Treatment of super oxide dismutase by a regression methoddownloads.hindawi.com/journals/jamc/1986/761764.pdf · JournalofAutomaticChemistry/JournalofClinical LaboratoryAutomation,

Journal of Automatic Chemistry/Journal of Clinical Laboratory Automation, Volume 8, Number (January-March 1986), pages 28-31

Treatment of super oxide dismutase assay bya regression method

Ph. NirdeCentre d’immunologie & de biologie parasitaire, Unit[ mixte INSERM U167,CNRS 624, Institute Pasteur, BP 245, 59019 Lille Cedex, France

Introduction

The superoxide dismutase (SOD, EC 1.15.1.1) is a widelydistributed enzyme in all aerobic cells [1 and 2]. It is theprincipal protective enzyme against oxygen toxicity andacts by catalysing the removal of superoxide radical(02--) [3 and 4]. The assay of SOD using Xanthine-Xanthine oxidase-Ferricytochrome C was described byMcCord and Fridovich in 1969 [5]. Since, this spectro-scopic method has been in use for SOD studies in both themedicine and biology.

The assay is based on the rate of reduction of ferricyto-chrome C measured spectrophotometrically, but this rateof reduction is not proportional to the amount of enzymeadded. Therefore samples must be concentrated ordiluted to obtain 50% ofinhibition ofthe rate ofreductionofferricytochrome C: one enzyme unit [5]. So this methodis not suitable for biologists working on scarce materialswhere storage of samples, to have enough material for anassay, may be prejudicial to the enzyme molecule.

In order to make the assay available for all samples, aminicomputer program has been developed. Becausesamples need not be concentrated nor diluted, thisprogram provides a rapid and a useful calculation for thedetermination of the amount of SOD in samples,especially for biological extracts with low quantities. Inaddition, the sensitivity of the assay has been improvedby a factor of 30 with this computer-aided approach.

Hardware configuration

The WANG 2200 MVP model has a user memory of45 Kbytes. Only 14 K bytes are necessary for the residentprogram and the variables. This model has an integratedCRT/keyboard which displays 24 lines on screen, each 80characters in length. The computer is equipped with afast printer (2221W WANG) for hard copies and a harddisk unit for storing the program.

Software

The WANG BASIC language allows 14 matrix opera-tions. These operations are performed on numeric arraysaccording to the rules of linear algebra and can be used

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for the solution of systems of non-singular homogenouslinear equations. The ’MAT INV’ matrix statementcauses matrix inversion by the Gauss-Jordan eliminationmethod. A matrix can be inverted in a significantlyshorter time than is possible with BASIC programs.Indeed, whereas other minicomputers store their pro-gram text exactly as it is entered by the programmer, theWANG BASIC interpreter converts into one-byte ’textatom’ each word of the text program. Thus, the atomizedlines permit faster program executionnlines are morecompact and can be more rapidly scanned, for example,inverting a 7 x 7 matrix requires 0"20 s. Because no filesare used for this logiciel, this program can be easilyadapted to BASIC microsoft language.

Mathematical expressions

Rate ofreduction offerricytochrome C: least squares estimation

The model, for calculating the rate of reduction offerricytochrome C at a known enzyme amount, is:

y=a+bx (1)where y is the absorbance and x the time whenabsorbance is set up. In the least squares estimation, theparameters a and b are chosen so that the value:

Q Z[y-(a + b x)] 2 is minimum.

This condition occurs when the following partial deriva-tives are zeroing:

)Q6a 6b

Thus, 6Q

6Q=o6b

Zy- na- bZx=O

Zy.x a Zx b Zx2 0

a (bZx Zy)/n

bYx.y (Zx. Zy)/nZx9 + (Zx)Un

Relationship between rate of reduction offerricytochrome C andenzyme amount

The p-degree polynomial regression model used with oneindependent variable is"

y=a0+ alx+a2x2 + +axP (2)where ai is called the partial regression coefficient [6].

