Vol. 42, No.6APPLIED AND ENVIRONMENTAL MICROBIOLOGY, Dec. 1981, p. 936-9430099-2240/81/120936-08$02.00/0

Use of a Fractional Factorial Design to Evaluate Interactionsof Environmental Factors Affecting Biodegradation Rates

TIMOTHY E. FANNIN,lt MICHAEL D. MARCUS,lt DONALD A. ANDERSON,2 ANDHAROLD L. BERGMANl*

Department ofZoology and Physiology' and Department of Statistics,2 University ofWyoming, Laramie, Wyoming 82071

Received 10 April 1981/Accepted 9 August 1981

For investigation ofmain and interactive effects of six experimentally controlledenvironmental factors on phenol biodegradation in a shake-flask system, a largelyneglected statistical procedure was applied. A major benefit resulting from theapplication of the orthogonal, fractional factorial design is that the number ofexperiments necessary to evaluate multifactor interactions is limited. In our

investigation, the required number of experiments was reduced to 81 from the324 necessary with conventional factorial designs; information was sacrificed foronly 3 of 15 possible two-factor interactions. Six experimentally controlled factorswere investigated at two or three treatment levels each; the six factors were (1)amount of phenol substrate, (2) amount of bacterial inoculum, (3) filtration ofinoculum, (4) type of basal salts medium, (5) initial pH of basal salts medium,and (6) flask closure. Significant main effects were found for factors 1, 2, and 4;whereas significant interactive effects were found only for factor 2 with factor 3and for factor 2 with factor 5. Our results suggest that the application of thesestatistical designs will greatly reduce the number of experiments necessary toevaluate multifactor effects on degradation rates during optimization of bothhazard screening systems and waste treatment systems.

An important problem in evaluating the fatesof chemicals in aquatic ecosystems is the influ-ence of environmental or experimental factorson microbial degradation rates. Such factors in-fluencing degradation rates include the bacterialinhibition by the test compound (6, 8), the num-ber and physiological state of bacteria as a func-tion of nutrients (9, 15, 18), and the seasonalstate of bacterial development (2). Interactionsamong these and other factors can cause widevariations in degradation kinetics. Analyzing theinfluence of each factor on realized degradationrates can be very complex when two or morefactors are influencing degradation. With con-ventional factorial analysis, the number of ex-periments required to test the effects of evenfour or five different factors is prohibitive forroutine screening of chemicals.The purpose of this paper is to demonstrate

the use of an orthogonal, fractional factorialdesign to evaluate the effects of six environmen-tal factors on experimental degradation rates.Fractional factorial designs allow testing of a

t Present address: Wyoming Game and Fish Commission,Water Pollution Laboratory, Lander, WY 82520.

t Present address: Western Aquatics, Inc., Laramie,WY 82070.

number of factors and their interactions simul-taneously with a substantial reduction in thenumber of individual experiments (experimentalruns) required, but without loss of importantinformation (3, 4). The example that we presentanalyzes effects on the maximum degradationrate for phenol, a known biodegradable com-pound (12, 16), caused by three quantitativefactors (amount of phenol substrate, amount ofbacterial inoculum, and pH of basal salts me-dium [BSM]) and three qualitative factors (typeof BSM, filtration of bacterial inoculum, andtype offlask closure, i.e., screw-capped or cotton-stoppered flasks). Two of the environmental fac-tors (filtration and flask closure) were tested attwo treatment levels; the remaining four factorswere tested at three levels each. With conven-tional factorial procedures, one full replicate ofthis experiment would involve 22 x 34 = 324experimental runs to test the individual influ-ences (main effects) of the six environmentalfactors plus the 15 possible two-factor interac-tions among the six factors. In comparison, theorthogonal, fractional factorial design that weused to analyze the main effects and two-factorinteractions required only 81 experimentalruns-243 fewer runs than for a conventionalfactorial analysis.

