Vol. 44, No. 6APPLIED AND ENVIRONMENTAL MICROBIOLOGY, Dec. 1982, p. 1374-13840099-2240/82/121374-11$02.00/0Copyright C 1982, American Society for Microbiology

Kinetics of Hydrogen Consumption by Rumen Fluid,Anaerobic Digestor Sludge, and Sedimentt

JOSEPH A. ROBINSONt AND JAMES M. TIEDJE*

Department of Microbiology and Public Health, Michigan State University, East Lansing, Michigan 48824

Received 26 May 1982/Accepted 3 September 1982

Michaelis-Menten kinetic parameters for H2 consumption by three methano-genic habitats were determined from progress curve and initial velocity experi-ments. The influences of mass transfer resistance, endogenous H2 production,and growth on apparent parameter estimates were also investigated. Kineticparameters could not be determined for undiluted rumen fluid and some digestorsludge from gas-phase measurements of H2, since mass transfer of H2 across thegas-liquid interface was rate limiting. However, accurate values were obtainedonce the samples were diluted. H2 consumption by digestor sludge with a longretention time and by hypereutrophic lake sediment was not phase transferlimited. The Km values for H2 uptake by these habitats were similar, with means

of 5.8, 6.0, and 7.1 ,uM for rumen fluid, digestor sludge, and sediment, respective-ly. Vmax estimates suggested a ratio of activity of approximately 100 (rumenfluid):10 (sludge):1 (sediment); their ranges were as follows: rumen fluid, 14 to 28mM h-1; Holt sludge, 0.7 to 4.3 mM h-1; and Wintergreen sediment, 0.13 to 0.49mM h-1. The principles of phase transfer limitation, studied here for H2, are thesame for all gaseous substrates and products. The limitations and errors associat-ed with gas phase determination of kinetic parameters were evaluated with a

mathematical model that combined mass transport and Michaelis-Menten kinet-ics. Three criteria are described which can be used to evaluate the possibility thata phase transfer limitation exists. If it does not exist, (i) substrate consumptioncurves are Michaelis-Menten and not first order, (ii) the Km is independent ofinitial substrate concentration, and (iii) the Km is independent of biomass (Vmax)

and remains constant with dilution of sample. Errors in the Michaelis-Mentenkinetic parameters are caused by endogenously produced H2, but they were

<15% for rumen fluid and 10% for lake sediment and digestor sludge. Increases inVmax during the course of progress curve experiments were not great enough toproduce systematic deviations from Michaelis-Menten kinetics.

Hydrogen is a key intermediate in the degra-dation of organic matter, affecting both the rateof this process and the nature of the end prod-ucts (4, 12, 34, 35). Due to the central role of H2in methanogenic habitats, the kinetics of H2consumption has received considerable atten-tion in the past few years, with most investiga-tors concentrating on H2 kinetics in eutrophiclake (29, 33) and marine (1, 2, 20) sediments andanaerobic digestor sludge (16, 26). H2 kinetics inthe rumen has been studied to a lesser extent (7,10, 13).Many investigators, particularly those study-

ing H2 kinetics in digestor sludge (16, 26), over-

t Journal article no. 10347 of the Michigan AgriculturalExperiment Station.

t Present address: JAR, Department of Civil Engineering,Montana State University, Bozeman, MT 59717.

looked the influence mass transfer resistancemay have had on their experiments. That masstransfer of gaseous substrates (e.g., 02) can limitmicrobial activity and growth has been under-stood for some time (3, 22, 23). But microbiolo-gists investigating H2 kinetics in methanogenichabitats have often implicitly assumed that theirincubation systems circumvented potentiallyrate-limiting movement of H2 across the gas-liquid interface. Gross overestimates of half-saturation constants (viz., Ki,m Ks) result if dataobtained under mass transfer (phase transfer)-limited conditions are used to compute estimatesof these parameters. Ngian et al. (21) havedemonstrated that mass transfer resistance cansignificantly increase apparent transport Km val-ues for organisms that form aggregates in biolog-ical reactors. They argue, as does Shieh (27),that mass transfer resistances must be eliminat-

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FIG. 1. Gas recirculation system used for H2 consumption and endogenous production experiments. Theheavier line indicates the path of gas circulation between sample flask and H2 GC sampling loop. Components aredetailed in the text.

