APPuED MICROBIOLOGY, Mar., 1967, p. 257-265Copyright © 1967 American Society for MiCrobiology

Kinetics and Mechanism of Bacterial Disinfectionby Chlorine Dioxide,1

MELVIN A. BENARDE, W. BREWSTER SNOW, VINCENT P. OLIVIERI, AND

BURTON DAVIDSONBio-Engineering Laboratory, Department of Civil Engineering, and Department of Chemical Engineering,

Rutgers * The State University, New Brunswick, New Jersey

Received for publication 11 July 1966

Survival data are presented for a fecal strain of Escherichia coli exposed to threeconcentrations of chlorine dioxide at four temperatures. Chick's first-order reac-

tion equation is generalized to a pseudo nth-order model. Nonlinear least squares

curve-fitting of the survival data to the nth order model was performed on an ana-

logue computer. The data were observed to follow fractional order kinetics withrespect to survival concentration, with an apparent activation energy of 12,000cal/mole. Initial experiments support the thesis that the mechanism of chlorinedioxide kill occurs via disruption of protein synthesis.

Although Joseph Lister is generally consideredthe initiator of practical disinfection procedures,it was Kronig and Paul's classic paper (8) thatfirst described a quantitative procedure for thestudy of disinfection. Ten years later, Madsenand Nyman (9), followed by Chick a year later(4), established a mathematical model for chem-ical disinfection of microbial populations. Thesetwo papers suggested the analogy between veloc-ity of microbial disinfection and a unimolecularor first-order reaction that has remained themodel for all subsequent investigations.During the intervening 50 years, refinements in

technique have been reported, and hypothesesas to the mechanism of microbial destruction havebeen postulated. In 1946, Green and Stumpf (5)proposed that chlorine brought about microbialdeath by inactivating the enzymes needed foroxidation of glucose. Knox et al. (7) suggestedthe enzyme triase-phosphate dehydrogenase asthe prime target of chlorine disinfection. As yet,however, direct biological proof of any of thetheories has been unavailable. As Wyss recentlynoted (10), "The field of disinfection is a leisurelyone." The study described herein offers a modifiedmathematical treatment for chemical disinfectionof bacterial populations, as a result of a uniqueand rapid sampling procedure, organic-free solu-tions, quantitative spectrophotometric determina-tions of low doses (fractions of a milligram perliter) of disinfectant, and chemical reactor theoryand design.

1 Presented in part at the IX International Congressof Microbiology, Moscow, USSR, 24-30 July 1966.

Additionally, results of biological experimentsthat complement the mathematical interpretationof the rate curves point to the mechanism of thelethal lesion. The investigation described hereinis a direct outgrowth of an earlier report by Be-narde et al. (1) which reported substantial killat orders of magnitude far less than the 30-minend point usually used in disinfection studies. Thisseemed to indicate that a primary target was af-fected by C102. This supposition led to the designof an apparatus that would permit determinationof percentage survival after intervals measured inseconds. With proven effectiveness of this ap-paratus, an investigation of temperature effectson the efficiency of disinfection was undertaken.In this series, the following constants were used:pH, 6.5; cell density, 15,000 per milliliter; andorganic-free menstruum. Variables were CG02concentration, temperature, and time of contact.

MATER1ALS AND METHODS

The procedure for the preparation of organic-freedistilled water (OFD) and glassware, generation ofaqueous solutions of pure C102, stopping the disin-fection reaction, washing bacterial cells, and stand-ardizing their density was continued as previouslyreported (3). To obtain samples at intervals as shortas 5 sec, the reaction assembly required considerablemodification. The original apparatus consisted of twohypodermic syringes, each with a two-way flap valveassembly, permitting rapid drawing and dispensing ofsamples from the reaction vessel. It could not beoperated fast enough to remove samples at 5-secintervals. To achieve such rapid sampling, a closedpressurized system was designed to operate within a

constant-temperature water bath. Figure 1 is a com-

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FiG. 1. Complete view of the reaction assembly.

