ABSTRACT

The involvement of Shewanella spp. in biocorrosion is often attributed to their Fe(III)-reducing properties, but they could also affect corrosion by using metallic iron as an electron donor. Previously, we isolated Shewanella strain 4t3-1-2LB from an acetogenic community enriched with Fe(0) as the sole electron donor. Here, we investigated its use of Fe(0) as an electron donor with fumarate as an electron acceptor and explored its corrosion-enhancing mechanism. Without Fe(0), strain 4t3-1-2LB fermented fumarate to succinate and CO2, as was shown by the reaction stoichiometry and pH. With Fe(0), strain 4t3-1-2LB completely reduced fumarate to succinate and increased the Fe(0) corrosion rate (7.0 ± 0.6)-fold in comparison to that of abiotic controls (based on the succinate-versus-abiotic hydrogen formation rate). Fumarate reduction by strain 4t3-1-2LB was, at least in part, supported by chemical hydrogen formation on Fe(0). Filter-sterilized spent medium increased the hydrogen generation rate only 1.5-fold, and thus extracellular hydrogenase enzymes appear to be insufficient to explain the enhanced corrosion rate. Electrochemical measurements suggested that strain 4t3-1-2LB did not excrete dissolved redox mediators. Exchanging the medium and scanning electron microscopy (SEM) imaging indicated that cells were attached to Fe(0). It is possible that strain 4t3-1-2LB used a direct mechanism to withdraw electrons from Fe(0) or favored chemical hydrogen formation on Fe(0) through maintaining low hydrogen concentrations. In coculture with an Acetobacterium strain, strain 4t3-1-2LB did not enhance acetogenesis from Fe(0). This work describes a strong corrosion enhancement by a Shewanella strain through its use of Fe(0) as an electron donor and provides insights into its corrosion-enhancing mechanism.
IMPORTANCE Shewanella spp. are frequently found on corroded metal structures. Their role in microbial influenced corrosion has been attributed mainly to their Fe(III)-reducing properties and, therefore, has been studied with the addition of an electron donor (lactate). Shewanella spp., however, can also use solid electron donors, such as cathodes and potentially Fe(0). In this work, we show that the electron acceptor fumarate supported the use of Fe(0) as the electron donor by Shewanella strain 4t3-1-2LB, which caused a (7.0 ± 0.6)-fold increase of the corrosion rate. The corrosion-enhancing mechanism likely involved cell surface-associated components in direct contact with the Fe(0) surface or maintenance of low hydrogen levels by attached cells, thereby favoring chemical hydrogen formation by Fe(0). This work sheds new light on the role of Shewanella spp. in biocorrosion, while the insights into the corrosion-enhancing mechanism contribute to the understanding of extracellular electron uptake processes.

INTRODUCTION

Corrosion of iron-based structures entails major costs worldwide, of which about 20% are related to microbially influenced corrosion (MIC) (1). Microorganisms can affect corrosion through various mechanisms, including metabolizing corrosion products or the metal itself (24). Under anoxic conditions, corrosion of metallic iron [Fe(0)] leads to the formation of hydrogen: Fe(0) + 2H+ → H2 + Fe2+G°′ = −10.6 kJ · mol−1) (reaction A). Initially, it was assumed that microorganisms induce corrosion by consuming hydrogen, rendering reaction A thermodynamically more favorable (the so-called cathodic depolarization theory) (5). Recently, it has become clear that some strains must have a more efficient mechanism to withdraw electrons from Fe(0), as they strongly induced corrosion while related hydrogen-consuming strains did not (69). Both the sulfate-reducing strain IS4 (Desulfopila corrodens) and the Methanobacterium strain IM1 likely use metallic iron directly as an electron donor by means of an extracellular electron transfer (EET) mechanism (2, 1012). In contrast, the methanogen Methanococcus maripaludis releases extracellular enzymes, such as hydrogenases, which adsorb to the electroactive surface and catalyze reaction A (13). While these efficient EET mechanisms are undesired in the context of iron corrosion, they are of interest for the development of biotechnological applications. Microbial electrosynthesis, for instance, powers the microbial production of valuable chemicals from CO2 with a cathode, which is a solid electron donor like Fe(0) (14, 15). Deutzmann and Spormann (16) showed that microbial electrosynthesis of acetate and methane could be improved by using the corrosion-enhancing strain IS4 in coculture with an acetogen or a methanogen, respectively. So far, the number of iron-corroding microorganisms known to efficiently withdraw electrons from Fe(0) is limited (3), while a better understanding of their electron uptake mechanisms is required to assess MIC and develop biotechnological applications.
Shewanella spp. are environmentally ubiquitous (17) and are well known for their ability to use solid electron acceptors, including Fe(III) oxides and anodes (18). Their EET mechanism involves the Mtr pathway, i.e., an electron conduit that transports electrons across the outer membrane by a series of membrane-associated c-type cytochromes (1820). The Mtr pathway allows Shewanella species to directly interact with solid electron acceptors, while they also excrete flavins acting as dissolved electron shuttles (21). Shewanella spp. can also use solid electron donors, such as cathodes, with oxygen or fumarate as an electron acceptor (2224). Investigations using the model strain Shewanella oneidensis MR-1 showed that this strain directly withdraws electrons from a cathode by reversing the electron flow of the Mtr pathway (23), possibly by redox bifurcation of the involved flavins (25). So far, only cell maintenance, but not growth, could be associated with the cathodic electron uptake by strain MR-1 (26).
Shewanella spp. also play a role in MIC, as they are often found on corroded structures (2730). Their involvement in MIC has been attributed mostly to their Fe(III)-reducing properties, which can either enhance or inhibit corrosion (31, 32). Fe(III) reduction can remove the protective Fe(III) oxide layer on steel (33), while the released Fe(II) could scavenge oxygen and diminish corrosion (34). In addition, several studies showed that Shewanella spp. can consume the abiotically generated hydrogen on Fe(0) (30, 35, 36). As Shewanella spp. can use a cathode as electron donor (2224), it seems likely that they can also use other solid electron donors, such as Fe(0). Only recently, it was suggested that strain MR-1 used carbon steel as an electron donor under nitrate-reducing conditions (37). Until now, however, the mechanisms used by Shewanella spp. to withdraw electrons from Fe(0) have not been investigated, and the importance of this process to MIC remains unclear.
Previously, we isolated a new Shewanella strain from an acetogenic community enriched with metallic iron as the sole electron donor (J. Philips, E. Monballyu, S. Georg, K. De Paepe, A. Prévoteau, K. Rabaey, and J. B. A. Arends, submitted for publication). This Shewanella strain, 4t3-1-2LB, which is highly similar to Shewanella fodinae (Fig. 1), did not metabolize Fe(0) with CO2 and water as the only possible electron acceptors. For that reason, the use of metallic iron as an electron donor by strain 4t3-1-2LB was investigated in this work with the addition of fumarate as an electron acceptor (see Fig. S1A in the supplemental material). The mechanism used by strain 4t3-1-2LB to enhance corrosion was explored with a series of bottle experiments, as well as electrochemical measurements and scanning electron microscopy (SEM) (Fig. S1B). In addition, the role of strain 4t3-1-2LB in the acetogenic enrichment was investigated by testing cocultures of strain 4t3-1-2LB and an acetogenic isolate (Fig. S1C). This study describes a strong increase of the rate of corrosion by a Shewanella strain through its use of Fe(0) as the electron donor when a suitable electron acceptor is present.
FIG 1
FIG 1 Maximum-likelihood phylogenetic tree showing the relatedness of Shewanella strain 4t3-1-2LB to representative 16S rRNA gene sequences of all Shewanella species currently classified in the RDP, Silva, and NCBI databases. The 16S rRNA gene was PCR amplified using primers 63F and 1378R and the tree was constructed as described elsewhere (Philips et al., submitted).

