (Fig. 1B). In non-limitingsubstrate supply the biofilm grows, but it starts to shrinkwhen the sub-strate is depleted. This is due to biomass maintenance, a process imple-mented in the model by considering the energy consumption forsustaining the biofilm and its activity. In the presence of acetate themaintenance also slows down the biofilm growth, but this biomass-consuming process becomes clearly visible after the complete substrateoxidation, when the biofilm thickness decreases. The model-derivedmaximum growth rate of anode respiring Geobacter biofilms of 0.022–0.029 h−1 (Fig. 1B) is in the range of other reported anaerobic growthrates based on acetate, e.g. of 0.010–0.018 h−1 [55,56] Another inter-esting result is the calculated metabolic efficiency of biomass build-up, fcat, i.e. the moles of acetate needed to generate 1 C-mol of biomass.Expectedly, the metabolic efficiency remained nearly constant (fcat =2.2–2.3) during the course of the experiment (Fig. 1B), since the biofilmwas relatively thin and thus no external factors were limiting (e.g. ace-tate diffusion, pH, redox potential and biofilm matrix conductivity).However, when acetate is depleted, the maintenance requirementsdominate the metabolism, leading to a remarkable increase in fcat andbiofilm shrinkage (Fig. 1B).

When fitting the model to the measured current–time curve in aniterative approach a number of available input parameters were varied.Thereby the fitting of maximum current density and duration of thecurrent production in a certain fed-cycle were main fitting criteria.Generally, the following parameters could play a role in the metabolicactivity and thus current production of electroactive microbial biofilms:(i) concentration of cytochromes (i.e. redox centers) in the biofilm

0 2 4 6 80.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

J / (

mA

cm

-2)

t / d

+1 mM acetate

0 2 4 6 80.020

0.022

0.024

0.026

0.028

0.030

t / d

L F /

m

CA

c- /

mM

max

/ h-1

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

f cat

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0

2

4

6

8

10

12

0 2 4 6 80.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

J / m

A c

m-2

t / d

CR/RH = 1 mM

CR/RH

= 10 mM

CR/RH = 100 mM

CR/RH = 300 mM

CR/RH = 1 M

0 2 4 6 80

2

4

6

8

10

12

14

L F /

m

t / d

CR/RH = 1 mM

CR/RH = 10 mM

CR/RH = 100 mM

CR/RH = 300 mM

CR/RH

= 1 M

0 2 4 6 80.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

J / m

A c

m-2

t / d

k0c = 10-7 s-1

k0c = 0.001 s-1

k0c = 0.03 s-1

k0c = 0.1 s-1

k0c = 1 s-1

k0c = 10 s-1

0 2 4 6 80

2

4

6

8

10

12

L F /

m

t / d

k0c = 10-7 s-1

k0c = 0.001 s-1

k0c = 0.03 s-1

k0c = 0.1 s-1

k0c = 1 s-1

k0c = 10 s-1

A B

C D

E F

Fig. 1. Simulation results of microbial anodes based on direct electron transfer. The Geobacter sulfurreducens biofilm was fed initially with 1 mM acetate and two subsequent substrateadditions (1 mM acetate each). (A) Modeled current density (solid line) and experimental data from Bond & Lovley [54] (dotted line). (B) Resulting modeled maximum growth rate(μmax, dotted blue line), multiplication factor for anabolic reaction (fcat, green chain-dotted line), acetate concentration in the bulk liquid (CAc−, solid red line) and resulting biofilm thick-ness (LF, dashed black line). (C–D) Simulated current density and biofilm thicknesswith several values for the total cytochrome concentration (CR/RH). (E–F) Simulated current density and

biofilm thickness with several values for the standard heterogeneous electron transfer rate from biofilm to electrode ðk0c Þ. The experimental data are taken from [54] and the modelparameters are listed in Tables 1 and S1.

198 B. Korth et al. / Bioelectrochemistry 106 (2015) 194–206

(CR=RH), (ii) substrate affinity constant (KAc−), (iii) electron transfer ki-

netics (k0c , k0e), (iv) biofilm conductivity (σM) and (v) intracellular elec-

tron transfer kinetics (k f ;m, kr;m).

