A framework for modeling electroactive microbial biofilms performing direct electron transfer Benjamin Korth, Luis F.M. Rosa, Falk Harnisch, Cristian Picioreanu PII: DOI: Reference:

S1567-5394(15)00034-1 doi: 10.1016/j.bioelechem.2015.03.010 BIOJEC 6827

To appear in:

Bioelectrochemistry

Received date: Revised date: Accepted date:

17 November 2014 24 March 2015 30 March 2015

Please cite this article as: Benjamin Korth, Luis F.M. Rosa, Falk Harnisch, Cristian Picioreanu, A framework for modeling electroactive microbial biofilms performing direct electron transfer, Bioelectrochemistry (2015), doi: 10.1016/j.bioelechem.2015.03.010

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ACCEPTED MANUSCRIPT A framework for modeling electroactive microbial biofilms performing direct electron transfer Benjamin Kortha, Luis F. M. Rosaa, Falk Harnischa,*, Cristian Picioreanub a

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UFZ – Helmholtz-Centre for Environmental Research, Department of Environmental Microbiology, Permoserstrasse 15, 04318 Leipzig, Germany b Department of Biotechnology, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands. Correspondence to: * Falk Harnisch: [email protected], Tel.: +49 341 235 – 1337, Fax: +49 341 235 – 1351

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Abstract

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

Keywords:

model, bioelectrochemical systems, electrochemically active microbial biofilms, extracellular electron transfer, microbial electrochemical technologies

Graphical Abstract

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ACCEPTED MANUSCRIPT 1. Introduction

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Microbial extracellular electron transfer (EET) describes the ability of microorganisms to connect their cellular metabolism with the flow of electrons in their surroundings [13]. EET is now believed to play a key-role for natural redox-cycles [3, 4], but it has also attracted ever increasing attention for its technical exploitation [5]. This interest and the associated progress in research and development during the last decade led to the foundation of the emerging field of microbial electrochemical technologies (MET) [6]. MET now cover different concepts of applications ranging from its archetype the microbial fuel cell (MFCs) [7, 8] via bioelectrochemical resource recovery [9, 10] and microbial electrosynthesis [11] to biocomputing [12]. In line with the technological advancement, the discovery of the underlying fundamentals of EET has made significant progress, resulting in detailed knowledge on different hierarchical levels from biofilms via cells to organelles and molecules [2]. However, there are still largely untapped areas and one future key to success will be the continuing standardization, cross-validation and benchmarking of the individual results [13]. This also holds true for the central elements of all bioelectrochemical systems (BES), the microbial electrodes. These electrodes are comprised of electroactive microorganisms (also referred to as electricigens [14] on anodes and electrotrophs on cathodes [15]) able to perform EET and thereby creating the link between microbial physiology and the flow of electric current. Different modes of EET are known including most prominently the direct electron transfer (DET) [16, 17]. DET requires a physical contact between the microorganism and the electrode, usually in a biofilm on the electrode surface. DET is not only restricted to microorganisms at the electrode surface transferring electrons with trans-membrane cytochrome complexes [18, 19], as “long-range” DET can also be performed from more distant locations of the biofilm. One possible mode of long-range DET occur via so-called nanowires or conductive pili [20-22] or other cellular appendages [23]. The most common model system for DET-based microbial electrocatalysis is the anodic oxidation of acetate by Geobacter. Even for this model system, comprising pure culture studies (e.g. [24-26]) as well as Geobacter dominated mixed cultures generated by electrochemically driven selection [27, 28], different and sometimes contradictory EET results ([29-33]) have been shown, leading to the proposal of different mechanisms of electron transfer. So far, different numerical models have been proposed for microbial fuel cells (e.g. [34-36]) or for electroactive microbial biofilms (e.g. [37-39]). For the latter, the existing models represent either the 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-based electrodes possessing a metal-like conductive matrix: i) connecting electrochemistry with microbial metabolism, ii) allowing modeling biofilm growth and current production as well as the voltammetric response, and iii) representing processes at different hierarchical (i.e. microscopic and macroscopic) levels in a biofilm. Model applications in different conditions on experimental results from studies obtained by various research groups are presented. Macroscopic performance and properties of the biofilm (current density, coulombic efficiency, biofilm thickness development) in response to different experimental conditions are described. Furthermore, microscopic effects such as formation of concentration, pH and redox gradients are evaluated in order to get principle insights into the thermodynamics and kinetics of electroactive microorganisms. 2

ACCEPTED MANUSCRIPT 2. Model description 2.1. Biological, electrochemical and chemical reactions

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2.1.1. Substrate conversion

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For modeling purposes, the metabolism of electroactive microorganisms can be separated into several steps: the energy-yielding catabolic reaction, the biomassproducing anabolism and the electron transfer from the intracellular reduction equivalent NADH to c-type outer surface cytochromes, which deliver the electrons to a biofilm conductive matrix and finally to the anode [42-44] (Scheme 1A). For example, acetate, Ac , is considered here both the microbial carbon and electron source. If the redox couple NAD+/NADH is the intracellular electron acceptor [45], then the overall catabolic reaction of acetate oxidation (eq. (1)) can be assumed to occur with a double Michaelis-Menten reaction rate, rbio (mol Ac m-3 s-1) (eq.(2)):

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Ac- + 4H2O + 4NAD+  4NADH + 2HCO3- + 5H+ C AcCNAD+ max rbio  qAc-CF,X  qAcCF,X C Ac-  K Ac- CNAD+  KNAD+

(1) (2)

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max K Ac- and KNAD+ are the half-rate coefficients for acetate and NAD+, qAcis the -1 -1 maximum biomass specific substrate uptake rate (mol Ac C-mol X s ) and the biomass concentration in the biofilm is CF,X .Further, qAc- (mol Ac C-mol X-1 s-1) is the acetate uptake rate per biomass.

Here Scheme 1.

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2.1.2. Intracellular electron transfer

Following the catabolic reduction of NAD+ to NADH (eq. (1)) the electrons are transferred via multiple redox carriers, like cytochromes and the quinone pool, to the terminal immobile redox centres that are as c-type outer surface cytochromes. Here this entire redox chain is modeled as cytochromes possessing two oxidation states, R and RH [37] (eq. (3) and Scheme 1A). The redox centres are assumed to be transmembrane cytochromes and therefore using a 1H+/1e- transfer mechanism [46, 47]. kf,m   NAD+ + 2RH NADH + H+ + 2R  rm (3)  kr,m

The reversible reaction rate rm is here simply expressed as function of concentrations of involved chemical species and rate coefficients kf,m and kr,m : 2 rm  kf,mCNADHCH+CR2  kr,mCNAD+CRH

(4)

In this model, tuned for anodic biofilms, the forward reaction rate has been assumed to be much faster than the reverse one. 3

ACCEPTED MANUSCRIPT 2.1.3. Extracellular electron transfer to the conductive matrix

