A kinetic model for bacterial Fe(III) oxide reduction in batch cultures

Transcription

1 WATER RESOURCES RESEARCH, VOL. 39, NO. 4, 098, doi:0.029/2002wr0032, 2003 A kinetic model for bacterial Fe(III) oxide reduction in batch cultures Eric L. Hacherl and David S. Kosson Department of Civil and Environmental Engineering, Vanderbilt University, Station B, Nashville, Tennessee, USA Robert M. Cowan Department of Environmental Sciences, Rutgers, The State University of New Jersey, New Brunswick, New Jersey, USA Received 5 March 2002; revised 25 March 2002; accepted 25 September 2002; published 22 April [] A model has been developed describing the microbial reduction of solid-phase electron acceptors (Fe(III) oxides) as well as dissolved electron acceptors (chelated Fe(III) or organic electron shuttles) in Shewanella alga BrY. The model utilized a multiple-substrate, Monod kinetics formulation. The Monod description of solid Fe(III) reduction requires a normalization of surface Fe concentration to biomass concentration in order to describe the bioavailable Fe(III) concentration. The model also contains provisions for irreversible sorption of Fe(II) to Fe(III) oxide surfaces and for the precipitation of Fe(III) carbonates. The loss of bioavailable Fe(III) due to sorption of Fe(II) was found to be minor, even for highly sorptive amorphous Fe(III) oxyhydroxides. However, the final extent of microbial reduction is very sensitive to the rate of siderite precipitation, assuming that siderite precipitation could partially occlude Fe(III) surface sites. The use of a multisubstrate Monod kinetics model enabled an evaluation of the effects of electron shuttles on solid Fe(III) reduction. Because the electron shuttle is recycled, very small additions can greatly increase the overall rate of solid Fe(III) reduction. INDEX TERMS: 65 Global Change: Biogeochemical processes (4805); 4840 Oceanography: Biological and Chemical: Microbiology; 4842 Oceanography: Biological and Chemical: Modeling; 485 Oceanography: Biological and Chemical: Oxidation/reduction reactions; KEYWORDS: dissimilatory iron reduction, multiple Monod kinetics, siderite precipitation, Fe(II) sorption, bioavailability, electron shuttle, anthraquinone disulfonic acid (AQDS) Citation: Hacherl, E. L., D. S. Kosson, and R. M. Cowan, A kinetic model for bacterial Fe(III) oxide reduction in batch cultures, Water Resour. Res., 39(4), 098, doi:0.029/2002wr0032, Introduction [2] In anoxic subsurface environments many types of bacteria are capable of utilizing Fe(III) oxides, hydroxides and oxyhydroxides (hereafter collectively referred to as Fe(III) oxides) as their electron acceptor, reducing solid Fe(III) to more soluble Fe(II). Reductive dissolution of solid Fe(III) can have the secondary effect of releasing adsorbed or coprecipitated inorganic contaminants such as heavy metals and radionuclides [Luoma and Davis, 983; Singh and Subramanian, 984; Tessier et al., 985; Gadd, 996]. This secondary effect is most dramatic in shallow subsurface environments that undergo cycles of oxidation and reduction, since they contain the youngest or most biologically available amorphous or slightly crystalline oxyhydroxides [Schwertmann and Taylor, 989]. Ultimately, a model is desirable which can predict the mobility of oxide-associated radionuclides and heavy metals in anoxic or periodically reduced subsurface environments as an aide to understanding system behavior under different management scenarios. However, this requires an independent understanding of the biogeochemistry of the microbial Fe(III) reduction process, the nature of the association between the Fe(III) oxides and the inorganic contaminants, and the mass transfer and reaction kinetics of the system components. The association of Fe(III) oxides and inorganic contaminants is a function of the unique Fe(III) oxides present, the chemical properties of the inorganic contaminant and the history of their association, which determines whether the contaminants are surface attached or are coprecipitated. [3] For microbial reactions governed by enzymatic controls, Monod kinetics can often provide a good empirical representation of reaction rates [Monod et al., 949]. For this rate formulation, the reaction rate is dependent on the concentration of a limiting species according to: dc dt ¼ X ^m C b K s þ C Y g ðþ Now at Sterile Process Technology and Engineering, Merck & Co., Inc., West Point, Pennsylvania, USA. Copyright 2003 by the American Geophysical Union /03/2002WR0032 HWC 3 - This equation is a generalized expression in which refers to the concentration of some limiting substrate, which can be a carbon source, energy source or electron acceptor. [4] Microbial Fe(III) reduction relies on one or more membrane-bound electron transport proteins to mediate