Ph. Nirde Treatment of SOD assay by a regression method

For eachyi, xi ofN data points, p + sets ofsimultaneouslinear equations can be written down"

Zy= a0 N+ al Y.x + + apYx a0 Zx + a ]x2 + + apZxy= ao Zx2 + a Z x3 + + al)

Zxty ao Zxl + a ZxP+1 + + ap

ZxP +1

Zxp+2

Zx’.

The numerical coefficient on the right side (i.e. Z) forma matrix M which determinant is D. These coefficientsinvolve only the xs.

NZx

Zx

Zx ZxPZx ZxP +

Zx3 Zxp +

Xx + Xx2.

Those on the left also involved theys. Resolution ofsuch asystem is mde by Cramer’s method: the determinants ofthe ith partial regression coefficient, Di, are:

O0

Xy Xx XxXy.x Xx2 Xx+

Xy.x2 Xxa Xx+

Xy.xt YxP+1 ..x2*P

Yx Yy.x Yx+ 1Yx2Zy.x 2.x+

NZxyx

Zx Zx, + Zy.xp

Thus, the partial coefficient regressions are"

ao Do al D1/D, at) Dt/D

The expression of the polynomey P(X) is:

Y x .Do/D + x .D1/D Jr x .D/D + + xP .Dt)/D

The root of such a polynomial regression is found bysuccesive iterations on the standard curve. In this case,two rates ofreduction ofcytochrome C from the standardare considered, including the rate of reduction of cyto-chrome C from the sample. If X1 and X2 are thecorresponding enzyme amounts of the standard, theseminimum and maximum values respectively enclose theunknown enzyme amount of the sample. For eachiteration a halfdecrease of the segement (X1, X2) (i.e. X3

(X1, X2)/2) is considered, which encloses the unknownenzyme value. If the calculated rate of reduction ofcytochrome C from X3 is higher than the rate ofreductionof cytochrome C from the sample, X1 X2 is set asshown in figure 1. Another iteration is performed until thecalculated rate ofreduction is the same as the sample withan approximation of 10-4. This method convergesrapidly.

v_+ "4,

ql

Figure 1. Calculation of the polynomial’s root by iterations.

Program description

Standard curve

As shown in figure 2, for a known enzyme concentration aset of experimental data points, xi (time) and yi (absor-bance) are introduced. The coefficients Yx, Zy, Zx andZx.y are calculated in a subroutine. Finally, the coefficientb of equation 2 (i.e. the slope of the straight line) iscomputed; b represents the rate of reduction of ferricy-tochrome C for a known enzyme amount.

Another subroutine computes the elements Zx andZy.xi-used for polynomial regression. When only alpha-numeric characters are keyed, the operator exits this partof the program and matrix and determinants are com-puted. The standard curve equation is then calculatedand samples can be analysed.

inputenzyme

subroutine 1[

Figure 2. Flowchart ofpolynomial fitting.

29


Sample analysis

For samples, as for standard points, the rate of reductionof ferricytochrome C is calculated using a least squaresestimation. This program allows the input ofreplicates bythe FOR/NEXT loop. The mean value is calculated andthe corresponding enzyme amount is computed bysuccessive iterations in subroutine 2. Experimentalparameters, such as initial extraction volume, assayvolume and dilution, are integrated for the final calcula-tion of the enzyme amount. Results are then printed.After the last sample is calculated the curve is plotted.

Results

The polynomial curve is fitted with 11 experimentalstandards whose enzyme amounts are equidistant on thex-axis. Standards have been chosen so that the maximumand minimum rate of reduction of cytochrome C coversthose of the samples. All experimental standard pointsare plotted on a curve (characters ’O’)--see figure 3. Inthese experiments, samples (character ’+’) were a knowndilution mixture of a standard solution. In this way wecould verify that the calculated enzyme amount forsamples was in good agreement with the real enzymecontent. This was so throughout the whole range of0-100% inhibition of the standard curve (table I).