plete view of the apparatus. The water bath contain-ing the reaction vessel and the spectrophotometerthat was operated in conjunction with the samplingapparatus are shown. Figure 2 shows the entire as-sembly ready for use. Figure 3 is a schematic repre-sentation of all the essential components of the system.Pressure on the system was generated by adding tapwater to a filter flask in a closed system, and was used(i) to force the C102 solution rapidly into the reactionvessel containing the bacterial suspension and (ii) toforce samples from the reaction vessel into the spec-trophotometer cuvette and into the bacterial sampletubes. Mixing of the bacterial suspension and theCl02 solution was rapid and thorough because of thepressure under which the latter was forced into thereaction vessel. Individual sterile units of reactionvessel and separatory funnel were used for eachexperimental run. The bacterial samples were col-lected in sterile test tubes containing sterile sodiumthiosulfate (Na2S203) solution. Bacterial samplingoccurred after 5, 10, 15, 20, 25, 30, 60, and 300 sec ofcontact. The spectrophotometer sample was drawn 3sec after initial mixing. Changes in C102 concentrationwere recorded through the 5-min test period.

All glassware, buffered dilution OFD, and C102solutions were kept at the temperature of the experi-mental run before and up to the moment of use. Thetemperature of these materials and of the reactionvessel was maintained within 10.1 C. Each experi-mental run was replicated three times at the followingC102 concentrations: 0.25, 0.50, and 0.75 mg/liter.The initial concentration of these C102 solutions wasmade up in double strength to compensate for the1 :1 dilution obtained by mixing equal volumes of cellsuspension and C102 solution. The strength of eachsolution was verified spectrophotometrically justbefore the start of each experimental run.

RESULTS

Figure 4 is a plot of survival with time andtemperature, when 0.75 mg/liter of C102 wasused. It is apparent that the disinfectant efficiency

varies directly with temperature. A similar rela-tionship was observed at 0.50 and 0.25 mg/liter(Fig. 5 and 6). To obtain 99% kill, a concentra-tion of 0.25 mg/liter required 110 sec at 5 C, 74sec at 10 C, 41 sec at 20 C, and 16 sec at 30 C-almost four times as rapid at 30 C as at 5 C. Atthe 99.9% level, the time required for disinfectionbetween 5 and 30 C increased to five times asmuch (21 sec at 30 C versus 150 sec at 5 C).

In the same Qlo range, 20 to 30 C, the calculatedQio values (based on the 30% kill level) were 1.67for 0.5 mg/liter and 1.23 for 0.75 mg/liter. In the10 to 20 C range, the Qlo values were 1.06 for both0.50 and 0.75 mg/liter. The Qlo values varied withdosage and temperature; consequently, we mustbe cautious in using Qlo as an index of relative re-action rates. Increasing the concentration of C102tended to decrease markedly the time needed forkill. At the 99% level, 0.75 mg/liter required only14 sec at 30 C versus 60 sec at 5 C. It is also ap-parent that these plots do not yield straight lines,indicating deviations from simple first-order re-actions. Therefore, to ascertain the best reactionorder, a more sophisticated treatment is war-ranted.From these data, it would be helpful to develop

a mathematical model that bioengineers would beable to use in the design of disinfection equip-ment. In these models, concern is always for thequantification of these nonlinear kinetic param-eters. Toward this end, it would be desirable torely on the classical approaches that correlatecomplex chemical reaction rate data with tem-perature and concentration. Chick (4) suggestedthis type of calculation, which was followed forthe past 60 years. However, during the past 10years, advances in kinetic models have been devel-oped.

Kinetic models. The overall rate of Escherichia

FIG. 2. Reaction assemblyiready for use.

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FIG. 3. Schematic representation of the essential components ofthe reaction assembly.

coli kill with chlorine dioxide is influenced by atleast three basic factors, namely, (i) mass transferof C102 in the liquid to the E. coli liquid interface,(ii) chemisorption of the disinfectant at selectiveactive centers on the cell surface, and (iii) surfaceand intrasurface diffusion of the activated chemi-sorbed complex with attendant chemical attackon cellular elements. Elucidation of disinfectionmechanisms from kinetic data is considerablyencumbered by the possibility that several stepsmay be rate-controlling. It is important, therefore,before kinetic modeling is employed, to determinewhether a physical step, such as mass transfer orintrasurface diffusion, or a chemical step, such aschemical attack on cellular elements, is rate-con-trolling; otherwise, curve-fitting would become ameaningless task.

Since most chemical rate processes, as opposedto purely physical mass transfer or diffusion proc-esses, are strongly temperature-sensitive, deter-mination of rate-controlling steps can be facili-tated by observing the effect of increased temper-ature on the overall rate of kill. In this study, astrong temperature effect was observed. This sug-

gests, as an initial hypothesis, that chemical re-sistance controls the overall rate of kill. Further-more, adequate stirring of the reactive mixtureeliminated mass transfer in the liquid phase as therate-controlling step. These phenomenologicalfacts and the hypothesis of a chemical rate-con-trolling mechanism serve as a convenient pointof departure for meaningful kinetic modeling.