2 HWC 3-2 HACHERL ET AL.: KINETICS OF BACTERIAL Fe(III) REDUCTION the process [Arnold et al., 990; Gorby and Lovley, 99; Lovley et al., 99; Myers and Myers, 993, 997]. Similar proteins are probably responsible for soluble electron shuttle reduction (e.g. anthrquinone-2,6-disulfonic acid (AQDS)) as well [Newman and Kolter, 2000]. Therefore it is reasonable to assume that microbial reduction of both soluble Fe(III) (available as chelated or complexed Fe(III)) and electron shuttles would both follow typical Monod behavior. Solid Fe(III) reduction is difficult to model using Monod kinetics. Presently, only first-order rate equations have been used to describe microbial Fe(III) oxide reduction kinetics [Roden and Urrutia, 999; Liu et al., 200a]. Both research groups have described the Fe(III) reduction rate normalized to estimates of free Fe(III) oxide surface area: ds Fe 2þ dt ¼ k red X Fe 3þ ;fss Notably, the Monod representation can be reduced to a firstorder representation in the restricted region where C K s in (). The first-order constant and the Monod parameters are related by: k red = ^m/y g K s. [5] Reactive transport models commonly assume that microbial Fe(III) reduction obeys first-order kinetics with respect to primary organic energy substrates [Berner, 980; Wersin et al., 99; van Cappellen and Wang, 995, 996; Hunter et al., 998]. This assumption implies that the bioavailability of organic carbon, not microbial substrate utilization, is rate limiting; again this is a limiting case of Monod kinetics in which S K s. For readily available substrates, Monod kinetics in terms of substrate concentration would still be valid. Multiple substrate Monod kinetics has not been investigated in terms of electron acceptor availability for Fe(III)-reducing microorganisms. [6] The kinetics of microbial Fe(III) reduction also is impacted by abiotic processes. For example, dissolved Fe(II) produced from Fe(III) reduction can impact the overall rate and extent of the reduction process through sorption of Fe(II) to Fe(III) oxides and through precipitation of siderite (FeCO 3 ). It is well documented that goethite and Fe(III) oxides in subsurface materials have a high capacity for sorption of free Fe(II) [Urrutia et al., 998, 999; Zachara et al., 2000]. Typically this sorption can be represented over broad dissolved Fe(II) concentrations by using a Freundlich type isotherm [Urrutia et al., 999]. At lower dissolved Fe(II) concentrations a Langmuir type isotherm may be sufficient [Liu et al., 200a]. Sorption of Fe(II) (in the form of Fe(OH) 2 compounds) to Fe(III) oxides may also be the first step in the formation of magnetite (Fe 3 O 4 )[Tamaura et al., 983; Roden and Zachara, 996; Cooper et al., 2000], which is a common biogenic end product under appropriate ph and Eh conditions. [7] Siderite can either nucleate on Fe(III) oxide surfaces or nucleate in solution with different effects on microbial Fe(III) reduction. Surface assisted nucleation on goethite crystals [Stumm, 992] reduces the bioavailable Fe(III) via surface site occlusion, whereas precipitation in solution may increase bioavailable Fe(III) by shifting the sorbed Fe(II) equilibrium toward Fe(II) desorption [Fredrickson et al., 998]. [8] In this paper we develop a model framework relating several of the most important biogeochemical processes, particularly ones that are most likely to be rate limiting, in a ð2þ simplified microcosm system to provide an improved understanding of the relationship between microbial Fe(III) reduction and abiotic geochemical reactions with the resulting Fe(II). This kinetic model utilizes multisubstrate Monod kinetics in which the limiting substrate is actually the electron acceptor. Solid Fe(III), chelated Fe(III) or oxidized electron shuttles serve as potential electron acceptors. Bacterial production of carbon dioxide (hence bicarbonate) leads to the potential precipitation of siderite, which may occur on oxide surfaces. In addition, soluble Fe(II) sorbs to Fe(III) oxide surfaces. Available oxide surface sites are affected by the reversible siderite precipitation and irreversible adsorption processes. A diagram of the physical system described by this model is shown in Figure. Model parameters are varied over ranges representative of literature reported values in order to test the sensitivity of the model to the biogeochemical features. The model is also used to investigate the potential limits to solid Fe(III) bioavailability that are commonly observed in Fe(III) reduction experiments. 2. Mathematical Development 2.. Model Overview [9] In this model, Fe(III) (aq), Fe(III) oxides and soluble electron shuttles are all potential electron acceptors for bacterial respiration. The sole carbon and energy source is the electron donor lactate (CH 3 CHOHCOO ). Lactate is incompletely oxidized to acetate (CH 3 COO ) and carbon dioxide (CO 2 ), with some of the carbon diverted to biomass (C 5 H 7 O 2 N). This representation of lactate oxidation was chosen since the organism on which this model is based, Shewanella alga BrY, is incapable of completely oxidizing lactate [Caccavo et al., 992]. Carbon dioxide is in equilibrium with bicarbonate (HCO 3 ) and is referenced as such. The stoichiometry of Fe(III) reduction and biomass formation (on an electron mole basis) is given by: FeðIIIÞþ0:25 þ Y b=ea CH3 CHOHCOO þ 0:05Y b=ea NH3 þ 0:5 0:5Y b=ea H2 O ¼ FeðIIÞþ0:25HCO 3 þ 0:25 þ Y b=ea CH3 COO þ :25H þ þ 0:05Y b=ea C5 H 7 O 2 N ð3þ Electron shuttles (e.g. AQDS) can be represented by a similar equation but they may have the potential to accept more electrons than Fe(III) [Hacherl et al., 200] and they require different yield coefficients. The stoichiometry in (3) is dependent on the initial carbon substrate and the organism of interest, and could be modified to accommodate alternate substrates or microbial species. [0] Iron(III) reduction generates dissolved Fe(II) through reductive dissolution. Dissolved Fe(II) then partitions into the solid phase via sorption and siderite (FeCO 3 ) precipitation. Sorbed Fe(II) is assumed to coat solid phase Fe(III) and reduce the pool of bioavailable Fe(III) in the ratio of 2 Fe(III): Fe(II), the ratio found in magnetite. Siderite precipitation occurs only when the solution is supersaturated with respect to ferrous iron and carbonate. [] Bacterial reduction of electron shuttles produces soluble chemical species capable of reducing Fe(III) abiotically. The Fe(II) (aq) resulting from this redox transformation is subject to the same reactions as Fe(II) produced biogenically.

3 HACHERL ET AL.: KINETICS OF BACTERIAL FE(III) REDUCTION HWC 3-3 Figure. Diagram of Fe(III) reduction system as formulated in mathematical model. [2] In all, this model computes the fate of four solid components and five dissolved components, numbered consecutively for reference within the model. The four solids are: () biomass, (2) Fe(III) oxides, (3) adsorbed Fe(II), and (4) siderite. The five aqueous components are: (5) dissolved Fe(III) as a chelated/complexed species, (6) dissolved Fe(II) as a free ion or a chelated/complexed species, (7) oxidized electron shuttle (AQDS), (8) reduced electron shuttle (AHDS), and (9) dissolved bicarbonate Kinetic Reactions [3] In this model we consider only the electron acceptor utilization to be rate limiting, so there is no need for Monod representation of organic carbon utilization. Thus, at all times organic carbon is present in sufficient excess that reduction is zero order with respect to substrate. We have done this to allow experimental determination of the kinetics associated with Fe(III) bioavailability and reduction. The model incorporates microbial reduction kinetics from three potential electron acceptors: solid Fe(III) oxide, chelated Fe(III) and any other electron accepting species that can act as an electron shuttle. The electron shuttle must satisfy two criteria: () it must be soluble and (2) it must have a reduction potential between that of the Fe(III)/Fe(II) couple and the substrate/co 2 couple. [4] All three of the electron acceptors behave according to Monod kinetics, equation (); however, systems contain- Table. Surface Properties of Fe(III) Oxides a Property AFO MSA-Gt LSA-Gt Surface area [m 2 g ] 600 b 55 c 22 d Unit cell formula Fe(OH) 3 FeOOH FeOOH Unit cell weight [g mole ] Calculated surface site density [mole sites (mole oxide) ] K f 0.45 d 2.0 c 3 d N f 0.08 d 0.6 c 0.43 d a AFO, amorphous ferric oxyhydroxide; MSA-Gt, medium surface area goethite; LSA-Gt, low surface area goethite. b Roden and Zachara [996]. c Urrutia et al. [998]. d Hacherl et al. [200]. Figure 2. Sorption of dissolved Fe(II) to AFO and LSA goethite as a function of time. Sorbed Fe(II) is calculated as the difference between total Fe(II) and dissolved Fe(II).