The cytochrome concentration in the biofilm is clearly a critical andsensitive model parameter. Low cytochrome concentrations slow downthe biofilm growth and subsequently lower also the current production(Fig. 1C–D). For a detailed discussion about cytochrome concentration,see Section 3.3: concentration of redox active centers. Furthermore,cytochrome concentration is directly linked to the biomass concentra-tion within the biofilm and thus influences the resulting biofilmthickness and the current production (SI Fig. S2E–F). Biomass concen-tration in electroactive microbial biofilms shows strong variabilityamong cultivation conditions [57,58] and therefore we used an accept-ed standard value for anaerobic biofilms [53]. From the qualitative

estimation based on the model results compared with current data(see Fig. 1A and C–D), the cytochrome concentration used in the follow-ingwas 300mM. This obtained value is in the same order of magnitudecompared to values calculated and derived fromEsteve-Núñez et al. [59](for details, please see SI 1.3). Other parameters show only a minorimpact on the biofilm growth and current production. Alterations of

the heterogeneous electron transfer rate (k0c ) by several orders ofmagnitude compared to the literature values [48] show no remarkablechange in the biofilm growth and current production (Fig. 1E–F). Onlyif the heterogeneous electron transfer ratewas unrealistically decreasedto 10−7 s−1 it would become growth limiting (Fig. 1F). In contrast,

alterations in the heterogeneous electron transfer rate k0c have a consid-erable effect during cyclic voltammetry, as it is shown in Section 3.3.Likewise, the homogeneous electron transfer rate (cell/biofilm, k0e )

199B. Korth et al. / Bioelectrochemistry 106 (2015) 194–206

and the biofilm conductivity do not reveal a significant effect on the bio-film growth (SI Fig. S1) within the studied range of value. Themetabolicparameters remained untapped in the calibration of the model due tothe lack of input parameters. So far, the metabolism of Geobacter is notcomprehensively described and no data about enzyme turnover ratesand Michaelis–Menten constants of enzymes are available. Hence, themodel focused on electrochemical parameters to help in the inter-pretation of recent experimental data. Nevertheless, the parametertesting on several metabolic properties (intracellular electron transfer(k f ;m, kr;m), half-saturation coefficient for acetate (KAc‐), biomass con-centration (C F;X)) revealed also a great influence on the model calcula-tions (SI Fig. S2). A faster intracellular electron transfer increased thebiofilm growth (SI Fig. S2A–D) but an increased half-saturation coeffi-cient for acetate slowed down growth and current production (SIFig. S2E–F).

3.2. Spatial resolution on the biofilm level

In addition tomacroscopic variables, i.e. current production, coulom-bic efficiency and biofilm thickness, themodel also reveals biofilmprop-erties at the micro scale, i.e. concentration profiles, pH and redoxpotential along the biofilm depth. The microscale properties, however,are often more difficult to be obtained experimentally. Fig. 2A, Cshows experimental results reported by Franks et al. [60] on the pHpro-file inGeobacter biofilms of a given thickness (70 μm)during anodic res-piration, conditions in which a current density of 2.2 A m−2 wasreached. The pH profile was calculated with the model for the same

0 10 20 30 40 50 60 706.0

6.2

6.4

6.6

6.8

7.0

pH

0 10 20 30 40 50 60 705.8

6.0

6.2

6.4

6.6

6.8

7.0

pH

LF / m

A B

DCL

F / m

Fig. 2.Modeled and experimental pH profiles and the respective redox profiles for themodeledcorresponding redox profiles (concentration of oxidized (CR, solid lines) and reduced cytochromand different bicarbonate buffer composition ðC0;HCO−

3¼ 1–50 mMÞ. 1 mM (orange lines), 5 m

and experimental (dotted line) pH profiles and the corresponding redox profiles (profiles of oxwith a constant bicarbonate buffer composition C0;HCO−