RESULTS

Shewanella strain 4t3-1-2LB converts fumarate in the presence and absence of Fe(0).

The first experiment evaluated the use of Fe(0) as the electron donor by strain 4t3-1-2LB with fumarate as the electron acceptor (see Fig. S1A in the supplemental material). In abiotic controls with Fe(0), the fumarate concentration remained constant, while no other volatile fatty acids (VFAs) were formed (Fig. 2A). Very recently, Fe(0) was reported to abiotically reduce CO2 to acetate and other VFAs at high temperatures and CO2 pressures (38), but the conditions in our experiments likely did not favor such reactions. In our abiotic controls, the hydrogen concentration increased linearly over time with a rate (0.49 ± 0.04 mmol of electron equivalents [meeq] · liter−1 · day−1 over 14 days) (Fig. 2A) that was highly similar to that observed in our other study (0.48 ± 0.05 meeq liter−1 · day−1) (Philips et al., submitted). Dissolved Fe(II) concentrations remained low and did not increase concomitantly with the hydrogen concentration, likely because part of the Fe(II) precipitated as Fe(II) carbonates or oxyhydroxides (whitish precipitates were visible). In the abiotic controls, the iron powder remained loose (there was visual turbidity upon shaking) throughout the experiment (see Fig. S2 in the supplemental material).
FIG 2
FIG 2 Change of fumarate, succinate, malate, hydrogen, and dissolved Fe(II) concentrations, expressed as 10−3 electron equivalents per volume of the liquid phase (meeq · liter−1), over time for abiotic controls with fumarate (A), Shewanella strain 4t3-1-2LB in the presence of Fe(0) powder and fumarate (B), and Shewanella strain 4t3-1-2LB with fumarate but in the absence of Fe(0) (C). Plotted values are averages from triplicate bottles, and error bars show the standard deviation.
In the presence of Fe(0), strain 4t3-1-2LB immediately started to reduce fumarate to succinate, while malate was transiently formed (Fig. 2B). As long as fumarate or malate was present (until day 11), succinate concentrations increased quasilinearly with an average rate of 3.43 ± 0.10 meeq · liter−1 · day−1. Final succinate concentrations were equal to the initial fumarate concentration (20 mM). Hydrogen concentrations were below the detection limit (<0.06 meeq liter−1 or 0.04% [vol/vol] in the headspace) as long as succinate was being produced, but they started to increase after fumarate depletion (day 11). These findings show that fumarate reduction was at least in part supported by hydrogen consumption. Dissolved Fe(II) concentrations initially increased to a level higher than that in the abiotic controls, but they decreased after day 6 (Fig. 2B), likely due to precipitation of Fe(II) salts, just as in the abiotic controls. During fumarate reduction, the liquid phase was colored slightly yellow (Fig. S2), possibly because of Fe(III) formation. Dissolved Fe(III) concentrations in this study were always low in comparison to Fe(II) concentrations, which hindered their accurate measurement by the used method (39). Upon fumarate depletion, the liquid phase turned colorless again and became clear (with no turbidity upon shaking), because all iron powder aggregated at the bottom of the bottle (Fig. S2). A second addition of fumarate (20 mM) led to similar concentration changes (see Fig. S3 in the supplemental material). The yellow color of the liquid phase appeared again during fumarate reduction and disappeared after fumarate depletion. The iron powder remained aggregated at the bottom of the bottle and became overlaid with a dark green layer of precipitates (Fig. S2).
Strikingly, in the absence of Fe(0), strain 4t3-1-2LB also converted fumarate to succinate (Fig. 2C). Malate was again formed transiently, but succinate production started only after an initial lag phase, and the final succinate concentrations were 20.5% ± 4.4% lower than the initial fumarate concentrations (day 14) [final succinate concentrations in the absence of Fe(0) were significant lower than those in the presence of Fe(0), based on a Student t test [P < 0.01]). Fumarate conversion continued after a second fumarate addition (Fig. S3), demonstrating that the reduction of fumarate was not just supported by the limited amount of yeast extract present in the medium [0.1 g · liter−1, which corresponds to 18 meeq · liter−1, assuming that yeast extract has the typical chemical composition of biomass (C5H7O2N) and is completely oxidized (40)]. In the absence of Fe(0), Shewanella visibly grew and remained planktonic (with an optical density increase from 0.01 to a maximum of 0.16).
Fumarate conversion by strain 4t3-1-2LB in the presence and absence Fe(0) was further analyzed by determining the CO2 content in the headspace and the pH at the end of the experiment (day 25, after two conversions of 20 mM fumarate) (Fig. 3). In abiotic controls without Fe(0), the CO2 content remained similar to the initial level (10%) (Fig. 3A). In abiotic controls with Fe(0), the CO2 content had decreased to 4.7% ± 0.4% over 25 days, likely because CO2 was partly removed from the headspace by Fe(II) carbonate formation. Fumarate conversion by strain 4t3-1-2LB in the presence of Fe(0) led to a much lower CO2 level (final headspace content, 0.4% ± 0.1%) than in the abiotic controls, suggesting that more Fe(II) carbonate precipitates had been formed or possibly that CO2 had been consumed by a biological process (S. fodinae can grow with bicarbonate as a carbon source [41]). In contrast, in the absence of Fe(0), fumarate conversion by strain 4t3-1-2LB increased the CO2 content (final headspace content, 14.4% ± 0.3%) in comparison to the initial level, demonstrating the production of CO2 (an additional 0.20 ± 0.01 mmol CO2 in the headspace). Furthermore, there were clear differences in the pH between the different treatments (Fig. 3B). In abiotic controls without Fe(0), the pH remained close to the initial value of 7.20 [the pKa of 3-(N-morpholino)propanesulfonic acid (MOPS)], while in abiotic controls with Fe(0), the pH slightly increased (final pH, 7.30 ± 0.01). Fumarate conversion by strain 4t3-1-2LB with Fe(0) led to a significant increase of the pH to 7.91 ± 0.06 (Student t test, P < 0.01), while without Fe(0), the pH (7.13 ± 0.02) had slightly decreased in comparison to the initial value.
FIG 3
FIG 3 Headspace CO2 content (A) and pH in the liquid phase (B) at the end of the experiment (day 25) for the different treatments shown in Fig. 2 and S3 as well as an abiotic control without Fe(0). Plotted values are averages from triplicate bottles, and error bars show the standard deviation.
These differences in stoichiometry, pH, and CO2 content show that strain 4t3-1-2LB converted fumarate differently with and without Fe(0). As discussed in detail below, fermentation of fumarate to succinate and CO2 most likely occurred in the absence of Fe(0) (with fumarate as an electron acceptor and donor), while the complete reduction of fumarate to succinate occurred in the presence of Fe(0). This shows that strain 4t3-1-2LB could use Fe(0) as the electron donor. Furthermore, the rate of succinate formation by strain 4t3-1-2LB with Fe(0) as an electron donor was (7.0 ± 0.6)-fold higher than the hydrogen formation rate under abiotic conditions (Fig. 2), demonstrating that strain 4t3-1-2LB significantly increased the Fe(0) corrosion rate in comparison to abiotic conditions (significant difference based on a Student t test [P < 0.001]). The real corrosion enhancement factor might even have been higher than 7.0 ± 0.6, since the higher pH at the end of the fumarate conversion by strain 4t3-1-2LB with Fe(0) (Fig. 3) implies a lower chemical hydrogen formation rate (reaction A).
The use of Fe(0) as an electron donor by strain 4t3-1-2LB was also evaluated with other electron acceptors, including sodium nitrate, trimethylamine oxide (TMAO), and dimethyl sulfoxide (DMSO) (all at 20 mM). Nitrate and TMAO, however, led to a strong chemical oxidation of the iron powder (clear from the extensive brown precipitation) (4244), while DMSO did not support the growth of strain 4t3-1-2LB (results not shown).