4 HWC 3-4 HACHERL ET AL.: KINETICS OF BACTERIAL Fe(III) REDUCTION Table 2. Kinetics Model for Microbial Fe(III) Reduction a Components Process (), X b (2), X Fe 3+ (4), X Fe 2+ (5), S Fe 3+ (6), S Fe 2+ (7), S Es+ (8), S Es (9), S HCO3 Process Rate (a), biomass growth on 20 Y b/xfe + 4 Term solid Fe (b), biomass growth on 20 Y b/sfe + 4 Term 2 chelated Fe (c), biomass growth on 20 Y b/es Term 3 electron shuttle (d), abiotic Fe reduction k W Fe 3+S Es (e), Fe(II) precipitation k 2 ( ) (VW) k 2 ((K 2 ) /2 K /2 2 ) 2 (WHM) (f ), Fe(II) dissolution K 2 X Fe 2+( ) < (g), biomass decay bx b a Ordinary differential equations can be derived from this matrix for eight of the nine components considered in the model. Component (3), sorbed Fe(II), 0 0 has no associated rate expression. Term W Fe 3þ 0 SEsþ A. Y b=es ^m Esþ K SEsþ ð Þ þ K SEsþ ð Þ X b K SðhÞ W þ K SEsþ ð Þ Fe 3þ K S ð Fe 3þ Þ S Fe3þ þsesþ K SðhÞ þ K SðhÞ K S ð Fe 3þ X b W Fe 3þ Þ S Fe 3þ þ K SðÞ K SEsþþ X b SEsþ ð Þ W Fe 3þ A. Term 2 20Xb Y b=sfe ^m Fe K S Fe 3þ ð S Fe 3þ K Þ þ S ð Fe 3þ K Þ X b K SðhÞ W þ S ð Fe 3þ Þ Fe 3þ K SEsþþS SEsþ ð Þ Fe 3þ A. Term 3 ing more than one electron acceptor will be affected by interactions between the acceptors. The two interactions considered are () competition by multiple electron acceptors for the active site, decreasing the observed utilization rate of the individual electron acceptors, and (2) fortuitous electron acceptor utilization from the presence of multiple available electron acceptors, increasing the observed overall electron utilization rate to greater than the utilization rates for individual electron acceptors. Electron acceptor utilization is due to all species present [Smouse, 980; Cowan, 994; Guha et al., 999]: m t ¼ Xn m i i¼ ð4þ coverage of this surface. Therefore, we have normalized bioavailable Fe(III) to surface area and surface coverage by bacteria, such that the concentration of solid Fe(III) used in equation (5) is: C FeðIIIÞ;solid ¼ X b W Fe 3þ where W Fe 3+ is a measure of the total number of reactive Fe(III) surface sites. W Fe 3+ can be calculated from the oxide surface area, unit cell weight, and surface site density, which is dependent on the type of oxide present (Table ). We ð6þ where n is the number of electron acceptors and m i is the specific utilization rate of electron acceptor i: 0 C i m i ¼ ^m i K Si þ Pn K Si K Sj C j j¼ [5] The apparent concentration of the solid Fe(III) oxides is a function Fe(III) surface area and bacterial C A ð5þ Table 3. Initial Conditions Used in Simulations Variable Initial Condition X b a X Fe X Fe 2+ 0 S Fe S Fe 2+ 0 S Es S Es 0 S HCO3 0 a Approximately 0 8 cells ml. Figure 3. Determination of first-order rate constant for the abiotic reduction of Fe(III) oxides by reduced electron shuttle (AHDS).

5 HACHERL ET AL.: KINETICS OF BACTERIAL FE(III) REDUCTION HWC 3-5 Table 4. Parameter Base Values and Units Used in Kinetics Model Simulations Parameter Base Value Units Y b/xfe a mol biomass (mol Fe(III) (s) ) Y b/sfe a mol biomass (mol Fe(III) (aq) ) Y b/es b mol biomass (mol shuttle) 0.09 c mole Fe(III) (mol surface Fe(III) hr) Fe a hr Es b hr K S(h) 0.2 c mol biomass (mol surface Fe(III)) K S(Fe 3+ ) a mol Fe(III) L K S(Es+) b mol e equivalent L k 672 b (mol surface Fe(III) hr) k 2 (WHM) d NA k 2 (VW) e mol Fe(II) (s) L hr k e hr K e NA b 0 3b hr a Liu et al. [200b]. b This work. c Calculated for this analysis using data from Roden and Zachara [996]. d Wajon et al. [985]. e van Cappellen and Wang [995]. derive a solid substrate utilization equation by substituting equation (6) into equation (): W Fe 3þ dx Fe 3þ dt 0 ¼ ^h X b W Fe 3þ K SðhÞ þ X b W Fe 3þ Such an expression is supported by data on solid Fe(III) oxide reduction rates versus initial Fe(III) concentration published by [Roden and Zachara, 996, Figure 3]. The rate constant used in the analysis presented here is based on regression analysis of this data. [6] The approach of measuring Monod parameters in single electron acceptor systems and applying them to the multiple electron acceptor system is valid assuming () the microbial community is in the same physiological state in the mixed system as it is in the single electron acceptor system, and (2) the electron acceptors all use a common enzyme system [Guha and Jaffe, 996]. [7] The major Fe(II) mineral species found in Fe(III) reducing systems are siderite and magnetite [Bell et al., 987; Roden and Lovley, 993]. Magnetite precipitation is accounted for empirically in this model, as discussed later. C A ð7þ Figure 4. Fe speciation during microbial reduction with concurrent siderite precipitation. Siderite precipitation was modeled using VW and WHM formulations and compared to the case of no siderite precipitation. There were no further interactions between siderite and Fe(III) oxides after precipitation. Sorption was irreversible. Iron species are (a) total (available plus unavailable) solid Fe(III), (b) dissolved Fe(II), (c) Fe(II) as siderite, and (d) sorbed Fe(II).