The cytochromes can change redox states by electron transfer with the biofilm conductive matrix (Scheme 1A, B): f,e   RH R + e- + H+   kr,e

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(5)

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re = kf,eCRCH+  kr,eCRH

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The Butler-Volmer equation is assumed for re (mol R m-3 s-1) and derived as a single electron transfer process between the two redox states of the cytochromes: (6)

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

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F   kf,e  ke0 exp    EM  ERθ'    RT  F   kr,e  ke0 exp 1     EM  ERθ'   RT  

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where ke0 is a standard rate for the electron transfer from the cytochromes to the biofilm matrix [48],  is the transfer coefficient and ERθ' is the standard redox potential of the redox centres. This model assumes the cytochromes are in full contact with the conductive matrix, i.e. there is no resistance in this electron transfer. So far, two main approaches exist for modeling the electron transfer rate of electroactive microbial anodes: Nernst-Monod (N-M) equation (e.g. [39, 49]) and Butler-Volmer (B-V) equation (e.g. [37, 50]). Due to the advantage of a more general approach, in the present model we chose 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 the terminal (heterogeneous) electron transfer is not rate-limiting [51]. A detailed discussion on this can be found in SI 1.4. 2.1.4. Electrical conduction in the biofilm

It was assumed that the microbial cells transfer electrons via cytochromes to a conductive biofilm matrix. The “wires” of the conductive matrix conducting electrons from cells to electrode (here an anode, Scheme 1B) are insulated from the electrolyte contained in the biofilm, so that the electrolyte potential EL and the conductive matrix potential EM are not influencing each other. Electrical conduction is represented by the Ohm’s law, which defines the electric current density J proportional with the gradient of potential EM by the conductivity  M , while maintaining electroneutrality (see SI 2.1): J   M

dEM dx

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d 2EM  reF = 0 dx 2

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Transfer of electrons by microbial redox centres to the conductive matrix with rate re (Scheme 1B) provides the current over the biofilm length, dJ dx  re F . With the current source defined by the Butler-Volmer equations (6)-(7) the electron balance in the conductive matrix takes the form of eq. (9):

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

Finally, the conductive matrix transfers electrons to the electrode with a rate rc

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(mol-e m-2 s-1) being a function of the electrode/matrix overpotential ( EA  EM ) and an

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standard electron transfer rate kc0 , different from the cell-matrix transfer rate coefficient ke0 . The homogeneous electron transport between cell and biofilm matrix and within the biofilm is achieved by similar redox species - in contrast to the heterogeneous electron transfer occurring between the redox centres and the anode [48]: (10)

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 F F     rc  kc0Lh CR exp   EA  EM   CRH exp 1     EA  EM   RT  RT    

The current continuity condition at the electrode ( x 0 ) is therefore rcF   M dEM dx

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and the anodic current density is calculated as JA  rcF . 2.1.5. Anabolism and microbial growth

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The microbial growth stoichiometry was derived using the thermodynamic principles described by Heijnen and Kleerebezem [52]. The energy released by the catabolic reaction (eq.(1)) is utilized by the microbial anabolism (Scheme 1A, eq.(11)): Ac- +4H2O+4NAD+  2HCO3- +5H+ +4NADH

0.525Ac- +0.2NH+4 +0.275H+  CH1.8O0.5N0.2 +0.05HCO +0.4H2O 3

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θ' Gan

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θ' θ' The Gibbs energies Gcat and Gan at pH 7 and 298 K were calculated with values of

Gfθ' 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 of NAD+/NADH couple was estimated from the respective θ' standard potential (SI 1.1). Gcat is positive for standard conditions but after correction for local reaction conditions it becomes negative, therefore making biomass growth possible. To produce biomass, part of the gained catabolic energy

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fcat

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The overall growth stoichiometry then becomes:

  fcat  0.525 Ac-  0.2NH4+  4 fcat NAD+   4fcat  0.4 H2O

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 CH1.8O0.5N0.2  2fcat  0.05HCO3-  4 fcatNADH   5 fcat  0.275 H+  0

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

3 Gcat / 8  4.5  69000  1 1   exp      max Gdiss R  T 298   

(14)

mAc- 

4.5  69000  1 1   exp      Gcat R  T 298   

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max 

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max Using a Herbert-Pirt relationship and the growth stoichiometry (eq.(13)), the qActakes the form of eq. (16), which can be further used in eq. (2): max qAc  fcat  0.525  max  mAc(16)

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Finally, the biomass specific conversion rate in any point in the biofilm follows:

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1 qAc-  mAc-    fcat  0.525

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The biological conversion rates of compounds rbio,y  qy CF,X ,

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qNADH  4 fcat   4 mAc-  qNAD+ ,

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qHCO3-  2 fcat  0.05   2 mAc- ,

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qH+   5 fcat  0.275   5 mAc- . 2.1.6. Chemical reactions

Several acid-base equilibria (water, acetate, phosphate and carbonate) were accounted for within the biofilm and bulk electrolyte with most importantly allowing to estimating pH-value. These fast equilibria were mathematically described by using rate expressions, as described in Supplementary Information, SI 2.1.

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Mass balances 2.2.1. Biomass (biofilm growth)

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The biofilm thickness increases in time due to biomass production or decreases as a result of endogenous metabolism or maintenance. The net biomass generation is described by the rate rbio,X   CF,X and transport within the biofilm is dominated by

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convection (velocity uF ), so that the biomass conservation in a one-dimensional biofilm domain becomes [53]:   uFCF,X  CF,X   rbio,X t x

(18)

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By assuming a constant biomass density in the biofilm, CF,X , and a zero-velocity

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condition at the electrode surface ( uF  0 at x 0 ), equation (18) can be integrated to obtain the speed of the biofilm surface advancement due to net biomass generation ( uF  uLF at x  LF , Scheme 1B): LF

rbio,X dx C 0 F,X

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With uLF calculated at each time step, the change of biofilm thickness results from integrating eq. (20) from an initial thickness LF,0 : dLF  uLF dt

(20)

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If desired, rates of biomass detachment from and attachment to the biofilm can be added to the right-hand-side of eq.(20) in future [53].

2.2.2. Electron mediators and fixed redox centres

The balance equations for cytochromes ( CF,R and CF,RH ) and NAD+/NADH ( CF,NAD+ and

CF,NADH ) in each point x in the biofilm are similar to the biomass balances and consider the relevant rates rF,R  2rm,R  re,R , rF,RH  2rm,RH  re,RH , rF,NAD+  rbio,NAD+  rm,NAD+ and rF,NADH  rbio,NADH  rm,NADH . Thus, effective rates change within the biofilm depending on the environmental variables, like electric potential and cytochrome concentration.

2.2.3. Solutes in biofilm

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Dissolved chemical species in the biofilm, each with a local concentration CF,y (x , t) , are characterized by spatial concentration gradients. The Nernst-Planck equations with diffusion and ion migration, coupled with the electroneutrality condition (see Supplementary Information 2.1), were used for transport and reaction of ions and neutral molecules in the biofilm, as detailed in Supplementary Information SI 2.2. At the biofilm surface all concentrations are equal with those in bulk liquid, while at the electrode surface zero-flux is set.