3¼ 5 mM

� and different diffusion atte

imental data are taken from Franks et al. [60,85]. The model parameters are listed in Tables 1 a

current density, but at different buffer compositions (detailed parame-ters in Table S2), mimicking the flow chamber experiments from [60].While the pH remains almost constant in the bulk liquid, a pH gradientbuilds up in the biofilm, which increases with a lower buffer capacity(Fig. 2A). Furthermore, an important factor determining solute profilesin the biofilm is the attenuation of diffusion coefficients within the bio-film compared with those in water (i.e. an “effective” diffusion coeffi-cient in the biofilm). Simulations presented in Fig. 2C show howdecreased diffusivities of all chemical species can lead to substantialacidification at the electrode surface, for the same bulk electrolyte solu-tion. However, a comparison between modeled and measured pH canonly remain here at a qualitative level, because: (i) the effective diffu-sion coefficient is likely to change as a function of biofilm density [61],(ii) the solution speciation depends in reality on dissociation equilibriaof many other chemical species present in the medium, as well as (iii)on the buffering capacity of the biofilm cells and its polymeric matrix.All these phenomena can presently not be included in the model.

The redox gradient, i.e. ratio of oxidized and reduced cytochromes,for which contradictory experimental data exist [62–66], is of specialinterest for microbial electrodes. The mode of electron transfer, e.g.soluble mediators, electron hopping or metal-like conductivity,is assumed to play a major role in the formation of redox gradients,i.e. indicates if redox gradients will arise. A few model approachesalready focused on soluble electron mediators using Fick's diffusionand Nernst–Planck's electromigration for these solutes and thereforefor electron transport and reported electron mediator gradients of con-centration [34,41]. For direct electron transfer two hypotheses exist:electron hopping and metal-like conductivity. An electron hopping

0 10 20 30 40 50 60 700.0

0.2

0.4

299.6

299.8

300.0

CR, C

RH /

mM

0 10 20 30 40 50 600.0

0.3

0.6

299.4

299.7

300.0

CR, C

RH /

mM

LF / m

LF / m

biofilms. (A–B) Calculated (solid lines) and experimental (dotted line) pH profiles and thees (CRH, dashed lines)) for biofilms with a constant diffusion attenuation factor (εD= 0.5)

M (red lines), 10 mM (green lines), and 50mM (blue lines). (C–D) Calculated (solid lines)idized (CR, solid lines) and reduced cytochromes (CRH, dashed lines)) for modeled biofilmsnuation factors (εD = 0.1–0.8). 0.1 (orange), 0.2 (red), 0.5 (green), and 0.8 (blue). Exper-nd S2.

Table 1Summary of all parameters their symbols, values and units used throughout the model.

Parameter description Symbol Value Units Source

Microbial kinetics and thermodynamicsHalf-saturation coefficient for acetate KAc− 0.1 mol Ac−/m3 ChosenHalf-saturation coefficient for acetate KNADþ 0.1 mol NAD+/m3 ChosenStandard Gibbs energy catabolic reaction ΔGθ0

cat32.2 kJ/mol Ac− [52]

Standard Gibbs energy anabolic reaction ΔGθ0an

29.56 kJ/C-mol X−1 [52]

Maximum Gibbs energy dissipation in metabolism ΔGmaxdiss −432 kJ/C-mol X−1 [52]

Acid–base reactionsEquilibrium constants

– Water dissociation KOH− 10−14 mol2/L2 [86]– CO2 hydrolysis KHCO−

310−6.6 mol/L [86]

– Acetic acid dissociation KAc− 10−4.756 mol/L [86]– H2PO4

− dissociation KHPO−24

10−7.21 mol/L [86]

Rate constants– Water dissociation kOH‐ 108 mol/m3 s Arbitrarily large value– CO2, acetic acid and H2PO4

− dissociation kHCO−3; kAc− ; kHPO−2

4107 1/s Arbitrarily large values

Electrochemical kinetics and electrical propertiesStandard (homogeneous) electron transfer rate (cell/biofilm conductive matrix) k0e 1.2 1/s [48]

Standard (heterogeneous) electron transfer rate (biofilm/electrode) k0c 0.03 1/s [48]

