Advertisement

Modeling Microbial Electrosynthesis

  • Benjamin Korth
  • Falk Harnisch
Chapter
Part of the Advances in Biochemical Engineering/Biotechnology book series (ABE, volume 167)

Abstract

Mathematical modeling is an overarching approach for assessing the complexity of microbial electrosynthesis (MES) and for complementing the relevant experimental research. By describing and linking compartments, components, and processes with appropriate mathematical equations, MES and the corresponding bioelectrodes and complete bioelectrochemical systems can be analyzed and predicted across several temporal and local scales. Thereby, insights into fundamental phenomena and mechanisms, in addition to process engineering and design can be obtained. However, a substantial lack of knowledge about extracellular electron transfer mechanisms and electrotrophic microorganisms presumably prevented the development of adequate models of MES, especially of biocathodes, so far. To propel efforts regarding this demanding task, this chapter provides a comprehensive overview of the relevant compartments, components and processes, appropriate model strategies, and a discussion on potential modeling pitfalls. By adapting an established approach to assessing the energetics of microorganism, an instruction for calculating stoichiometry, thermodynamics, and kinetics, with the example of electro-autotrophic growth at cathodes, is presented. Models of bioanodes and fundamental electrochemical equations are described to provided strategies for calculating cathodic electron-uptake reactions and connecting them to the microbial metabolism. Finally, differential equations are detailed for coupling the distinct compartments of a bioelectrochemical system. Although MES comprises anodic and cathodic reactions, the present chapter focuses on biocathodes representing a functional connection between cathode and electron-accepting microorganisms.

Graphical Abstract

Keywords

Autotrophy Biocathode Cathodic extracellular electron transfer Microbial electrochemical technologies Microbial fuel cells 

List of Symbols

AC

Cathode area, m2

AG

Gas–liquid–interface area, m

α

Charge transfer coefficient

\( {C}_{F,i}^0 \)

Initial concentration of the ith component in the inflow of a chemostat, mol m−3

Ci

Concentration of the ith component, mol m−3

CA, i

Concentration of the ith component in the anodic reactor volume, mol m−3

CB, i

Concentration of the ith component within biofilm, mol m−3

CC, i

Concentration of the ith component in cathodic bulk volume, mol m−3

CG, i

Concentration of the ith component in the gas phase, mol m−3

CDBL, i

Concentration of the ith component in the diffusion boundary layer, mol m−3

CFeed, i

Concentration of the ith component in added liquid during a fed-batch process, mol m−3

CX

Biomass concentration, C-mol m−3

CX, i

Concentration of the ith biomass fraction, C-mol m−3

DB, i

Diffusion coefficient of the ith component within the biofilm, m2 s−1

DDBL, i

Diffusion coefficient of the ith component within the diffusion boundary layer, m2 s−1

Det

Effective electron diffusion coefficient, m2 s−1

DM, i

Diffusion coefficient of the ith component through the membrane, m2 s−1

E0

Standard potential for biochemical standard conditions (1 mol L−1 of respective reactants, 298.15 K, 101.325 kPa, pH = 7), V

EB

Potential of the conductive biofilm matrix, V

EC

Cathode potential, V

\( {E}_i^f \)

Formal potential of the ith component, V

EKA

Potential for the half-maximum rate, V

EL

Potential of the liquid phase within the biofilm, V

\( {E}_{\mathrm{MED}}^{0\prime } \)

Standard potential of redox mediators for biochemical standard conditions (1 mol L−1 of respective reactants, 298.15 K, 101.325 kPa, pH = 7), V

ε0

Dielectric constant of the vacuum, 8.85 × 10−12 F m−1

εM

Dielectric constant of the membrane, F m−1

F

Faraday constant, 96,485.34 C mol−1

fCat

Multiplication factor for catabolic reaction

FFlow

Flow rate, m3 s−1

ΔG

Gibbs free energy, kJ mol−1

ΔfG0

Standard Gibbs free energy of formation for biochemical standard conditions (1 mol L−1 of respective reactants, 298.15 K, 101.325 kPa, pH = 7), kJ mol−1

ΔRG0

Standard Gibbs free energy of reaction for biochemical standard conditions (1 mol L−1 of respective reactants, 298.15 K, 101.325 kPa, pH = 7), kJ mol−1

ΔRGAn

Gibbs free energy of the anabolic reaction, kJ mol−1

ΔRGCat

Gibbs free energy of the catabolic reaction, kJ mol−1

ΔGDiss

Gibbs free energy dissipation, kJ mol−1

ΔH

Enthalpy, kJ mol−1

ΔfH0

Standard enthalpy of formation for biochemical standard conditions (1 mol L−1 of respective reactants, 298.15 K, 101.325 kPa, pH = 7), kJ mol−1