6 HWC 3-6 HACHERL ET AL.: KINETICS OF BACTERIAL Fe(III) REDUCTION Figure 5. Fe speciation during microbial reduction with concurrent siderite precipitation. Siderite precipitation is modeled using VW and WHM formulations and compared to the case of no siderite precipitation. Available Fe(III) was depleted due to siderite precipitation in a : stoichiometry. Sorption was irreversible. Iron species are (a) total (available plus unavailable) solid Fe(III), (b) dissolved Fe(II), (c) Fe(II) as siderite, and (d) sorbed Fe(II). Based on our experimental design [Hacherl et al., 200] we found that there was little possibility for the supersaturation and precipitation of vivianite (Fe 3 (PO 4 ) 2 8H 2 O) at the low phosphate levels used in our media (0.5 mm total PO 4 ). Also, vivianite has only been experimentally observed in ferric citrate media [Fredrickson et al., 998]. [8] Two formulations for a siderite precipitation rate law were found in the literature. Van Cappellen and Wang (VW) have used a formulation based on a linear rate law with 2 respect to the degree of supersaturation of Fe(II) and CO 3 in the aqueous phase [van Cappellen and Wang, 995]. Alternatively, Wajon, Ho and Murphy (WHM) have used a formulation depending on a linear rate law with respect to the square of relative aqueous phase supersaturation [Wajon et al., 985]. The WHM model was determined empirically from samples containing calcium carbonate minerals (aragonite). The precipitation rates found in this model are greater than those observed in systems containing no natural aragonite. Thus, the VW model is considered to be more general. [9] It has been hypothesized that siderite precipitation does not occlude any solid Fe(III) sites, but instead acts as an Fe(II) sink [Fredrickson et al., 998]. We have also considered the case in which siderite precipitates on and partially occludes active Fe(III) reduction sites. Siderite precipitation is relatively slow and will not affect initial rates in laboratory experiments with short durations, but is likely to affect results in natural systems or in experiments with longer time frames. [20] As a first approximation, reduction of solid Fe(III) by electron shuttles is assumed to be first order in electron shuttle concentration and first order in available solid Fe(III) surface sites, based on our preliminary experimental evidence. To complete the electron shuttle cycle, the model includes a Monod rate of biotic electron shuttle reduction Equilibrium Reactions [2] For low-surface area goethite and amorphous Fe(III) oxyhydroxide the rate of sorption is nearly instantaneous relative to the timescale of interest for our model (Figure 2), so Fe(II) sorption and the concurrent loss of bioavailable Fe(III) is treated at each time step as an equilibrium process. The sorption data indicates a Freundlich type isotherm [Urrutia et al., 999; Hacherl et al., 200] described by: X Fe 2þ ;s W Fe 3þ ¼ K f S Nf Fe 2þ Loss of bioavailable Fe(III) due to Fe(II) sorption is assumed to follow magnetite stoichiometry of one mole of ð8þ

7 HACHERL ET AL.: KINETICS OF BACTERIAL FE(III) REDUCTION HWC 3-7 Figure 6. Fe speciation during microbial reduction with concurrent siderite precipitation. Siderite precipitation is modeled using VW and WHM formulations and compared to the case of no siderite precipitation. Available Fe(III) was depleted due to siderite precipitation in a 2: stoichiometry. Sorption was irreversible. Iron species are (a) total (available plus unavailable) solid Fe(III), (b) dissolved Fe(II), (c) Fe(II) as siderite, and (d) sorbed Fe(II). Fe(III) lost for every two moles of Fe(II) sorbed. Based on this assumption, sorption is considered to be irreversible, although in several cases our results are compared to a reversible sorption model. Fe(II) sorption is assumed to occur uniformly on all surfaces. The precipitation of magnetite is implicitly incorporated into the model by the empirical coefficient relating the Fe(II) sorption to loss of bioavailable solid Fe(III). [22] Similarly, we included Fe(II) sorption to biomass as another potential sink. Sorption isotherms are presented in the literature for two strains of Shewanella: S. alga BrY [Urrutia et al., 998], and S. putrefaciens CN32 [Liu et al., 200b]. This sorption is considered to be irreversible since it is assumed that Fe(II) will continue to sorb to dead cells and our model does not include a degradation rate for cell biomass. [23] Equilibrium also exists among the dissolved inorganic carbon (DIC) species. All inorganic carbon enters the model through the biological conversion of organic substrates to CO 2. Dissolved inorganic carbon is represented in the model as bicarbonate per equation (3). For determination of supersaturation, the dissolved carbonate concentration is equal to (at ph 7) [O Neill, 993]: S CO 2 3 ¼ S HCO 3 ð9þ [24] Note that the model is actually calculating total inorganic carbon and representing it as bicarbonate, which is the dominant species at ph Modeling Strategy [25] The full kinetic model contains four solid components and five aqueous components, participating in seven kinetically controlled processes and a single equilibrium exchange. These components and the kinetic process rates are listed in Table 2. Table 2 was developed assuming lactate as the sole carbon source, ammonia as the source of biomass nitrogen, and a biomass chemical composition of C 5 H 7 O 2 N. Table 2 is written on a molar basis and assumes that one mole of electron shuttle is capable of accepting two modes of electrons. The governing differential equations can be derived from Table 2 by multiplying each component cell by the associated process rate in the right-hand column and summing the components within a column (i.e., a matrix product of components and process rates). As an example, dissolved Fe(II) (species (6)) is involved in the most processes of the nine species considered and has the most complex differential equation. The differential equation describing the kinetics of dissolved Fe(II) formation in a supersaturated ferrous carbonate solution governed by VW precipitation kinetics (note that siderite precipitation