Forward rate for the intracellular electron transfer from NADH to redox centers k f ;m 3 × 107 m9/mol3 s ChosenReverse rate constant for the intracellular electron transfer from redox centers toNAD+

kr;m 1 × 10−10 m6/mol2 s Chosen

Standard redox potential of the redox centers Eθ0R

−0.136 V (SHE) [70]

Transfer coefficient for redox rate α 0.5 –Length of direct biofilm/electrode electron transfer layer Lh 1 μm Chosen length of a typical

microbial cellElectrode potential EA

b V (SHE) Variable by caseb

Biofilm matrix conductivity σM 0.5 S/m [21]

Biofilm propertiesInitial biofilm thickness LF0

b μm Variable by caseb

Biomass concentration in the biofilm C F;X 2000 C-mol/m3 ChosenConcentration oxidized/reduced redox centers CR/RH 300 mol/m3 Chosen for chronoamperometry

1, 3 mol/m3 Chosen for cyclic voltammetryConcentration NAD+/NADH CNADþ=NADH 20 mol/m3 Adapted from [87]Biofilm area and electrode area AA

b cm2 Variable by caseb

Diffusion coefficients in water– Acetate DAc− 1.1 × 10−9 m2/s [88,89]– Acetic acid DAcH 1.3 × 10−9 m2/s [88,89]– Cl− DCl− 2.0 × 10−9 m2/s [88,89]– Na+ DNaþ 1.3 × 10−9 m2/s [88,89]– H+ DHþ 9.3 × 10−9 m2/s [88,89]– OH− DOH− 5.3 × 10−9 m2/s [88,89]– CO2 DCO2 1.9 × 10−9 m2/s [88,89]– HCO3

− DHCO−3

1.2 × 10−9 m2/s [88,89]– H2PO4

− DH2PO−4

1.2 × 10−9 m2/s [88,89]– HPO4

2− DHPO−24

1.0 × 10−9 m2/s [88,89]

Reduction factor for diffusion coefficient in the biofilm εD 0.5 – [90]

Bulk liquidBulk liquid volume VB

b L Variable by caseb

Initial concentrations in bulk liquid and biofilma

– Total acetate C0;Ac− ;Tb mol/m3 Variable by caseb

– Total carbonate C0;HCO−3 ;T

b mol/m3 Variable by caseb

– Total phosphate C0;H2PO−4 ;T

b mol/m3 Variable by caseb

– Cl− C0;Cl− 5 mol/m3 Chosen– H+ C0;Hþ 10−7 mol/L If not stated otherwiseb

Transport through membraneMembrane area AM 2 cm2 ChosenDiffusion coefficients in membrane

– H+ DM;Hþ 5.3 × 10−10 m2/s [91]– Na+ DM;NAþ 2.1 × 10−10 m2/s [91]

Membrane thickness LM 100 μm [91]Membrane electric permittivity εM 1.8 × 10−10 F/m [91]Ion concentration in the cathodic solution

– H+ CC;Hþ C0;Hþ mol/m3 Chosen– Na+ CC;Naþ C0;Naþ mol/m3 Chosen

Other constantsFaraday constant F 96485.34 C/molUniversal gas constant R 8.31 J/mol KWork temperature T 298 K If not stated otherwiseb

200 B. Korth et al. / Bioelectrochemistry 106 (2015) 194–206

201B. Korth et al. / Bioelectrochemistry 106 (2015) 194–206

approach with fixed electron mediators (e.g. similar to a redox-polymer [67,68]) and a respective electron diffusion coefficient wasused by Strycharz et al. and resulted in the occurrence of redox gradi-ents due to limiting electron transfer between the bound mediators[40]. Experimental and modeling results from Richter et al. supportthis modeling approach, but these studies also suggest that the homo-geneous electron transfer is limited by the diffusion of counter ionswithin the biofilm [25,40]. An alternative to Fick's law formodeling “dif-fusive” electron transport is Ohm's law of conductivity. Only Marcus etal. and Fischer et al. used this approach for modeling the electron trans-fer performing electric conduction within the biofilm but did also notcomment on the evolution of redox gradients [39,49]. In themodel pre-sented here, based on metal-like conductivity, the electron transfer isdriven by an electric field and with the parameters derived from litera-ture (Table 1) no redox gradients arise, i.e. gradients of the ratio of oxi-dized and reduced cytochromes (Figs. 2B, D, S3, and S4). In thefollowing, severalmodel parameterswere tested to reveal potential fac-tors influencing the redox gradient. For instance, the standard