ed if biological parameters, independent of reac-tion vessel geometries, are to be estimated.Thus, we initially examined the influence thatinterphase movement of H2 has on apparentkinetic parameters (viz., Ki, Vmax) when con-sumption of H2 is monitored in the gaseousphase and determined the magnitude of errorsassociated with Michaelis-Menten kinetic pa-rameters calculated from data obtained underphase transfer-limited conditions. We developeda model (PHASIM) to evaluate effects of masstransfer resistance on Michaelis-Menten kineticparameters. The model is generally useful sinceit describes the influence that mass transferresistance has on substrate consumption occur-ring in one phase of a multiphase system, wherethe substrate partitions among the variousphases (gas, liquid, or solid).The other goals of the present study were as

follows: (i) to compare the kinetics of H2 con-sumption in rumen fluid, hypereutrophic lakesediment, and anaerobic sludge; and (ii) to as-sess the influence that endogenous H2 produc-tion and growth have on apparent Michaelis-Menten kinetic parameters for H2.

MATERIALS AND METHODS

Habitats sampled. Samples of rumen fluid wereobtained from a fistulated cow that was fed daily 5.44kg of hay ad libitum. Samples of rumen fluid werewithdrawn from the cow according to a previouslydescribed procedure (23); a cheesecloth screen re-duced the proportion of particulate solids from thatfound in vivo. Samples were usually obtained beforefeeding to minimize variability in endogenous H2 pro-duction rates. Rumen fluid was used within 30 minafter it was collected.

Anaerobic digestor sludge was obtained from mu-nicipal waste treatment plants in Holt and Portland,Mich. Lake sediment samples were taken from thepelagic zone of hypereutrophic Wintergreen Lake(Hickory Corners, Mich.), using an Eckman dredge.Mason jars were completely filled with the samplesand sealed with metal canning lids. Samples werestored at 5 to 10°C for 1 week or less before beingused.

Experimental apparatus for measurement of H2 andCH4. All experiments were performed with the gasrecirculation system depicted in Fig. 1, which is pat-terned after the one described by Kaspar and Tiedje(15). Five hundred-milliliter volumes of undiluted ru-men fluid, diluted rumen fluid, Wintergreen sediment,or digestor sludge were anaerobically transferred to a2-liter flask, using a modification of the Hungatetechnique (11). The flask was stoppered, placed in awater bath (held at 39°C for rumen fluid, 30°C forsludge, or 9°C for sediment), and attached to the gasrecirculation system. Before the beginning of eachexperiment, the head space of the flask was flushedout the vent with CO2 (for rumen fluid), 30% C02-70%Ar (for sludge), or 5% C02-95% Ar (for sediment) forabout 15 to 30 min. Trace levels of 02 were removedfrom the sparge gas by passing it through hot copperfilings. After the flushing period, the gas recirculationsystem was closed and head space of the flask wasrecirculated, via a bellows-type pump (Universal Elec-tric Co., Owosso, Mich.), through a 3-ml gas samplingloop in a Carle AGC-111 gas chromatograph (GC)(Carle Instruments Inc., Anaheim, Calif.). A magneticstirrer set at near-maximal speed mixed the aqueousphase in the 2-liter flask. Argon, at a flow rate of 20 mlmin- , was used as the carrier gas for the Carle GC,and gas separation was made by using two tandemcolumns held at 30°C; the first column was Porapak T(1.2-m length, 3.2-mm inside diameter), and the sec-ond was molecular sieve 5A (2.7-m length, 3.2-mminside diameter). Injections were automatically per-

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4

c 3 l \-RASR

81 \ L~~~LIMBE \0

v1 L0L

0 30 60 90 120 10Time Units

FIG. 2. Theoretical curves for phase transfer- andnontransfer-limited gaseous substrate consumption.The two curves were generated with the PHASIMmodel. Note that depletion of a saturating concentra-tion of a gaseous substrate is first order under transfer-limited conditions.

formed with a timer (Carle Instruments Inc.) attachedto the valve switching mechanism in the H2 GC. TheH2 retention time was ca. 3 min. After the H2 passedthrough the microthermistor detector, the gas flowwas reversed by the timer, and the rest of the gassample (including the CH4 in the original 3-ml injec-tion) was backflushed to a Varian 600-D GC (VarianInstrument Group, Walnut Creek, Calif.) equippedwith a flame ionization detector. The backflush stream

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of Ar, at a flow rate of 40 ml min-', served as thecarrier gas for the second (CH4-detecting) GC, and gasseparation in this instrument was effected with a 1.5-m(3.2-mm-inside diameter) column of Porapak Q atroom temperature. H2 and CH4 peak areas weredetermined with integrators. The pressure transducer(Unimeasure, Grants Pass, Ore.) was used to checkfor leaks in the gas recirculation system.Bunsen coefficients, for the three temperatures of

incubation, were calculated with an equation thatdescribes the solubility of a gas as a function oftemperature (32).