Figure 3. Graph ofpolynomial model. Because using a typewriterinstead ofa plotter when experimental and calculated points havethe same value all the points are plotted as ’. ’for theoretical curve,’o’for standard points and ’+ ’for samples.

Discussion

The polynomial regression model is attractive because itis possible to approximate almost any function, such asthe enzymatic assay for SOD. However, restrictions mustbe kept in mind when using such a mathematical model.The data on the X-axis occurs at equally spaced intervals,and in many cases the approximation is valid only in theregion of the data, hence extrapolations are hazardous.

30

Table 1. Results obtained using the mathematical model.December, 1984. Exper.: Polynomial adjustment.

SUPEROXIDE DISMUTASE SOLUTION USED micro g/ml 21195 units/mg

.Volume Initial speed Qty Sigma Units

0.000 micro 0.0234 D.O/mn 0.00 0.0000

5.000 micro 0.0214 D.O/mn 0.1059

10.000 micro 0.0194 D.O/mn 10.00 0.2129

20.000 micro 0.0170 D.O/mn 20.00 0.4239

40.000 micro 0.0122 D.O/mn 40.00 0.8478

60.000 micro 0.0100 D.O/mn 60.00 1.2717

1.695680.000 0.0082 D.O/mn 80.00

100.000 micro 0.0072 D.O/mn 100.00 g. 2.1195

120.000 micro 0.0064 D.O/mn 120.00 2.5434

150.000 micro 0.0036 D.O/mn 150.00 g. 3.1792

233.3

Sample Initial Initial Total Total specificDilut. Siqma S.O.D

volume speed Inhibit. units activity

pl 0.25 .02340 D.O/mn I/ 0.00 0.0000

pl 0.25 .02290 D.O/mn 1% I/ 1.09 0.0231 23182.03 U/mg

l 0.25 .02250 D.O/mn I/ 2.10 0.0447 22354.10 U/mg

pl 0.25 .02140 D.O/mn I/ 5.01 0.1063 21277.79 U/mg

l 0.25 .01940 D.O/mn 16 I/ 10.78 0.2285 22850.85 U/mg

pl 0.25 .01740 D.O/mn 25 I/ 17.34 g. 0.3676 24506.71U/mg

20 l 0.5 ml .01700 D.O/mn 27 I/ 20.00 g. 0.4239 21195.00 U/mg

l 0.25 ml .01220 D.O/mn 47 I/ 41.48 0.8792 21981.53 U/mg

60 l 0.25 ml .01000 D.O/mn I/ 60.00 g. 1.2717 21195.00 U/mg

80 M1 0.25 .00820 D.O/mn I/ 80.62 g. 1.7088 21360.58 U/mg

100 ul 0.25 .00720 D.O/mn 69 I/ 100.15 g. 2.1228 21228.11U/mg

120 l 0.25 .00640 D.O/mn 72 I/ 120.00 2.5434 21195.00 U/mg

150 pl 0.25 .00360 D.O/mn 84 I/ 149.98 3.1789 21192.93 U/mg

From eight standard points onwards, the six degreepolynomial gives satisfactory results for the SOD assay.The best results are obtained with 11 data points.

The reason for the development ofa polynomial fitting forthe SOD assay was the lack of methods available forstudying biological material whose SOD content is verylow. Whereas one unit was previously needed in thevolume assay (50% of inhibition), 0"03 units are nowsufficient with the polynomial fitting. Thus, the sensitiv-ity of the enzymatic assay has been improved by a factorof 30. Assays can be performed on very little material andthe program may be a useful tool for clinicians andresearchers. Indeed, this treatment of SOD assay hasallowed the detection of Cu/Zn SOD and Mn SOD inhuman Schistosoma mansoni [7]--so the biological role ofthese enzymes in S. mansoni can now be investigated.Furthermore, in tumor biology, low levels of SOD,particularly extra-cellular SOD (EC-SOD), have beenrecently reported, rarely in ostensibly normal human celllines, but rather frequently in malignant cell lines [8].Moreover, in clinical pneumology, modifications of theoxidant-antioxidant system within the human broncho-alveolar macrophages by intracytoplasmic mineral parti-cules occur, in particular for SOD in coal-worker’spneumoconiosis and silicosis [9]. The assay systemdescribed should permit a more vapid and detailedinvestigations in these fields.