heterogeneous electron transfer rate (k0c ) of the “electron gates” at theelectrode surface is supposed to play a key role, as this may limit theelectron flow in the biofilm layers more distant to the electrode surface.Within the wide range of values tested, the heterogeneous electrontransfer rate to the electrode limited the biofilm growth and microbialmetabolism only, if drastically decreased (Fig. 1E–F). Even then, almostno redox gradients arise (SI Fig. S4A–B) across a 12 μm thick biofilm.Only if the biofilm becomes remarkably thicker and the heterogeneouselectron transfer rate is slower than experimentally measured[48], reduced cytochromes accumulate near the electrode and aredox gradient evolves (SI Fig. S3A–B). Certainly, other parameterscould impact the formation of redox profiles in reality. For instance,buffer conditions and the diffusion of ionswithin the biofilm (especiallyprotons) and consequently the pH profile inside the biofilm influencesslightly the ratio of oxidized and reduced cytochromes (Fig. 2B, D).Therefore, not the electron, but the counter ion (mainly H+) transportmay govern the overall activity, which is in line with indicationsfrom several experimental studies [69]. One also may speculatethat the biofilm conductivity is crucial for the formation of a redoxgradient. However, even a decrease of the biofilm matrix conductiv-ity to semiconductor-like values led to only a minor redox gradient(SI Fig. S3C). These model results support recent experiments, whichalso did not lead to observable redox gradients and subsequentlyassumed other bottlenecks for current production in Geobacter basedbiofilms, i.e. metabolic constraints or different control mechanisms forelectron flow between pure and mixed Geobacter cultures [62].Nevertheless, it is still subject of investigation whether electron hoppingor metal-like conductivity is the mechanism for electron transfer withina specific biofilm. Although the proposed biofilm model is based onmetal-like conductivity and as such it shows no redox gradients, othermodels based on different electron transfer modes may lead to redoxgradients. Thus, a coupling of the presented metabolic calculationswith electron hopping as alternative mode of EET could help clarifyingthis open question in future.

3.3. Biofilm electron transfer

One frequently used method to study the mechanisms of microbialextracellular electron transfer is cyclic voltammetry (CV) [70]. CVhas been applied in several studies to Geobacter based biofilms [31,70,71] and models to interpret cyclic voltammograms have beendeveloped [25,40,41], for both turnover and non-turnover conditions(i.e. voltammetries obtained in the presence and absence of the

Notes to: Table 1a The other initial concentrations result from electroneutrality C0;Naþ

� �, mole balances and

b These values have been adapted for the respective example (see, Individual results and re

microbial substrate, respectively). The introducedmodeling frameworkcan also be used for modeling cyclic voltammograms and to study mi-crobial electron transfer properties. In the following the results of its ap-plication on a set of non-turnover CV curves from the recent study ofJana et al. [72] harboring a comprehensive data set for thin (5 μm) andthick (50 μm) biofilms (Fig. 3A and B respectively), and turnover CVdata from Fricke et al. [70] (Fig. 4A–B) are shown. These studies werechosen in order to fulfill the criteria of comparability with the modelset-up, because for planar electrodes the geometric area can be easilyused as an input parameter. Most other studies used 3D electrodes(foam, fiber brush) for the experiments (e.g. [73–75]), which cannotbe directly used because it leads to the question, how bacterial accessi-ble surface area is defined.

The fitting criteria used to calibrate the model parameters usingthese sets of data included: (i) peak current densities, (ii) formal poten-tial (in turnover CV), or the oxidation and reduction peak potentials (innon-turnover CV), (iii) the area of the respective oxidation and/or re-duction peak in turnover CVs (this area is directly related to the numberof cytochromes involved in the dynamic electron transfer process innon-turnover conditions) and (iv) the peak separation from the formalpotential (Ep−E0) for non-turnover CVs as function of the scan rate (v),which reflects the electron transfer kinetics.