Initial velocity and progress curve experiments. Forinitial velocity experiments, rumen fluid (diluted andundiluted) was incubated with five different initial H2concentrations. Consumption of H2 was monitored at10-min intervals for 2 h, and initial velocity estimateswere obtained by evaluating the first derivatives of thebest-fit lines for H2 disappearance at t = 0. Estimatesof Km and Vmax for H2 consumption were determinedfrom initial velocity-substrate concentration (v-s)pairs, using (i) an unweighted Lineweaver-Burk analy-sis, (ii) the direct linear plot of Cornish-Bowden (9),and (iii) a nonlinear regresrsion analysis that involvedfitting the v-s pairs directly to a rectangular hyperbola(6). For progress curve experiments, a saturatingconcentration of H2 (calculated from K,,, estimatesdetermined by Hungate et al. [13] and Strayer andTiedje [29]) was incubated with diluted rumen fluid,Holt sludge, or Wintergreen sediment. The H2 concen-tration was monitored until it had decreased to 10% orless of the value measured at the first time point. Vmaxand Km estimates were calculated from the progress

120 240 360Minutes

480

FIG. 3. Gaseous-phase data for phase transfer-limited (first-order) H2 consumption by undiluted rumen fluid(URF) and Portland sludge (PS) and nontransfer-limited (mixed-order) H2 consumption by 20-fold-diluted rumenfluid (DRF). The solid lines are best-fit one-term exponential (undiluted rumen fluid and Portland sludge) andtheoretical Michaelis-Menten curves (diluted rumen fluid) calculated from the data.

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sis. Rates of H2 production were calculated duringtimes when the endogenous H2 pool, which was con-comitantly measured with CH4, had attained an ap-proximately steady-state condition.

Phase-transfer model. If the rate at which a gaseoussubstrate crosses the gas-liquid interface is slowerthan the rate of biological consumption, then substrateconsumption is phase transfer limited and approxi-

H%<S mately first order, whether the initial substrate con-

RF H centration is greater than the Km or not. But if the rateof interface transfer is rapid enough to supply thebiological demand, then substrate consumption willnot be transfer limited, and the kinetic pattern ob-

3 6 9 12 15 served will be controlled by the biological process. InHour-s this case, and assuming that the biological processHour~s exhibits saturation kinetics, a Michaelis-Menten prog-

ress curve will be observed for gaseous substrateconsumption.We developed a model (PHASIM) to elucidate con-

ditions leading to phase transfer limitations for con-sumption of a gaseous substrate. The model consistsof two differential equations. The first equation de-scribes consumption of a gaseous substrate in the gas

Ws phase: dG/dt = -kla(BG - A), where G is theconcentration of the gaseous substrate in the gasphase, A is the concentration of the gaseous substratedissolved in the aqueous phase, kla is the volumetrictransfer coefficient, B is the Bunsen absorption coeffi-cient, and t is time. The equation derives from Fick'sfirst law of diffusion (23, 31) and, in its most general

5 10 15 20 25 form, describes mass transport across any interphaseHour-s

FIG. 4. Calculated aqueous-phase data for Michae-lis-Menten H2 consumption by diluted rumen fluid(RF), Holt sludge (HS), and Wintergreen sediment(WS). The solid lines are theoretical curves calculatedwith the Vmax and Km estimates obtained from nonlin-ear analysis of the progress curve data and illustratethe high precision with which the kinetic constantswere estimated.

curve data, using a computer program that performeda nonlinear regression analysis of Michaelis-Mentenprogress curve data (M. Betlach, Ph.D. thesis, Michi-gan State University, East Lansing, 1979), accordingto the procedure outlined by Duggleby and Morrison(8). H2 Vmax values for rumen fluid were multiplied bythe dilution factor required to overcome the phasetransfer limitation.Measurement of endogenous H2 production rates.