ΔRH0

Standard enthalpy of reaction for biochemical standard conditions (1 mol L−1 of respective reactants, 298.15 K, 101.325 kPa, pH = 7), kJ mol−1

Hcp

Henry’s law proportionality coefficient defined via concentration and partial pressure, mol m−3 Pa−1

j

Current density, A m−2

j0

Exchange current density, A m−2

JB, i

Flux of the ith component at interface biofilm/cathodic reactor volume, mol m−2 s−1

JG, i

Flux of the ith component at gas–liquid interface, mol s−1

JM, i

Flux of the ith component through membrane, mol m−2 s−1

JMed, x

Flux of redox mediators at layer x, mol m−2 s−1

\( {k}_{\mathrm{Het}}^0 \)

Standard (heterogeneous) electron transfer rate constant at biofilm–electrode interface, s−1

kf, kr

Forward and reverse reaction rate constants for chemical equilibrium reactions, s−1

kL

Liquid-phase mass transfer coefficient, mol m−2 s−1

kox, kred

Electron transfer rate constants for the oxidation and reduction rate in the Butler–Volmer equation, cm s−1

KAH/A−

Equilibrium constant for the acid-base pair AH/A

Ki

Monod affinity constant of the ith component, mol m−3

K1,K2

Parameters in the Butler–Volmer–Monod equation

κB

Biofilm matrix conductivity, S m−1

LB

Biofilm thickness, m

LH

Thickness of the cell layer directly in contact with the electrode, m

LM

Membrane thickness, m

Mi

Added ith component in a continuous flow or fed-batch mode, mol m−3 s−1

mS

Substrate specific maintenance rate, mol C-mol−1 s−1

μmax

Maximum growth rate, s−1

μ

Growth rate, s−1

NC

Number of carbon atoms in the carbon source

ni

Amount of the ith component, mol

η

Overpotential, V

pi

Partial pressure of the ith component, Pa

\( {q}_i^{\mathrm{max}} \)

Maximum biomass-specific uptake rate of the ith component, mol C-mol−1 s−1

pKA

Logarithmic acid dissociation constant

qi

Biomass-specific uptake rate of the ith component, mol C-mol−1 s−1

R

Universal gas constant, 8.31 J mol−1 K−1

req, i

Chemical equilibrium rate of the ith component, mol m−3 s−1

ri

Total conversion rate of the ith component, mol m−3 s−1

rB, i

Net rate of the ith component within the biofilm summarizing all rates, mol m−3 s−1

rDecay

Biomass decay rate, C-mol m−3 s−1

rMed,Ox

Total redox mediator oxidation rate, mol m−3 s−1

rMed,Red

Total redox mediator reduction rate at the cathode, mol s−1

rCyt,Red

Reduction rate of cytochromes within the biofilm, mol m−3 s−1

rX

Biomass production rate, C-mol m−3 s−1

ΔS

Entropy, kJ mol−1

t

Time, s

T

Temperature, K

TS

Standard temperature, 298.15 K

uX

Velocity of the biofilm thickness increase, m s−1

uB

Velocity of the biofilm surface increase, m s−1

VC

Cathodic reactor volume, m3

VFeed

Volume of added liquid, m3

vi

Stoichiometric factor of the ith component

Yi

Stoichiometric factor of the ith component in the overall growth reaction, mol C-mol−1

γD

Degree of reduction of the carbon source

x

Distance of a layer within biofilm or the diffusion boundary layer from the cathode, x = 0 is designated as the cathode surface, m

xi

Mole fraction of the ith compound

z

Number of transferred electrons

zi

Charge of the ith component

Notes

Glossary

Boundary condition

Allocation of a defined value (Dirichlet boundary condition, e.g., concentration) or of a derivative of a solution (Neumann boundary condition, e.g., flux) to the border between a compartment and the external world or to a border between two compartments to connect these compartments.

Compartment

Defined one-, two- or three-dimensional section of a model (e.g., biofilm and reactor volume) with specifically assigned parameters and variables.

Component

A charged or uncharged chemical species (e.g., acetate, bicarbonate, redox mediator, other ions) or sum of chemical species (e.g., biomass).

Educt

Starting component of a chemical reaction.

Flux

Transport phenomenon describing the rate of movement of a component per area (e.g., flux of a component through a membrane).

Global

A parameter/variable valid for all compartments of a model.

Grid

Entirety of spatial fragments constituting a compartment and defining the spatial resolution of the compartment.

Local

A parameter/variable valid only for a certain compartment of the model.

Locality

Specific position (x, y, z) within a compartment.

Mass balance

Equation that considers all transport and transformation reactions of a component and thus fulfills the conservation of mass. Needs to be established for every component in every compartment.

Parameter

A given value for biological/physical/chemical processes or properties.

Product

End component of a chemical reaction.

Reactant

Starting or end component of a chemical reaction.

Reactor volume

Denotes the cathodic compartment of a bioelectrochemical system in this chapter.