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2.2.4. Solutes in bulk electrolyte

Concentrations of solutes in the bulk liquid, CB,y (t) , change in time. The balance

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equations in the bulk volume ( VB ) include contributions from acid-base reactions in the bulk liquid, ion flux exchanged with the biofilm ( JF,y ) through the area exposed to the bulk ( AA ), the flux through the membrane ( JM,y ) with the membrane surface area

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( AM ) and, possibly, new medium additions or substitutions, all detailed in SI 2.3. Here Table 1.

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

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3. Results and Discussion

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The presented modeling framework has been applied on experimental data from various studies by different research groups. Thereby, for each study case-specific input parameters were considered, such as electrode size, buffer composition, acetate concentration, etc. These parameters are listed in the respective supplementary information sections. 3.1. Macroscopic level: Biofilm growth and current production Here Figure 1.

This first model application demonstrates how the modeling framework allows describing two of the most important performance parameters of microbial anodes: current density (J) and coulombic efficiency (CE). Figure A shows the current production in time measured for a Geobacter biofilm by Bond & Lovely [54] as well as the best fit model results (details on fitting see below). The measured and modeled current curves are very similar and, in terms of maximum current density, almost identical (36 µA cm-2). When considering a complete digestion of the initially provided substrate (acetate) as well as the two substrate additions at day 4 and day 5, the achieved coulombic efficiency (CE) can be calculated. The experimental values (CE = 86.6 % and CE = 90.3 % for the first and second cycle, respectively) are also very close to the modeled ones (CE = 90.4 % and CE = 89.8 %). Furthermore, the biofilm thickness is calculated, a parameter usually not easy to measure in vivo and in real time (Fig. 1B). In non-limiting substrate supply the biofilm 8

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grows, but it starts to shrink when the substrate is depleted. This is due to biomass maintenance, a process implemented in the model by considering the energy consumption for sustaining the biofilm and its activity. In the presence of acetate the maintenance also slows down the biofilm growth, but this biomass-consuming process becomes clearly visible after the complete substrate oxidation, when the biofilm thickness decreases. The model-derived maximum growth rate of anode respiring Geobacter biofilms of 0.022-0.029 h-1 (Figure 1B) is in the range of other reported anaerobic growth rates based on acetate, e.g. of 0.010-0.018 h-1 [55, 56] Another interesting 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,

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the metabolic efficiency remained nearly constant ( fcat = 2.2 - 2.3) during the course of the experiment (Figure 1B), since the biofilm was relatively thin and thus no external factors were limiting (e.g. acetate diffusion, pH, redox potential and biofilm matrix conductivity). However, when acetate is depleted, the maintenance requirements dominate the metabolism, leading to a remarkable increase in fcat and biofilm shrinkage (Figure 1B). When fitting the model to the measured current-time curve in an iterative approach a number of available input parameters were varied. Thereby the fitting of maximum current density and duration of the current production in a certain fed-cycle were main fitting criteria. Generally, the following parameters could play a role in the metabolic activity and thus current production of electroactive microbial biofilms: (i) concentration of cytochromes (i.e. redox centres) in the biofilm ( CR/RH ), (ii) substrate

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affinity constant ( K Ac- ), (iii) electron transfer kinetics ( kc0 , ke0 ), (iv) biofilm conductivity (  M ) and (v) intracellular electron transfer kinetics ( kf,m , kr,m ).

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The cytochrome concentration in the biofilm is clearly a critical and sensitive model parameter. Low cytochrome concentrations slow down the biofilm growth and subsequently lower also the current production (Figure 1C-D). For a detailed discussion about cytochrome concentration see Section 3.3: Concentration of redox active centres. Furthermore, cytochrome concentration is directly linked to the biomass concentration within the biofilm and thus influences the resulting biofilm thickness and the current production (Figure SI 2E-F). Biomass concentration in electroactive microbial biofilms shows strong variability among cultivation conditions [57, 58] and therefore we used a accepted standard value for anaerobic biofilms [53]. From the qualitative estimation based on the model results compared with current data (see Figure 1A and 1C-D), the cytochrome concentration used in the following was 300 mM. This obtained value is in the same order of magnitude compared to values calculated and derived from Esteve-Núñez et al. [59] (Fore details please see SI 1.3). Other parameters show only a minor impact on the biofilm growth and current production. Alterations of the heterogeneous electron transfer rate ( kc0 ) by several orders of magnitude compared to the literature values [48] show no remarkable change in the biofilm growth and current production (Figure 1E-F). Only if the heterogeneous electron transfer rate was unrealistically decreased to 10 -7 s-1 it would become growth limiting (Figure 1F). In contrast, alterations in the heterogeneous electron transfer rate kc0 have a considerable effect during cyclic voltammetry, as it is shown in section 3.3. Likewise, the homogeneous electron transfer rate (cell/biofilm, ke0 ) and the biofilm conductivity do not reveal a significant effect on the biofilm growth (Figure S1) within the studied range of value. The metabolic parameters remained untapped in the calibration of the model due to the lack of input parameters. So far, 9

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the metabolism of Geobacter is not comprehensively described and no data about enzyme turnover rates and Michaelis-Menten constants of enzymes are available. Hence, the model focused on electrochemical parameters to help in the interpretation of recent experimental data. Nevertheless, the parameter testing on several metabolic properties (intracellular electron transfer ( kf,m , kr,m ), half-saturation coefficient for acetate ( K Ac- ), biomass concentration ( CF,X )) revealed also a great influence on the model calculations (SI Figure S2). A faster intracellular electron transfer increased the biofilm growth (SI Figure S2A-D) but an increased halfsaturation coefficient for acetate slowed down growth and current production (SI Figure S2E-F).