Experiments to determine endogenous concentrationsand rates of H2 production by rumen fluid, digestorsludge, or lake sediment were essentially the same as

the progress curve and initial velocity experiments,except that H2 was not added. Rates of endogenousCH4 production were calculated by fitting the CH4concentration data to linear or one-term power curves

and evaluating the first derivatives of these equations.Rates of endogenous H2 production were calculatedfor rumen fluid, sewage sludge, and lake sediment byfirst multiplying the CH4 production rates by 4 andthen assuming that 100o (10), 30%o (14, 28), and 37%(17), respectively, of the CH4 generated in thesehabitats comes from chemolithotrophic methanogene-

TABLE 1. Summary of Michaelis-Menten kineticparameters for rumen fluid, Holt digestor sludge, and

Wintergreen sedimentaAnaerobic habitat V.,, (mM h-1)b Km (pLM)c

Rumen fluid 28.3 ± 0.37 9.08 ± 0.2613.3 ± 0.15 7.19 ± 0.3019.8 ± 0.71 6.00 ± 0.6414.6 ± 0.39 4.31 ± 0.4113.5 ± 0.21 4.23 ± 0.2317.0 ± 0.70 4.21 ± 0.50

Holt digestor sludge 0.70 ± 0.01 6.80 ± 0.304.30 ± 0.22 6.72 ± 0.852.98 ± 0.08 6.22 ± 0.432.55 ± 0.04 6.12 ± 0.262.29 ± 0.10 5.85 ± 0.593.26 ± 0.16 4.42 ± 0.66

Wintergreen sediment 0.49 ± 0.01 8.58 ± 0.490.13 ± 0.01 5.63 ± 0.38

a Parameter estimate ± SE*t value (95% confidenceinterval); each pair of parameter estimates was deter-mined from a minimum of 12 data pairs. Note that SEsare approximate, since the integrated form of theMichaelis-Menten model is nonlinear, and were calcu-lated assuming no correlation among the measurementerrors.

b Values are corrected for any dilutions required toovercome phase transfer limitations and are for totalconsumption per unit volume of sample assayed.

c Estimates are for H2 dissolved in the aqueousphase, calculated from gaseous-phase data using Bun-sen absorption coefficients for pure water.

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FIG. 5. Dependence of apparent H2 Km on magni-tude of the biological sink under phase transfer- andnontransfer-limited conditions. Points are Km esti-mates calculated from both linear and nonlinear analy-ses of five initial velocity-H2 concentration data pairs.Along with apparent Km determined from initial veloc-ity experiments are plotted Km estimates obtainedfrom progress curves performed at dilutions of 20 or

greater, to demonstrate equivalence of these two ki-netic approaches once H2 consumption is not phasetransfer limited.

boundary (e.g., gas-liquid interface). The rate of bio-logical consumption was assumed to conform to Mi-chaelis-Menten kinetics. The following equation de-scribes the behavior of the substrate dissolved in theaqueous phase: dAldt = kla(BG - A) - [VmaxAI(K,n +A)], where Vmax is the maximum rate of consumptionof A and Km is the half-saturation constant for sub-strate consumption. The model also allowed for en-

dogenous production of the substrate and a doubling ofVmax with time, the latter simulating growth during theperiod of substrate consumption. Solution curves(viz., G versus t, A versus t) for the above differentialequations were estimated by using a fourth-orderRunge-Kutta technique (5). Our model is similar to onepreviously described for 02 uptake by growing cells ina shake flask (30).

Figure 2 depicts the results of two PHASIM simula-tions. When the k1a was less than the V ..ax, then phasetransfer-limited consumption occurred. On the otherhand, a Michaelis-Menten progress curve resultedwhen the k1a was greater than the Vmax. Parametervalues for these simulations were chosen arbitrarily.In general, Michaelis-Menten kinetics result if the klais greater than the Vmax, whereas gaseous substrateconsumption is first order when a phase transferlimitation exists. When the kia and Vaax are similar inmagnitude, then the kinetic pattern is a combination offirst order and Michaelis-Menten kinetics.

Consumption of H2 by rumen fluid, sediment,and sludge. Consumption of initially saturatinglevels of H2 by undiluted rumen fluid and Port-land digestor sludge was first order and thusphase transfer limited (Fig. 3). Coefficients ofdetermination (r2) of 1.00 were obtained whenthese data were fitted to one-term exponentialequations. H2 progress curve data for Portlandsludge and undiluted rumen fluid could not befitted to the integrated Michaelis-Menten equa-tion due to their strictly first-order nature.We chose dilution as a means of circumvent-