Based on these fitting criteria a comprehensive parameter testingwas performed. The parameters found to bemost important for the cor-rect model description of turnover as well as non-turnover CVs were:(i) the concentration of cytochromes, i.e. redox centers, in the biofilm(CR/RH, Figs. 3E–F and 4C) and (ii) the heterogeneous electron transfer

rate (k0c , Figs. 3G–H and 4D).

3.3.1. Concentration of redox active centersInterestingly, to obtain a reasonable representation of both the

voltammetric peak areas and peak current densities for the modeledCVs (Figs. 3A–B, 4A), the concentration of cytochromes had to belowered to 3 mM (non-turnover) and 1 mM (turnover), comparedto the necessary 300 mM when modeling biofilm growth (seeSection 3.1). This indicates that only a certain “share” of the redoxcenters participate in the electron transfer during CVmeasurements,i.e. they are available for fast responses when using voltammetry. Inturnover CVs the concentration of cytochromes does not change con-siderably the peak currents, but has a significant impact on the for-mal potential (Fig. 4C) and promotes the occurrence of a peak paircentered at ~0 V (vs. SHE) superimposed to the turnover CV-curve(Fig. 4C). This phenomenon also appears with faster scan rates for aconstant cytochrome concentration (Fig. 4F). As previously reported[40], this peak pair may be associated to slow acetate oxidation that islimiting catalytic current production. In this context Strycharz et al.also speculate that rather other intracellular processes, i.e. reduction ofthe cytochrome pool, may limit current generation and that substrateoxidation is comparable fast [40].Within the currentmodel the electrontransfer limitation related to the peak formation was caused by sub-strate oxidation rather than by internal electron transfer (SI Fig. S7).Further, one may speculate that the periplasmic pool of redox com-pounds, e.g. quinones, acts as a redox buffer between the cell and theterminal transfer proteins to the electrode [76].

The fact that differing cytochrome concentrations are needed torepresent biofilm growth, turnover CVs and non-turnover CVs –while all other intrinsic parameters are constant – leads to anotherimportant question:

What are the “active” redox centers, i.e. these that can exchangeelectrons with the electrode, during a certain electrochemicalmeasurement?

equilibrium relations (C0;AcH, C0;Ac− , C0;CO2, C0;HCO−

3, C0;H2PO

−4, C0;HPO−2

4, C0;OH− ).

spective SI).

202 B. Korth et al. / Bioelectrochemistry 106 (2015) 194–206

-0.4 -0.2 0.0 0.2 0.4

0

20

40

60

80

J /

A c

m-2

EA / V (vs. SHE)

-0.4 -0.2 0.0 0.2 0.4

0

100

200

300

400

500

JE

-1

/ arb

. uni

ts

EA/ V vs. SHE

-0.4 -0.2 0.0 0.2 0.4

0

20

40

60

80

100

120

140

J /

A c

m-2

EA / V (vs. SHE)

CR/RH

= 0.1 mM

CR/RH

= 0.5 mM

CR/RH

= 1 mM

CR/RH

= 5 mM

CR/RH

= 10 mM

-0.4 -0.2 0.0 0.2 0.4

0

10

20

30

40

50

60

70

80

90

J /

A c

m-2

EA / V (vs. SHE)

k0c = 10-3 s-1

k0c = 0.1 s-1

k0c = 1.2 s-1

k0c = 10 s-1

k0c = 100 s-1

-0.4 -0.2 0.0 0.2 0.4

0

10

20

30

40

50

60

70

80

90

J /

A c

m-2

EA / V (vs. SHE)

k0e = 0.001 s-1

k0e = 0.1 s-1

k0e = 1.2 s-1

k0e = 10 s-1

k0e = 100 s-1

-0.4 -0.2 0.0 0.2 0.4

0

20

40

60

80

100

J /

A c

m-2

EA / V (vs. SHE)

