ARTICLE pubs.acs.org/est
Model to Couple Anaerobic Process Kinetics with Biological Growth Equilibrium Thermodynamics Perry L. McCarty†,‡,* and Jaeho Bae‡ † ‡
Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305, United States Department of Environmental Engineering, Inha University, Namgu, Yonghyun dong 253, Incheon, Republic of Korea
bS Supporting Information ABSTRACT: Monod kinetics indicates a substrate concentration limit (Smin) at biological growth equilibrium where growth is just balanced by decay. A relationship between Smin and the Gibbs free energy available at growth equilibrium (ΔGE) was introduced into the Monod model and applied directly to chemostat cultures. Results from four anaerobic mixed-culture chemostat studies yielded ΔGE of 17.7 ( 2.2 kJ/mol acetate converted to methane. ΔGE for propionate syntrophs in propionate-fed cultures was 8.0 ( 3.1 kJ/mol propionate, compared with that of 3.0 ( 0.9 kJ/mol H2 for the hydrogenotrophs present. With ethanol present, however, ΔGE for the hydrogenotrophs became more favorable, 6.1 ( 1.6 kJ/mol H2, while ΔGE for propionate became positive even though propionate was consumed, suggesting an alternative interspecies electron transport route. The results suggest that Smin, normally considered a function of an organism’s intrinsic rate characteristics, is also a function of solution characteristics, and this is likely the case for the substrate affinity coefficient, K, as well. A comparison between ΔGE and Smin and reported threshold thermodynamic and concentration limits, leads to the conclusion that ΔGE and Smin represent lower and upper bounds, respectively, on such values. This study indicates that knowledge gained from pure-culture studies applies well to more complex natural anaerobic systems.
’ INTRODUCTION Anaerobic organic transformation processes are of environmental interest 14 and are useful as well for treatment of organic contaminants.5,6 These processes generally require multiple groups of microorganisms working together to transform primary substrates to end products such as methane.7 With methanogenic processes, most of the energy contained in the primary substrate remains in the methane formed, leaving relatively little to support the multiple life processes of the substrate transforming organisms, each receiving only a portion of the small amount of energy released. With so little energy available, these biological reactions generally occur very close to thermodynamic equilibrium, forcing a close syntrophic relationship between the organisms involved.1,2,4,710 The multitude of individual steps results in the formation of different intermediate degradation products as well as a thermodynamically controlled lower limits on the concentrations of each (Scrit), limits below which each of the various reaction products tend not to be degraded. Such limits have been estimated from resting-cell studies.7,9,1113 The resulting threshold thermodynamic values (ΔGcrit) have been related to a biological quantum of energy, the minimum energy required to sustain biological growth, a value that is thought in turn to be related to the energy required to form ATP, the biological carrier of energy for cell growth and maintenance.1,2,8 Considerable research has been conducted over the past two decades to better learn of the processes controlling threshold r 2011 American Chemical Society
limits, thermodynamics being a key variable addressed.1,7,9,14 Also addressed has been the impact of these factors on rates of reaction.1,3 Many have stated that the unmodified Monod or MichaelisMenten expressions for rate of substrate utilization do not apply to these reactions,12,13,15,16 and arbitrary modifications of one kind or another have been made to cause utilization rates to approach zero as S approaches the threshold value (Scrit).13,16 However, the Monod expression for organism growth and decay itself without modification yields a minimum substrate concentration (Smin) at which organism growth and decay are just balanced, that is at a point of biological equilibrium. Here, we investigate the thermodynamics of this growth equilibrium state, evaluate its associated growth equilibrium Gibbs free energy value (ΔGE) and determine its magnitude and variability for a few key substrates and intermediate products. Since poising a system for study at growth equilibrium is difficult to do, we have developed kinetic relationships that have allowed us to estimate Smin and ΔGE from the results of normal chemostat studies, which we have done using previously reported mixed-culture results. We then compare the ΔGE and Smin values so obtained with ΔGcrit and Scrit values reported in the literature with pure-culture Received: March 18, 2011 Accepted: July 8, 2011 Revised: June 15, 2011 Published: July 08, 2011 6838