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FACTORIAL DESIGN FOR BIODEGRADATION ANALYSIS 937

MATERIALS AND METHODSLaboratory procedures. Table 1 shows the treat-

ment levels applied for each of the six selected envi-ronmental factors used in our experiments. Includedare the codes which correspond to each treatmentlevel. These codes are again used in Table 2 to indicatethe level for each environmental treatment assignedto each of the 81 flasks. The experimental flasks wererandomly assigned the sequence numbers 1 to 81 andthen, in the order of these sequence numbers, weredivided into nine sets of nine flasks each. Over 5succeeding weeks, these nine experimental sets werecompleted at two per week for 4 weeks, and the ninthset was completed during week 5. Sterile controls wererun each week to estimate the influence ofphotochem-ical reactions or volatilization on the disappearance ofphenol from the flasks.The bacterial population used for the experimental

inoculum was collected from an oil refinery settlingpond near Sinclair, Wyo. A mixture of 4 liters of waterand 2 liters of sediment was allowed to settle for 15min before 200-ml samples of the supernatant weredispensed into 250-ml Teflon-capped flasks, whichwere then stored in darkness at 40C. Each flask ofsupernatant supplied the inoculum for one set of nineexperimental flasks.The pH of each BSM solution (Table 3) was ad-

justed to ±0.1 pH unit of the required experimentalvalue with 1 N HCI or 1 N NaOH. Appropriateamounts of BSM were then added to acid-washed,250-ml Erlenmeyer flasks to provide a final 200-mlvolume of medium, phenol, and inoculum. Capped orcotton-plugged flasks were autoclaved at 121°C and at15 lb/in2 for 20 min. After the flasks were cooled toroom temperature, phenol stock solution (16 g of Mal-

TABLE 1. Experimental treatments, codes fortreatment levels, and corresponding treatment levels

used in phenol degradation experimentsEnvironmental factor Code' Treatment level

Amt of phenol 0 100 mg/litersubstrate 1 200 mg/liter

2 400 mg/liter

Amt of bacterialinoculum

Initial pH

Flask closure

Inoculum filtration

BSMb

0 lml1 5ml2 10ml

0 -1 pH unit, BSM1 pH unit, BSM2 +1 pH unit, BSM

0 Cotton plug1 Screw cap

0 Unfiltered1 Filtered

0 R&V1 LDH2 V&D

linckrodt phenol per liter of sterile distilled water) andbacterial inoculum were added in appropriate experi-mental volumes with sterile syringes. When requiredby the experimental design, the inoculum was filteredwith sterile Gelman type A-E glass fiber filters duringinjection into the flasks.

Experimental flasks and sterile controls were placedon a gyratory shaker at 100 rpm in a continuous 4,300-lx white fluorescent light at 28 ± 2°C. One-millilitersamples were collected at 0 and 24 h and every 8 to 10h thereafter until either the phenol was completelydegraded or 100 h had elapsed. Collected samples wereplaced in acid-washed, Teflon-capped vials and pre-served with 2 ml of a CuSO4-H3PO4 solution (0.43 g ofCuSO4 per ml of 2% H3PO4) to give a final samplepreservative concentration of 0.86 g of CuSO4 per literatpH4 (1).

Samples were analyzed for residual phenol with ahigh-performance liquid chromatograph by using asthe elution solvent either MeOH-water (60:40) orCH3CN-water (50:50) at 2 ml/min through a 30-cm,u-C18 reverse-phase column and an ultraviolet detectorat 254 nm. Ten-microliter subsamples were injectedusually immediately after preservation, but alwayswithin 12 h. The concentration (milligrams per liter)of phenol in the sample was determined by measuringthe sample peak height and comparing it with a stan-dard curve which was prepared daily.Maximum degradation rate determinations.

The phenol concentration values from the high-per-formance liquid chromatograph analyses were con-verted to percentages of initial concentration for eachexperiment. These values were then plotted as a func-tion of elapsed time for the respective experiments(see Fig. 1). For each of these plots, two characteristicintervals were apparent, a lag or induction period (2)and a maximum degradation period. For each experi-ment, the duration of these periods was estimated byinspection. Using least-squares regression analysis ofthe second interval, we estimated the maximum deg-radation rate which occurred in each of the 81 exper-iments.