If it is assumed that the law of mass action ap-plies to biochemical reactions in the same way itapplies to homogeneous liquid-phase reactions,then for a pseudo-unimolecular model the kineticexpression becomes

1 dVc- - - = kc

For the E. coli system studied, equation 1 statesthat the rate of disappearance of E. coli cells perunit volume per unit time in the reactor is pro-portional to the concentration (active mass) ofcells present at any time in the system, the systemhere being the liquid mixture in the reactor at anytime. If the volume of the system is nearly con-stant, which would be the case for batch reactors

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According to the "Chickian" philosophy, it iscustomary to analogue equation 3 as follows:

_dN =kN

ilI10 t

>

UUo

' 0

o 11101

o 25 solo0 200 300

CONTACT TIME IN SECONDS (SEC.)FIG. 4. Effect of temperature on disinfection with

0.75 mg of chlorine dioxide per liter (pH 6.5; IS,O00cells per milliliter).

with no sample removal, equation 1 becomes

(6)

where N = number, not concentration, of sur-viving cells in system. Proceeding as before for thevariable volume case, equation 6 becomes

dN kl(N)n dlnV N=ii l'(N) - ~dt-N (7

Equation 7 in no way resembles-equation 5, andfurthermore k values from the two equations arefundamentally different because of the units andmathematical form of the differential equations.Even if volume were constant, equations 5 and 7are still different and define different k values. Therelationship between the two k parameters forvariable volume systems is

k' = (N)l-n dltV + k(V)l-n (8)

It is indeed puzzling why Chick (4), for example,insisted on using N, the number of living cells inthe system, in equation 1 as the active mass. Evenmore puzzling is the fact that many unknowingexperimenters, after Chick (4), apparently used cin place of N when calculating k. The conclusion

dcdt (2)

which is the classical "Chick's Law" expressionfor disinfection. If the order is other than simplefirst-order, then equation 2 must be modified ac-cordingly; for example,

dc kcn (3)

where n = any real number.Now consider the general case where contin-

uous removal of a sample from the system causesthe volume to change according to a volume de-crease law, V = V(t). Equation 3 would become

dVc dV- dt tdt

k 10'-

cnU1)I.

0Jl'w

(4)

which reduces to

-dc k(c)n (5)

Apparently, the case where volume was constantis identical to the case where volume was variable,providing that concentration variables are usedthroughout.

-. * *

0 25 50 loo 200 300

CONTACT TIME IN SECONDS (SEC.)FIG. 5. Effect of temperature on disinfection with

0.50 mg of chlorine dioxide per liter (pH 6.5; 15,000cells per milliliter).

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10-

10 ]

-J

5:

C-) -I>cn

10-1

,2

!O3

*i~~~~~~'5"lUg 9'~~~%loolUg 9'~~~~~~~I

3mg 9

I32c I

0 25 50 100

CONTACT TIME IN

FiG. 6. Effect of temperature0.25 mg of chlorine dioxide per icells per milliliter).

to be drawn from these observtion 5 represents the least cmodel of the chemical law of nlations based on N as opposeident, because V(t) has to be knaccount mathematically.The emphasis in this paper

ting or goodness of fit, but rafor developing a rate expressone form of the classical lawhereas equation 13 does not I

dation, and is therefore on m(than is equation 3.

In curve-fitting, one can alvmathematical rate expressionEness of fit. Equation 5 shouldstarting point from which fudepart.

Parameter estimation. Bearfully aware that our experimiwarrant sophisticated statisticfitting techniques, and detaileand mechanism elucidation.primarily with showing a norcan be used with this type of cFor fixed values of temp

chlorine dioxide concentratiparameters in equation 5, kmated from a "least squares e

criterion, based on a linearized form, is

mi in - _t-nk"f- nai (9)t[( dt)i]

where k" = kcon- , cO = initial cell concentration,

Coand c~= -. The corresponding "normal equa-

tions" aremnm

m* Ilnk" + Wiln& In= (10)EiE ( dt i

andm m

Z ln(j) . Ink" + E (Ina,)2 * ni i

=E Ii*In (-C) (11)o Parameter estimation from equations 10 and

*| 11 serves to indicate a starting grid-point from200 300 which nonlinear search on an analogue computerSECONDS (SEC.) can be initiated. Of course, k" and n could be