dx.doi.org/10.1021/es2009055 | Environ. Sci. Technol. 2011, 45, 6838–6844
Environmental Science & Technology
ARTICLE
systems, and examine the impact of the formulations developed on growth kinetics. Of particular interest was to learn the extent to which knowledge gained from studies with pure-culture systems applies to complex natural methanogenic systems. Relationship Between Kinetics and Thermodynamics at Growth Equilibrium. The Monod model for growth of microorganisms is as follows,17 μ ¼ μm
S b K þ S 1
b μm b
1
ð2Þ
The Gibbs free energy for the reaction to convert Smin to end products is not zero, but has some value, here termed the growth equilibrium value (ΔGE), which has a relationship to system chemistry as indicated by the Nernst equation, Q0 ΔGE ¼ ΔGo þ RTln ½Smin
ð3Þ
Where ΔGE (kJ) is the reaction Gibbs free energy/mol of substrate under culture conditions, ΔGo is the standard free energy for that reaction, R is the universal gas constant (0.008314 kJ/K mol), T (K) is temperature, and Q0 represents the Nernst quotient of all reaction products and reactants except for the absence of substrate [Smin], which is included separately. Solving for [Smin] gives, o ΔG ΔGE ½Smin ¼ Q 0 exp ð4Þ RT Equation 4 indicates that Smin normally considered a function of an organism’s intrinsic rate characteristics, is also a function of solution characteristics. This has been noted by others to be the case with Scrit as well.7,9,20 Similarly, as can be seen by combining eqs 2 and 4, one or more of the rate parameters must also be influenced by solution characteristics. Studies by Min and Zinder 12and Jetten et al.13 suggest that for acetoclastic methanogens higher organism Scrit values are associated with higher effective K values. If we assume that K is the only rate parameter affected, we can find its relationship with solution chemistry by solving the combination for K, ! μm b 0 ΔG0 ΔGE Q exp ð5Þ K ¼ b RT Chemostat Kinetics and Thermodynamics. ΔGE can be evaluated directly from chemostat studies. A chemostat is operated at a given solids retention time (θx, d), which in the absence of recycle is equal to the hydraulic detention time or its inverse, the dilution rate D (d1). At a given θx, the net growth rates of all organisms in a chemostat are the same and concentrations of products and reactants reach steady-state values that are invariant with time. Analogous to eq 4, the substrate
primary
substrate
substrate
concentration
θx (d)
T (°C)
sourceb
primary sludge acetate and
18.1 g CODa/L 0.026 to 0.052 M each
7.560 2060
2035 2035
c d
propionate
ð1Þ
where μ (d ) is net organism growth rate, μm (d ) is the maximum specific growth rate, K (M) is the substrate affinity, b (d1) is organism decay rate, and S (M) is the concentration of the reaction limiting substrate, here taken to be the organism’s electron donor. The substrate concentration that results when net growth rate μ is zero, Smin,18,19 is given by, Smin ¼ K
Table 1. Mixed-Culture Chemostat Results Evaluated and Operational Characteristics of Each
glucose
0.05 to 0.10 M
7.530
35
e
ethanol and
0.05 and 0.10 M each
515
35
f
propionate a
Chemical oxygen demand. b Data obtained from Ph.D. Dissertations at Stanford University, Stanford, CA, as follows: (c) O'Rourke, J. T. “Kinetics of Anaerobic Waste Treatment at Reduced Temperatures” 1968, (d) Lawrence, A. W. “Kinetics of Methane Fermentation in Anaerobic Waste Treatment” 1967, (e) Bae, J. “Studies of Substrate Perturbation on the Methanogenesis of Glucose” 1991, (f) Smith, D. P. “Hydrogenotrophic Control in Methanogenic Processes” 1987.
concentration SD at θx is given by, o ΔG ΔGD 0 ½SD ¼ Q exp RT
ð6Þ
Here, ΔGD is the Gibbs free energy/mol of a given substrate at a given θx. Based upon mass balance for a chemostat and Monod kinetics (eq 1), [SD] has the following relationship to chemostat operating parameters,17 ½SD ¼ K
1 þ bθx θx ðμm bÞ 1
ð7Þ
Solving eq 7 for K and setting the result equal to the right side of eq 5, and then solving for ΔGE yields: ΔGE ¼ ΔGo
0 Q 1 þ bθx μm b þ RTln b ½SD θx ðμm bÞ 1 ð8Þ
ΔGE so determined can be used to estimate Smin for a given substrate from eq 4 and for K from eq 5. Combining and rearranging the last three equations yields, 1 þ bθx μm b ΔGD ΔGE ¼ RTln b θx ðμm bÞ 1 ð9Þ Thus, the difference between reaction Gibbs free energy at a given θx and the Gibbs growth equilibrium free energy is the same for organisms having the same maximum growth and decay rates. ΔGE represents the free energy obtained per mol of substrate consumed that is used for cell maintenance, while that given by eq 9 is the amount used for net cell growth. As θx approaches infinity, eq 9 approaches zero, the energy available then is only ΔGE, all of which is used for cell maintenance.