Orthogonal, fractional factorial design. The ex-perimental design for the 81 treatment combinations(Table 2) came from the extensive set of tables forfractional factorial designs ptepared by Connor andYoung (4). In our particular experiment, three two-factor interactions were thought to be unimportantand consequently were excluded in the design. Theseinteractions were flask closure with inoculum filtra-tion, flask closure with BSM, and inoculum filtrationwith BSM. The remaining 12 two-factor interactionsand all main effects were tested.We assumed the magnitude of all three-factor and

higher-order interactions to be negligible when com-pared with main effects and two-factor interactions.Consequently, we did not analyze for interactions ofthree factors and above. This assumption seems veryreasonable considering the variables involved. Thebulk of experimental evidence over a spectrum ofresearch fields indicates that three-factor and higher-order interactions often have negligible influences inthe statistical model (e.g., see discussion in reference3). However, main effects and two-factor interactionsare aliased (completely confounded) with these

a See Table 2 for use of treatment level codes.b See Table 3 for medium descriptions.

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938 FANNIN ET AL. APPL. ENVIRON. MICROBIOL.

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FACTORIAL DESIGN FOR BIODEGRADATION ANALYSIS 939

TABLE 3. BSM solutions used in phenoldegradation experiments

Component ConcnComponent ~~~~~~(g/liter)R&VaNaHCO3 0.125KH2PO4 0.1NH4C1 0.07Na2SiO3- 9H20 0.0465FeSO4. 7H20 0.01MnCl2.4H20 0.007ZnSO4. 7H20 0.0015Vitamin-free Casamino Acids 0.01

(Difco Laboratories)Distilled water To 1 literAdjust to pH 8

LHDbKNO3 1.0MgSO4 *7H20 0.2NaCl 1.0K2HPO4 1.0Tap water To 1 literAdjust to pH 7 to 7.2

V&DcNH4NO3 1.0K2HPO4 1.0KH2PO4 1.0MgSO4 * 7H20 0.2CaCl2 0.001FeCl3.6H20 (saturated solution) 2 dropsDistilled water To 1 literAdjust to pH 7a Medium for detecting phenol-degrading bacteria.bMedium for bacteria oxidizing liquid hydrocar-

bons.c Voroshilova and Dianova medium.

higher-order interactions, and if these higher-order-interaction effects are present, they introduce statis-tical bias into our estimates. All desired effects couldbe estimated, and 35 degrees of freedom were initiallyavailable for estimating the error variance. In theactual analysis, some degrees of freedom for nonsig-nificant treatment interactions were pooled with error.This pooling is a common practice for such analysesinvolving nonsignificant quantitative factors.Environmental factor main effects. The SPSS

BREAKDOWN package (11) was used to calculatethe mean maximum degradation rate from the maxi-mum degradation rate determined for each flask foreach treatment level of each environmental factor.The effects of factor interactions in the experimentalflasks were removed during the calculation of thesemeans because of the orthogonal design. Mean deg-radation rates were then plotted as a function of eachof the six experimental factors (see Fig. 2). A horizontalrelationship among datum values on such a plot qual-itatively indicates no difference in maximum degra-dation rates for the treatment levels tested.Environmental factor interaction effects. Mean

degradation rates for each pair of treatment levels

(e. g., 1 ml of bacterial inoculum and 100 mg of phenolsubstrate per liter) were calculated with the BREAK-DOWN program for the 12 pairs of environmentalfactors having testable interactions based on the sta-tistical design that we used. The orthogonal design ofa fractional factorial analysis removes influences offactors other than the pair of interest during thecalculation of sample means. Once computed, themeans for each of the 12 pairs of interacting factorswere plotted to qualitatively determine which testableinteractions might have significant influences on max-imum degradation rates (see Fig. 4). Each plot resultedin a graphical representation of two or three datumsets, depending on the number of treatment levelsincluded in the environmental factors being compared.When the plots of the datum sets are parallel, there isan indication of no interaction between the pair ofenvironmental factors. Nonparallel plots indicateprobable significant interactions.

Determination of statistical significance.Whereas plots from SPSS BREAKDOWN analysesqualitatively indicate whether maximum degradationrates were influenced by variation in treatment levelsfor environmental factors and by factor interactions,any observed differences may or may not be statisti-cally significant. To test for statistical significance, weused the SPSS REGRESSION program (11). Theterms used in the regression model included an inter-cept term, a linear term for each environmental factorhaving three treatment levels, linear and quadraticterms for factors having three treatment levels, andcross products of these terms corresponding to thetestable environmental factor interactions. In theregression analysis, each term was subjected to an F-test for significance. It should be noted that the sumsof squares are statistically independent, again becauseof the orthogonal design. Both linear and nonlinearquadratic effects were tested in the model because aquadratic effect may be significant even though thelinear effect is not. All main, environmental factoreffects were retained in the regression model for dis-cussion, as were interaction effects for which one ormore of the corresponding terms were significant.