Transformation

Process changing the chemical nature of a component (e.g., chemical equilibrium reaction, oxidation, biomass synthesis).

Transport

Process changing the position of a component (e.g., diffusion and migration).

Variable

A value for biological/physical/chemical processes or properties calculated according to local parameters and variables (e.g., local concentrations, temperature).

References

  1. 1.
    National Research Council (1990) Ground water models: scientific and regulatory applications. Press NA, Washington, DCGoogle Scholar
  2. 2.
    Wanner O, Eberl HJ, Morgenroth E, Noguera DR, Picioreanu C, Rittmann BE, van Loosdrecht MCM (2006) Mathematical modeling of biofilms. Scientific and Technical Report no 18. IWA PublishingGoogle Scholar
  3. 3.
    Schröder U, Harnisch F, Angenent LT (2015) Microbial electrochemistry and technology: terminology and classification. Energy Environ Sci 8(2):513–519.  https://doi.org/10.1039/c4ee03359k CrossRefGoogle Scholar
  4. 4.
    Nevin KP, Woodard TL, Franks AE, Summers ZM, Lovley DR (2010) Microbial electrosynthesis: feeding microbes electricity to convert carbon dioxide and water to multicarbon extracellular organic compounds. MBio 1(2):e00103-10.  https://doi.org/10.1128/mBio.00103-10 CrossRefPubMedPubMedCentralGoogle Scholar
  5. 5.
    Rabaey K, Rozendal RA (2010) Microbial electrosynthesis – revisiting the electrical route for microbial production. Nat Rev Microbiol 8(10):706–716.  https://doi.org/10.1038/nrmicro2422 CrossRefPubMedGoogle Scholar
  6. 6.
    Kazemi M, Biria D, Rismani-Yazdi H (2015) Modelling bio-electrosynthesis in a reverse microbial fuel cell to produce acetate from CO2 and H2O. Phys Chem Chem Phys 17(19):12561–12574.  https://doi.org/10.1039/c5cp00904a CrossRefPubMedGoogle Scholar
  7. 7.
    Kracke F, Krömer JO (2014) Identifying target processes for microbial electrosynthesis by elementary mode analysis. BMC Bioinformatics 15:410.  https://doi.org/10.1186/s12859-014-0410-2 CrossRefPubMedPubMedCentralGoogle Scholar
  8. 8.
    Pandit AV, Mahadevan R (2011) In silico characterization of microbial electrosynthesis for metabolic engineering of biochemicals. Microb Cell Factories 10(76):1–14.  https://doi.org/10.1186/1475-2859-10-76 CrossRefGoogle Scholar
  9. 9.
    Marcus AK, Torres CI, Rittmann BE (2007) Conduction-based modeling of the biofilm anode of a microbial fuel cell. Biotechnol Bioeng 98(6):1171–1182.  https://doi.org/10.1002/bit.21533 CrossRefGoogle Scholar
  10. 10.
    Picioreanu C, Head IM, Katuri KP, van Loosdrecht MC, Scott K (2007) A computational model for biofilm-based microbial fuel cells. Water Res 41(13):2921–2940.  https://doi.org/10.1016/j.watres.2007.04.009 CrossRefPubMedGoogle Scholar
  11. 11.
    Zhang X-C, Halme A (1995) Modelling of a microbial fuel cell process. Biotechnol Lett 17(8):809–814.  https://doi.org/10.1007/BF00129009 CrossRefGoogle Scholar
  12. 12.
    Flynn JM, Ross DE, Hunt KA, Bond DR, Gralnick JA (2010) Enabling unbalanced fermentations by using engineered electrode-interfaced bacteria. MBio 1(5):e00190–e00110.  https://doi.org/10.1128/mBio.00190-10 CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    Do TQN, Varničić M, Hanke-Rauschenbach R, Vidaković-Koch T, Sundmacher K (2014) Mathematical modeling of a porous enzymatic electrode with direct electron transfer mechanism. Electrochim Acta 137:616–626.  https://doi.org/10.1016/j.electacta.2014.06.031 CrossRefGoogle Scholar
  14. 14.
    Volesky B, Votruba J (1992) Modeling and optimization of fermentation processes, vol 1. 1st edn. Elsevier Science, AmsterdamGoogle Scholar
  15. 15.
    Krieg T, Madjarov J, Rosa LFM, Enzmann F, Harnisch F, Holtmann D, Rabaey K (2017) Reactors for microbial electrobiotechnology. In: Harnisch F, Holtmann D (eds) Bioelectrosynthesis. Advances in biochemical engineering/biotechnology. Springer, BerlinGoogle Scholar
  16. 16.