estimated from a nonlinear "least squares" analy-liter (pH 6.5; 15)000 sis on a digital computer, but this procedure

would require use of nonlinear search techniques,which are, in fact, equivalent in "art" form to thetwo-step parameter estimation procedure out-

rations is that equa- lined above for the analogue computer.onfusing analogue The scaled analogue computer diagram fornass action. Formu- equation 5 with c = ecO and k" = kcon-1 is givend to c are not pru- by Fig. 7, and the results are summarized in Tableown and taken into 1 and in Fig. 8 and 9. The goodness-of-fit crite-

rion in Fig. 8 and 9 is based on the minimum-is not on curve-fit- squared error between analogue curve and experi-tther on the criteria mental points. The results indicate that reaction;ion. Equation 3 is order with respect to time of contact varies withw of mass action, both temperature and C102 concentration. Fur-have any such foun- thermore, numerical results from the linearizedore tenuous ground least-squares analysis did not agree well at all with

the analogue computer values except at 32 C. Theways uncover many values of n were kept constant at the values com-s with equal good- puted from 10 and 11 because it was observedbe viewed only as a that curve-fitting errors were more sensitive to k"ture theorizing can than they were to n. This also provided a basis for

comparing k values from two different methods ofin mind that we are analysis. Since n was found to be relatively unim-ental data may not portant, an Arrhenius activation energy plot wascal analysis, curve- attempted with the assumption that variance ind kinetic modelling order of reaction did not invalidate the estimationWe are concerned of the activation energy. The results from thisilinear method that analysis showed that the activation energy wasdata. 12,000 cal/mole, independent of C102 concentra-erature and initial tion.ion, the unknown The kinetic model, equation 5 with parameterand n, can be esti- values from Table 1, points the way toward futurexrror" analysis. The research in the area of C102 disinfection. First of

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v6 0.100+ 0_ T

ABSCISSA TIME BASE = 5 SEC/IN FOR X-Y PLOTTERORDINATE BASE= I VOLT FULL- SCALE

FIG. 7. Scaled analogue computer diagram for equation 5.

all, it was assumed that C102 was the excess re-active component whose concentration changewith time of kill did not vary as significantly asthe E. coli concentration. This condition led to thepseudo nth order formulation of equation 5.

TABLE 1. Summary of curve-fitting from equations10 and 11 and figs. 8 and 9

nfrom k" from k' from Fig. 8C102 n rm k rm and 9 with n

concna Temp equations equations from equations10 and 11 10 and 11 10 and It

0.5 32 0.634 0.160 0.11820 0.394 0.074 0.04810 0.538 0.074 0.0285 0.522 0.039 0.013

0.75 32 0.689 0.179 0.17520 0.773 0.171 0.07810 0.858 0.195 0.039b5 0.614 0.071 0.046

a Data at 0.25 mg/liter were not included, asit did not appear to follow the power law rateexpression.

b Questionable data point not following tem-perature trend.

Future research should aim at elucidating theeffects of including C102 concentration, in thekinetic model, on curve-fitting the data. Further-more, the order of reaction with respect to initialconcentration of E. coli cells should be determinedto ascertain whether reaction intermediates inhibit

-I

5

i

ocJLIJJ

CHLORINE DIOXIDE 0.75 mg/liter------ ANALOG COMPUTER DRAWN

CONTACT TIME IN SECONDS (SEC)

FIG. 8. Effect of temperature on disinfection with0.75 mg of chlorine dioxide per liter.

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0

0

6 X - ANALOG COMPUTER DRAWN

0

0.3

0.2 'o2oso *

0

0004

0o. T i>' '0.2

15 20 25 30 35 40 45 55 60

CONTACT TIME IN SECONDS (SEC)

FiG. 9. Effect of temperature on disinfection with0.50 mg ofchlorine dioxide per liter.