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3.2. Spatial resolution on the biofilm level In addition to macroscopic variables, i.e., current production, coulombic efficiency, biofilm thickness, the model also reveals biofilm properties at the micro scale, i.e., concentration profiles, pH, redox potential along the biofilm depth. The micro scale properties, however, are often more difficult to be obtained experimentally. Figure 2A,C shows experimental results reported by Franks et al. [60] on the pH profile in Geobacter biofilms of a given thickness (70 µm) during anodic respiration, conditions in which a current density of 2.2 A m-2 was reached. The pH profile was calculated with the model for the same current density, but at different buffer compositions (detailed parameters in Table S2), mimicking the flow chamber experiments from [60]. While the pH remains almost constant in the bulk liquid, a pH gradient builds up in the biofilm, which increases with a lower buffer capacity (Figure 2A). Furthermore, an important factor determining solute profiles in the biofilm is the attenuation of diffusion coefficients within the biofilm compared with those in water (i.e., an "effective" diffusion coefficient in the biofilm). Simulations presented in Figure 2C show how decreased diffusivities of all chemical species can lead to substantial acidification at the electrode surface, for the same bulk electrolyte solution. However, a comparison between modelled and measured pH can only remain here at a qualitative level, because: (i) the effective diffusion coefficient is likely to change as a function of biofilm density [61], (ii) the solution speciation depends in reality on dissociation equilibria of 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. Here Figure 2. The redox gradient, i.e. ratio of oxidized and reduced cytochromes, for which contradictory experimental data exist [62-66], is of special interest for microbial electrodes and so far not modeled for a biofilm possessing metal-like conductivity. 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 gradients1, i.e. indicates if redox gradients will arise. A few model approaches already focused on soluble electron mediators using Fick’s diffusion and Nernst-Planck’s electromigration for these solutes and therefore for electron transport and reported electron mediator gradients of concentration [34, 41]. For direct electron transfer two hypotheses exist: electron hopping and metal-like conductivity. An electron hopping approach with fixed electron mediators (e.g. similar to a redox-polymer [67, 68]) and a respective electron diffusion coefficient was used by Strycharz et al. and resulted in the occurrence of redox gradients due to limiting electron transfer between the bound 10

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mediators [40]. Experimental and modeling results from Richter et al. support this modeling approach, but these studies also suggest that the homogeneous electron transfer is limited by the diffusion of counter ions within the biofilm [25, 40]. An alternative to Fick’s law for modeling “diffusive” electron transport is Ohm’s law of conductivity. Only Marcus et al. and Fischer et al. used this approach for modeling the electron transfer performing electric conduction within the biofilm but did also not comment on the evolution of redox gradients [39, 50]. In the model presented here, based on metal-like conductivity, the electron transfer is driven by an electric field and with the parameters derived from literature (Table 1) no redox gradients arise, i.e. gradients of the ratio of oxidized and reduced cytochromes (Figure 2B, D and SI Figure S3, S4). In the following, several model parameters were tested to reveal potential factors influencing the redox gradient. For instance, the standard heterogeneous electron transfer rate ( kc0 ) of the “electron gates” at the electrode surface is supposed to play a key role, as this may limit the electron flow in the biofilm layers more distant to the electrode surface. Within the wide range of values tested, the heterogeneous electron transfer rate to the electrode limited the biofilm growth and microbial metabolism only, if drastically decreased (Figure 1E-F). Even then, almost no redox gradients arise (SI Figure S4A-B) across a 12 µm thick biofilm. Only if the biofilm becomes remarkably thicker and the heterogeneous electron transfer rate is slower than experimentally measured [48], reduced cytochromes accumulate near the electrode and a redox-gradient evolves (SI Figure S3A-B). Certainly, other parameters could impact the formation of redox profiles in reality. For instance, buffer conditions and the diffusion of ions within the biofilm (especially protons) and consequently the pH profile inside the biofilm influences slightly the ratio of oxidized and reduced cytochromes (Figure 2B, D). Therefore, not the electron, but the counter ion (mainly H+) transport may govern the overall activity, which is in line with indications from several experimental studies [69]. One also may speculate that the biofilm conductivity is crucial for the formation of a redox gradient. However, even a decrease of the biofilm matrix conductivity to semiconductor-like values led to only a minor redox gradient (SI Figure S3C). These model results support recent experiments, which also did not lead to observable redox gradients and subsequently assumed other bottlenecks for current production in Geobacter based biofilms, i.e. metabolic constraints or different control mechanisms for electron flow between pure and mixed Geobacter spp. cultures [62]. Nevertheless, it is still subject of investigation whether electron hopping or metal-like conductivity is the mechanism for electron transfer within a specific biofilm. Although the proposed biofilm model is based on metal-like conductivity and as such it shows no redox gradients, other models based on different electron transfer modes may lead to redox gradients. Thus, a coupling of the presented metabolic calculations with electron hopping as alternative mode of EET could help clarifying this open question in future. 3.3. Biofilm electron transfer One frequently used method to study the mechanisms of microbial extracellular electron transfer is cyclic voltammetry (CV) [70]. CV has been applied in several studies to Geobacter based biofilms [31, 70, 71] and models to interpret cyclic voltammograms have been developed [25, 40, 41], for both turnover and nonturnover conditions (i.e. voltammetries obtained in the presence and absence of the microbial substrate, respectively). The introduced modeling framework can also be used for modeling cyclic voltammograms and to study microbial electron transfer properties. In the following the results of its application on a set of non-turnover CV 11

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curves from the recent study of Jana et al. [72] harboring a comprehensive data set for thin (5 µm) and thick (50 µm) biofilms (Figure 3A and Figure 3B respectively), and turnover CV data from Fricke et al. [70] (Figure 4A-B) are shown. These studies were chosen in order to fulfill the criteria of comparability with the model set-up, because for planar electrodes the geometric area can be easily used as an input parameter. Most other studies used 3D electrodes (foam, fiber brush) for the experiments (e.g. [73-75]), which cannot be directly used because it leads to the question, how bacterial accessible surface area is defined. The fitting criteria used to calibrate the model parameters using these sets of data included: (i) peak current densities, (ii) formal potential (in turnover CV), or the oxidation and reduction peak potentials (in non-turnover CV), (iii) the area of the respective oxidation and/ or reduction peak in turnover CVs (this area is directly related to the number of cytochromes involved in the dynamic electron transfer process in non-turnover conditions) and (iv) the peak separation from the formal potential (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 testing was performed. The parameters found to be most important for the correct model description of turnover as well as non-turnover CVs were: (i) the concentration cytochromes, i.e. redox centres, in the biofilm ( CR/RH , Figures 4E-F and 5C) and (ii) the

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heterogeneous electron transfer rate ( kc0 , Figures 4G-H and 5D). Concentration of redox active centres. Interestingly, to obtain a reasonable representation of both the voltammetric peak areas and peak current densities for the modeled CVs (Figure 3 A-B, 5A), the concentration of cytochromes had to be lowered to 3 mM (non-turnover) and 1 mM (turnover), compared to the necessary 300 mM when modeling biofilm growth (see section 3.1). This indicates that only a certain "share" of the redox centers participate in the electron transfer during CV measurements, i.e. they are available for fast responses when using voltammetry. In turnover CVs the concentration of cytochromes does not change considerably the peak currents, but has a significant impact on the formal potential (Figure 4C) and promotes the occurrence of a peak pair centered at ~ 0 V (vs. SHE) superimposed to the turnover CV-curve (Figure 4C). This phenomenon also appears with faster scan rates for a constant cytochrome concentration (Figure 4F). As previously reported [40], this peak pair may be associated to slow acetate oxidation that is limiting catalytic current production. In this context Strycharz et al. also speculate that rather other intracellular processes, i.e. reduction of the cytochrome pool, may limit current generation and that substrate oxidation is comparable fast [40]. Within the current model the electron transfer limitation related to the peak formation was caused by substrate oxidation rather than by internal electron transfer (SI Figure S7). Further, one may speculate that the periplasmic pool of redox compounds, e.g. quinones, acts as a redox buffer between the cell and the terminal transfer proteins to the electrode [76]. The fact that differing cytochrome concentrations are needed to represent biofilm growth, turnover CVs and non-turnover CVs - while all other intrinsic parameters are constant - leads to another important question: What are the “active” redox centres, i.e. these that can exchange electrons with the electrode, during a certain electrochemical measurement? For simplicity reasons this modeling platform considered only one species of a c-type cytochrome possessing one mid-point potential, and transferring one electron per molecule at a time, as cellular redox centres. In reality, Geobacteraceae are known 12