ing the transfer limitation. Rumen fluid wasdiluted to various degrees with artificial saliva(19) and incubated with a saturating concentra-tion of H2. H2 consumption by 20-fold-dilutedrumen fluid conformed to Michaelis-Menten ki-netics (Fig. 3) and thus was not phase transferlimited. These experiments were repeated sever-al times, and it was found that the criticaldilution factor required to overcome phasetransfer-limited consumption of H2 was between10- and 20-fold. The Vmax (corrected for dilu-tion) and Km for H2 consumption by rumen fluidwere calculated from the data depicted in Fig. 4to be 28 mM h-1 and 9.1 ,uM, respectively.Hydrogen consumption by undiluted Winter-

green sediment and Holt digestor sludge exhibit-ed Michaelis-Menten kinetics (Fig. 4). Con-sumption of added H2 by sediment wasoccasionally phase transfer limited (data notshown), but this was due to the relatively highviscosity of sediment rather than to the presenceof a large biological sink. Estimates of Vmax andKm for diluted rumen fluid, Holt sludge, andWintergreen sediment were determined via non-linear regression analysis. The goodness-of-fit ofthe nontransfer-limited H2 depletion data to theintegrated Michaelis-Menten equation is illus-trated in Fig. 4. Km estimates for the anaerobichabitats investigated ranged from 4 to 9 ,uMdissolved H2 (Table 1). Vmax for H2 consumptionby rumen fluid, eutrophic sediment, and anaero-bic digestor sludge varied from 0.1 to 28 mmol oftotal H2 consumed liter-1 h-1, with rumen fluidhaving the highest potential H2-consuming ca-pacity and Wintergreen sediment having thelowest (Table 1).

Effect of phase transfer limitation on H2 Km.The error associated with H2 Km estimates for aphase transfer-limited system was evaluatedfrom initial velocity data obtained for undilutedand diluted rumen fluid. Each batch of rumenfluid was incubated with five different initial H2concentrations. Substrate disappearance wasmonitored for 2 h, and initial velocity estimateswere calculated from slopes of the best-fitcurves at t = 0. The apparent H2 Km estimates

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HYDROGEN KINETICS IN ANAEROBIC HABITATS 1379

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PHASIM Model Data

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FIG. 6. Effect of increases in endogenous substrateproduction (A) and Vmax with time (B) on Michaelis-Menten progress curves. All theoretical curves weregenerated by PHASIM for gaseous substrate con-sumption under nontransfer-limited conditions. Thelowest curve in (A) is the case for no endogenous H2production, with the succeeding curves above this onerepresenting linear endogenous H2 production ratesequal to 5, 10, 15, and 20%o of the Vmax for substrateconsumption. The uppermost curve in (B) is identicalto the lowest curve in (A) and represents the situationwhere Vmax remains constant over the course of theprogress curve. The lower succeeding curves depictthe patterns of substrate consumption where Vmaxdoubles within 100, 75, 50, and 25% of the total timerequired for the control progress curve to be 99ocomplete.

were markedly dependent on the rumen fluidconcentration when H2 consumption was trans-fer limited (Fig. 5). In addition, H2 Km estimateswere dependent on the initial H2 concentration:the higher the initial substrate concentration, thegreater the apparent H2 Km. Once the phasetransfer limitation was overcome, H2 Km valuesremained relatively constant with increasing di-lution (Fig. 5) and were independent of the initialH2 concentration, as expected.

Influence of endogenous H2 production on V.,.and Km. The effect of endogenous H2 production

on Vmax and Km estimates was investigated withthe PHASIM model. Several simulations wererun with the same Vmax and Km values, but withincreasing linear rates of H2 production (Fig.6A). After the simulated data were generated,they were analyzed, using the same nonlinearregression program used in analyzing experi-mental data, to obtain estimates of the kineticparameters. Rates of endogenous productionthat were a greater percentage of the maximumrate of substrate consumption produced lesserror in estimates of Vmax than Km (Fig. 7). Theapparent Km values increased with increasingrates of endogenous substrate production,whereas apparent Vmax values decreased withincreasing rates of substrate production. In theabsence of endogenous substrate production,the kinetic parameters calculated from simulateddata equalled the parameter values plugged intothe PHASIM model for that particular simula-tion.To assess the error in calculated Vmax and Km