’ METHOD OF ANALYSIS Using Microsoft Excel spread sheets, values for ΔGE, K, and Smin were calculated using eqs 2 through 9, and data from mixed-culture anaerobic chemostat studies contained in four doctoral dissertations (Table 1). The studies varied widely in primary substrate type and concentrations used, temperatures of operation, and θx. The anaerobic 6839
dx.doi.org/10.1021/es2009055 |Environ. Sci. Technol. 2011, 45, 6838–6844
Environmental Science & Technology
ARTICLE
Table 2. Energy Reactions Used in This Analysis and Their Standard Free Energies and Enthalpies Per Mole Substrate at 25 °C reaction no.
ΔGo (kJ)
reaction
I
+ CH3COO (aq)+H fCH4(g)+CO2(g)
II
+ CH3CH2COO (aq)+H +1/2H2Of7/4CH4(g)+5/4CO2(g)
III
CH3CH2COO (aq)+1/2H2OfCH3COO(aq)+3/4CH4(g)+1/4CO2(g)
IV
CH3CH2COO (aq)+2H2OfCH3COO(aq)+3H2(g)+Co2(g)
V
H2(g)+1/4CO2(g)f1/4CH4(g)+1/2H2O
ΔHo (kJ)
75.76
+17.89
102.19
19.34
26.43
37.23
+71.65
+152.29
32.69
63.17
Table 3. Summary of Average and Standard Deviations of ΔGE Values Determined for Reactions I, II, and III reaction I substrate
a
n
ΔGE (kJ/mol)
reaction II
reaction III
ΔGE (kJ/mol)
a
n
ΔGE (kJ/mol)
a
n
primary sludge
10
16.3 ( 0.8
10
42.3 ( 1.2
10
21.6 ( 1.6
acetate and propionate glucose
15 3
17.4 ( 2.3 15.1 ( 2.3
5 3
42.9 ( 4.0 41.9 ( 4.8
5 3
17.4 ( 2.3 21.7 ( 1.7
ethanol and propionate
6
16.7 ( 1.0
4
42.8 ( 1.0
4
21.3 ( 1.6
overall average
34
17.7 ( 2.2
22
42.5 ( 2.5
22
20.6 ( 2.4
95% confidence limits
16.9 to 18.5
41.4 to 43.6
19.5 to 21.7
Number of different steady-state operational conditions used in deriving respective ΔGE average and standard deviation. For each steady-state condition, average concentrations of reactants and products were used in determining ΔGE for that condition. a
treatment of complex materials involves multiple reactions and organisms. Only three reactions were evaluated here, ones for which the analytical data were sufficient for evaluation. These include the two methanogenic substrates (acetate and H2) and propionate, which is converted by syntrophic organisms to acetate and H2. Only data for which θx was equal to or greater than twice the washout rate [θx g 2/(μm b)] were used in the evaluation as substrate concentrations at lower θx values tend to be high and quite sensitive to θx, creating the possibility for significant error. The five energy reactions associated with propionate oxidation to acetate and hydrogen and ultimate conversion of acetate and hydrogen to methane along with their Gibbs standard free energy and enthalpy values at 25 °C are listed in Table 2. Reaction II represents the overall conversion of propionate to methane, a reaction requiring all three organism groups, while Reaction III for propionate conversion to acetate and methane, requires two organism groups. These were evaluated in order to learn how organism interactions might affect outcomes for ΔGE and Smin. Reactions I, IV, and V are each carried out by a single organism group. The only parameters that needed to be assumed for this evaluation are μm and b. For acetate and propionate using organisms, μm at 35 °C was taken to equal 0.35 d1 and b was taken as 0.018 d1, both of which are typical average values.6 Temperature corrections to μm and b were made assuming a doubling of each with each 10 °C rise in temperature. Temperature corrections to ΔGo were made using ΔHo and the van’t Hoff equation. Activity corrections to ionic species molar concentrations were made using an estimate of ionic strength and the Debye H€uckel relationship (see Supporting Information). The fugacities of gaseous components were taken to equal their partial pressures in atm. A sensitivity analysis was conducted in order to determine the effect of changes in μm and b on ΔGE, K, and Smin.