8 HWC 3-8 HACHERL ET AL.: KINETICS OF BACTERIAL Fe(III) REDUCTION Figure 7. Fe speciation during microbial reduction with concurrent siderite precipitation. Siderite precipitation is modeled using VW and WHM formulations and compared to the case of no siderite precipitation. Available Fe(III) was depleted due to siderite precipitation in a : stoichiometry. Sorption was reversible. Iron species are (a) total (available plus unavailable) solid Fe(III), (b) dissolved Fe(II), (c) Fe(II) as siderite, and (d) sorbed Fe(II). and dissolution cannot occur simultaneously) is derived by multiplying the coefficients for processes a, b, d, and e by the appropriate process rate in the right-hand column and summing the Fe 0 ¼ W Fe 3þ ^h 0 þ 20X b ^m Y Fe 3þB K SFe ð 3þ K SðhÞ þ K SðhÞ K SFe ð 3þ Þ Þ þ K SFe ð 3þ Þ þ 2k W Fe 3þS ES k 2 ð Þ K SðhÞ X b W Fe 3þ S Fe 3þ þ K SðhÞ S Esþ þ X b K SEsþ ð Þ S Fe 3þ X b W Fe 3þ þ K SFe ð 3þ Þ K SEsþ ð W Fe 3þ C A C A S Esþ þ S Fe 3þ Þ ð0þ 3. Materials and Methods 3.. Cultures and Media [26] All biological parameter measurements were performed using a pure culture of Shewanella alga BrY, grown in the dark under anoxic conditions as described previously [Hacherl et al., 200]. The sole carbon source provided in the media was lactate (20 mm) Sorption Isotherms [27] Sorption isotherms were conducted as described previously [Hacherl et al., 200]. In order to determine the time necessary for equilibrium these experiments were repeated with equilibration times of min, 3 min, 0 min, 30 min, 00 min, 300 min and 000 min Abiotic Electron Shuttle Kinetics [28] The rate of abiotic Fe(III) reduction by AQDS was determined by adding the reduced form, anthraquinol-2,6- disulfonic acid (AHDS) to a known mass of Fe(III) oxide under anaerobic conditions and monitoring the AHDS concentration as a function of time [Hacherl et al., 200]. The order and rate constant for the reaction was determined per the methods described by Fogler [992]. This procedure was conducted for several different oxides (e.g. hematite, goethite) Monod Parameter Determination [29] Monod kinetic parameters were determined for dissolved Fe(III) and for AQDS by measuring the rate of accumulation of reduced species in anaerobic, batch systems immediately after inoculation with S. alga BrY.

9 HACHERL ET AL.: KINETICS OF BACTERIAL FE(III) REDUCTION HWC 3-9 Figure 8. Fe speciation resulting from changes to the siderite precipitation rate constant, k 2. The precipitation rate constant was varied over five orders of magnitude. Iron species are (a) total (available plus unavailable) solid Fe(III), (b) dissolved Fe(II), (c) Fe(II) as siderite, and (d) sorbed Fe(II). Replicate batch microcosms were prepared according to the method described by Hacherl et al. [200]. The initial concentration of electron acceptor was varied such that there were sufficient data in the zero- and first-order regions to obtain satisfactory parameter estimations. Monod kinetics parameters for chelated Fe(III) were determined using ferric citrate as the Fe(III) source. 4. Results and Discussion [30] The nine differential equations along with the sorption equilibrium equation were solved using an ordinary differential equation solver package (STELLA 7.0, High Performance Systems, Inc.), using Euler s method. Initial concentrations were set according to common concentrations used in our experiments or found in the literature (Table 3). Single and multiple electron acceptor simulations were conducted. Solid Fe(III), as amorphous Fe(III) oxyhydroxide, was chosen for the single electron acceptor simulations. Multiple electron acceptor simulations included solid/dissolved Fe(III) and solid Fe(III) with AQDS/AHDS as the electron shuttle capable of accepting two moles of electrons per mole of shuttle. [3] The Monod kinetic parameters for chelated Fe(III) and soluble electron shuttles were determined by regression to initial rate data collected at different initial electron acceptor concentrations. Abiotic reduction of Fe(III) by reduced electron shuttles was described by first-order kinetics (Figure 3). Parameter values determined experimentally or taken from the literature are reported in Table 4. [32] Freundlich isotherm coefficients for Fe(II) sorption to mineral phases were available for amorphous oxyhydroxide (AFO), medium surface area goethite (MSA-Gt), and low surface area goethite (LSA-Gt) (Table ). Sorption to Fe(III) oxides was rapid and for the purpose of our model it was assumed to be instantaneous (Figure 2). Both irreversible and reversible sorption behaviors were simulated. Sorption of Fe(II) to biomass was represented using both Freundlich and Langmuir isotherms. 4.. Siderite Precipitation Models and Sorption Behavior in Single Electron Acceptor Simulations [33] Siderite precipitation was modeled with each of the two kinetic formulations previously described (VW and WHM models). In addition to these two kinetic formulations, we also considered two possible scenarios for the effect of siderite precipitation on Fe(III) reduction. In one scenario, it was assumed that siderite acted only as a sink for aqueous Fe(II), thereby limiting the sorption of Fe(II) onto Fe(III) oxides (Figure 4). In the other scenario, siderite precipitation was assumed to occur on the Fe(III) oxide surface, depleting the bioavailable Fe(III) in either a : or a 2: stoichiometry (Figures 5 and 6). These simulations were performed assuming irreversible mineral sorption (i.e. for-