    Picioreanu C, Loosdrecht M, Heijnen J (1998) Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol Bioeng 58:101–116.  https://doi.org/10.1002/(SICI)1097-0290(19980405)58:1<101::AID-BIT11>3.0.CO;2-M CrossRefPubMedGoogle Scholar
  17. 17.
    Leader JJ (2004) Numerical analysis and scientific computation 1st edn. Pearson Education, New YorkGoogle Scholar
  18. 18.
    Hellweger FL, Clegg RJ, Clark JR, Plugge CM, Kreft JU (2016) Advancing microbial sciences by individual-based modelling. Nat Rev Microbiol 14(7):461–471.  https://doi.org/10.1038/nrmicro.2016.62 CrossRefPubMedGoogle Scholar
  19. 19.
    Gimkiewicz C, Hunger S, Harnisch F (2016) Evaluating the feasibility of microbial electrosynthesis based on Gluconobacter oxydans. ChemElectroChem 3(9):1337–1346.  https://doi.org/10.1002/celc.201600175 CrossRefGoogle Scholar
  20. 20.
    Koch C, Harnisch F (2016) What is the essence of microbial electroactivity? Front Microbiol 7:1–5.  https://doi.org/10.3389/fmicb.2016.01890 CrossRefGoogle Scholar
  21. 21.
    Von Stockar U (2013) Biothermodynamics – the role of thermodynamics in biochemical engineering. EPFL Press, LausanneCrossRefGoogle Scholar
  22. 22.
    Von Stockar U, Maskow T, Liu J, Marison IW, Patino R (2006) Thermodynamics of microbial growth and metabolism: an analysis of the current situation. J Biotechnol 121(4):517–533.  https://doi.org/10.1016/j.jbiotec.2005.08.012 CrossRefGoogle Scholar
  23. 23.
    Von Stockar U, Liu JS (1999) Does microbial life always feed on negative entropy? Thermodynamic analysis of microbial growth. Biochim Biophys Acta 1412:191–211.  https://doi.org/10.1016/S0005-2728(99)00065-1 CrossRefGoogle Scholar
  24. 24.
    Maskow T, Paufler S (2015) What does calorimetry and thermodynamics of living cells tell us? Methods 76:3–10.  https://doi.org/10.1016/j.ymeth.2014.10.035 CrossRefPubMedGoogle Scholar
  25. 25.
    LaRowe DE, Amend JP (2015) Power limits for microbial life. Front Microbiol 6:718.  https://doi.org/10.3389/fmicb.2015.00718 CrossRefPubMedPubMedCentralGoogle Scholar
  26. 26.
    Schink B (1997) Energetics of syntrophic cooperation in methanogenic degradation. Microbiol Mol Biol R 61(2):262–280Google Scholar
  27. 27.
    Von Stockar U, Marison IW (1991) Large-scale calorimetry and biotechnology. Thermochim Acta 193:215–242.  https://doi.org/10.1016/0040-6031(91)80185-L CrossRefGoogle Scholar
  28. 28.
    Korth B, Maskow T, Picioreanu C, Harnisch F (2016) The microbial electrochemical Peltier heat: an energetic burden and engineering chance for primary microbial electrochemical technologies. Energy Environ Sci 9(8):2539–2544.  https://doi.org/10.1039/c6ee01428c CrossRefGoogle Scholar
  29. 29.
    Heijnen JJ, van Dijken JP (1992) In search of a thermodynamic description of biomass yields for the chemotrophic growth of microorganisms. Biotechnol Bioeng 39:833–858.  https://doi.org/10.1002/bit.260390806 CrossRefPubMedGoogle Scholar
  30. 30.
    Heijnen JJ, van Dijken JP (1993) Response to comments on “in search of a thermodynamic description of biomass yields for the chemotropic growth of microorganisms”. Biotechnol Bioeng 42:1127–1130.  https://doi.org/10.1002/bit.260420916 CrossRefGoogle Scholar
  31. 31.
    VanBriesen JM (2002) Evaluation of methods to predict bacterial yield using thermodynamics. Biodegradation 13:171–190.  https://doi.org/10.1023/A:1020887214879 CrossRefPubMedGoogle Scholar
  32. 32.
    Monod J (1949) The growth of bacterial cultures. Annu Rev Microbiol 3:371–394.  https://doi.org/10.1146/annurev.mi.03.100149.002103 CrossRefGoogle Scholar
  33. 33.
    Heijnen JJ, Kleerebezem R (2010) Bioenergetics of microbial growth. In: Flickinger MC (ed) Encyclopedia of industrial biotechnology: bioprocess, bioseparation and cell technology. Wiley, Hoboken, NJ.  https://dx.doi.org/10.1002/9780470054581.eib084
  34. 34.