’ RESULTS AND DISCUSSION ΔGE Values. Detailed tables of chemostat results, model inputs, and computations used in this evaluation are contained
Table 4. Summary of ΔGE Values (kJ/mol Substrate) for Reactions III, IV, and V primary substrate propionate glucose
ethanol + propionate ethanol
θx (d)
Reaction III
Reaction IV
Reaction V
15
22.6
13.4
1.7
10
22.7
7.9
3.0
30
21.1
6.5
4.1
10 7.5
20.3 23.6
5.8 6.6
2.9 3.3
15
20.5
+2.4
6.2
10
19.5
+5.1
6.3
15
7.6
10
7.2
5
3.4
in the Supporting Information, only summaries are provided here. Values for ΔGE for the first three reactions listed in Table 2 are summarized in Table 3. ΔGE values for the last three reactions for the two chemostats with H2 measurements are summarized in Table 4. Concerning the Table 3 values, the relative precision of the values is reflected in the 12% or less standard deviations for the averages and the relatively small range of the 95% confidence limits. This was unexpected since the primary substrates used were quite different in composition and concentration, as were θx values and chemostat operating temperatures, neither of which produced statistically significant differences from the averages. Interestingly, reactions II and III, carried out by three and by two different organism groups, respectively, still resulted in somewhat invariant ΔGE values. Somewhat different results come from the two mixed-culture studies for which H2 partial pressure measurements were available (Table 4). However, the number of measurements available was limited and the resulting ΔGE values were not as invariant as in Table 3. For the hydrogenotrophic methanogens (Table 4, Reaction V), ΔGE was more negative in the presence of ethanol 6840
dx.doi.org/10.1021/es2009055 |Environ. Sci. Technol. 2011, 45, 6838–6844
Environmental Science & Technology
ARTICLE
Table 5. Summary of K and Smin Values Determined for Reaction I, II, and IIIa K (mg/L) substrate
a
Reaction I
Reaction II
Smin (mg/L) Reaction III
Reaction I
Reaction II
Reaction III
primary sludge
135 ( 43
87 ( 34
87 ( 34
7.3 ( 2.3
4.7 ( 1.9
4.7 ( 1.9
acetate and propionate
222 ( 145
34 ( 35
34 ( 35
12 ( 8
1.9 ( 1.9
1.9 ( 1.9
glucose
70 ( 47
127 ( 192
127 ( 192
3.8 ( 2.6
6.9 ( 10
6.9 ( 10
ethanol and propionate
103 ( 31
90 ( 31
90 ( 31
5.6 ( 1.7
4.9 ( 1.7
4.9 ( 1.7
overall average
159 ( 112
83 ( 74
83 ( 74
8.6 ( 6.1
4.5 ( 4.0
4.5 ( 4.0
95% confidence limits
118 to 200
48 to 118
48 to 118
6 to 11
2.6 to 6.4
2.6 to 6.4
Number of measurements for each substrate is the same as in Table 3. Values shown represent averages and standard deviations.
Table 6. Summary of K and Smin Values for Reactions IV and V Reaction IV K
primary substrate
Smin
Reaction V K
Smin
θx (d) (mg/L) (mg/L) (105 atm) (105 atm)
propionate
15 10
116 116
6.3 6.3
25 42
1.3 2.2
glucose
30
22
1.2
39
2.1
10
12
0.6
24
1.3
349
18.9
27
1.4
15
70
3.8
132
7.0
10
58
3.2
135
7.1
15
209
11.0
10 5
180 40
9.5 2.1
7.5 ethanol + propionate ethanol
(6.1 ( 1.6 kJ/mol H2) than in its absence (3.0 ( 0.9 kJ/mol H2). This more favorable ΔGE would enable the hydrogenotrophs to competitively obtain a better share of the energy available from ethanol conversion to acetate and methane. However, ΔGE for propionate conversion to acetate and H2 in the presence of ethanol (Table 4, Reaction IV) became positive, quite different than the average 6.1 ( 1.6 kJ/mol H2 in other cultures. Also, substrate concentrations under these chemostat operating conditions (see Supporting Information) were used to compute ΔGD values for Reaction IV, and were found to be almost zero (0.6 and 2.2 kJ/mol H2), effectively blocking this route of interspecies electron transport, yet propionate was consumed. An alternate interspecies electron transport route is likely involved, probably through formate.21,22 While formate information was not available to test this hypothesis, support is provided by De Bok et al.,23 who reported that Syntrophobacter fumaroxidans, a propionate syntroph, possesses both formate dehydrogenase and hydrogenases that are both expressed on all substrates tested. They concluded that both H2 and formate are involved in the central metabolism of this organism, and that both may serve as interspecies electron carriers. K and Smin Concentrations. Values for K and Smin, determined using eqs 4 and 5, are summarized in Tables 5 and 6. The variations found were not as great as might be expected considering the range of substrates and concentrations involved. The K and Smin values for propionate were the same for a given chemostat condition whether using Reactions II, III, or IV. The values obtained for all three substrates are typical of reported values,6,13,24