10 HWC 3-0 HACHERL ET AL.: KINETICS OF BACTERIAL Fe(III) REDUCTION Figure 9. Fe speciation resulting from changes in the maximum solid Fe(III) reduction rate, ^h. Siderite precipitation was modeled using VW kinetics. The reduction rate constant was varied from hr. Iron species are (a) total (available plus unavailable) solid Fe(III), (b) dissolved Fe(II), (c) Fe(II) as siderite, and (d) sorbed Fe(II). mation of magnetite) and no biomass sorption. Simulation results for reversible sorption cases and simulation results involving biomass sorption are discussed later. [34] During our simulations we consistently observed three characteristic trends to the siderite precipitation models (Figure 4). First, siderite precipitation could not begin until the Fe(III) oxide surfaces were saturated with sorbed Fe(II), that is, until the sorbed Fe(II) concentration had reached a maximum. At that point, dissolved Fe(II) began to accumulate in the system to an extent great enough that it became supersaturated with respect to siderite. Second, siderite precipitation began almost immediately after sorption sites were saturated for the WHM model, whereas there was a lag of approximately h before siderite precipitation began with the VW model. Third, siderite precipitation was always more rapid according to the WHM model than to the VW model, leading to a greater final amount of Fe(II) in the siderite phase for the WHM model. These last two points are inherent in the mathematical formulations of the two models, but they are more obvious when compared using these simulations. [35] When siderite precipitation acted solely as a sink for dissolved Fe(II), the Fe(III) reduction rate and final Fe(III) oxide concentration were unaffected by siderite precipitation (Figure 4a). Endpoint dissolved Fe(II) concentrations were in the range of mm, with the highest concentrations corresponding to the case in which there was no siderite precipitation (Figures 4b and 4c). Fe(III) oxide surfaces became saturated with sorbed Fe(II) to essentially the same concentration (Figure 4d). Therefore, any additional Fe(II) phase, such as siderite, was formed at the expense of dissolved Fe(II). [36] When siderite precipitation was allowed to occlude the Fe(III) oxide surface at a : stoichiometry, the initial Fe(III) reduction rate was the same for all three cases, but the extent of reduction decreased as a function of siderite precipitation (Figure 5a). The WHM model caused Fe(III) reduction to cease after about 70% of the total Fe(III) was reduced, compared to 80% reduction for the VW model and over 85% for the model that did not allow siderite precipitation. Siderite precipitation had a similar effect on dissolved Fe(II) concentration in this case (Figure 5b) as it did in the first case (i.e., the WHM model maintained the lowest solution Fe(II) concentrations). The mass of siderite formed in this case was less than in the previous case because Fe(III) reduction stopped earlier due to site occlusion (Figure 5c). [37] To test the effect of occlusion stoichiometry on Fe(III) reduction rates and extents, the simulations were repeated with the stoichiometry increased to 2: mol Fe(III) occluded per mol siderite precipitated (Figure 6). This resulted in a further decrease in the extent of Fe(III) oxide reduction, in direct proportion to the stoichiometry

11 HACHERL ET AL.: KINETICS OF BACTERIAL FE(III) REDUCTION HWC 3 - Figure 0. Fe speciation resulting from changes in the maximum solid Fe(III) reduction rate, ^h. Siderite precipitation was modeled using WHM kinetics. The reduction rate constant was varied from hr. Iron species are (a) total (available plus unavailable) solid Fe(III), (b) dissolved Fe(II), (c) Fe(II) as siderite, and (d) sorbed Fe(II). (Figure 6a). However, for the WHM model, the dissolved Fe(II) concentrations decreased by only about 20% (Figure 6b) and the siderite concentrations decreased by less than 5% (Figure 6c), compared to the : stoichiometry. There was little change in dissolved Fe(II) or siderite concentrations for the VW model, compared to the : stoichiometry. The remaining simulations in this paper were conducted with a : stoichiometry. [38] The results presented so far were all obtained based on the assumption that sorption was irreversible, resulting in magnetite formation. To test this hypothesis, we repeated each of the simulations using a reversible sorption model. The results were consistent for all simulations; therefore, only one representative case is presented here (Figure 7). For reversible sorption, sorbed Fe(II) concentrations were always less than 2 mm by the end of the simulation (500 h). In Figure 7d the sorption maximum is reached at the same time as in the corresponding irreversible case (Figure 5d). At this point, although dissolved Fe(II) concentration is increasing the total available Fe(III) oxide surface is decreasing. Although the mass sorbed per unit mass sorbent was continuing to increase past this time, the total mass of sorbent was decreasing, causing a concurrent decrease in the total mass sorbed. [39] Reversible sorption led to greater Fe(III) oxide reduction (less than 0% difference compared to the irreversible case), approximately 5% greater dissolved Fe(II) concentrations and approximately 0% greater siderite concentrations. Since the maximum sorbed Fe(II) concentration, generally approximately 3 mm, was less than 0% of the total Fe(II) produced during the simulations it is not a major phase for Fe(II). The remaining simulations in this paper were conducted assuming that sorption was irreversible, thus allowing a mechanism for magnetite precipitation in the model. [40] There was no observable difference in any of the simulations when biomass sorption was included in the model. This results from the lower affinity for Fe(II) to cells than to Fe(III) oxide minerals on a per gram basis, and the significantly lower biomass compared to the mineral mass. As a rough estimate, [Urrutia et al., 998] report a sorption maximum of 0.25 mmol Fe(II) g goethite, compared to a biomass sorption maximum of 0.0 mmol Fe(II) g on a dry cell weight basis. We initialized our system with approximately 4.5 g L of goethite and approximately 0.04 g L of biomass. This leads to micromolar concentrations of biomass-sorbed Fe(II) Parameter Sensitivity for Single Electron Acceptor Simulations (Amorphous Fe(III) Oxyhydroxide) [4] Using the VW model and assuming siderite precipitation occluding Fe(III) at a : ratio, Fe(II) speciation was evaluated as a function of the siderite precipitation rate