Malate complexes Fe(II), but this does not explain the enhanced Fe(0) corrosion by strain 4t3-1-2LB.

Some organic compounds, including malate, are known to form complexes with ferric and ferrous iron (45, 46). For this reason, abiotic controls with 20 mM malate or succinate were investigated (Fig. S1A). Abiotic controls with succinate (Fig. 4A) showed concentration changes very similar to those of the abiotic controls with fumarate (Fig. 2A). The hydrogen concentration increased with an average rate of 0.40 ± 0.01 meeq · liter−1 · day−1 (over 21 days), while dissolved Fe(II) concentrations remained low. With malate, however, the dissolved Fe(II) concentration increased with an average rate of 0.34 ± 0.03 meeq · liter−1 · day−1 (over 21 days), almost proportionally to the hydrogen formation rate (0.26 ± 0.03 meeq · liter−1 · day−1, over 21 days) (Fig. 4B). The flushing of the headspace at the start of the experiment, which removed hydrogen but not Fe(II), explains the higher dissolved Fe(II) concentration at day 0 in comparison to the initial hydrogen concentration (Fig. 4B). The increasing dissolved Fe(II) concentration with malate suggests that malate was able to keep all Fe(II) formed in solution by complexation. The chelating properties of malate were also clear from liquid samples exposed to air. Oxygen in the air oxidized the dissolved Fe(II) in the samples to Fe(III), which usually resulted in an extensive brown precipitation, but with malate, liquid samples were only slightly colored brown and remained completely clear (see Fig. S4 in the supplemental material). In addition, malate diminished the abiotic hydrogen formation rate (0.26 ± 0.03 meeq · liter−1 · day−1) in comparison to those with fumarate and succinate (Fig. 2A and 4; see Fig. 9) (significant differences, based on Student t tests with a P value of <0.01). With both malate and succinate, the pH at the end of the experiments was similar to that with fumarate (results not shown); thus, the difference in hydrogen formation rates is not pH related. Most likely, the complexing properties of malate also explain its lower hydrogen formation rate, which is discussed further below. The formation of malate, therefore, is not an explanation for the strongly increased rate of Fe(0) corrosion by strain 4t3-1-2LB with fumarate as the electron acceptor.
FIG 4
FIG 4 Change of malate, succinate, hydrogen, and dissolved Fe(II) concentrations, expressed in 10−3 electron equivalents per volume of the liquid phase (meeq · liter−1), over time for abiotic controls with Fe(0) and succinate (A) or malate (B). Plotted values are averages from triplicate bottles, and error bars show the standard deviation.

Cells attached to Fe(0) are responsible for fumarate reduction.