although reported values tend to vary so greatly that judgment as to model accuracy in their prediction is not possible. While the primary substrates here were quite different in composition, methane, carbon dioxide, and bicarbonate end product concentrations were quite similar among the four studies, and this may be a factor leading to the relatively small range of values found here. In only one of the studies evaluated had model fitting been done to determine kinetic parameters for acetate and propionate,25 the average reported acetate K value for the five separate chemostat evaluations at 35 °C was 168 ( 28 mg/L. With the approach developed here K was essentially the same (159 ( 112 mg/L). That reported for propionate from the two propionate chemostats was 32 ( 15 mg/L versus a somewhat higher 87 ( 74 found in this study. The reported μm and b values from that study had averages of 0.35 ( 0.11 d1 and 0.017 ( 0.004 d1, respectively, the same as assumed for this analysis. Insufficient data were available to make a reasonable comparison between K values at other temperatures, although reported values tended to be higher than determined from the approach developed here. An important factor leading to large variations in K and Smin values is the poor precision in measuring low concentrations of acetate, propionate, and H2. Considering these experimental difficulties, the approach developed here appears to be within reasonable agreement with the traditional methods. Sensitivity Analysis. A sensitivity analysis was conducted to determine the effect of the only two assumed coefficients for this model, μm and b, on the values obtained for ΔGE, K, and Smin. The two coefficients were independently doubled or halved and the resulting maximum percentage changes in the computed values were determined for Reactions I, III, and V (Table 7). Changes in μm and b for a given reaction impacted all values of ΔGE for that reaction, but the changes were relatively minor and no greater than given by the overall standard deviations listed for ΔGE. For example with Reaction I, doubling the 35 °C value of μm from 0.35 d1 to 0.7 d1 caused the average ΔGE to decrease from 17.7 kJ to 19.6 kJ/mol acetate. No growth rates at 35 °C as high as 0.7 d1 for acetoclastic methanogens could be found in the literature, and so 19.6 kJ/mol would appear to be beyond a lower bound with acetate. Halving μm to 0.175 d1 increased ΔGE to 16.3 ( 0.8 kJ/mol acetate, which is well within a standard deviation of the average value. Doubling μm and b for acetoclastic methanogens also decreased by 6% the ΔGE values for the propionate syntrophs. Syntroph kinetics are closely linked to their end-product-using partners as noted by others.1,2 Percentage changes in K and Smin were much greater than that in ΔGE and consistent with the near linear relationship between these coefficients and μm and b as indicated by eq 2. 6841
dx.doi.org/10.1021/es2009055 |Environ. Sci. Technol. 2011, 45, 6838–6844
Environmental Science & Technology
ARTICLE
Table 7. Sensitivity of ΔGE, K, and Smin to Doubling and Halving of μm and b valuesa ΔGE variable changed
Reaction I
Reaction III
12
6
K Reaction V
Reaction I
Reaction III
230
160
Smin Reaction V
Reaction I
Reaction III
54
67
Reaction . V
μm Reaction I Reaction III
+5
124 1
Reaction V
4 125
6
b Reaction I Reaction III Reaction V
8
6
49
14
76
49
+5 12
57 7
38
45
a
Values represent percentage changes and equal 100 times the difference between the changed and base average value divided by the lowest of the two. Plus or minus values indicate parameter increases or decreases with increase in μm or b, respectively. Blank spaces indicate no change occurred.
Relationship Between Growth Equilibrium and Threshold Thermodynamics. There is considerable literature addressing
substrate threshold limits, Scrit, and thermodynamic limits ΔGcrit.1,2,7,8,22 The question arises as to what if any relationship might exist between these limits and growth equilibrium values, Smin and ΔGE, as defined here? If one begins with a culture flask containing just below a Smin concentration of a substrate and introduces into it a single organism that can use that substrate for energy and growth, no substrate will be consumed. At that concentration, the organism decay rate will exceed its growth rate and no growth will occur. A single organism has little capacity to consume a substrate at a measurable rate. In this case, Smin and Scrit would be the same. This would also be the case with plug-flow through a fixed-bed column, such as in an aquifer, where organisms remain in place while a substrate passes through. As substrate decreases in its passage through the media, a Smin concentration is eventually reached, at which point the concentration would again be too small to support biological growth,26 and again, Smin would equal Scrit. In geological settings with very low delivery of substrate to confined microorganisms or in chemostat reactors operating with very high θx, a fixed population of organisms might survive obtaining just sufficient energy for survival with substrate concentration remaining poised near Smin. Here, again, Smin and Scrit would be the same. However, it is possible to arrive at concentrations below Smin, leading to a lower apparent Scrit value. Substrate consumption need not cease at Smin and reaction ΔG need not be as negative as ΔGE for substrate consumption. A relatively large active population being exposed to a concentration less than Smin would be under starvation conditions, but could still consume substrate, at least temporarily, thus lowering the concentration below Smin so that reaction free energy becomes less negative than ΔGE.27,28 Indeed, it would be possible theoretically to lower the concentration until the reaction free energy became zero. In a different approach than used here with a chemostat coculture converting ethanol to acetate and methane, Seitz et al.29 extrapolated measured ΔGD values to zero dilution (infinite θx, in effect offering another approach for estimating ΔGE). The ΔGE value so found for the hydrogenotroph, Methanobacterium bryantii was 9.1 kJ/mol H2, somewhat more negative than found in this study with the mixed culture growing on ethanol (Table 4). They also extrapolated the change in ΔGD values with increase in θx to a theoretical point at which substrate utilization rate would be zero, and obtained a less negative 7.5 kJ/mol H2. This is close to the threshold value of 7.2 kJ/mol H2 they found from batch