RESULTS AND DISCUSSION

Both lag and maximum degradation phasesare indicated on the example plot from 1 of the81 phenol degradation experiments shown inFig. 1. Maximum degradation rates in percent-ages of initial phenol concentrations per hour(absolute values of the slopes for maximum deg-radation phases) for each of the 81 experimentsare presented in Table 2. The results of thestatistical analysis for the experiment are sum-marized in Table 4. Included in this table are F-test values for all selected environmental factormain effects and test values for those interac-tions which were statistically significant and hadat least one degree of freedom. For those envi-ronmental factors having three treatment levels,both linear and quadratic components are pre-sented. Similarly, both linear and quadratic

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APPL. ENVIRON. MICROBIOL.

100 LAG PHASE components are presented for interactions of thefactor treatments. Figures 2 and 3 provide graph-ical representations of the main effects, and Fig.4 presents the two statistically significant inter-

75actions found between environmental factors. Itshould be remembered that a nonsignificantmain effect would plot as a nearly horizontalstraight line, and nonsignificant interactions re-sult as almost parallel plots. Based on results

50 from the control flasks, photochemical reactionsor volatilization had a negligible importance inthe disappearance of phenol from the flasks.

MAXIMUM The maximum degradation rate was affected25 DEGRADATION significantly by three experimental treatments:

PHASE the amount of substrate, i.e., phenol concentra-tions; the type of BSM; and the amount ofbacterial inoculum. With increasing concentra-

0c tions of phenol substrate, the maximum degra-0 20 40 60 dation rate decreased significantly for both lin-

TIME (hrs)ear and quadratic analyses (Table 4). Phenolwas the only bacterial carbon source in our

Exampleplot ofphenol degradation in one experiments, but bacterial growth rate can betal flask showing division into lag and inhibited by high phenol concentrations (6, 7,degradation phases. 19). We found that as the phenol concentration

TABLE 4. Summary of statistical analyses for influences on maximum phenol degradation rates byenvironmental factor main effects and significant interaction effects.

Degreesoof Mean sum of F valueFactor freedom squaresMain effect

Substrate amt 2 69.4 34.7 61.96aLinear 1 61.85 61.85 110.45aQuadratic 1 7.55 7.55 13.48a

BSM 2 8.52 4.26 7.61aInoculum amt 2 4.75 2.38 4.24b

Linear 1 3.07 3.07 5.48bQuadratic 1 1.68 1.68 3.00

Initial pH 2 1.59 0.795 1.42Linear 1 1.17 1.17 2.09Quadratic 1 0.42 0.47 0.75

Flask closure 1 1.95 1.95 3.48Inoculum filtration 1 1.22 1.22 2.18

Significant interactioncInoculum amt vs 4 8.34 2.08 3.72a

initial pHLinear x linear 1 2.21 2.21 3.95Linear x quadratic 1 1.14 1.14 2.04Quadratic x linear 1 0.14 0.14 0.25Quadratic x quadratic 1 4.85 4.85 8.66a

Inoculum amt vs inoculum 2 3.41 1.75 3.12filtration

Linear x linear 1 3.28 3.28 5.86aQuadratic x linear 1 0.13 0.13 0.23

Error 64 37.34 1.497P < 0.01.P < 0.05.

'Nonsignificant two-factor interactions pooled with error.

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FACTORLAL DESIGN FOR BIODEGRADATION ANALYSIS 941

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media contain ferrous iron, and both had signif-icantly faster phenol degradation rates than thelow-iron LHD medium (0.1 mg of Fe per liter).However, the concentration of iron in V&D me-dium may have been high enough to inhibitbacterial growth, resulting in a lower maximumdegradation rate than that observed with R&Vmedium. Thus, although several componentsdiffered among the media (Table 3), ferrous ironconcentrations might have been an importantfactor affecting the maximum phenol degrada-tion rates in our experimental media. Appar-ently, the R&V medium contains a more optimaliron concentration for phenol degradation.