The corrosion-enhancing mechanism of strain 4t3-1-2LB was first explored by exchanging the medium of strain 4t3-1-2LB growing on Fe(0) and fumarate (Fig. S1B). After the depletion of 20 mM fumarate (day 12), the liquid phase was replaced with 40 ml fresh anaerobic defined medium, while the aggregated iron powder remained in the bottle. Bottles were briefly flushed with N2-CO2 gas to remove any hydrogen. After the medium exchange, 20 mM fumarate or no electron acceptor was added. With the addition of fumarate, succinate formation after the medium exchange continued without a lag phase and with a rate (5.04 ± 0.07 meeq · liter−1 · day−1 between days 12 and 19) even higher than that before the medium exchange (4.15 ± 0.06 meeq · liter−1 · day−1 during the first 7 days) (significantly different based on a Student t test [P < 0.01]) (Fig. 5A). These findings suggest that attached cells were responsible for the fumarate reduction, as planktonic cells were removed from the liquid phase. Moreover, the glass and the liquid phase were always completely clear (Fig. S2), suggesting that the cells must have been attached to the Fe(0) powder. Accordingly, SEM imaging showed attachment of cells to the Fe(0) powder (Fig. 6). Rod-shaped cells were seen clustered together in cavities of the iron powder particles. The Fe(0) surface was largely covered by precipitates of various sizes and shapes. The outside of the Shewanella cells looked coarse, which possibly indicates that precipitates had also formed on the outer surfaces of the cells.
FIG 5
FIG 5 Change of fumarate, malate, succinate, hydrogen, and dissolved Fe(II) concentrations, expressed in 10−3 electron equivalents per volume of the liquid phase (meeq · liter−1), for the medium exchange test with Shewanella strain 4t3-1-2LB. At day 12, the liquid phase was replaced by fresh medium (40 ml) with 20 mM fumarate (A) or without fumarate (B), while the Fe(0) powder was retained in the bottle. Plotted values are averages from triplicate bottles, and error bars show the standard deviation.
FIG 6
FIG 6 SEM image of Shewanella strain 4t3-1-2LB cells clustered together in a cavity of an iron powder granule after 14 days of growth with fumarate as the electron acceptor. Arrows point to cells (C) or precipitates (P).
The increased electron uptake from Fe(0) by strain 4t3-1-2LB could be mediated by hydrogen or formate (13). Without the addition of an electron acceptor after the medium exchange, hydrogen was formed at a rate (0.70 ± 0.10 meeq · liter−1 · day−1 between days 12 and 22) (Fig. 5B) higher than the abiotic hydrogen formation rate (a significant difference based on a Student t test [P < 0.0001]; the pHs were similar) (Fig. 2A), but still much lower than the succinate formation rate after exchanging the medium and adding fumarate (Fig. 5A). Similar hydrogen formation rates were obtained when the medium was not exchanged after fumarate depletion (results not shown). Formate concentrations always remained low (<1 meeq · liter−1) in this study (results not shown). Consequently, the strong increase of the corrosion rate by strain 4t3-1-2LB cannot be explained solely by a kinetic stimulation of the hydrogen (or formate) formation reaction on the Fe(0) surface, for instance, by adsorbed extracellular hydrogenase (or formate dehydrogenase) enzymes.
The results of the medium exchange also suggest that no dissolved, self-excreted redox mediators were involved in the electron uptake from Fe(0) by strain 4t3-1-2LB. This was confirmed by electrochemical measurements on filtered liquid samples. Cyclic voltammograms measured with a glassy carbon rotating-disk electrode (scan rate, 10 mV · s−1; rotation speed, 2,000 rpm) were similar for strain 4t3-1-2LB grown with Fe(0) and fumarate and for an abiotic control with Fe(0); nevertheless, there were strong differences in the height of peaks, likely related to Fe(II) reduction and oxidation (see Fig. S5A in the supplemental material). Addition of 10 μM riboflavin to the filter liquid samples, i.e., an exogenous dissolved redox mediator, resulted in an additional sigmoidal feature in the voltammogram, which was otherwise absent (Fig. S5B). This further confirmed that strain 4t3-1-2LB did not excrete dissolved redox mediators to the liquid phase at a detectable concentration in our experiments (47).

Defined spent medium slightly increases the hydrogen formation rate.

The corrosion-enhancing mechanism of strain 4t3-1-2LB was further assessed by investigating the effect of filter-sterilized spent medium on the corrosion of Fe(0) (Fig. S1B). The medium removed in the medium exchange experiment was filter sterilized and placed in bottles with 5 ml medium and 2 g Fe(0) powder (spent defined medium). Dissolved Fe(II) concentrations remained low in these bottles (Fig. 7A), while hydrogen was formed at a rate (0.72 ± 0.03 meeq · liter−1 · day−1, over 24 days) similar to the hydrogen formation rate after the medium exchange without fumarate addition (Fig. 5B) and higher than the abiotic hydrogen formation rate (Fig. 2A) (a significant difference based on a Student t test [P < 0.01]; the pHs were similar). The increase in the hydrogen formation rate could be due to the catalytic effect of extracellular hydrogenase enzymes present in the spent medium (13). However, their catalyzing effect on the hydrogen formation reaction is alone insufficient to explain the large increase in the rate of corrosion by strain 4t3-1-2LB with fumarate as an electron acceptor.
FIG 7
FIG 7 Change of fumarate, malate, succinate, hydrogen, and dissolved Fe(II) concentrations, expressed in 10−3 electron equivalents per volume of the liquid phase (meeq · liter−1), over time for spent defined medium (A) and spent LB medium (B) (both filter sterilized) added to fresh Fe(0) powder. Plotted values are averages from triplicate bottles, and error bars show the standard deviation.
In addition, spent Luria-Bertani (LB) medium was tested by adding 1 ml filter-sterilized supernatant of Shewanella cells aerobically grown in LB (no fumarate addition) to bottles with 40 ml anaerobic defined medium with fumarate and Fe(0) powder. The bottles were briefly flushed with N2-CO2 gas to remove traces of oxygen. The fumarate concentrations in these bottles exponentially decreased, and fumarate was incompletely converted into only malate (Fig. 7B). No fumarate conversion occurred in controls to which fresh LB medium was added (results not shown). The hydrogen formation rate (0.26 ± 0.01 meeq · liter−1 · day−1, between days 0 and 21) and the linearly increasing dissolved Fe(II) concentrations (Fig. 7B) were similar to those in abiotic controls with malate (Fig. 4B). These results suggest that the spent LB medium contained fumarate hydratase enzymes (catalyzing the reversible hydration of fumarate to malate) (discussed below), most likely resulting from the lysis of the cells grown in the LB medium, but no hydrogenase enzymes affecting the Fe(0) corrosion rate.

Shewanella strain 4t3-1-2LB does not increase acetogenesis from Fe(0) by an Acetobacterium isolate.