culture studies with this organism and to the ΔGE value found here with mixed ethanol cultures. We conclude that growth-equilibrium ΔGE as defined here sets a lower (more negative) bound on ΔGcrit and a higher concentration bound on Scrit. Also indicated by eq 4, Smin is a function of solution chemistry as well as ΔGE. For example, the ΔGE values found for H2 (Table 4) of 3.0 ( 0.9 kJ/mol H2 in the absence of ethanol and of 6.1 ( 1.6 kJ with ethanol are within the range of the nine values for ΔGcrit from field and culture studies reported by others.30 The range there reported for ΔGcrit was 2.4 to 10.8 kJ/mol of H2 with an average of 5.2 ( 2.9 kJ, values covering the same range as the ΔGE values obtained using the approach developed here. Similarly, the values determined here for Smin, ranging from 1.3 105 to 11 105 atm and averaging 4.5 ( 3.6 105 atm for hydrogenotrophic methanogens are similar to values reported for Scrit from 11 field and laboratory studies, with a range of 0.3 105 to 10.0 105 atm, and averaging 5.8 ( 3.2 105 atm as summarized by Pavlostathis and Giraldogomez.6 Similar comparisons for acetate and propionate between modeled results from chemostat studies as determined here and summaries provided by others 6,30,31 and largely based upon pure and coculture studies also indicate good agreement. Thus, while values for ΔGE and Smin are concluded to represent bounds on ΔGcrit and Scrit, values reported for the latter often tend to be similar to the former. Mixed-cultures tended to respond in a manner similar to that found with pure single and cocultures. One other aspect of ΔGE noted here is that the lower values found for hydrogenotrophs in ethanol oxidation compared with those found with propionate oxidation alone demonstrates that ΔGE values can differ significantly with organism as well as ecological conditions. A lower intrinsic ΔGE can permit a hydrogenotrophic methanogen to compete better for energy with an energetic substrate such as ethanol, but a higher value is more desirable when only a low energy substrate such as propionate is available. The ecological significance of such differences has been well demonstrated by differences in ΔGcrit found for acetoclastic methanogens.12,13,3234 Acetate Scrit values for Methanosaeta range from 0.4 to 4.1 mg/L, while the range for Methanosarcina is from 15 to 130 mg/L.6 This tendency for Methanosaeta to dominate with low acetate concentrations, but with dominance of Methanosarcina at higher acetate concentrations confirms that ΔGcrit, which is related to Scrit, is in some cases, if not all, an intrinsic property of the organisms themselves, a property that can have important ecological significance. 6842
dx.doi.org/10.1021/es2009055 |Environ. Sci. Technol. 2011, 45, 6838–6844
Environmental Science & Technology Biological Energy Quantum. While it has been suggested that a bacterium needs a minimum of about 20 kJ per mol of substrate transformed in order to exploit for growth the free energy released by a reaction,2 a so-called “quantum of energy” for a living cell as required to form ATP, the direct application of this concept has been called into question with syntrophic microorganisms.1,4,8,30 Reports where significantly less energy/ mol substrate has been found available are given for ethanol syntrophs (5.0 to 8.0 kJ),29 butyrate syntrophs (4.5 ( 1.9 kJ),9 and propionate syntrophs (3 to 15 kJ).35 The ΔGE values from this study with mixed-cultures tend to agree with the latter observations. Based upon the 20 kJ quantum concept, propionate conversion should yield a minimum of 20 kJ per mole propionate conversion to acetate and H2, another 20 kJ/mol for conversion of acetate to methane, and an additional 15 kJ for conversion of 3 mols H2 to methane, representing a total of 55 kJ/mol propionate. However, in this mixed-culture evaluation, the average ΔGE for the overall conversion of propionate to methane found was only 43 kJ/mol (Reaction II, Table 3), that for conversion of propionate to acetate and methane was 20.6 kJ/mol (Reaction III, Table 3), and that for the single organism conversion of propionate to acetate and H2 in propionate-fed cultures was only 8.0 kJ/mol (Reaction IV, Table 4), all similar to findings for syntrophs by others, but less than expectations with the 20 kJ/mol concept. However, the average values found here of 17.7 ( 2.2 kJ/mol acetate conversion and of 4.6 ( 2.1 kJ/mol for H2 oxidation are similar to the suggested quantum values.