Increasing the amount of bacterial inoculumcaused a significant linear increase in the maxi-mum degradation rate (Table 4; Fig. 2b). Thiscan be explained simply: when larger bacterialpopulations are initially present in the inoculum,

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pH ALTERATIONS OF BSM (UNITS)FIG. 2. Main effects ofquantitative environmental

factors on the maximum degradation rates forphenol.

was increased from 100 to 400 mg/liter, themaximum degradation rate was reduced (Fig.2a), suggesting bacterial growth inhibition.The type of BSM significantly influenced the

maximum degradation rate of phenol in the or-

der R&V > V&D >> LHD (Table 4; Fig. 3a),with R&V modified from Ralston and Vela (15)and V&D and LHD modified from Rodina (17).Kostyaev and Baronkina (9) maintain that bac-terial activity for degrading phenol under oth-erwise equal conditions depends on the concen-

tration of biogenic elements (e.g., nitrogen andphosphorus) in the media. Even though LHDand V&D media contained the highest nitrogenand phosphorus concentrations, the highestmean values for maximum degradation rateswere observed in the R&V medium. Ralston andVela (15) observed that media either lackingferrous iron or having ferrous iron concentra-tions greater than 10 mg/liter inhibit the growthof phenol-degrading bacteria. Both R&V (2 mgof Fe per liter) and V&D (20 mg of Fe per liter)

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APPL. ENVIRON. MICROBIOL.

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faster substrate consumption rates will result(9).Two factor interactions significantly affected

the maximum rate of phenol degradation. Thesigniflcant interactions were the amount of bac-terial inoculum versus the initial pH of BSMand the amount of bacterial inoculum versus theinoculum filtration (Table 4, Fig. 4). The effectof pH was not significant for 1 ml of bacterialinoculum, as indicated by the flat plot for the 1-ml inoculum level in Fig. 4a. Maximum degra-dation rates observed at this inoculum level werelow compared with those observed at 5- and 10-ml inoculum levels (Fig. 2b). There were signif-icant interactions between the inoculum amountand pH when 5 and 10 ml of bacterial inoculumwere used with the specified pH values and pHvalues 1 unit below those specified. This signifi-cant interaction is indicated by the crossing ofplots for 5- and 10-ml inoculum amounts in Fig.4a. With the specified pH, faster degradationoccurred with 5 ml of inoculum, but at values 1pH unit lower, the 10-ml inoculum level yieldedgreater rates. We know of no reason for this

interaction. At all inoculum levels with a pH 1unit above that specified for BSM, similar deg-radation rates were observed.Whereas inoculum filtration did not have a

significant main effect on the maximum degra-dation rate, there was a significant interactionbetween inoculum amount and inoculum filtra-tion (Table 4). This significant interaction isindicated by the crossing of plots in Fig. 4b.Whereas the unfiltered inoculum yielded a fastermean degradation rate when 10 ml of inoculumwas used, the filtered inoculum had a more rapiddegradation rate with 1 or 5 ml of bacterialinoculum. The lower rates of maximum degra-dation observed with 1 ml of unfiltered inoculumcompared with 1 ml of filtered inoculum couldindicate substrate competition of other organiccompounds with phenol, but if substrate com-petition was the sole cause of the reduced deg-radation rates, one would expect even lowerrates with higher concentrations of competingsubstrates in the 5- and 10-ml inocula, a responsewhich was not observed. If, however, the surfacearea available for bacterial growth had a simul-taneous, opposing, and somewhat stronger effectthan did organic substrate competition on deter-mining maximum degradation rates, one wouldexpect an increase in the degradation rate withincreasing concentrations of unfiltered inocu-lum, as observed. Until filtration, the bacterialinoculum contained enough suspended particu-lates to make it quite turbid, and filtration re-sistance increased noticeably due to the filterclogging at inoculum volumes greater than 5 ml.Therefore, the faster degradation rates foundwith the unfiltered 10-ml inocula compared withthe filtered 10-ml inocula may have resultedfrom removing surface-area-supplying sedi-ments or numbers of bacteria from the inocula.For a clear identification of the reason for theinteraction between inoculum amounts and in-oculum filtration, additional experiments are re-quired; without them, the interaction remainsconfounded.Based on the statistical analyses (Table 4) and