It was previously found that a corrosion-enhancing strain (sulfate-reducing strain IS4) improved the electron transfer from a cathode for acetogenesis (16). In order to investigate whether Shewanella strain 4t3-1-2LB played a similar role in the acetogenic enrichment from which it was isolated, acetogenesis from Fe(0) by cocultures of Shewanella strain 4t3-1-2LB and Acetobacterium strain 73-4-6p-4 was investigated (Fig. S1C). Acetobacterium strain 73-4-6p-4 by itself produced acetate at an average rate of 0.85 ± 0.19 meeq · liter−1 · day−1 (over 21 days), while hydrogen concentrations remained below the detection limit (Fig. 8A). This acetate production rate corresponds to a (1.77 ± 0.43)-fold corrosion enhancement in comparison to hydrogen formation under abiotic conditions, which is similar to results from our other study (Philips et al., submitted). Adding Acetobacterium strain 73-4-6p-4 and Shewanella strain 4t3-1-2LB together from the start of the experiment resulted in a similar acetate production rate (0.80 ± 0.05 meeq · liter−1 · day−1, over 21 days) (Fig. 8B). Also, when Acetobacterium strain 73-4-6p-4 was added after strain 4t3-1-2LB had reduced 20 mM fumarate, acetogenesis had a similar rate (0.83 ± 0.04 meeq · liter−1 · day−1, between days 14 and 35) (Fig. 8C). These results show that strain 4t3-1-2LB was not able to enhance acetogenesis from Fe(0) by Acetobacterium strain 73-4-6p-4.
FIG 8
FIG 8 Change of acetate, formate, fumarate, malate, succinate, and hydrogen concentrations, expressed in 10−3 electron equivalents per volume of the liquid phase (meeq · liter−1), over time with Acetobacterium strain 73-4-6p-4 (A), Shewanella strain 4t3-1-2LB and Acetobacterium strain 73-4-6p-4 inoculated together at day 0 (B), and Acetobacterium strain 73-4-6p-4 inoculated at day 14 after Shewanella strain 4t3-1-2LB had completed the reduction of 20 mM fumarate (C). Plotted values are averages from triplicate bottles, and error bars show the standard deviation. Note the different scale of the x axis for panel C.
For comparison, all product formation rates, i.e., approximations for the corrosion rates, obtained in this study are summarized in Fig. 9.
FIG 9
FIG 9 Comparison of product formation rates (meeq · liter−1 · day−1) with Fe(0) (as described in the text), which are approximations for the corrosion rate. S., Shewanella strain 4t3-1-2LB; A., Acetobacterium strain 73-4-6p-4. The letters in the bars indicate statistically different groups as determined with a Duncan test (α = 0.05); corrosion rates increase in alphabetical order.

DISCUSSION

Shewanella strain 4t3-1-2LB ferments fumarate to succinate and CO2 in the absence of Fe(0).

Shewanella strain 4t3-1-2LB was able to convert fumarate to succinate in the presence and absence of Fe(0) (Fig. 2). Differences in stoichiometry, pH, and CO2 content suggested that different metabolic processes occurred with and without Fe(0) (Fig. 2 and 3). In the absence of an electron donor, strain 4t3-1-2LB most likely performed a fumarate fermentation by coupling the reduction of six moles of fumarate to succinate with the oxidation of one mole of fumarate to CO2G°′ values were calculated as described by Madigan et al. [48]): 7C4H2O42− + 8H2O → 6 C4H4O42− + 4HCO3 + 2H+G°′ = −63.09 kJ · mol−1 fumarate) (reaction B). In the presence of Fe(0) as the electron donor, the complete reduction of fumarate to succinate coupled to the oxidation of Fe(0) is thermodynamically more favorable than fumarate fermentation: C4H2O42− + Fe(0) + 2H+ → C4H4O42− + Fe2+G°′ = −85.23 kJ · mol−1 fumarate) (reaction C). These reactions are in good agreement with the pH evolutions observed in our experiments (Fig. 3). In addition, the measured formation of 0.20 mmol CO2 in the headspaces of bottles of strain 4t3-1-2LB in the absence of Fe(0) corresponds well with the expected increase of 0.34 mmol based on reaction B, as part of the formed CO2 remained in solution as bicarbonate. Moreover, the theoretical stoichiometry of 6:7 (86%) for succinate-fumarate is in agreement with the observed ratio (80%), as part of the fumarate was likely used for biomass formation.
The same fumarate fermentation reaction (reaction B) was reported for Providencia rettgeri (49), Malonomonas rubra (50), and Syntrophobacter fumaroxidans (51). Besides fumarate fermentation, S. fumaroxidans can also couple the complete reduction of fumarate to succinate with the oxidation of electron donors, such as hydrogen. Geobacter sulfurreducens converts fumarate to succinate with a 1:0.8 stoichiometric ratio in the absence of an electron donor, but it is unable to grow with this reaction (52). In addition, Shewanella amazonensis is able to grow on fumarate in the absence of an electron donor (J. Gralnick, unpublished results), suggesting that fumarate fermentation may be common within the genus Shewanella. Consequently, experiments studying microbial conversions with fumarate as an electron acceptor should always carefully evaluate whether decreasing fumarate concentrations are due to the oxidation of an electron donor or due to fumarate fermentation.

Transient formation of malate leads to Fe(II) and Fe(III) complexation and diminishes the abiotic hydrogen formation rate.