12 HWC 3-2 HACHERL ET AL.: KINETICS OF BACTERIAL Fe(III) REDUCTION Figure. Fe(III) reduction and Fe(II) speciation for various Fe(III) oxides. Siderite precipitation was modeled using VW kinetics. Iron species are (a) total (available plus unavailable) solid Fe(III), (b) dissolved Fe(II), (c) Fe(II) as siderite, and (d) sorbed Fe(II). constant, k 2, which was varied over five orders of magnitude (Figure 8). Simulation results show that the full range of effect that this parameter had on the extent of Fe(III) reduction was represented by a single order of magnitude variation in either direction from the baseline value of mole Fe(II) (s) L hr as reported by van Cappellen and Wang [995] (Figure 8a). The highest precipitation rate resulted in more than twice the final Fe(III) oxide concentration as compared to the lowest precipitation rate. The same trends were observed in the final extent of production of dissolved Fe(II) and siderite. That is, varying k 2 from to could capture the full range of variability. The precipitation rate constant had no effect on sorbed Fe(II) concentration (Figure 8d). [42] As a consequence of the above observations, model sensitivity to the values of the Monod parameters was also examined for both VWand WHM kinetics (Figures 9 and 0). In a natural environment it is realistic to expect a wide range of observed biological reduction rates given the diversity of dissimilatory iron reducing bacteria (DIRBs). The effects of ^h and K S(h) were numerically nearly equal and opposite because of the low biomass-to-solid ratio (as defined in equation (6)) used in these simulations. At very high biomass-to-solid Fe(III) ratios the effect of K S(h) becomes negligible. The Monod parameters, ^h and K S(h), had a significant impact on Fe(III) reduction rate even when they were varied only by a factor of two. A higher maximum specific growth rate, or a lower half-saturation constant, led to more rapid Fe(III) reduction (Figures 9a and 0a) and faster production of dissolved Fe(II) (Figures 9b and 0b). For clarity, we are only presenting the results of variation in the maximum specific growth rate in Figures 9 and 0. The extent of Fe(III) reduction was only slightly affected by variations in the specific growth rate parameter for the VW model, and unaffected in the WHM model; however, the final extent of reduction was greater in all cases for the VW model. This is due to the significant impact that siderite precipitation has on the overall availability of Fe(III) oxides. The rate of Fe(III) reduction was roughly first order with respect to the biomass-to-solid Fe(III) ratio because of the low values of this ratio Comparative Single Electron Acceptor Simulations With Goethite [43] Simulations were carried out for MSA-Gt and LSA- Gt to compare with AFO results. Again, both the VM and WHM siderite precipitation models were simulated, assuming precipitated siderite occluded Fe(III) sites at a : ratio. Model simulations were conducted using sorption isotherm coefficients (Table 4) and calculated Fe(III) site densities specific for each of the three minerals (Table ). For both models, initial Fe(III) reduction rate decreased as a function of surface area, from AFO with a surface area of approx-

13 HACHERL ET AL.: KINETICS OF BACTERIAL FE(III) REDUCTION HWC 3-3 Figure 2. Fe(III) reduction and Fe(II) speciation for various Fe(III) oxides. Siderite precipitation was modeled using WHM kinetics. Iron species are (a) total (available plus unavailable) solid Fe(III), (b) dissolved Fe(II), (c) Fe(II) as siderite, and (d) sorbed Fe(II). imately 600 m 2 g to LSA-Gt with a surface area of approximately 20 m 2 g (Figures and 2). About 80% of the initial Fe(III) oxide was reduced with the VW model. The total extent of goethite reduction (both types) was equivalent between the two models. [44] AFO reduction under the WHM model ceased after approximately 70% of the initial mass was reduced. In other words, the extent of Fe(III) reduction was actually greater for the crystalline oxides. This is the result of the balance between Fe(II) sorption and siderite precipitation. Although siderite precipitation is relatively slow, for the crystalline Fe(II) oxides dissolved Fe(II) production and concurrent sorption was slower than for the AFO mineral. In addition, sorption capacity was much lower for the goethite minerals than for AFO. Except for the case of AFO reduction governed by WHM kinetics, the final dissolved Fe(II) and siderite concentrations were equal between the two kinetics models. [45] Recently, it was reported that the Fe(II) sorption capacity of goethite decreased with increasing goethite concentration, leading to a model in which available Fe(III) sites depended empirically on the initial Fe(III) oxide concentration [Liu et al., 200a]. The assumption required for this model was that particle aggregation at higher oxide concentrations caused the physical exclusion of bacteria from many surface sites, decreasing the oxide availability, and that this phenomenon was in proportion to the loss of sorption sites due to aggregation. When we corrected our initial Fe(III) oxide concentration based on the variable sorption isotherm [Liu et al., 200a], our model generated total and dissolved Fe(II) concentrations slightly less than the experimental data (Figure 3). At high goethite concentrations the initial rates generated in our model were slower than those indicated by the experimental data. [46] For 00 mm goethite, we were able to generate excellent simulations of the Liu data by doubling the maximum specific Fe(III) oxide reduction rate, ^h (Figure 3). This is reasonable since the rate of Fe(III) citrate reduction for their organism, S. putrefaciens CN32, was significantly higher than for S. alga BrY [Liu et al., 200b]. Presumably, the rate of goethite reduction was also greater, although there is not enough data in the literature to estimate ^h and K S(h) for this strain. It must be noted that, at this higher ^h the behavior of the dissolved Fe(II) concentration was not consistent with experimental data. Our model predicted that dissolved Fe(II) concentration would decrease after 200 hours, since the Fe(II) production rate was decreasing while the siderite precipitation rate was relatively constant. It is likely that if siderite precipitation were a surface-mediated process, aggregation at high goethite loadings would lead to fewer siderite precipitation sites and slower siderite precipitation in much the same manner as it led to fewer