the rate of kill or whether an autocatalytic mech-anism prevails. The strong temperature effect ob-served in this study has already pointed out thechemical nature of the rate of kill, as opposed topurely physical controlling steps. An activationenergy of 12,000 cal/mole is certainly reasonableif the assumption of variable order of reactiondoes not affect E. The value of the activationenergy reported herein is more reflective of thetrue activation energy than those commonly re-

ported based on either of the following kineticequations:

or

-dN =kNtdt

dt

Biological studies of mechanism. The develop-ment of the kinetic model was predicated on an

assumption that pseudo nth order kinetics de-scribed the rate of reaction and its temperaturedependence. This model attempts to explain theoverall mechanism. The individual steps, how-ever, which comprise the overall mechanism re-

main to be elucidated. For this reason, attemptswere made to discover the biological pathwaytaken by C102 that might explain the rate-control-ling step.The velocity of disinfection, shorter by far than

previously reported values, and the strong oxidiz-ing character of C102 suggested that chemical dis-ruption of the bacterial cell wall was the likelymechanism. If the cell wall was severely breached,protein and nucleic acid should be released intothe menstruum in sufficient quantity to yieldcharacteristic peaks in the 260- and 280-m,u region

on spectrophotometric analysis. To ascertain thefact of protein and nucleic acid peaks, untreatedwashed cells were disrupted mechanically in asonic oscillator. The response was sufficientlylarge to force the pen off the chart. Upon a 1:10dilution, a peak was traced at 260 and 280 m,.At this point, C102 was added to the solution. Onfurther analysis, no changes in tracings occurred,indicating no demonstrable reaction betweenC102, protein, or nucleic acid.A large harvest of cells was suspended in OFD-

phosphate buffer (pH 6.5). These cells were centri-fuged and washed three times. The washed cellswere treated with C102 for 5 min. They were thencentrifuged into a pellet, leaving a clear super-natant liquid. A sample of the supernatant solu-tion was placed in a 10-cm cuvette for analysis.The added length of the light path increased sensi-tivity 10-fold. The absence of absorbance peaksin the 260- and 280-mA region indicated that pro-tein and nucleic acid had not been released fromthe cells. It was concluded that C102 did not pro-duce leakage of cell contents and apparently didnot oxidize proteinaceous material to other prod-ucts. At about this time, we learned of Bring-mann's work, reported in 1953 (3), which showedvia electron photomicrographs that no visiblechanges in cell wall integrity occurred to chlorine-treated celLs.Our disinfection curves were then shown to

Robert J. Kuchler, Department of Bacteriology,Rutgers University. He suggested that destruc-tion in 5 to 10 sec was about the same time re-quired for protein synthesis, and that the lethallesion in that interval might well be due to a hit ona primary target, such as protein synthesis. Haggis(6) noted that synthesis of a single hemoglobinmolecule required 5 to 10 sec.To test the hypothesis that protein synthesis

might be involved, "4C-labeled phenylalanine wasadded to Braun's (2) minimal essential medium(MEM) for E. coli, containing approximately 109cells, in an ice-water bath. This was immediatelyplaced in a 37 C water bath and allowed to incu-bate. At intervals, samples were withdrawn andadded to hot trichloroacetic acid to precipitateprotein. Chlorine dioxide was then added to thesystem, and samples were again withdrawn atintervals to trichloroacetic acid. Counts of the"4C-containing protein showed wide differencesin protein synthesis between C102- and MEM-treated cells.To establish firmly this observation, a second

trial was carried out. This time, "4C-labeled valinewas added to cells in an ice-water bath. To obtainmeaningful data on the rate of protein synthesis,with and without C102 treatment, an apparatuswas designed that permitted withdrawal of sam-

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z

'Iz

0

I I I I I I

10 12 13 14 15

ELAPSED TIME IN MINUTES (MIN)

FIG. 10. Effect of chlorine dioxide on proteinsynthesis.

ples at 10-sec intervals. From the results of thisexperiment (Fig. 10), it is clear that C102 mark-edly inhibits protein synthesis, and apparentlydoes so abruptly. A lag phase is not seen. Thisindicates the lethal lesion to be directly related toprotein synthesis, rather than inactivation of an

enzyme system in the catabolism of glucose,wherein protein, sufficient to produce a lag phase,would be expected to be synthesized.