Malate was transiently formed during the conversion of fumarate by strain 4t3-1-2LB, independently of the presence of Fe(0) (Fig. 2). Hydration of fumarate to malate is a reversible reaction that does not require energy and is normally catalyzed by the enzyme fumarate hydratase (fumarase). This enzyme participates in the tricarboxylic acid (TCA) cycle of many organisms, including Shewanella spp. (53). This or a similar enzyme was released by strain 4t3-1-2LB during aerobic growth in LB medium (likely by cell lysis), as the spent LB medium also converted fumarate to malate (Fig. 7B). Fumarate conversion by G. sulfurreducens also led to transient formation of malate (52).
Malate is known to form stable complexes with Fe(II) and Fe(III), which prevents Fe(II) and Fe(III) precipitation at circumneutral pH (45, 46, 54). In our experiment, this was clear from the increase of the dissolved Fe(II) concentration proportionally to the hydrogen concentration in abiotic controls with malate (Fig. 4B). Malate was likely capable of keeping Fe(II) in solution as long as its concentration was higher than the Fe(II) concentration (46), which explains why dissolved Fe(II) concentrations decreased after day 2 to 6 with strain 4t3-1-2LB growing on Fe(0) and fumarate (Fig. 2B and 5).
Complexation of Fe(III) by malate could also explain the yellow color of the liquid phase during fumarate reduction by strain 4t3-1-2LB (see Fig. S2 in the supplemental material), as Fe(III) is usually not soluble. As described above, dissolved Fe(III) concentrations were low in this study and could not be accurately measured. It is not clear if the formed Fe(III) resulted from the oxidation of Fe(II) by trace amounts of oxygen intruded into the bottles or possibly by strain 4t3-1-2LB itself. Based on the color of the crust overlaying the aggregated Fe(0) powder (Fig. S2), green rust formation possibly occurred. This further suggests the presence of Fe(III), as green rust is typically a mixture of Fe(II) and Fe(III) hydroxides. Interestingly, various Shewanella strains were already reported to form green rust by reducing Fe(III) oxides (55, 56). Further mineralogical characterizations will be required to verify if the dark green crust indeed consisted of green rust.
Malate also diminished the abiotic hydrogen formation rate in comparison to those with fumarate and succinate (Fig. 4 and 9). Several organic anions, including malate, were already described as good inhibitors of steel corrosion (57). This is likely due to the adsorption with their functional groups on the Fe(0) surface, thereby partially blocking the access for water, which is required for corrosion (58).
Our results show that corrosion rates cannot be correctly assessed from dissolved Fe(II) concentrations alone [for instance, higher dissolved Fe(II) concentrations but a lower hydrogen formation rate in abiotic controls with malate versus fumarate (Fig. 4B and 9)], even though this often occurs in biocorrosion studies. As an alternative to a destructive extraction of Fe(II) and Fe(III) with acid, the addition of a biologically inert chelator, such as EDTA, could help with correctly assessing corrosion rates in MIC studies by keeping Fe(II) and Fe(III) in solution. Nevertheless, the possible effect of such a chelator on the corrosion process itself needs to be well understood first.

Shewanella strain 4t3-1-2LB possibly uses a direct EET mechanism.

Strain 4t3-1-2LB had an Fe(0) corrosion rate significantly higher than that of any of the abiotic controls or spent-medium tests (Fig. 9). Hydrogen consumption was at least in part responsible for fumarate reduction by strain 4t3-1-2LB, as hydrogen concentrations remained below the detection limit during succinate formation (Fig. 2B). Deutzmann et al. (13) previously demonstrated that cell-free spent medium of Methanococcus maripaludis enhanced the hydrogen and formate formation from Fe(0). In addition, our upcoming study found that the increased hydrogen generation by filter-sterilized spent medium could explain the Fe(0) corrosion enhancement by several acetogens (Philips et al., submitted). The components in the spent medium responsible for this increased hydrogen generation are likely free extracellular hydrogenase enzymes, which adsorb on the electroactive surface and catalyze the formation of hydrogen (13, 59, 60). Also in this study, spent defined medium increased the rate of hydrogen formation from Fe(0) in comparison to the abiotic hydrogen formation rate (Fig. 9). A similar increased hydrogen formation rate was measured after exchanging the medium without adding an electron acceptor. Nevertheless, these rates were much lower than the rate of corrosion by strain 4t3-1-2LB with fumarate (Fig. 9). Consequently, the corrosion-enhancing mechanism of strain 4t3-1-2LB cannot be based solely on a kinetic stimulation of the chemical hydrogen formation reaction on the Fe(0) surface by extracellular components (Fig. 10).
FIG 10
FIG 10 Schematic overview of different possible mechanisms for electron uptake from Fe(0) by strain 4t3-1-2LB, contradicted or suggested by the results of this study.
Interestingly, spent LB medium led to a decreased hydrogen formation rate, due to the formation of malate (0.26 ± 0.01 meeq · liter−1 · day−1) (Fig. 7B and 9). Shewanella spp. do not express hydrogenases during aerobic growth (LB medium) (61), while during anaerobic growth on Fe(0), strain 4t3-1-2LB likely expressed hydrogenases to consume the chemically formed hydrogen. This shows that strong differences in the presence and concentration of extracellular enzymes can arise from different types of spent medium and different growth conditions, which will be of major importance for further studies investigating microorganisms whose EET mechanism relies on extracellular enzymes.
Exchanging the medium (Fig. 5A), as well as electrochemical measurements (see Fig. S5 in the supplemental material), showed that the corrosion-enhancing mechanism of strain 4t3-1-2LB was also not based on the excretion of dissolved redox mediators (Fig. 10). In contrast, exchanging the medium of S. oneidensis MR-1 grown on an anode strongly diminished its current production (62), demonstrating the importance of electron shuttling by its excreted flavins (21). Flavins possibly also played a role in catalyzing cathodic oxygen reduction by Shewanella loihica (24), while Shewanella putrefaciens likely did not use a redox mediator to reduce oxygen with cathodic electrons (22).
Both the medium exchange experiment and SEM imaging showed that cells were attached to the Fe(0) powder (Fig. 5 and 6). For this reason, it is possible that strain 4t3-1-2LB used a direct mechanism to obtain electrons from Fe(0) (Fig. 10). This could entail a reversal of the Mtr pathway, similarly as was described for S. oneidensis MR-1 reducing fumarate or oxygen with a cathode as an electron donor (23, 25, 26). Those studies, however, first grew strain MR-1 on an anode, after which the electrode potential was lowered and fumarate or oxygen was added, followed by the examination of the mechanism within hours. This experimental procedure could have strongly affected the EET mechanism used by strain MR-1. Moreover, the reversal of the Mtr pathway was recently found not to support cell growth but to support only cell maintenance (26). In our experiments, strain 4t3-1-2LB grew with Fe(0) as an electron donor (not experimentally measured), as it would otherwise have favored fumarate fermentation. Further investigations, for instance, using mutant strains and electrochemical characterizations of cells grown on cathodes, will be required to assess whether a reversal of the Mtr pathway could be involved in the uptake of extracellular electrons by strain 4t3-1-2LB.
Finally, another plausible explanation for the corrosion enhancement by strain 4t3-1-2LB could be that attached cells scavenge hydrogen on the Fe(0) surface and thereby cause a thermodynamic shift of reaction A (Fig. 10). This cathodic depolarization theory has in recent literature been contested by the finding that only strains isolated with Fe(0) were found to enhance corrosion, while typical hydrogen-consuming strains did not (2, 6, 8, 9). Those studies, however, did not evaluate differences in the hydrogen threshold (minimum hydrogen level allowing microbial growth) between strains, even though it seems likely that enrichments with Fe(0) lead to strains better adapted to use low hydrogen concentrations than strains enriched with a hydrogen overpressure. Fumarate reducers typically have one- and two-orders-of-magnitude-lower hydrogen thresholds than methanogens and acetogens, respectively (63). Possibly this explains the much higher corrosion enhancement factor obtained in this study in comparison to that of acetogens (Fig. 8A). Further investigations, for instance, testing mutant strains incapable of hydrogen consumption (64), will be required to investigate the involvement of hydrogen in the electron uptake mechanism of strain 4t3-1-2LB.