v = 0.1 mV s-1

v = 1 mV s-1

v = 5 mV s-1

v = 10 mV s-1

v = 20 mV s-1

A B

C D

E F

Fig. 4. Comparison between simulation results of microbial anodes and results obtained from Fricke et al. [70] in cyclic voltammetry experiments under turnover conditions. (A) Modeled(solid line) and experimental (dashed line) cyclic voltammogram recorded at 5mV s−1 from−0.5 to 0.5 V vs. SHE. Experimental data is taken from [49]. (B) Corresponding first derivativeof themodeled (solid line) and experimental (dashed line) CV. (C) Modeled current density with several values for the total cytochrome concentration (CR/RH). (D)Modeled current den-sity with several values for the standard heterogeneous electron transfer rate ðk0c Þ. (E) Modeled current density with several values for the standard homogeneous electron transfer rate (k0e).(F) Modeled current density with several scan rates (v). A solid line in the parameter analysis indicates the voltammogram obtained with the best fitting set of parameters compared toFricke et al. One parameter at the time was varied in the simulations. Model parameters are listed in Tables 1 and S4.

203B. Korth et al. / Bioelectrochemistry 106 (2015) 194–206

For simplicity reasons this modeling platform considered only onespecies of a c-type cytochrome possessing one mid-point potential,and transferring one electron per molecule at a time, as cellular redoxcenters. In reality, Geobacteraceae are known for producing more than100 different types of cytochromes (with most cytochromes possessingmore than one electron binding haem domains) [77] and different

Fig. 3. Comparison betweenmodeled cyclic voltammograms and experimentally obtained by Jaand (B) thick biofilms (50 μm)at different scan rates.Modeleddata (solid lines) is compared to e40mV s−1 (green), and 60mV s−1 (black). Respective peak separation analysis for (C) thin andfrom Jana et al. (dotted lines). (E) Modeled current density with several values for the total cytovalues for the total cytochrome concentration (CR/RH) for a 50 μmbiofilm. (G) Modeled current5 μmbiofilm. (H)Modeled current densitywith several values for the heterogeneous electron trconductivities (σM) for a 5 μmbiofilm. (J)Modeled current densitywith various biofilmmatrix cvoltammogram obtained with the best fitting set of parameters compared to Jana et al. (scan raeters are listed in Tables 1 and S3.

electron transfer mechanisms, e.g. 1H+/1e− mechanism or 1H+/2e−

mechanism. Recent experimental data suggest that several respiratorypathways with different cytochromes exist in parallel. Each pathway isable to transfer electrons to an external electron acceptor in accordanceto the applied anode potential [78,79]. Furthermore, the amount ofcytochromes may change with biofilm age and vary over the biofilm

na et al. [72] in the absence of acetate (non-turnover conditions). (A) Thin biofilms (5 μm)xperimental data obtained from Jana et al. (dotted lines). 5mV s−1 (blue), 20mVs−1 (red),(D) thick biofilms. Modeled data (solid lines) is compared to experimental data obtainedchrome concentration (CR/RH) for a 5 μmbiofilm. (F) Modeled current density with severaldensity with several values for the standard heterogeneous electron transfer rate (k0c ) in aansfer rate (k0c) for a 50 μmbiofilm. (I)Modeled current densitywith various biofilmmatrixonductivities (σM) for a 50 μmbiofilm. The solid line in the parameter analysis indicates thete of 60 mV s−1). One parameter at the time was varied in the simulations. Model param-

204 B. Korth et al. / Bioelectrochemistry 106 (2015) 194–206

thickness [18,80] and cytochromes can have different functions withinthe microbial cell. Generally, in addition to their role in extracellularelectron transfer, cytochromes are involved in further metabolic path-ways and there indications for charge storage function within the bio-film [81]. Further on, other redox carriers like the quinone pool areinvolved, being only in contact with the electrode via a chain of redoxcarriers. All these redox carriers possess not only individual formalpotentials, but also specific electron transfer rates etc. As a consequencea certain species of cytochrome will only exchange electrons with theelectrode (i.e. be responsive to the measurement) when the drivingforce (i.e. the electrode potential) aswell as the time needed for electrontransfer is sufficient. As more data becomes available, the model couldbe extended with different numbers and types of cytochromes (withdifferent redox potentials) and additional internal electron transfer pro-cesses, so that more complex non-turnover CV shapes can be obtainedthan those in Fig. 3A–B.