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for producing more than 100 different types of cytochromes (with most cytochromes possessing more than one electron binding haem domains) [77] and different electron transfer mechanism, e.g. 1H+/ 1e- mechanisms or 1H+/ 2emechanisms. Recent experimental data suggest that several respiratory pathways with different cytochromes exist in parallel. Each pathway is able to transfer electrons to an external electron acceptor in accordance to the applied anode potential [78, 79]. Furthermore, the amount of cytochromes may change with biofilm age and vary over the biofilm thickness [18, 80] and cytochromes can have different functions within the microbial cell. Generally, in addition to their role in extracellular electron transfer, cytochromes are involved in further metabolic pathways and there indications for charge storage function within the biofilm [81]. Further on, other redox carriers like the quinone pool are involved, being only in contact with the electrode via a chain of redox carriers. All these redox carriers possess not only individual formal potentials, but also specific electron transfer rates etc. As a consequence a certain species of cytochrome will only exchange electrons with the electrode (i.e. be responsive to the measurement) when the driving force (i.e. the electrode potential) as well as the time needed for electron transfer is sufficient. As more data becomes available, the model could be extended with different numbers and types of cytochromes (with different redox potentials) and additional internal electron transfer processes, so that more complex non-turnover CV shapes can be obtained than those in Figures 3A-B. Electron transfer rate. The heterogeneous electron transfer rate ( kc0 ) does, within the

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range of 0.001 s-1 to 10 s-1, not alter the biofilm growth (Figure 1E-F). The value kc0 = 0.03 s-1, reported in [48] and used for modeling biofilm growth and current production (Section 3.1), did not result in good description of the CV experiments. Only using values of about 1.2 s-1 for the heterogeneous electron transfer rate (similar to the homogeneous electron transfer rate coefficient) provided a reasonable agreement with the experimental data (Figure 3A-D and Figure 4A-B). In turnover CV curves the formal potential of the cytochromes is shifted to more positive values the slower the heterogeneous electron transfer rate is set (Figure 4D). The same observations are made for the homogeneous (cell/biofilm) electron transfer rate ( ke0 , Figure 4E). However, kc0 and ke0 considerably change the electrochemical reversibility, expressed in peak separation in non-turnover CV curves (Figure 3G-H and Figure S5A-B). Most voltammetric studies do only allow to get access to the apparent electron transfer rate [31, 70, 71] and only a few studies describe kinetic mechanisms that can distinguish between homogeneous and heterogeneous electron transfer [48]. The electron transfer rate depends on other factors as well, including for instance the electrode material [82], its crystallographic orientation, or the different electron tunneling distance between the electrode and the iron centre [83]. Therefore, the model should be adapted for a more detailed description of the extracellular electron transfer process. It was also found that biofilm matrix conductivity (  M ) could influence the outcome of the modeled voltammetric response, but only when approaching semiconductor-like values [84] (Figure 3I-J and SI Figure S6C). It is obvious that a thicker biofilm produces more current (Figure 3 and SI Figure S6A), but it also shifts the formal potential to more positive values due to the build-up of ohmic resistance in the biofilm (SI Figure S6B, e.g. [25]). 13

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A modeling framework for microbial anodes composed of electroactive microbial biofilms based on direct electron transfer was developed and used for interpretation of experimental observations on Geobacter based biofilms from several independent sources focusing on electrochemical data, as the kinetics of the metabolism of Geobacter is not comprehensively described and metabolic parameters could not be included extensively The novelty of the proposed model consists in its combined description of biofilm growth and performance at constant electrode potentials with a voltammetric characterization (i.e. dynamic potential conditions). It is shown that during biofilm growth under previously reported experimental conditions no redox gradients and only weak pH gradients should form. Furthermore, while for growth conditions the heterogeneous electron transfer rate is not a sensitive parameter, when modeling CVs this rate has to be within the range of the homogeneous electron transfer rate. In general, the concentration of cellular redox carriers (here denominated as cytochromes) proved to be the most sensitive parameter and therefore the key for data fitting. Thereby the concentration of “active” (i.e., “electrochemically accessible”) redox carriers that participate in the heterogeneous electron transfer to the electrode differs strongly between constant potential and voltammetric conditions. This may imply that an important share of the cellular redox carriers may act solely as "electron pool" that can only release/ accept electrons at lower rates than the rate of the extracellular electron 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 of anodes of complex geometries, with biofilms composed of a diverse microbiomes and thus complex food webs, as well as DET-based cathodes, and full bioelectrochemical systems.

Acknowledgments F.H. acknowledges support by the BMBF (Research Award “Next generation biotechnological processes - Biotechnology 2020+”) and the Helmholtz-Association (Young Investigators Group). This work was supported by the Helmholtz-Association within the Research Programme Renewable Energies.

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[77] B.A. Methe, K.E. Nelson, J.A. Eisen, I.T. Paulsen, W. Nelson, J.F. Heidelberg, D. Wu, M. Wu, N. Ward, M.J. Beanan, R.J. Dodson, R. Madupu, L.M. Brinkac, S.C. Daugherty, R.T. DeBoy, A.S. Durkin, M. Gwinn, J.F. Kolonay, S.A. Sullivan, D.H. Haft, J. Selengut, T.M. Davidsen, N. Zafar, O. White, B. Tran, C. Romero, H.A. Forberger, J. Weidman, H. Khouri, T.V. Feldblyum, T.R. Utterback, S.E. Van Aken, D.R. Lovley, C.M. Fraser, Genome of Geobacter sulfurreducens: metal reduction in subsurface environments, Science, 302 (2003) 1967-1969. [78] C.E. Levar, C.H. Chan, M.G. Mehta-Kolte, D.R. Bond, An inner membrane cytochrome required only for reduction of high redox potential extracellular electron acceptors, MBio, 5 (2014) e02034. [79] R.A. Yoho, S.C. Popat, C.I. Torres, Dynamic Potential-Dependent Electron Transport Pathway Shifts in Anode Biofilms of Geobacter sulfurreducens, Chem. Sus. Chem., 7 (2014) 3413-3419. [80] A.E. Franks, R.H. Glaven, D.R. Lovley, Real-time spatial gene expression analysis within current-producing biofilms, Chem. Sus. Chem., 5 (2012) 1092-1098. [81] N.S. Malvankar, T. Mester, M.T. Tuominen, D.R. Lovley, Supercapacitors Based on cType Cytochromes Using Conductive Nanostructured Networks of Living Bacteria, Chem. Phys. Chem., 13 (2012) 463-468. [82] K.J. Vetter, Electrochemical kinetics: theoretical and experimental aspects, Academic Press Inc., 1968. 20

ACCEPTED MANUSCRIPT [83] B. Maestro, J.M. Ortiz, G. Schrott, J.P. Busalmen, V. Climent, J.M. Feliu, Crystallographic orientation and electrode nature are key factors for electric current generation by Geobacter sulfurreducens, Bioelectrochemistry, 98 (2014) 11-19.