14 HWC 3-4 HACHERL ET AL.: KINETICS OF BACTERIAL Fe(III) REDUCTION [48] The addition of an electron shuttle as an alternative electron acceptor greatly affected the overall rate of microbial Fe(III) reduction. Since the rate of electron shuttle reduction is higher than the rate of solid Fe(III) reduction (due to better bioavailability) and the electron shuttle can be recycled, even small concentrations can have quite dramatic impacts (Figure 5). In this simulation a maximum of only 0.2 mm electron shuttle was added to the base system. The presence of the electron shuttle merely as an alternative electron acceptor (k = 0) had no significant inhibitory impact on Fe(III) reduction rate (data obscured by simulation with S Es+ = 0 mm). However, when the electron shuttle was able to mediate abiotic Fe(III) reduction the effect was dramatic (Figure 5a). Available Fe(III) was completely reduced about 0 times faster with 0.2 mm electron shuttle. Even with only 0.02 mm shuttle, the available Fe(III) was completely reduced in about half the time. The rates of dissolved Fe(II) and siderite production were altered by the addition of electron shuttle; however, the final extent of dissolved Fe(II) production was unchanged (Figure 5b). Figure 3. Simulation of MSA goethite reduction using model parameters, Fe(III) oxide availability, and experimental data from Liu et al. [200a]. Initial goethite concentrations of 5, 0, or 00 mm as Fe(III) were used for both the experiment and model simulations. Initial biomass was equivalent to cells ml. Initial inorganic carbon content was 32 mm from bicarbonate buffer and headspace CO 2, Siderite precipitation was modeled using VW kinetics. Iron species are (a) total Fe(II) and (b) dissolved Fe(II). sorption sites. Our model does not account for the availability of siderite nucleation sites Multiple Electron Acceptor Simulations [47] Simulations were carried out with solid Fe(III) at 50 mm and chelated Fe(III) in solution at various initial concentrations from 0 to 50 mm using the VW model (Figure 4). Chelated Fe(III) is more available to bacteria than solid Fe(III), and as expected, the presence of chelated Fe(III) inhibited the reduction of solid Fe(III) oxides (Figure 4a). Dissolved Fe(II) concentration and siderite production increased in almost direct proportion to the amount of chelated Fe(III) added to the system (Figures 4b and 4c). Siderite precipitation caused a dramatic decrease in available solid Fe(III), such that at the highest chelated Fe(III) concentration simulated, less than 60% of the initial solid Fe(III) was bioavailable. Total Fe(II) sorption was slightly greater when chelated Fe(III) was available, due to higher Fe(II) concentrations early in the simulations before sorption sites could be depleted by solid Fe(III) reduction (Figure 4d). 5. Conclusions [49] Once solid Fe(III) reduction was complete under the constraints of the base model parameters (Tables 3 and 4), 70% of the Fe(II) produced was in the dissolved phase and 20% in the siderite phase. The remaining 0% of the Fe(II) produced was sorbed to Fe(III) oxides. Of the initial solid Fe(III) in the system, only 0% was unavailable (due to Fe(II) mineral precipitation and Fe(II) sorption) at the end of the simulation. Most batch microcosm experiments of biological Fe(III) reduction demonstrate far more unreducible Fe(III), indicating that there is another cause of the loss of reducing capability, or that the estimates for Fe(II) precipitation and sorption are too low. Besides Fe(II) sorption to Fe(III) oxides, two possibilities that have been suggested are loss of specific bacterial reduction capacity due to sorption of Fe(II) to cell surfaces [Urrutia et al., 998] or loss of solid Fe(III) reactive sites due to precipitation of siderite on Fe(III) oxide surfaces [Roden and Zachara, 996]. Although we investigated the impact of biosorption as a sink for Fe(II), we were not able to evaluate the impact of this sorption on the capacity of a cell to reduce Fe(III) since it was not clear how sorbed Fe(II) would affect model parameters. Fe(II) sorption to bacteria may in fact change some of the assumptions necessary for the use of Monod kinetics. [50] Siderite precipitation was investigated using two kinetics models. Siderite formation has little impact on the initial rate of Fe(III) reduction since there is very little CO 2 initially in the system with which Fe(II) can precipitate. However, it is apparent that microbial CO 2 production even at low levels is sufficient to control the extent of Fe(III) reduction in a way that Fe(II) adsorption alone cannot. The effect of siderite precipitation on Fe(III) reduction and the resulting speciation of Fe(II) was much greater than the effect of Fe(II) sorption. This is in spite of the difference in the assumed stoichiometry of the two processes: two moles of Fe(III) were made unavailable by adsorption of one mole of Fe(II) whereas only one mole of Fe(III) was made unavailable by precipitation of one mole of siderite.

15 HACHERL ET AL.: KINETICS OF BACTERIAL FE(III) REDUCTION HWC 3-5 Figure 4. Fe(III) reduction in a mixed system containing solid and chelated Fe(III) as electron acceptors. Siderite precipitation was modeled using VW kinetics. Iron species are (a) total (available plus unavailable) solid Fe(III), (b) dissolved Fe(II), (c) Fe(II) as siderite, and (d) sorbed Fe(II). [5] This model highlights the importance of the interaction between siderite and Fe(III) oxides. In spite of slow precipitation rates, siderite occlusion of available Fe(III) sites can dramatically affect the extent of oxide reduction and it was the major cause of the loss of available Fe(III) oxides. Recent studies [Liu et al., 200a] indicate that some of the siderite produced is associated with Fe(III) oxides, but that there were also discrete siderite crystals not associated with Fe(III) oxides. More experimental findings, particularly the fraction of Fe(III) sites that are occluded by siderite precipitation (on a mole per mole basis) and the relationship between surface-precipitated and solution-precipitated siderite, are required in order to appropriately model this system. [52] This model also demonstrates the dramatic increases in Fe(III) reduction rates that are possible as a result of electron shuttle activity. Even minor electron shuttle additions cause dramatic increases in the rate of Fe(III) oxide reduction. The use of multiple electron acceptor Monod kinetics will allow this model to be extended to natural soil systems in which it is common to find solid Fe(III) oxides in association with organic matter which can act as both a complexing agent and an electron shuttle. [53] This model compares favorably with literature data for goethite reduction once the initial Fe(III) concentration is corrected for particle aggregation. However, it fails to capture the loss of microbial activity that is typically observed in batch systems if the system is not corrected for aggregation. For example, there is much evidence to indicate that only 0 60% of the total Fe(III) present in a batch microcosm is ultimately bioavailable, while many of our simulations indicate ca. 90% available [Lovley and Phillips, 986; Roden and Zachara, 996; Fredrickson et al., 998; Zachara et al., 998]. Also, dissolved Fe(II) concentrations generated by this model are higher than those observed experimentally, although this is in part due to the greater overall reduction of Fe(III) in the model and may or may not be due to a phenomenological effect not included in the model. In a natural soil system, the aggregation of Fe(III) oxides is not likely, since they exist primarily as surface coatings on soil particles. In addition, soils will have an inherent Fe(II) sorption capacity that is not associated with Fe(III) oxides. It would not be feasible for soil systems to use sorption capacity as an estimate of bioavailability. The multiple-substrate Monod kinetic model provides an excellent tool for evaluating the relative impact of biogeochemical processes related to microbial Fe(III) reduction. Notation X b biomass concentration, mole C 5 H 7 O 2 NL. X Fe 3+ solid-phase Fe(III) concentration, mole Fe(III) L.