    Liu Y (2007) Overview of some theoretical approaches for derivation of the Monod equation. Appl Microbiol Biotechnol 73(6):1241–1250.  https://doi.org/10.1007/s00253-006-0717-7 CrossRefPubMedGoogle Scholar
  35. 35.
    Von Stockar U (2010) Biothermodynamics of live cells: a tool for biotechnology and biochemical engineering. J Non-Equil Thermodyn 35(4):415–475.  https://doi.org/10.1515/jnetdy.2010.024 CrossRefGoogle Scholar
  36. 36.
    Roels JA (1980) Application of macroscopic principles to microbial metabolism. Biotechnol Bioeng 22(12):2457–2514.  https://doi.org/10.1002/bit.260221202 CrossRefGoogle Scholar
  37. 37.
    Egli T (2015) Microbial growth and physiology: a call for better craftsmanship. Front Microbiol 6:1–12.  https://doi.org/10.3389/fmicb.2015.00287 CrossRefGoogle Scholar
  38. 38.
    Vanysek P (2001) CRC handbook of chemistry and physics 82nd edn. CRC Press, Boca RatonGoogle Scholar
  39. 39.
    Fultz ML, Durst RA (1982) Mediator compounds for the electrochemical study of biological redox systems: a compilation. Anal Chim Acta 140:1–18.  https://doi.org/10.1016/S0003-2670(01)95447-9 CrossRefGoogle Scholar
  40. 40.
    Heijnen JJ, van Loosdrecht MCM, Tijhuis L (1992) A black box mathematical model to calculate auto- and heterotrophic biomass yields based on Gibbs energy dissipation. Biotechnol Bioeng 40(10):1139–1154.  https://doi.org/10.1002/bit.260401003 CrossRefGoogle Scholar
  41. 41.
    Harnisch F, Freguia S (2012) A basic tutorial on cyclic voltammetry for the investigation of electroactive microbial biofilms. Chem Asian J 7(3):466–475.  https://doi.org/10.1002/asia.201100740 CrossRefPubMedGoogle Scholar
  42. 42.
    Simonte F, Sturm G, Gescher J, Sturm-Richter K (2017) Extracellular electron transfer and biosensors. In: Harnisch F, Holtmann D (eds) Bioelectrosynthesis. Advances in biochemical engineering/biotechnology. Springer, BerlinGoogle Scholar
  43. 43.
    Rosenbaum M, Aulenta F, Villano M, Angenent LT (2011) Cathodes as electron donors for microbial metabolism: which extracellular electron transfer mechanisms are involved? Bioresour Technol 102(1):324–333.  https://doi.org/10.1016/j.biortech.2010.07.008 CrossRefPubMedGoogle Scholar
  44. 44.
    Pous N, Koch C, Colprim J, Puig S, Harnisch F (2014) Extracellular electron transfer of biocathodes: revealing the potentials for nitrate and nitrite reduction of denitrifying microbiomes dominated by Thiobacillus sp. Electrochem Commun 49:93–97.  https://doi.org/10.1016/j.elecom.2014.10.011 CrossRefGoogle Scholar
  45. 45.
    Kracke F, Vassilev I, Krömer JO (2015) Microbial electron transport and energy conservation – the foundation for optimizing bioelectrochemical systems. Front Microbiol 6:1–18.  https://doi.org/10.3389/fmicb.2015.00575 CrossRefGoogle Scholar
  46. 46.
    Madigan MT, Martinko JM, Bender KS, Buckley DH, Stahl DA, Brock T (2014) Brock biology of microorganisms 14th edn. Pearson Education, New YorkGoogle Scholar
  47. 47.
    Jin Q, Bethke CM (2007) The thermodynamics and kinetics of microbial metabolism. Am J Sci 307:643–677.  https://doi.org/10.2475/04.2007.01 CrossRefGoogle Scholar
  48. 48.
    Hamelers HV, Ter Heijne A, Stein N, Rozendal RA, Buisman CJ (2011) Butler-Volmer-Monod model for describing bio-anode polarization curves. Bioresour Technol 102(1):381–387.  https://doi.org/10.1016/j.biortech.2010.06.156 CrossRefPubMedGoogle Scholar
  49. 49.
    Picioreanu C, Katuri KP, van Loosdrecht MCM, Head IM, Scott K (2009) Modelling microbial fuel cells with suspended cells and added electron transfer mediator. J Appl Electrochem 40(1):151–162.  https://doi.org/10.1007/s10800-009-9991-2 CrossRefGoogle Scholar
  50. 50.
    Strycharz SM, Malanoski AP, Snider RM, Yi H, Lovley DR, Tender LM (2011) Application of cyclic voltammetry to investigate enhanced catalytic current generation by biofilm-modified anodes of Geobacter sulfurreducens strain DL1vs. variant strain KN400. Energy Environ Sci 4(3):896–913.  https://doi.org/10.1039/c0ee00260g CrossRefGoogle Scholar