estimates for filtered rumen fluid, arising fromendogenously produced H2, rates of H2 produc-tion were determined for this methanogenic hab-itat. These rates were subsequently used tocalculate potential errors in the kinetic parame-ters, using Fig. 7. Undiluted rumen fluid (500 ml)was incubated in the gas recirculation system,and H2 and CH4 concentrations were monitored(Fig. 8). Best-fit curves were calculated for theCH4 data, and the first derivatives of thesecurves were evaluated at times when endoge-nous H2 concentrations were measured. Endog-enous rates of ruminal H2 production were cal-culated by multiplying calculated CH4production rates by 4 and then assuming that100% of total CH4 production derives fromchemolithotrophic methanogenesis (10). Ratesof H2 production for undiluted rumen fluid, overthe period of time the H2 pool size was relativelyconstant (Fig. 9), ranged from 0.7 to 0.9 puM h-1(Fig. 8). These rates equal 4 and 5%, respec-tively, of the average ruminal Vmax for H2 con-sumption. Thus, potential errors in the H2 Kmfor rumen fluid, after taking into account thepossible error associated with the Vmax estimate,ranged from 10 to 15%. In similar experimentswith Holt sludge and Wintergreen sediment, wecalculated maximum potential errors in H2 Kmvalues to be less than 10%.

Steady-state dissolved H2 concentrationswere typically 0.1 ,iM for diluted rumen fluid(Fig. 9), 0.05 ,uM for Holt sludge (Fig. 10), andgenerally less than 0.01 ,M for Wintergreensediment (when detectable). These are 40-fold ormore below the H2 Km estimates. Figures 9 and10 also show that added H2 is consumed untilthe concentration reaches the endogenous H2level found in replicate batches.

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soPHASIM Model Data 4

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30 ] Error in Km 2,

Error inVi , 8

30 8

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Endogenous S Production Ra+e as % of VMCx

FIG. 7. Errors in apparent Vmax (A) and Km (B)resulting from concomitant endogenous H2 productionduring the course of progress curve experiments. Eachtheoretical curve was generated from 60 separatesimulations, all of which were run under nontransfer-limited conditions.

Effect of growth on H2 Vmax and Km estimates.The effect of growth on the shape of nontransfer-limited H2 consumption was examined with thePHASIM model. Again, the kinetic parameters,with the exception of Vmax, were constant for allsimulations. For each simulation, the initialVmax was the same, but the doubling time forVmax was decreased for succesive simulations. IfVmax increased by a minimum of 25% during thecourse of a simulated progress curve, thenenough sigmoidicity was introduced into thedata to prevent nonlinear regression analysis,using the Michaelis-Menten kinetic model (Fig.6B). We never observed a degree of sigmoidicityin our H2 consumption experiments, using ru-

men fluid, sediment, or sludge, that preventedanalyzing the progress curve data with our non-linear regression program.

DISCUSSIONWhen consumption of a gaseous substrate is

phase transfer limited, then the kinetic pattern isdictated by the rate of absorption of the gas.According to the fluid-film theory (23, 31), theabsorption rate of a gas by a liquid is linearlydependent on the difference between the equilib-rium concentration of the gas and its concentra-tion in the bulk of the liquid phase. If thesolubility of the gaseous substrate is low, suchas is the case for H2, then disappearance of thegas from the gaseous phase is approximatelyfirst order, regardless of the kinetic nature ofsubstrate consumption by cells in the liquidphase. H2 consumption by undiluted rumen flu-id, using our incubation system, was phasetransfer limited. H2 consumption could not besaturated, and apparent Km values, determinedfrom initial velocity experiments, exhibited a

strong dependence on both the initial substrateconcentration and the magnitude of the biologi-cal sink. Once the transfer limitation was over-come, H2 consumption could be saturated andKm values became relatively constant (5.8 ,uM).When gaseous substrate consumption is not

phase transfer limited, then gaseous phase con-centrations may be multiplied by a partitioncoefficient to obtain aqueous-phase substrateconcentrations, because the rate-limiting step isbiological consumption and not mass transport.We have found agreement between steady-stateaqueous-phase H2 concentrations calculatedfrom gaseous-phase data (Fig. 9 and 10) anddissolved H2 measured by a previously pub-lished technique (24). Similar results have alsobeen obtained for H2 progress curve experi-ments. Measurement of gaseous-phase compo-nents (albeit indirect) is usually preferred since itgenerally can be done with greater ease andprecision.H2 consumption by eutrophic Wintergreen