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[84] R.A. Serway, J.W. Jewett, Principles of Physics: A Calculus-Based Text 5ed., Cengage Learning, 2013.

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[85] D.R. Lovley, E.J.P. Phillips, Novel mode of microbial energy metabolism organic carbon oxidation coupled to dissimilatory reduction of iron, Appl. Environ. Microb., 54 (1988) 14721480.

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[86] J.K. D.J. Batstone, I. Angelidaki, S.V. Kalyuzhnyi, S.G. Pavlostathis, A. Rozzi,W.T.M. Sanders, H. Siegrist, V.A. Vavilin, Anaerobic Digestion Model No.1 (ADM1), IWA Task Group for Mathematical Modelling of Anaerobic Digestion Processes, IWA Publishing London, 2002.

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[87] X.Y. Yong, J. Feng, Y.L. Chen, D.Y. Shi, Y.S. Xu, J. Zhou, S.Y. Wang, L. Xu, Y.C. Yong, Y.M. Sun, C.L. Shi, P.K. OuYang, T. Zheng, Enhancement of bioelectricity generation by cofactor manipulation in microbial fuel cell, Biosens. Bioelectron., 56 (2014) 19-25.

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[88] J.S. Newmann, Electrochemical System, 2nd ed., Prentice Hall, Englewood Cliffs, NJ, 1991.

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[89] P. Vanysek, CRC handbook of chemistry and physics, 82 ed., CRC Press LLC, Boca Raton, 2001.

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[90] H. Horn, E. Morgenroth, Transport of oxygen, sodium chloride, and sodium nitrate in biofilms, Chem. Eng. Sci., 61 (2006) 1347-1356.

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[91] F. Harnisch, R. Warmbier, R. Schneider, U. Schröder, Modeling the ion transfer and polarization of ion exchange membranes in bioelectrochemical systems., Bioelectrochemistry, 75 (2009) 136-141.

List of figures Scheme 1:

(A) Biochemical reactions and electron transfer of a single cell embedded in the biofilm. The energy gained from acetate oxidation is partly used to build up + biomass (anabolism), partly used in the electron transfer via NAD /NADH and the fixed redox centres (c-type outer surface cytochromes) to the conductive matrix, and partly dissipated. (B) Electron transfer within the biofilm and the electrochemical boundary conditions. There are no molecular fluxes at the

21

ACCEPTED MANUSCRIPT electrode and the electrode potential is fixed to

E A . At the biofilm surface

(biofilm/liquid interface) the conductive biofilm matrix is insulated ( dEM / dx  0 ), the liquid potential EL takes a zero reference value and the

T

biofilm exchanges ions with the bulk liquid. The electrons transferred to the biofilm matrix are collected at the anode surface and result in the current density JA . The red line represents the conductive extrapolymeric biofilm matrix

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IP

performing metal-like conductivity. (C) Bulk liquid in the anode compartment. The anolyte is ideally mixed and cations are exchanged between anode and cathode compartments through a membrane (ion flux, JM,y ). There is exchange of ions and neutral molecules between biofilm and anode compartment

Simulation results of microbial anodes based on direct electron transfer. The Geobacter sulfurreducens biofilm was fed initially with 1 mM acetate and two subsequent substrate additions (1 mM acetate each). (A) Modeled current density (solid line) and experimental data from Bond & Lovley [54] (dotted line). (B) Resulting

NU

Figure 1:

(fluxes JF,y ).

modeled maximum growth rate ( max , dotted blue line), multiplication factor for

fcat , green chain-dotted line), acetate concentration in the bulk liquid ( C Ac- , solid red line) and resulting biofilm thickness ( LF , dashed black line). (C-

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anabolic reaction (

D

D) Simulated current density and biofilm thickness with 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 0

Modeled and experimental pH profiles and the respective redox profiles (profiles of oxidized ( CR ) and reduced cytochromes ( CRH )) for the modelled biofilms. (A-B) Calculated (solid lines) and experimental (dotted line) pH profiles and the corresponding redox profiles (concentration of oxidized ( CR , solid lines) and reduced

CE P

Figure 2

TE

from biofilm to electrode ( kc ). The experimental data are taken from [54] and the model parameters are listed in Table 1 and Table S1.

cytochromes ( CRH , dashed lines)) for biofilms with a constant diffusion attenuation

AC

factor (  D  0.5 ) and different bicarbonate buffer composition ( C0,HCO3-  1 - 50 mM ). 1 mM (orange lines), 5 mM (red lines), 10 mM (green lines), 50 mM (blue lines). (C-D) Calculated (solid lines) and experimental (dotted line) pH profiles and the corresponding redox profiles (profiles of oxidized ( CR , solid lines) and reduced cytochromes ( CRH , dashed lines)) for modelled biofilms with a constant bicarbonate buffer composition ( C0,HCO3-  5 mM ) and different diffusion attenuation factors (  D  0.1 - 0.8 ). 0.1 (orange), 0.2 (red), 0.5 (green), 0.8 (blue). Experimental data are from Franks et al. [60, 85]. The model parameters are listed in Table 1 and Table S2.

Figure 3

Comparison between modeled cyclic voltammograms and experimentally obtained by Jana et al. [72] in the absence of acetate (non-turnover conditions). (A) Thin biofilms (5 µm) and (B) Thick biofilms (50 µm) at different scan rates. Modeled data (solid lines) is compared to experimental data obtained from Jana et al. (dotted lines). -1 -1 -1 -1 5 mV s (blue), 20 mV s (red), 40 mV s (green), 60 mV s (black). Respective peak separation analysis for (C) thin and (D) thick biofilms. Modeled data (solid lines) is compared to experimental data obtained from Jana et al. (dotted lines). (E) Modeled current density with several values for the total cytochrome concentration ( CR/RH ) for a 5 µm biofilm. (F) Modeled current density with several values for the total cytochrome concentration ( CR/RH ) for a 50 µm biofilm. (G) Modeled current density with several

22

ACCEPTED MANUSCRIPT values for the standard heterogeneous electron transfer rate ( kc0 ) in a 5 µm biofilm. (H) Modeled current density with several values for the heterogeneous electron transfer rate ( kc0 ) for a 50 µm biofilm. (I) Modeled current density with various biofilm matrix conductivities (  M ) for a 5 µm biofilm. (J) Modeled current density with

T

various biofilm matrix conductivities (  M ) for a 50 µm biofilm. The solid line in the

MA

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Comparison between simulation results of microbial anodes and results obtained from Fricke et al. [70] in cyclic voltammetry experiments under turnover conditions. (A) Modelled (solid line) and experimental (dashed line) cyclic voltammogram -1 recorded at 5 mV s from 0.5 to -0.5 V vs. SHE. Experimental data is taken from [49]. (B) Corresponding first derivative of the modelled (solid line) and experimental (dashed line) CV. (C) Modeled current density with several values for the total cytochrome concentration ( CR/RH ). (D) Modeled current density with several values for the standard heterogeneous electron transfer rate ( kc0 ). (E) Modeled current density with several values for the standard homogeneous electron transfer rate ( ke0 ).