  51. 51.
    Lovley DR (2012) Electromicrobiology. Annu Rev Microbiol 66:391–409.  https://doi.org/10.1146/annurev-micro-092611-150104 CrossRefPubMedGoogle Scholar
  52. 52.
    Robinson JA, Trulear MG, Characklis WG (1984) Cellular reproduction and extracellular polymer formation by Pseudomonas aeruginosa in continous culture. Biotechnol Bioeng 26:1409–1417.  https://doi.org/10.1002/bit.260261203 CrossRefPubMedGoogle Scholar
  53. 53.
    Nielsen PH, Jahn A, Palmgren R (1997) Conceptual model for production and composition of exopolymers in biofilms. Water Sci Technol 36(1):11–19.  https://doi.org/10.1016/S0273-1223(97)00318-1 CrossRefGoogle Scholar
  54. 54.
    Laspidou CS, Rittmann BE (2002) A unified theory for extracellular polymeric substances, soluble microbial products, and active and inert biomass. Water Res 36:2711–2720.  https://doi.org/10.1016/S0043-1354(01)00413-4 CrossRefPubMedGoogle Scholar
  55. 55.
    Pinto RP, Srinivasan B, Manuel MF, Tartakovsky B (2010) A two-population bio-electrochemical model of a microbial fuel cell. Bioresour Technol 101(14):5256–5265.  https://doi.org/10.1016/j.biortech.2010.01.122 CrossRefPubMedGoogle Scholar
  56. 56.
    Popat SC, Torres CI (2016) Critical transport rates that limit the performance of microbial electrochemistry technologies. Bioresour Technol 215:265–273.  https://doi.org/10.1016/j.biortech.2016.04.136 CrossRefPubMedGoogle Scholar
  57. 57.
    Rabaey K, Rodriguez J, Blackall LL, Keller J, Gross P, Batstone D, Verstraete W, Nealson KH (2007) Microbial ecology meets electrochemistry: electricity-driven and driving communities. ISME J 1(1):9–18.  https://doi.org/10.1038/ismej.2007.4 CrossRefPubMedGoogle Scholar
  58. 58.
    Torres CI, Marcus AK, Lee HS, Parameswaran P, Krajmalnik-Brown R, Rittmann BE (2010) A kinetic perspective on extracellular electron transfer by anode-respiring bacteria. FEMS Microbiol Rev 34(1):3–17.  https://doi.org/10.1111/j.1574-6976.2009.00191.x CrossRefPubMedGoogle Scholar
  59. 59.
    Koch C, Harnisch F (2016) Is there a specific ecological niche for electroactive microorganisms? ChemElectroChem 3(9):1282–1295.  https://doi.org/10.1002/celc.201600079 CrossRefGoogle Scholar
  60. 60.
    Recio-Garrido D, Perrier M, Tartakovsky B (2016) Modeling, optimization and control of bioelectrochemical systems. Chem Eng J 289:180–190.  https://doi.org/10.1016/j.cej.2015.11.112 CrossRefGoogle Scholar
  61. 61.
    Bard AJ, Faulkner LR (2001) Electrochemical methods: fundamentals and applications 2nd edn. Wiley, New YorkGoogle Scholar
  62. 62.
    Marsili E, Baron DB, Shikhare ID, Coursolle D, Gralnick JA, Bond DR (2008) Shewanella secretes flavins that mediate extracellular electron transfer. Proc Natl Acad Sci U S A 105(10):3968–3973.  https://doi.org/10.1073/pnas.0710525105 CrossRefPubMedPubMedCentralGoogle Scholar
  63. 63.
    Mao L, Verwoerd WS (2014) Theoretical exploration of optimal metabolic flux distributions for extracellular electron transfer by Shewanella oneidensis MR-1. Biotechnol Biofuels 7(118):1–20.  https://doi.org/10.1186/s13068-014-0118-6 CrossRefGoogle Scholar
  64. 64.
    Guidelli R, Compton RG, Feliu JM, Gileadi E, Lipkowski J, Schmickler W, Trasatti S (2014) Defining the transfer coefficient in electrochemistry: an assessment (IUPAC Technical Report). Pure Appl Chem 86(2):245–258.  https://doi.org/10.1515/pac-2014-5026 CrossRefGoogle Scholar
  65. 65.
    Hamann CH, Hamnett A, Vielstich W (2007) Electrochemistry 2nd edn. Wiley-VCH Verlag GmbH & Co. KGaA, WeinheimGoogle Scholar
  66. 66.
    Lowy DA, Tender LM, Zeikus JG, Park DH, Lovley DR (2006) Harvesting energy from the marine sediment-water interface II. Kinetic activity of anode materials. Biosens Bioelectron 21(11):2058–2063.  https://doi.org/10.1016/j.bios.2006.01.033 CrossRefPubMedGoogle Scholar
  67. 67.