Several possibilities present themselves, forexample, inhibition of formation of amino acyladenylate, or inhibition of amino acid activation.These two steps might properly be considered asone possibility, and would be represented asfollows: amino acid + adenosine triphosphate-* adenosine monophosphate.amino acid, andsoluble ribonucleic acid (sRNA) + amino acid(20) -> sRNA-amino acid. A second possibilitycould occur at the ribosome level, represented bythe expression sRNA amino acid + ribosomes

-ransferase specific protein. A third possibilityenzymesmay be inactivation of messenger RNA, pre-venting translation of coded information. Afourth explanation that suggests itself is a struc-tural rather than a functional one: the destructionof the ribosome by C102. Consideration of Fig.10, however, tends to rule this out. Destructionof ribosomes should yield a loss in counts as cellcontents leak into the surrounding menstruum.Thus, inactivation of a functional process appearsmost likely.The key experiment that must now be under-

taken to ascertain conclusive direct proof of thesite of the lethal lesion requires a cell-free systememploying ribosomes obtained from disruptedhomogenates of E. coli. This experiment is nowin progress, and the results will be reported at a

later date.

A step in the direction of determining theeffect of C102 on cell constituents that are in-volved in protein synthesis was taken and can bereported at this time. Each of six amino acids(histidine, asparagine, phenylalanine, arginine,proline, and leucine) was treated with C102 for aperiod of 30 min. Samples were removed andspotted on sheets (8 by 8 inches) of Whatmanno. 1 filter paper. The chromatogram wasdeveloped in an Eastman sandwich chamber withbutanol-acetic acid-water (4:1:5). Amino acidswere detected with 0.5% ninhydrin in butanol.An untreated sample of each amino acid wasplaced on the filter paper alongside the treatedsamples. From the observed spots of both treatedand untreated amino acids, it was evident thatsize, color, and intensity were quite similar. Inaddition, RF values appeared equal. A secondset of amino acids was treated with C102, andsamples were removed every 30 sec for 5 min.Because C102 is volatile, none remained on thepaper after the spot dried. Again, the RF values,size, intensity and spot color did not differ withtime. From this set of experiments it was con-cluded that C102 apparently did not react withthe amino acids sufficiently to alter their char-acteristic structures. Consequently, we would notanticipate a C102-free amino acid reaction withinthe cell, -eliminating this as a possible reason fordepression of protein synthesis.

It is our belief that the ability to obtain samplesat 5-sec intervals, combined with the organic-freemenstruum, enabled us to observe the particularlyrapid bacterial destruction, which prompted theseries of experiments that pinpointed the mecha-nism of C102 disinfection. We believe this is thefirst time this has been demonstrated, and hopethat other investigators will undertake studies inthe important area of disinfection research.

ACKNOWLEDGMENTS

We express our appreciation for the analoguecomputation performed by A. F. Burkart and R. W.Bradshaw, Department of Chemical Engineering.

This investigation was supported by an unrestrictedgrant from the Olin Corp. and by Public HealthService training grant PHT-1-61A.

LITERATURE CITED1. BENARDE, M. A., B. M. ISRAEL, V. P. OLIVIERI,

AND M. L. GRANSTROM. 1965. Efficiency ofchlorine dioxide as a bactericide. Appl. Micro-biol. 13:776-780.

2. BRAUN, W. 1953. Bacterial genetics. W. B.Saunders & Co., London.

3. BRINGMANN, G. 1953. Electron microscopicfindings of the action of chlorine, bromine,iodine, copper, silver and hydrogen peroxide onE. coli. Z. Hyg. Infektionskrankh. 138:155-166.

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4. CHICK, H. 1908. An investigation of the laws ofdisinfection. J. Hyg. 8:92-157.

5. GREEN, D. C., AND P. K. STUMPF. 1946. A note onthe enzymatic method of estimating chlorine.J. Am. Water Works Assoc. 38:1306-1308.

6. HAGGIS, G. H. [ed.]. 1965. Introduction tomolecular biology. Protein synthesis (chapter12). John Wiley & Sons, Inc., London.

7. KNOX, W. E., P. K. STUMPF, D. E. GREEN, ANDV. H. AUERBACH. 1948. The inhibition ofsulfhydryl enzymes as the basis of the bacteri-cidal action of chlorine. J. Bacteriol. 55:451-458.

8. KRONIG, B., AND T. PAUL. 1897. The chemicalfoundation for the theory of poison reactionsand disinfection. Z. Hyg. Infektionskrankh.25:1-112.

9. MADSEN, T., AND M. NYMAN. 1907. On the theoryof disinfection. I. Z. Hyg. Infektionskrankh.57:388-404.

10. WYss, 0. 1961. Theoretical aspects of disinfectionby chlorine. Proc. Rudolfs Research Conf.Public Health Hazards of Microbial Pollutionof Water. Rutgers - The State Univ., NewBrunswick, N.J., p. 400-418.

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