CE P

TE

D

(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 to Fricke et al. One parameter at the time was varied in the simulations. Model parameters are listed in Table 1 and Table S4.

AC

Figure 4

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parameter analysis indicates the voltammogram obtained with the best fitting set of -1 parameters compared to Jana et al. (scan rate of 60 mV s ). One parameter at the time was varied in the simulations. Model parameters are listed in Table 1 and Table S3.

23

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ACCEPTED MANUSCRIPT

AC

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Scheme 1

24

ACCEPTED MANUSCRIPT

B

A 0.040

2.9

0.030

1.4

+1 mM acetate

12 2.8

0.030

1.2 0.028

0.026

0.024

2.3

0.010

0.022

2.1

SC R

2.2

0.005 0.000 2

4

6

8

t/d

D

C CR/RH = 1 mM CR/RH = 10 mM

0.035

CR/RH = 100 mM

0.030

CR/RH = 300 mM

0.025

LF / m

MA

J / mA cm-2

CR/RH = 1 M

0.020 0.015 0.010

2

0.0 -0.2

4

14

CR/RH = 1 mM

12

CR/RH = 100 mM

10

CR/RH = 1 M

D

0.000 2

4

t/d

6

0

8

t/d

CR/RH = 10 mM CR/RH = 300 mM

8 6 4

0.040

k0c = 10-7 s-1

0 8

0

0.030

k0c = 0.1 s-1 k0c = 1 s-1

0.025

k0c = 10 s-1

0.020

0.010 0.005 0.000 0

2

8

6

8

k0c = 0.001 s-1 k0c = 0.03 s-1

10

k0c = 0.1 s-1 k0c = 1 s-1

8

AC

0.015

6

k0c = 10-7 s-1

12

LF /m

k0c = 0.03 s-1

4

F

k0c = 0.001 s-1

0.035

2

t/d

CE P

E

6

TE

0

k0c = 10 s-1

6 4 2 0

4

6

8

0

t/d

2

4

t/d

Figure 1

25

6 4

2

0.005

J / mA cm-2

2

8

0.2

NU

0.040

0.4

0.020

0

0

0.6

CAc- / mM

2.4

0.015

T

2.5

0.8

IP

0.020

10

1.0

max / h-1

2.6

fcat

J / (mA cm-2)

2.7

0.025

LF / m

0.035

ACCEPTED MANUSCRIPT

A

B 300.0 7.0 299.8

6.4

0.4

0.2

6.2

0.0

6.0 0

10

20

30

40

50

60

0

70

LF /m

C

D

10

20

30

40

50

60

70

80

LF /m

NU

300.0

7.0

299.7

6.8

299.4

MA

CR, CRH / mM

6.6

pH

T

299.6

IP

pH

6.6

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CR, CRH / mM

6.8

6.4 6.2

5.8 10

20

30

40

0.3

0.0

70

0

10

20

30

LF /m

AC

Figure 2

60

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LF / m

50

TE

0

D

6.0

0.6

26

40

50

60

ACCEPTED MANUSCRIPT A

B 1.0

4

0.8 0.6 2

0.0 -0.2

0

T

0.2

J / A m-2

J / A m-2

0.4

-0.4

-0.8 -0.6

-0.4

-0.2

0.0

0.2

-4 -0.8

0.4

EA / V (vs. SHE)

-0.4

-0.2

0.0

0.2

0.4

EA / V (vs. SHE)

C

D

0.20

0.06

0.15

0.04

0.10

0.02

0.05

Ep-E0' / V

0.08

0.00

0.00

NU

Ep-E0' / V

-0.6

SC R

-1.0 -0.8

IP

-2 -0.6

-0.02 -0.04

-0.05 -0.10

-0.06

-0.15

-0.08

-0.20

0.01

0.1

MA

0.001

v / V s-1

E

0.001

0.01

F

40

20

0.1

v / V s-1

15 10

J / A m-2

D TE

J / A m-2

5 0

-5

CR/RH = 1 mM

-20

0

CR/RH = 3 mM

CR/RH = 0.5 mM

CR/RH = 50 mM

CR/RH = 1 mM

-10

CR/RH = 150 mM

-0.6

-0.4

0.0

0.2

-0.2

-0.4 -0.8

AC

0.2

-0.6

-0.4

-0.2

-0.4

-0.2

0.0

4 2

k0C = 0.3 s-1

0 -2

k0C = 0.03 s-1 k0C = 0.3 s-1

-4

k0C = 1.2 s-1

k0C = 1.2 s-1 k = 10 s

0.2

-6

-1

k = 100 s

0.0

0.4

6

k0C = 0.03 s-1

0 C 0 C

0.2

EA / V (vs. SHE)

8

k0C = 10 s-1 k0C = 100 s-1

-1

-8 -0.8

0.4

EA / V (vs. SHE)

I

CR/RH = 10 mM

-0.6

H

J / A m-2

0.4

0.0

CR/RH = 3 mM

-15 -0.8

0.4

EA / V (vs. SHE)

G

J / A m-2

-0.2

CE P

-40 -0.8

CR/RH = 300 mM

-0.6

-0.4

-0.2

0.0

0.2

0.4

EA / V (vs. SHE)

J

0.4

6 4

0.2

J / A m-2

J / A m-2

2 0.0

0 -2

M= 0.00005 mS cm-1

-0.2

M= 0.005 mS cm-1

M= 0.0005 mS cm-1

-0.4 -0.8

M= 5 mS cm

-0.6

-0.4

-0.2

0.0

0.2

M= 0.05 mS cm-1

-4

M= 0.5 mS cm-1

M= 0.5 mS cm-1 M= 5 mS cm-1

-1

-6 -0.8

0.4

EA / V (vs. SHE)

-0.6

-0.4

-0.2

0.0

EA / V (vs. SHE)

Figure 3

27

0.2

0.4

ACCEPTED MANUSCRIPT A

B 80

500 400

20

300 200 100

-0.4

-0.2

0.0

0.2

0.4

-0.4

EA / V (vs. SHE)