    Ly HK, Harnisch F, Hong SF, Schröder U, Hildebrandt P, Millo D (2013) Unraveling the interfacial electron transfer dynamics of electroactive microbial biofilms using surface-enhanced Raman spectroscopy. ChemSusChem 6(3):487–492.  https://doi.org/10.1002/cssc.201200626 CrossRefPubMedGoogle Scholar
  68. 68.
    Bader FG (1978) Analysis of double-substrate limited growth. Biotechnol Bioeng 20(2):183–202.  https://doi.org/10.1002/bit.260200203 CrossRefPubMedGoogle Scholar
  69. 69.
    Bae W, Rittmann BE (1996) A structured model of dual-limitation kinetics. Biotechnol Bioeng 49(6):683–689.  https://doi.org/10.1002/(SICI)1097-0290(19960320)49:6<683::AID-BIT10>3.0.CO;2-7 CrossRefPubMedGoogle Scholar
  70. 70.
    Deutzmann JS, Sahin M, Spormann AM (2015) Extracellular enzymes facilitate electron uptake in biocorrosion and bioelectrosynthesis. MBio 6(2):e00496-15.  https://doi.org/10.1128/mBio.00496-15 CrossRefPubMedPubMedCentralGoogle Scholar
  71. 71.
    Torres CI, Marcus AK, Parameswaran P, Rittmann BE (2008) Kinetic experiments for evaluating the Nernst-Monod model for anode-respiring bacteria (ARB) in a biofilm anode. Energy Environ Sci 42(17):6593–6597.  https://doi.org/10.1021/es800970w CrossRefGoogle Scholar
  72. 72.
    Richter H, Nevin KP, Jia H, Lowy DA, Lovley DR, Tender LM (2009) Cyclic voltammetry of biofilms of wild type and mutant Geobacter sulfurreducens on fuel cell anodes indicates possible roles of OmcB, OmcZ, type IV pili, and protons in extracellular electron transfer. Energy Environ Sci 2(5):506–516.  https://doi.org/10.1039/b816647a CrossRefGoogle Scholar
  73. 73.
    Rousseau R, Délia M-L, Bergel A (2014) A theoretical model of transient cyclic voltammetry for electroactive biofilms. Energy Environ Sci 7(3):1079–1094.  https://doi.org/10.1039/c3ee42329h CrossRefGoogle Scholar
  74. 74.
    Korth B, Rosa LF, Harnisch F, Picioreanu C (2015) A framework for modeling electroactive microbial biofilms performing direct electron transfer. Bioelectrochemistry 106(Pt A):194–206.  https://doi.org/10.1016/j.bioelechem.2015.03.010 CrossRefPubMedGoogle Scholar
  75. 75.
    Malvankar NS, Vargas M, Nevin KP, Franks AE, Leang C, Kim BC, Inoue K, Mester T, Covalla SF, Johnson JP, Rotello VM, Tuominen MT, Lovley DR (2011) Tunable metallic-like conductivity in microbial nanowire networks. Nat Nanotechnol 6(9):573–579.  https://doi.org/10.1038/nnano.2011.119 CrossRefPubMedGoogle Scholar
  76. 76.
    Renslow RS, Babauta JT, Majors PD, Beyenal H (2013) Diffusion in biofilms respiring on electrodes. Energy Environ Sci 6(2):595–607.  https://doi.org/10.1039/C2EE23394K CrossRefPubMedGoogle Scholar
  77. 77.
    Yates MD, Strycharz-Glaven SM, Golden JP, Roy J, Tsoi S, Erickson JS, El-Naggar MY, Barton SC, Tender LM (2016) Measuring conductivity of living Geobacter sulfurreducens biofilms. Nat Nanotechnol 11(11):910–913.  https://doi.org/10.1038/nnano.2016.186 CrossRefPubMedGoogle Scholar
  78. 78.
    Storck T, Virdis B, Batstone DJ (2015) Modelling extracellular limitations for mediated versus direct interspecies electron transfer. ISME J 10(3):621–631.  https://doi.org/10.1038/ismej.2015.139 CrossRefPubMedPubMedCentralGoogle Scholar
  79. 79.
    Renslow R, Babauta J, Kuprat A, Schenk J, Ivory C, Fredrickson J, Beyenal H (2013) Modeling biofilms with dual extracellular electron transfer mechanisms. Phys Chem Chem Phys 15(44):19262–19283.  https://doi.org/10.1039/c3cp53759e CrossRefPubMedPubMedCentralGoogle Scholar
  80. 80.
    Fischer KM, Batstone DJ, van Loosdrecht MCM, Picioreanu C (2015) A mathematical model for electrochemically active filamentous sulfide-oxidising bacteria. Bioelectrochemistry 102:10–20.  https://doi.org/10.1016/j.bioelechem.2014.11.002 CrossRefPubMedGoogle Scholar
  81. 81.
    Kadic E, Heindel TJ (2014) An introduction to bioreactor hydrodynamics and gas-liquid mass transfer. Wiley, Hoboken, NJCrossRefGoogle Scholar
  82. 82.