Ecological relevance and technological implications.

The genus Shewanella had only a low abundance (0.6%) in the acetogenic enrichment from which Shewanella strain 4t3-1-2LB was isolated (Philips et al., submitted). Nevertheless, Shewanella cells must have been active in the enrichment, as they survived five transfers of the enrichment and grew quickly once transferred to LB medium. Coculturing Shewanella strain 4t3-1-2LB with an Acetobacterium isolate did not increase acetogenesis from Fe(0) by the Acetobacterium strain (Fig. 8). In contrast, the corroding IS4 strain increased acetate and methane production in coculture with Acetobacterium woodii and M. maripaludis, respectively, on a cathode (16). Also, the composition of microbial communities on acetogenic cathodes has already led to the suggestion that extracellular electrons could be withdrawn by electrotrophs, such as Desulfovibrio spp., which pass them as hydrogen to acetogens (65). Our results show that strain 4t3-1-2LB definitely did not play such a syntrophic role. This is likely because it does not increase the formation of available hydrogen from Fe(0) (Fig. 5B), in contrast to, for instance, strain IS4 (6, 16). Consequently, the function of strain 4t3-1-2LB in the acetogenic community remains unclear. It is possible that it survived by consuming metabolites released by the acetogenic community, such as fumarate, possibly in mixotrophy with Fe(0) as the electron donor.
Shewanella spp. and related species are likely important for MIC, as they were present in biofilms on corroded steel (27, 66), dominated the microbial community of water exposed to metal materials (29), and have frequently been isolated from environments with corroded structures (28, 30, 67), as in our previous work (Philips et al., submitted). Until now, the importance of Shewanella spp. for MIC was mainly related to their Fe(III)-reducing properties. For this reason, their effect on corrosion was usually studied by the addition of a suitable electron donor, i.e., lactate (31, 3335, 66). Only a few studies examined the effect of Shewanella spp. on corrosion with the addition of electron acceptors, such as sulfite or ferric citrate (35) or nitrate (36, 37). Only small corrosion enhancements were found (1.3-fold with nitrate [measured after 20 h] [36] to 4.2-fold with sulfite [but with lactate present] [35]), which were indirectly linked to the metabolism of the Shewanella strains. Only recently, nitrate was reported to support Fe(0) oxidation by strain MR-1 (corrosion enhancement factor without lactate, about 1.3), but it remained unclear to what level corrosion was caused by the bacterial metabolism or by the corrosive effect of the produced nitrite (37). In contrast, our study found a strong ([7.0 ± 0.6]-fold) increase of the corrosion rate by a Shewanella strain solely by the use of Fe(0) as an electron donor in the presence of an electron acceptor (here fumarate). Fumarate likely occurs only in low concentrations in the environment, but Shewanella spp. can use various other electron acceptors, including environmentally ubiquitous oxygen, nitrate, or Fe(III). The effect of these electron acceptors on MIC by Shewanella spp. should be reevaluated, as our study suggests that Shewanella spp. could strongly aggravate corrosion. Future studies should also use more-realistic iron-based materials (for example steel coupons), instead of Fe(0) powder as used in this study, to correctly assess the possibly large contribution of Shewanella spp. to biocorrosion.
Besides its undesirable induction of corrosion, strain 4t3-1-2LB could be of interest for biotechnological applications, such as microbial conversions powered by cathodes. Genetic systems exist for Shewanella spp., and their aerobic growth strongly simplifies cultivation in comparison to other model strains for cathodic conversions (68). Once its EET mechanism for electron uptake is well understood, our Shewanella strain could become an interesting candidate for genetic engineering toward a strain producing valuable end products on cathodes.

MATERIALS AND METHODS

Strains and growth conditions.

Shewanella strain 4t3-1-2LB and Acetobacterium strain 73-4-6p-4 were previously isolated from acetogenic enrichments, started from freshwater anoxic corrosion products with Fe(0) as the sole electron donor and CO2 and water as the only possible electron acceptors (Philips et al., submitted). Isolates were obtained by a novel plating procedure using agar plates with an Fe(0) powder top layer. Shewanella strain 4t3-1-2LB is highly similar to S. fodinae (99% identity, based on the near-full-length 16S rRNA gene sequence) (NCBI accession number MG835274) (Fig. 1), while Acetobacterium strain 73-4-6p-4 is closely related to A. wieringae and A. malicum (both 99% identity) (NCBI accession number MG835272) (Philips et al., submitted). Frozen stocks (−80°C, in 10% [vol/vol] DMSO) of Shewanella strain 4t3-1-2LB were revived in aerobic Luria-Bertani (LB) medium, while anaerobic DSMZ 135 medium with 1 g · liter−1 fructose was used to revive Acetobacterium strain 73-4-6p-4. Cultures were transferred once and were used in late log phase for inoculation (2.5%, [vol/vol] for all experiments). Before inoculation, cells were washed by centrifugation and brought into defined medium to avoid carryover of organic substrates. Washing of Acetobacterium cells was performed inside an anaerobic chamber (GP-Campus; Jacomex) with an N2-CO2 (90:10, vol/vol) atmosphere.

Corrosion experiments.