sediment and Holt sludge generally followedMichaelis-Menten kinetics. Nontransfer-limitedbehavior by Holt sludge was likely a result of itsunusually long retention time (38 days). Experi-ments with other sludges (e.g., Portland), havingmore typical retention times (17 to 21 days), allexhibited phase transfer-limited consumption ofH2. The H2 Km values for Wintergreen sedi-ments and Holt sludge fell within the rangeobserved for rumen fluid (Table 1). The H2 Vmaxvalues for total consumption by sediments andHolt sludge were approximately 100- and 10-foldlower, respectively, than those for rumen fluid(Table 1). The difference among the H2 Vmaxvalues is partially explained by the differenttemperatures of incubation. But the broad rangeamong the Vinax estimates primarily reflects thedensities of H2-consuming organisms, principal-ly methanogens, present in these habitats. TheVmax values for rumen fluid are probably under-estimates since solid particulates were partiallyremoved by sampling through cheesecloth. Thevariability among the H2 Km estimates probablyreflects variability in endogenous H2 productionrates, since the precision of Km estimates washigh (Table 1). This is supported by the repro-ducibility of Km estimates determined for Meth-anospirillum hungatei JF-1 and DesulfovibrioGll (coefficients of variation, approximately10% versus about 30% overall for the threehabitats studied [unpublished data]).Our H2 Km values for rumen fluid and eutro-

phic sediments are slightly higher than previous-ly published estimates. Strayer and Tiedje's (29)average Km for H2 consumption by Wintergreensediment was 2.5 ,uM. Hungate et al. (13) report-ed an average ruminal H2 Km of 1 ,M. In a seriesof competition experiments with FeCI2- and

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production were calculated by fitting a power curve to the CH4 production data, differentiating, and thenmultiplying the calculated instantaneous CH4 production rates by 4. Early high rates of H2 production partiallyresult from prior stripping out of the product and substrate gases during the sparging period (see text); later ratesreflect attainment of near steady-state conditions after H2 has again equilibrated between the two phases.

FeSO4-amended Wintergreen sediments, Love-ly et al. (17) determined H2 Km values for themethanogenic population that agree with ourestimates. Mass transfer resistance probably in-fluenced the above sediment H2 kinetic experi-ments to a minor extent since H2-consumingactivity is comparatively low in this methano-genic habitat, and these experiments used reac-tion vessels having large surface-to-sedimentvolume ratios. Interphase transport could nothave influenced H2 kinetic experiments per-formed by Hungate and co-workers (13) sincedissolved H2 was directly measured.

Half-saturation constants in the literature fordigestor sludge differ markedly compared withH2 Km estimates we obtained for anaerobicsludge. Half-saturation constants as high as 96kPa have been reported for H2 consumption byanaerobic sludge (26). This is equivalent to 720,uM at 25°C and 101-kPa total pressure, assum-ing that the gas and liquid phases were in equilib-rium. In a more recent study, Kaspar and Wuhr-mann (16) calculated that H2 consumption bydigestor sludge was half-saturated at 80 ,uM (11kPa). The high Km estimates for sludge probablywere determined under phase transfer-limitedconditions. Previous investigators have general-ly performed initial velocity-type experiments,analyzing their rate data with double-reciprocalplots, to obtain estimates of microbial kineticparameters. For transfer-limited systems, initial

velocity experiments can be performed and ex-cellent linear fits obtained when the data aretransformed for double-reciprocal analysis, eventhough the rate data are strictly first order. Thisis because the reciprocal of a first-order rateequation is a straight line. In initial velocityexperiments with transfer-limited rumen fluidwe have repeatedly obtained r2 values of 0.99 orbetter for double-reciprocal analyses of the data,but the parameter values determined for suchsystems are unrealistically high (Fig. 5).

Estimates of H2 Michaelis-Menten parametersare in error if endogenous H2 production con-comitantly occurs with consumption of addedH2. Under these conditions, overestimates ofKm and underestimates of V.max are obtainedfrom analysis of the progress curve data, withKm being the more sensitive of the two kineticparameters. In the present study, H2 Km valueswere maximally overestimated for rumen fluidby 15 and 10% for Holt sludge and Wintergreensediment. These error estimates were calculatedby using the endogenous H2 production ratesand average Vmax estimates for these three habi-tats and Fig. 7. It is interesting to note thatdifferences among the endogenous H2 levels forrumen fluid, sludge, and sediment paralleled theratios of the H2 Vmax values for these habitats.