D

80

J / A cm-2

60 40

-0.2

0.0

0.2

EA / V (vs. SHE)

k0e = 0.001 s-1

k0c = 100 s-1

0.4

k0c = 10 s-1

50 40 30

k = 0.1 s

-1

k = 1.2 s-1 k = 10 s-1 k = 100 s-1

50 40 30

AC

20

-0.4

-0.2

0 -0.4

-0.2

0.0

EA / V (vs. SHE)

F

100

80

J / A cm-2

0 e 0 e 0 e 0 e

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J / A cm-2

60

0.4

TE

E

0

k0c = 1.2 s-1

D

-0.4

10

0.2

k0c = 0.1 s-1

10

0

60

0.4

20

20

70

0.2

k0c = 10-3 s-1

70

MA

J /A cm-2

CR/RH = 10 mM

80

80

0.0

NU

CR/RH = 1 mM CR/RH = 5 mM

90

90

CR/RH = 0.1 mM CR/RH = 0.5 mM

100

-0.2

EA/ V vs. SHE

C 120

SC R

0

0

140

T

40

IP

J E -1 / arb. units

J /A cm-2

60

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

60

40

20

0 0.0

0.2

0.4

-0.4

EA / V (vs. SHE)

-0.2

0.0

0.2

EA / V (vs. SHE)

Figure 4

28

0.4

ACCEPTED MANUSCRIPT List of Tables

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

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Table 1

29

ACCEPTED MANUSCRIPT Value

Units

K AcKNAD+

0.1

mol Ac- / m3 Chosen

0.1

Standard Gibbs energy catabolic reaction

01 Gcat

32.2

mol NAD+ / Chosen m3 kJ / mol Ac- [52]

Standard Gibbs energy anabolic reaction

Gan01

29.56

Maximum Gibbs energy dissipation in metabolism Acid-base reactions Equilibrium constants - water dissociation

max Gdiss

-432

KOHKHCO3K AcKHPO4-2

- CO2 hydrolysis - acetic acid dissociation Rate constants - water dissociation

kJ / C-mol X [52] kJ / C-mol X [52]

10-14

mol2 / L2

[86]

10-6.6

mol / L

[86]

10

mol / L

[86]

10-7.21

mol / L

[86]

-4.756

MA

- H2PO4- dissociation

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Half-saturation coefficient for acetate

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Microbial kinetics and thermodynamics Half-saturation coefficient for acetate

Source

T

Symbol

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Parameter description

108 kOH7 kHCO3- , kAc- , kHPO4-2 10

1/s

AC

CE P

TE

D

- CO2, acetic acid and H2PO4dissociation Electrochemical kinetics and electrical properties Standard (homogeneous) electron transfer k 0 e rate (cell / biofilm conductive matrix) Standard (heterogeneous) electron transfer k 0 c rate (biofilm / electrode) Forward rate for the intracellular electron kf,m transfer from NADH to redox centres Reverse rate constant for the intracellular kr,m electron transfer from redox centres to NADH Standard redox potential of the redox ERθ' centres  Transfer coefficient for redox rate Length of direct biofilm/electrode electron L h transfer layer Electrode potential E

mol / m3 s

Arbitrarily large value Arbitrarily large values

1.2

1/s

[48]

0.03

1/s

[48]

3 107

m9 / mol3 s

Chosen

1 10-10

m6 / mol2 s

Chosen

-0.136

V (SHE)

[70]

0.5 1

m

b

V (SHE)

Chosen length of a typical microbial cell variable by caseb

A

Biofilm matrix conductivity

M

0.5

S/m

[21]

Biofilm properties Initial biofilm thickness

LF0

b

m

variable by caseb

Biomass concentration in the biofilm

CF,X

2000

C-mol / m3

Concentration oxidized/reduced redox centres

3

Concentration NAD+/NADH

CNAD+/NADH

20

mol / m3

Chosen for Chronoamperometry Chosen for Cyclic voltammetry Adapted from [87]

Biofilm area and electrode area

AA

b

cm2

variable by caseb

CR/RH

30

300

mol / m

1, 3

mol /m3

Chosen

ACCEPTED MANUSCRIPT Diffusion coefficients in water - acetate

- Cl+

2 2.0 10-9 m / s

[88, 89]

1.3 10-9 m / s

[88, 89]

T

9.3 10

-9

2

[88, 89]

2

5.3 10-9 m / s

[88, 89]

1.9 10

2

m /s

[88, 89]

2 1.2 10-9 m / s

[88, 89]

1.2 10

m /s

[88, 89]

2 1.0 10-9 m / s

[88, 89]

0.5

-

[90]

b

L

variable by caseb

C0,Ac-,T

b

mol / m3

variable by caseb

C0,HCO3-,T

b

mol / m3

variable by caseb

C0,H2PO4-,T

b

mol / m3

variable by caseb

C 0,Cl-

5

mol / m3

Chosen

SC R

-9

MA

-7

-9

2

C0,H+

10

mol / L

if not stated otherwiseb

Transport through membrane Membrane area

AM

2

cm2

Chosen

Diffusion coefficients in membrane - H+

DM,H+

2 5.310-10 m / s

[91]

DM,Na+

2 2.110-10 m / s

[91]

LM

100

- Na+

AC

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-H

[88, 89]

2

D

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- total phosphate

2 1.3 10-9 m / s

m /s

VB

Initial concentrations in bulk liquid and biofilma - total acetate - total carbonate

[88, 89]

NU

the biofilm Bulk liquid Bulk liquid volume

2 1.1 10-9 m / s

IP

DAc- acetic acid DAcH - Cl DCl+ - Na DNa+ + -H DH+ - OH DOH- CO2 DCO2 - HCO3 DHCO3- H2PO4 DH2PO42- HPO4 DHPO4-2 Reduction factor for diffusion coefficient in  D

Membrane thickness

Membrane electric permittivity Ion concentration in the cathodic solution - H+ - Na+ Other constants Faraday constant Universal gas constant Work temperature

a

M

m

[91]

1.810-10 F / m

[91] 3

Chosen Chosen

CC,H+

C 0,H+

mol / m

CC,Na+

C0,Na+

mol / m3

F R T

96485.34 C / mol 8.31 J / mol K 298 K

if not stated otherwiseb

The other initial concentrations result from electroneutrality ( C0,Na+ ), mole balances and

equilibrium relations ( C 0,AcH , C 0,Ac- , C0,CO2 , C0,HCO3- , C0,H2PO4- , C0,HPO4-2 , C0,OH- ). b These values have been adapted for the respective example (see individual results and respective SI)

31

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ACCEPTED MANUSCRIPT

AC

CE P

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D

Graphical abstract

32

ACCEPTED MANUSCRIPT Highlights

T

IP SC R NU MA D TE CE P



A modeling platform for direct electron transfer (DET) biofilms was developed Both constant and dynamic potential conditions can be described Model Geobacter anodes were compared to different experiments The concentration of cytochromes plays a key role for describing experimental data Different shares of cytochrome may be "active" during CA (300 mM) and CV (3 mM)

AC

   

33