Experiments were performed in 120-ml serum bottles with 40 ml anaerobic defined medium and 2 g Fe(0) powder (99%; Riedel-deHaën <212 μm, gray color]). The defined medium was composed as described elsewhere (Philips et al., submitted). The medium was made anoxic by boiling and N2-CO2 (90:10, vol/vol) gas sparging (at least 30 min) before it was brought under N2-CO2 gas flow into bottles with Fe(0) powder. This procedure prevented the oxidation of Fe(0) to Fe(III) upon exposure to oxygen and water. Once in the bottles, the medium was flushed for an additional 10 min. Bottles were autoclaved with the Fe(0) powder in the medium. Filter-sterilized 3-(N-morpholino)propanesulfonic acid (MOPS) (50 mM, brought to pH 7.2 with 10 M NaOH) and NaHCO3 (20 mM) were added after autoclaving. Bottles with iron powder were flushed with sterile N2-CO2 gas for 5 min just before the start of experiments to remove any hydrogen abiotically formed during the storage of the bottles. Sodium fumarate, succinate, or malate was added from filter-sterilized anoxic stock solutions at concentrations of 20 mM.
A first experiment tested fumarate conversion by Shewanella strain 4t3-1-2LB in the presence and absence of Fe(0) (see Fig. S1A in the supplemental material). In addition, abiotic controls with Fe(0) and fumarate, succinate, or malate were tested. A second series of experiments explored the corrosion-enhancing mechanism of strain 4t3-1-2LB (Fig. S1B). Medium was exchanged by replacing the liquid phase with 40 ml fresh anaerobic defined medium, while the iron powder was retained in the bottle. Afterwards, the bottles were briefly flushed with sterile N2-CO2 gas. The collected medium (spent defined medium) was filter sterilized (twice through a 0.2-μm sterile syringe filter) and added to new bottles containing 5 ml anaerobic defined medium and 2 g Fe(0) powder. In addition, filter-sterilized supernatant of strain 4t3-1-2LB aerobically grown in LB medium (spent LB medium) was added at 2.5% (vol/vol) to bottles with 40 ml anaerobic defined medium and 2 g Fe(0) powder, after which the bottles were briefly flushed. Electrochemical measurements on filtered liquid samples were performed using a rotating-disk electrode, as described elsewhere (Philips et al., submitted). Iron powder samples were prepared for scanning electron microscopy (SEM) (69) and visualized with a Phenom Pro SEM (70). A third experiment investigated Fe(0) corrosion by cocultures of Shewanella strain 4t3-1-2LB and Acetobacterium strain 73-4-6p-4 (Fig. S1C). Both strains were inoculated with 2.5% (vol/vol).
All experiments were performed in triplicate with static incubation at 28°C. Samples were collected once or twice a week for analysis of the headspace gas composition and VFA and dissolved Fe(II)/Fe(III) concentrations.

Chemical analyses.

The H2 and CO2 contents of gas samples (1 ml) were measured on a compact gas chromatograph (GC), as previously described (71). Liquid samples (1 ml, filtered through a 0.2-μm syringe filter [Chromafil Xtra]) were prepared for VFA or Fe(II)/Fe(III) analysis as reported elsewhere (Philips et al., submitted). VFA concentrations were measured on an ion chromatograph (72). Additional standards were prepared from sodium fumarate, malate, and succinate. Dissolved Fe(II)/Fe(III) concentrations were measured with an adapted phenanthroline assay (Philips et al., submitted). After the absorbance of the initial color reaction product was measured [dissolved Fe(II) concentration], a spatula tip of ascorbic acid powder was added to reduce Fe(III) to Fe(II), and the absorbance was measured again [dissolved Fe(II) + Fe(III) concentration]. The pH was measured with an InLab Semi-Micro pH electrode (Mettler Toledo), and optical densities were measured at 610 nm using a UV-visible spectrophotometer (Isis 9000; Dr Lange). To allow comparison, all hydrogen, fumarate, malate, succinate, acetate, and dissolved Fe(II) concentrations were expressed as 10−3 moles electron equivalents [assuming two electrons for each molecule of H2, fumarate, malate, succinate, and Fe(II) and eight electrons for each molecule of acetate] per volume of the liquid phase (meeq liter−1). As hydrogen has a low solubility (Henry coefficient of 7.8 · 10−4 M · atm−1 [73]), only its concentration in the headspace was considered in the calculations. Statistical tests were performing using SPSS Statistics.

ACKNOWLEDGMENTS

J.P. was funded by a postdoctoral grant from the Special Research Fund (BOF) of Ghent University. J.P., A.P., J.B.A.A., and K.R. were supported by the European Research Council via Starter Grant no. 310023 “ELECTROTALK.” K.D.P. was supported by the Research Foundation Flanders (SBO BRANDING) and the Special Research Fund (BOF) Concerted Research Actions (GOA, BOF12/GOA/008) from the Flemish Government. In addition, this project was supported by a King Abdullah University of Science & Technology (KAUST) Competitive Research Grant (OSR-2016-CRG5-2985-01).
We thank Jana De Bodt (Center for Microbial Ecology and Technology, Ghent University) for her help with sampling. We acknowledge Greet Van de Velde (Center for Microbial Ecology and Technology, Ghent University) for performing the ion chromatography analyses. We thank Pieter Candry and Jo De Vrieze (Center for Microbial Ecology and Technology, Ghent University) for the maintenance of the compact GC. SEM imaging was performed with the appreciated help of Silvia Hidalgo Martinez and Filip Meysman (University of Antwerp). We acknowledge Jeet Varia (Center for Microbial Ecology and Technology, Ghent University) for his useful comments that contributed to this work.

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Information & Contributors

Information

Published In

cover image Applied and Environmental Microbiology
Applied and Environmental Microbiology
Volume 84Number 2015 October 2018
eLocator: e01154-18
Editor: Shuang-Jiang Liu, Chinese Academy of Sciences
PubMed: 30054363

History

Received: 4 June 2018
Accepted: 21 July 2018
Published online: 1 October 2018

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Keywords

  1. Acetobacterium
  2. Shewanella fodinae
  3. biocorrosion
  4. complexation
  5. extracellular electron transfer mechanisms
  6. fumarate fermentation
  7. malate
  8. microbially influenced corrosion
  9. solid electron donors
  10. zero-valent iron

Contributors

Authors

Center for Microbial Ecology and Technology, Ghent University, Ghent, Belgium
Niels Van den Driessche
Center for Microbial Ecology and Technology, Ghent University, Ghent, Belgium
Kim De Paepe
Center for Microbial Ecology and Technology, Ghent University, Ghent, Belgium
Antonin Prévoteau
Center for Microbial Ecology and Technology, Ghent University, Ghent, Belgium
Jeffrey A. Gralnick
Department of Plant and Microbial Biology, University of Minnesota, St. Paul, Minnesota, USA
Jan B. A. Arends
Center for Microbial Ecology and Technology, Ghent University, Ghent, Belgium
Center for Microbial Ecology and Technology, Ghent University, Ghent, Belgium

Editor

Shuang-Jiang Liu
Editor
Chinese Academy of Sciences

Notes

Address correspondence to Korneel Rabaey, [email protected].

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