Errors in H2 Km and Vmax estimates are alsoproduced if there is a change in activity (i.e.,Vmax) during a progress curve experiment. In

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20-Fold DRF

Endo9enous H2 %a_~~~~~~~~~18

0 100 200 300Minu+es

400 500 600

FIG. 9. Relationship between endogenously produced H2 and H2 concentrations monitored during a progresscurve, using replicate suspensions of diluted rumen fluid (DRF). Triangles in lower graph are the points at theend of the progress curve that fall within the ordinate range in which endogenously produced H2 is plotted.

contrast to the effect of endogenous H2 produc-tion, an increase in Vmax (i.e., growth) with timeresults in underestimates and overestimates ofKm and Vmax, respectively, when progress curvedata are analyzed. Indeed, if Vnmax increases by aminimum of 25% during the course of substrateconsumption, then the resulting degree of sig-moidicity is sufficient to prevent analysis of thedata with the Michaelis-Menten model. H2 con-sumption by rumen fluid, Holt sludge, and Win-tergreen sediment exhibited no apparent sig-moidicity, and if Vmax increased during thecourse of any of our progress curve experi-ments, it was not enough to generate statisticallysignificant deviations from the Michaelis-Men-ten kinetic model.The influence of mass transport on microbial

activity is a general one, affecting both substrateconsumption and product formation in multi-phase systems. Thus, half-saturation constantsfor substrate consumption by either growing (25)or resting cells may have questionable signifi-cance unless it was established that conditionswere not phase transfer limited. Phase transferconsiderations are also important to productionof gaseous products (e.g., CH4, N20, N2) fromeither gaseous or nongaseous substrates. Pro-duction of a gaseous product from a gaseous

substrate mirrors the kinetic behavior of sub-strate consumption, whether a phase transferlimitation is in force or not. On the other hand,appearance of a gaseous product in a head spaceis rate limited if interphase transport is slowerthan the rate at which this product is formed inthe liquid phase from a nongaseous substrate.PHASIM can be used to model this situation byincluding a third differential equation to describenongaseous substrate consumption and by re-versing the order of the variables in the masstransport terms of the other two differentialequations.

Several criteria can be used to assess whethera phase transfer limitation is in force or not.First, under transfer-limited conditions con-sumption of an initially saturating concentrationof the substrate is approximately first order.Consumption of the substrate must be moni-tored until it is at least 85% complete to assurethat strictly first-order behavior can be distin-guished from Michaelis-Menten-type kinetics.Second, apparent Km values (obtained frominitial velocity studies) are markedly dependenton the magnitude of the biological sink (i.e.,Vmax) and the initial substrate concentrationunder transfer-limited conditions, and experi-ments should be designed to test for these possi-

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r-4 16lHc 12I

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HYDROGEN KINETICS IN ANAEROBIC HABITATS

HS

Endogenous H2

r~~~ -a

8 12Hours

16 20

FIG. 10. Relationship between endogenously produced H2 and H2 concentrations monitored during a

progress curve, using replicate samples of undiluted Holt sludge (HS). Triangles in lower graph are the points atthe end of the progress curve that fall within the ordinate range in which endogenously produced H2 is plotted.

bilities. If initial velocity studies are to be reliedupon, then the v-gaseous s data pairs should bedirectly fitted to a rectangular hyperbola (i.e.,the Michaelis-Menten equation) or a direct lin-ear plot should be constructed. Plotting of initialvelocity results for gaseous substrate consump-tion to a linearized form of the Michaelis-Men-ten equation (e.g., Lineweaver-Burk plot) doesnot alone allow a distinction to be made betweentransfer-limited substrate consumption and satu-ration kinetics. On occasion, substrate con-sumption is nearly transfer limited and progresscurve analysis of substrate consumption datayields Km estimates greater than the initial sub-strate concentration. This results from the datafitting first-order decay better than the Michae-lis-Menten model and is apparent when the dataare plotted against the theoretical Michaelis-Menten curve along with the best-fit exponentialequation. Last, apparent Km values determinedfrom initial velocity data should decrease withincreasing dilutions of the original liquid sample,converging to a constant value once the transferlimitation is overcome.For kinetic investigations of microbial pro-

cesses that involve gaseous substrates and prod-ucts, it is easier to monitor changes in theconcentrations of these compounds in the gas-

eous than in the liquid phase. But this is appro-priate only when it has been verified by thecriteria presented above that a phase transferlimitation does not exist.

ACKNOWLEDGMENTS

We thank Derek Lovley for helpful comments on sedimentH2 kinetics, Mike Klug for making available the facilities of hislaboratory at the Kellogg Biological Station in Hickory Cor-ners, Mich., and the Department of Animal Science for use oftheir fistulated cows.

This work was supported by National Science Foundationgrants DEB 78-05321 and DEB 81-09994.

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