’ SUMMARY The incorporation of growth equilibrium thermodynamics directly into to the Monod model for biological growth and decay (eq 1) as proposed here does not require a basic modification of that equation to make it fit observations of threshold values as has been the case with many other models. Using the model and data from several mixed-culture chemostat experiments with a variety of substrates, results were found that agree well with results and conclusions on threshold thermodynamic and concentration values obtained from single and simple combinations of pure anaerobic cultures. Such pure culture studies have provided a better fundamental understanding of how microorganisms work syntrophically at close to thermodynamic equilibrium to capture and share the small quantities of energy available. This study provides a demonstration that the basic principles so developed are applicable directly to complex anaerobic mixed culture systems containing numerous organisms working together in organic transformation where organism dominance changes to meet the ecological conditions imposed by their environment, whether natural or created in a biological wastewater treatment system. ’ ASSOCIATED CONTENT
bS
Supporting Information. Detailed data used for this analysis, method of computation and information on equations used. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
* Phone:1-650-723-4131; fax: 1-650-725-3164; e-mail: pmccarty@ stanford.edu.
ARTICLE
’ ACKNOWLEDGMENT This research was supported by the World Class University Program through the National Research Foundation of Korea, funded by the Ministry of Education, Science and Technology (grant number R33-2008-000-10043-0). ’ REFERENCES (1) Heimann, A.; Jakobsen, R.; Blodau, C. Energetic constraints on H2-dependent terminal electron accepting processes in anoxic environments: A review of observations and model approaches. Environ. Sci. Technol. 2010, 44 (1), 24–33. (2) Schink, B. Energetics of syntrophic cooperation in methanogenic degradation. Microbiol. Mol. Biol. Rev. 1997, 61 (2), 262–280. (3) Dassonville, F.; Renault, P. Interactions between microbial processes and geochemical transformations under anaerobic conditions: A review. Agronomie 2002, 22 (1), 51–68. (4) McInerney, M. J.; Sieber, J. R.; Gunsalus, R. P. Syntrophy in anaerobic global carbon cycles. Curr. Opin. Biotechnol. 2009, 20, 623–632. (5) Speece, R. E. Anaerobic Biotechnology for Industrial Wastewater Treatment. Environ. Sci. Technol. 1983, 17 (9), 416A–427A. (6) Pavlostathis, S. G.; Giraldogomez, E. Kinetics of anaerobic treatment—A critical review. Crit. Rev. Environ. Control 1991, 21 (56), 411. (7) McInerney, M. J., Anaerobic metabolism and its regulation. In Biotechnology; Kelly, D. R., Ed.; Wiley-VCH: Verlag, 1999; pp 456478. (8) Mcinerney, M. J.; Struchtemeyer, C. G.; Sieber, J.; Mouttaki, H.; Stams, A. J. M.; Schink, B.; Rohlin, L.; Gunsalus, R. P. Physiology, ecology, phylogeny, and genomics of microorganisms capable of syntrophic metabolism. Ann. N. Y. Acad. Sci. 2008, 1125, 58–72. (9) Jackson, B. E.; McInerney, M. J. Anaerobic microbial metabolism can proceed close to thermodynamic limits. Nature 2002, 415 (6870), 454–456. (10) Archer, D. B.; Powell, G. E. Dependence of the specific growth rate of methanogenic mutualistic cocultures on the methanogen. Arch. Microbiol. 1985, 141, 133–137. (11) Lovley, D. R. Minimum threshold for hydrogen metabolism in methanogenic bacteria. Appl. Environ. Microbiol. 1985, 49 (6), 1530– 1531. (12) Min, H.; Zinder, S. H. Kinetics of acetate utilization by 2 thermophilic acetotrophic methanogens—Methanosarcina sp. strain CALS-1 and Methanothrix sp strain CALS-1. Appl. Environ. Microbiol. 1989, 55 (2), 488–491. (13) Jetten, M. S. M.; Stams, A. J. M.; Zehnder, A. J. B. Acetate threshold values and acetate acivating enzymes in methanogenic bacteria. FEMS Microbiol. Ecol. 1990, 73, 339–344. (14) Hopkins, B. T.; McInerney, M. J.; Warikoo, V. Evidence for an anaerobic syntrophic benzoate degradation threshold and isolation of the syntrophic benzoate degrader. Appl. Environ. Microbiol. 