    Kayode Coker A (2001) Modeling of chemical kinetics and reactor design 1st edn. Gulf Publishing Company, Houston, TXGoogle Scholar
  83. 83.
    Harnisch F, Warmbier R, Schneider R, Schröder U (2009) Modeling the ion transfer and polarization of ion exchange membranes in bioelectrochemical systems. Bioelectrochemistry 75(2):136–141.  https://doi.org/10.1016/j.bioelechem.2009.03.001 CrossRefPubMedGoogle Scholar
  84. 84.
    Stenina IA, Sistat P, Rebrov AI, Pourcelly G, Yaroslavtsev AB (2004) Ion mobility in Nafion-117 membranes. Desalination 170(1):49–57.  https://doi.org/10.1016/j.desal.2004.02.092 CrossRefGoogle Scholar
  85. 85.
    Harnisch F, Schröder U (2009) Selectivity versus mobility: separation of anode and cathode in microbial bioelectrochemical systems. ChemSusChem 2(10):921–926.  https://doi.org/10.1002/cssc.200900111 CrossRefPubMedGoogle Scholar
  86. 86.
    Matemadombo F, Puig S, Ganigué R, Ramírez-García R, Batlle-Vilanova P, Dolors Balaguer M, Colprim J (2016) Modelling the simultaneous production and separation of acetic acid from CO2 using an anion exchange membrane microbial electrosynthesis system. J Chem Technol Biot 92:1211–1217.  https://doi.org/10.1002/jctb.5110 CrossRefGoogle Scholar
  87. 87.
    Gildemyn S, Verbeeck K, Slabbinck R, Andersen SJ, Prévoteau A, Rabaey K (2015) Integrated production, extraction, and concentration of acetic acid from CO2 through microbial electrosynthesis. Environ Sci Technol Lett 2(11):325–328.  https://doi.org/10.1021/acs.estlett.5b00212 CrossRefGoogle Scholar
  88. 88.
    Sander R (2015) Compilation of Henry’s law constants (version 4.0) for water as solvent. Atmos Chem Phys 15:4399–4981.  https://doi.org/10.5194/acp-15-4399-2015 CrossRefGoogle Scholar
  89. 89.
    Carroll JJ, Slupsky JD, Mather AE (1991) The solubility of carbon dioxide in water at low pressure. J Phys Chem Ref Data 20(6):1201–1209.  http://dx.doi.org/10.1063/1.555900 CrossRefGoogle Scholar
  90. 90.
    Henry W (1803) Experiments on the quantity of gases absorbed by water, at different temperatures, and under different pressures. Phil Trans R Soc Lond 93:29–274CrossRefGoogle Scholar
  91. 91.
    Smith FL, Harvey AH (2007) Avoid common pitfalls when using Henry’s law. Chem Eng Prog 103(9):33–39Google Scholar
  92. 92.
    Raoult F-M (1887) Loi générale des tensions de vapeur des dissolvants. Comptes Rendus 104:1430–1433Google Scholar
  93. 93.
    Nielsen J, Villadsen J (1994) Bioreactor modeling. Bioreaction engineering principles. Springer, New York.  https://doi.org/10.1007/978-1-4757-4645-7_9 CrossRefGoogle Scholar
  94. 94.
    Bond DR, Lovley DR (2003) Electricity production by Geobacter sulfurreducens attached to electrodes. Appl Environ Microb 69(3):1548–1555.  https://doi.org/10.1128/aem.69.3.1548-1555.2003 CrossRefGoogle Scholar
  95. 95.
    Von Stockar U, von der Wielen LAM (2003) Back to basics: thermodynamics in biochemical engineering. In: Von Stockar U et al (eds) Process integration in biochemical engineering. Advances in biochemical engineering/ biotechnology, vol 80. Springer, Berlin, pp 1–17.  https://doi.org/10.1007/3-540-36782-9_1 CrossRefGoogle Scholar
  96. 96.
    Beese-Vasbender PF, Nayak S, Erbe A, Stratmann M, Mayrhofer KJJ (2015) Electrochemical characterization of direct electron uptake in electrical microbially influenced corrosion of iron by the lithoautotrophic SRB Desulfopila corrodens strain IS4. Electrochim Acta 167:321–329.  https://doi.org/10.1016/j.electacta.2015.03.184 CrossRefGoogle Scholar
  97. 97.
    Venzlaff H, Enning D, Srinivasan J, Mayrhofer KJJ, Hassel AW, Widdel F, Stratmann M (2013) Accelerated cathodic reaction in microbial corrosion of iron due to direct electron uptake by sulfate-reducing bacteria. Corros Sci 66:88–96.  https://doi.org/10.1016/j.corsci.2012.09.006 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Environmental MicrobiologyHelmholtz-Centre for Environmental Research – UFZLeipzigGermany

Personalised recommendations