This mathematical model should be applied to researchstudies on SOD detection, purification, biological role,enzymatic regulation, as well as in a clinical contextwhere large numbers of samples are routinely assayed.

Acknowledgments

The author thanks Professor J. P. Dessaint for valuablediscussions and P. Fr(ssancourt for his skilled technicalassistance.


References

1. MCCORD, J. M. KEELE, B. B. JR. and FRIDOVITCH, 1.,Proceedings of the National Academy of Science, 68(5) (1971),1024.

2. FRXDOWCn, I., In Free Radicals in Biology, Ed Pryor, W. A.(Academic Press, New York, 1976), 1 239.

3. FRmowcn, I., McCoRD, J. M. and MICHELSON, A. M., InSuperoxide and Superoxide Dismutase, Eds. Michelson, A. M.,McCord, J. M. and Fridovich, I. (Academic Press, NewYork, 1977), p. 551.

4. FRIDOVICH, I., Science, 201 (1978), 875.

5. MCCORD, J. M. and FRIDOVICH, I., Journal of BiologicalChemistry, 244 (22) (1969), 6049.

6. FREVND, R.J. and MNTON, P. D., In Regression Methods, Ed.Owen, D. B. (Marcel Dekker, Inc. New York, 1979), 30159.

7. NRD., Pn., International Conference on ’Chemical com-munication and regulation of sexual reproduction, growth,and maturation in Schistosomes’ (Baltimore, 1985).

8. MARKLUND S. L., Journal ofClinical Investigation, 74 (1984),1398.

9. VotstN, C., WALLAERT, B., A.RTS, C. and GRosaos, J. M.,In Third International Workshop on the in vitro Effects ofMineralDusts (Springer Verlag, Berlin, 1985).

NEWJOURNALIn February 1986, The Royal Society ofChemistry will launch a new international periodical entitled Journal ofAnalytical Atomic Spectrometry (JAAS). Published bimonthly, JAAS will contain original research papers, shortpapers, communications and letters concerned with the development and ’analytical application of atomicspectrometric techniques. It will also include comprehensive reviews on specific topics, general information andnews of interest to analytical atomic spectroscopists including details of forthcoming conferences and bookreviews.An important feature ofJAAS will be the inclusion ofspecial reviews to be called Atomic Spectrometry Updates.These were formerly published in book form as part of Annual Reports on Analytical Atomic Spectroscopy,which will be discontinued following the introduction ofJAAS. The review will cover a number of key areasincluding environmental and agricultural materials; chemical and food materials; instrumentation; industrialchemicals and metals; atomisation and excitation; and minerals and refactories. Successive issues ofJAAS willreview the entire range of topics previously covered by ARAAS to provide a unique current appreciation ofdevelopments in analytical atomic spectrometry.

The Editor is Mrs Judith Drew, with Dr J. M. Harnly as US Associate Editor. The Editorial Board includes:

Professor J. M. Ottaway (Strathclyde, UK)Chairman

Dr M. S. Cresser (Aberdeen, UK)Dr L. C. Ebdon (Plymouth, UK)D. L. Miles (Wallingford, UK)Dr B. L. Sharp (Aberdeen, UK)Dr M. Thompson (London, UK)Dr A. M. Ure (Aberdeen, UK)and the Advisory Board:

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The 1986 subscription (ISSN 0267-9477) is 165 (UK) $319 (USA) and 182 (rest ofthe World). Orders to Royal Society ofChemistry, Distribution Centre, Blackhorse Road, Letchworth, Hertfordshire SG6 1HN, UK.

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Treatment of super oxide dismutase by a regression methoddownloads.hindawi.com/journals/jamc/1986/761764.pdf · JournalofAutomaticChemistry/JournalofClinical LaboratoryAutomation,