1995, 61 (2), 526–530. (15) Ahring, B. K.; Westermann, P. Kinetics of butyrate, acetate, and hydrogen metabolism in a thermophilic, anaerobic, butyrate-degrading triculture. Appl. Environ. Microbiol. 1987, 53 (2), 434–439. (16) Chong, S. C.; Liu, Y.; Cummins, M.; Valentine, D. L.; Boone, D. R. Methanogenium marinum sp. nov., a H2-using methanogen from Skan Bay, Alaska, and kinetics of H2 utilization. Antonie van Leeuwenhoek 2002, 81, 263–270. (17) Rittmann, B. E.; McCarty, P. L., Environmental Biotechnology: Principles and Applications; McGraw-Hill: New York, 2001; p 754. (18) McCarty, P. L., Energetics of organic matter degradation. In Microbiology of Polluted Waters, Chapter 5; Mitchell, R., Ed.; John Wiley and Sons: New York, 1972; Vol. II. (19) Rittmann, B. E.; McCarty, P. L. Model of steady-state-biofilm kinetics. Biotechnol. Bioeng. 1980, 22, 2343–2357. (20) Warikoo, V.; McInerney, M. J.; Robinson, J. A.; Suflita, J. M. Interspecies acetate transfer influences the extent of anaerobic benzoate 6843
dx.doi.org/10.1021/es2009055 |Environ. Sci. Technol. 2011, 45, 6838–6844
Environmental Science & Technology
ARTICLE
degradation by syntrophic consortia. Appl. Environ. Microbiol. 1996, 62 (1), 26–32. (21) Thiele, J. H.; Zeikus, J. G. Control of interspecies electron fow during anaerobic digestion: significance of formate transfer versus hydrogen transfer during syntrophic methannogenesis in flocs. Appl. Environ. Microbiol. 1988, 54 (1), 20–29. (22) Stams, A. J. M.; Plugge, C. M. Electron transfer in syntrophic communities of anaerobic bacteria and archaea. Nat. Rev. Microbiol. 2009, 7, 568–577. (23) de Bok, F. A. M.; Roze, E. H. A.; Stams, A. J. M. Hydrogenases and formate dehydrogenases of Syntrophobacter Fumaroxidans. Antonie van Leeuwenhoek 2002, 81, 283–291. (24) Mosche, M.; Jordening, H. J. Detection of very low saturation constants in anaerobic digestion: influences of calcium carbonate precipitation and pH. Appl. Microbiol. Biotechnol. 1998, 49 (6), 793. (25) Lawrence, A. W.; McCarty, P. L. Kinetics of methane fermentation in anaerobic treatment. J. Water Pollut. Control Federation 1969, 41 (2), R1–R17. (26) Rittmann, B. E.; McCarty, P. L. Evaluation of steady-statebiofilm kinetics. Biotechnol. Eng. 1980, 22, 2359–2373. (27) Hoehler, T. M.; Alperin, M. J.; Albert, D. B.; Martens, C. S. Apparent minimum free energy requirements for methanogenic archaea and sulfate-reducing bacteria in an anoxic marine sediment. FEMS Microbiol. Ecol. 2001, 38 (1), 33–41. (28) Labib, F.; Ferguson, J. F.; Benjamin, M. M.; Merigh, M.; Ricker, N. L. Anaerobic butyrate degradation in a fluidized-bed reactor—Effects of increased concentrations of H2 and acetate. Environ. Sci. Technol. 1992, 26 (2), 369–376. (29) Seitz, H. J.; Schink, B.; Pfennig, N.; Conrad, J. Energetics of syntrophic ethanol oxidation in defined chemostat cocultures. Arch. Microbiol. 1990, 155, 82–88. (30) Hoehler, T. M. Biological energy requirements as quantitative boundary conditions for life in the subsurface. Geobiology 2004, 2 (4), 205–215. (31) Conklin, A.; Stensel, H. D.; Ferguson, J. Growth kinetics and competition between Methanosarcina and Methanosaeta in mesophilic anaerobic digestion. Water Environment Research 2006, 78 (5), 486–496. (32) Zinder, S. H.; Cardwell, S. C.; Anguish, T.; Lee, M.; Koch, M. Methanogenesis in a thermophilic (58°C) anaerobic digestor: Methanothrix sp. as an important aceticlastic methanogen. Appl. Environ. Microbiol. 1984, 47 (4), 796–807. (33) Westermann, P.; Ahring, B. K.; Mah, R. A. Threshold acetate concentrations for acetate catabolism by aceticlastic methanogenic bacteria. Appl. Environ. Microbiol. 1989, 55 (2), 514–515. (34) Fukuzaki, S.; Nishio, N.; Nagai, S. Kinetics of the methanogenic fermentation of acetate. Appl. Environ. Microbiol. 1990, 56 (10), 3158–3163. (35) Scholten, J. C. M.; Conrad, R. Energetics of syntrophic propionate oxidation in defined batch and chemostat cocultures. Appl. Environ. Microbiol. 2000, 66 (7), 2934–2942.
6844
dx.doi.org/10.1021/es2009055 |Environ. Sci. Technol. 2011, 45, 6838–6844