3.3.2. Electron transfer rate

The heterogeneous electron transfer rate (k0c) does, within the rangeof 0.001 s−1 to 10 s−1, not alter the biofilm growth (Fig. 1E–F). The value

k0c ¼ 0:03 s−1, reported in [48] and used for modeling biofilm growthand current production (Section 3.1), did not result in gooddescription of the CV experiments. Only using values of about 1.2 s−1

for the heterogeneous electron transfer rate (similar to the homoge-neous electron transfer rate coefficient) provided a reasonable agree-ment with the experimental data (Figs. 3A–D and 4A–B). In turnoverCV curves the formal potential of the cytochromes is shifted to morepositive values the slower the heterogeneous electron transfer rate isset (Fig. 4D). The same observations are made for the homogeneous

(cell/biofilm) electron transfer rate (k0e, Fig. 4E). However,k0c andk0e con-

siderably change the electrochemical reversibility, expressed in peakseparation in non-turnover CV curves (Figs. 3G–H and S5A–B).

Most voltammetric studies do only allow to get access to the apparentelectron transfer rate [31,70,71] and only a few studies describe kineticmechanisms that can distinguish between homogeneous and heteroge-neous electron transfer [48]. The electron transfer rate depends onother factors as well, including for instance the electrode material [82],its crystallographic orientation, or the different electron tunneling dis-tance between the electrode and the iron center [83]. Therefore, themodel should be adapted for amore detailed description of the extracel-lular electron transfer process.

It was also found that biofilm matrix conductivity (σM) couldinfluence the outcome of the modeled voltammetric response, butonly when approaching semiconductor-like values [84] (Fig. 3I–J andSI Fig. S6C). It is obvious that a thicker biofilm produces more current(Fig. 3 and SI Fig. S6A), but it also shifts the formal potential tomore pos-itive values due to the build-up of ohmic resistance in the biofilm (SIFig. S6B, e.g. [25]).

4. Conclusions

A modeling framework for microbial anodes composed of electro-active microbial biofilms based on direct electron transfer was devel-oped and used for interpretation of experimental observations onGeobacter based biofilms from several independent sources focusingon electrochemical data, as the kinetics of the metabolism of Geobacteris not comprehensively described and metabolic parameters could notbe included extensively. The novelty of the proposed model consistsin its combined description of biofilm growth and performance atconstant electrode potentials with a voltammetric characterization(i.e. dynamic potential conditions). It is shown that during biofilmgrowth under previously reported experimental conditions no redoxgradients and only weak pH gradients should form. Furthermore, whilefor growth conditions the heterogeneous electron transfer rate is not asensitive parameter, when modeling CVs this rate has to be within the

range of the homogeneous electron transfer rate. In general, the concen-tration of cellular redox carriers (here denominated as cytochromes)proved to be the most sensitive parameter and therefore the key fordata fitting. Thereby the concentration of “active” (i.e. “electrochemicallyaccessible”) redox carriers that participate in the heterogeneous electrontransfer to the electrode differs strongly between constant potential andvoltammetric conditions. This may imply that an important share of thecellular redox carriers may act solely as “electron pool” that can onlyrelease/accept electrons at lower rates than the rate of the extracellularelectron transfer. Especially this latter finding has to be assessed further,and raises interesting questions on the microbial physiology.

This modeling framework may be extended with the description ofanodes of complex geometries, with biofilms composed of a diversemicrobiomes and thus complex food webs, as well as DET-based cath-odes, and full bioelectrochemical systems.

Acknowledgments

F.H. acknowledges support by the BMBF (Research Award “Nextgeneration biotechnological processes — Biotechnology 2020+”) andthe Helmholtz-Association (Young Investigators Group). This workwas supported by the Helmholtz-Association within the Research Pro-gramme Renewable Energies.

Appendix A. Supplementary data

Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.bioelechem.2015.03.010.

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