the inspection of main effect and interactionplots (Fig. 2 to 4), we can define the shake-flasksystem which provided the maximum degrada-tion rate. It included 200 ml of a modified R&Vmedium (15), 100 mg of phenol substrate perliter, and either 5 or 10 ml of bacterial inoculumfrom an oil refinery settling pond. With a 5-mlbacterial inoculum, the optimal initial pH of themedium was 7, and with a 10-ml inoculum, aninitial pH of 8 was most effective. The inoculumneed not be filtered if it is allowed to settle for15 min before inoculation. Flasks may be eitherscrew capped or cotton plugged and incubatedat about 28°C on a gyratory shaker at 100 rpm

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FACTORIAL DESIGN FOR BIODEGRADATION ANALYSIS 943

in continuous light.In this paper we demonstrate the use of an

orthogonal, fractional factorial design, coupledwith other statistical procedures, to determineoptimal conditions providing maximum degra-dation rates for phenol. This study was under-taken as part of our effort to develop a biologicalscreening system for effluents from advancedfossil fuel processes. However, we feel that theusefulness of such experimental designs to mi-crobiology is not limited to proposing and testingnew hazard screening or biological treatmentsystems. In studies in which an analysis of theeffects and interactions of many experimentaltreatments is required and in which it is alsopossible to sacrifice a small amount of this infor-mation, an orthogonal, fractional factorial designshould be strongly considered for the experi-ment. This design maximizes the amount ofinformation about the experiment and substan-tially reduces the number of experimental unitsrequired for analysis. Another example applyingfractional factorial designs to biological prob-lems has recently been published (14), and gen-eral discussions on the use of this statistical toolcan be found in many statistics texts (3, 5, 10,13).

ACKNOWLEDGMENTSWe thank J. S. Meyer for help with the analytical proce-

dures and helpful discussiono on many aspects of this paperand T. W. LaPoint and two anonymous reviewers for helpfulcomments on the manuscript.

The work upon which this paper was based was fundedthrough an interagency agreement between the U.S. Depart-ment of Energy and the U.S. Environmental ProtectionAgency under U.S. Department of Energy contracts EY-77-C-04-3913, ET-77-2-03-1761, and DE-AS20-79LC01761 withthe University of Wyoming. Support was also granted in partby an interagency agreement between the U.S. EnvironmentalProtection Agency and the University of Georgia SavannahRiver Ecology Laboratory.

LITERATURE CIED

1. American Public Health Association. 1975. Standardmethods for the examination of water and wastewater,

14th ed. American Public Health Association, Inc., NewYork.

2. Borighem, G., and J. Vereeken. 1978. Study of thebiodegradation of phenol in river water. Ecol. Model. 4:51-59.

3. Cochran, W. G., and G. M. Cox. 1957. Experimentaldesigns, 2nd ed. John Wiley & Sons, Inc., New York.

4. Connor, W. S., and S. Young. 1961. Fractional factorialdesigns for experiments with factors at two and threelevels. Natl. Bur. Stand. (U.S.) Appl. Math. Ser. 58:1-65.

5. Federer, W. T. 1955. Experimental design. MacmillanPublishing Co., New York.

6. Hill, G. A., and C. W. Robinson. 1975. Substrate inhi-bition kinetics: phenol degradation by Pseudomonasputida. Biotechnol. Bioeng. 17:1599-1615.

7. Jones, G. L, F. Jansen, and A. J. McKay. 1973. Sub-strate inhibition of the growth of bacterium NCIB 8250by phenol. J. Gen. Microbiol. 74:139-148.

8. Kimerle, R. A., and R. D. Swisher. 1977. Reduction ofaquatic toxicity of linear alkylbenzene sulfonate (LAS)by biodegradation. Water Res. 11:31-37.

9. Kostyaev, V. Y., and L. A. Baronkina. 1973. Decom-position of phenol in various media. Akad. Nauk SSSRInst. Biol. Vnutrennykh Dokl. Trudy. 24:178-181.(Translation available from National Technical Infor-mation Service as ORNL-TR-2337.)

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