and D. M. Servant The Polytechnic Wolverhampton WV1 lLY, England
I
Substoichiometry and Saturation Analysis
Radioactive isotope dilution analysis depends on the reduction of specific activity (disintegration rate per unit amount of material) of a radioactive tracer, in an identical chemical form with the analyte, when it is diluted with the non-radioactive analyte present in the analytical sample. The fundamental relation is Mx = Mt
($- I).
where M, is the amount of analyte, Mt is the amount of radioactive tracer added, St is the specific activity of the added tracer, and S, is the specific activity after mixing the tracer and sample. The two specific activities may be expressed as
and
...
where A is the absolute activity (disintegrations per unit time), and W is the amount of substance in the sample of which the activity is measured. The chief advantage of isotope dilution analysis in its classical form is that the whole of the analyte need not be isolated; the recovery, in a pure form, of only a sufficient sample of the mixture of tracer and analyte is required, t o allow a determination of specific activity. Thus the method has found its main applications where difficult isolations cause ooor recoveries. or where the removal of the whole of the ~--sample is forbidden, as in the in vivo measurement of blood volume. The method has not shared the low limits of detection which are a feature of many radiochemical methods, because of the necessity of obtaining a counting sample large enough for the measurement of W,, usually by weighing. The substoichiometric ~rocedureavoids this difficultv bv making the counting samples equal, through the use of identical hut stoichiometricallv inadeauate. . amounts of reaeent for chemical separation. Then ~
~
'Johannesson, J. K., Analyst, 86.72 (1961). 2Ruzicka,J., and Stary,J., At. Energ. Rev., 2,4 (1964). 3Ekins,R. P., The Practitioner, 207,312 (1971). "ewant, D. M., J. CHEM. EDUC., 51,550 (1974).
452 1 Journal of Chemical Education
~
~
M ~ = MS * ( ~ - I= )
AJ
(TJK-
=
,wt (AAm
and absolute activities may be used in place of specific activities. In practice the use of identical counting samples normally ensures constant counting efficiency, and the ohserved count rates can he used for At and A,. There is now no necessity to measure the amounts of the counting samples, and the much lower limits of detection associated with simple measurements of radioactivitv are ~otentiallvavailable. An early application of thiitechiique was that developed by Johannesson for the determination of chloride ion? Equal amounts of silver chloride were precipitated from two equal volumes of aqueous chloride labelled with chlorine-36, to one of which had been added the unknown in which chloride was to be determined. Equal amounts of precipitate were ensured by adding equal amounts of silver nitrate, less than stoichiometrically equivalent to the amount of radioactive chloride present in each solution. Precipitation methods present difficulties a t very low levels in inorganir analysis, and the chief advantage ofhhannesson's method lies in its convenience rather t han in a very low limit of detecticm. Kuzicka and Staw'have develooed methods which allow the determination of metal ions down to subnanogram levels in many cases. These methods depend on complexing the metal ions of the diluted and undiluted tracer samples with equal, substoichiometric amounts of a suitable reagent. The equal amounts of complex are then separated from the excess metal ions, either by solvent extraction or by ion exchange procedures, and are counted. Apart from the low limits of detection, such methods have the advantage of being extremely simple and convenient to carry out. Furthermore the substoichiometric principle ensures that there is no excess of complexing agent. If the latter is carefully chosen to complex more strongly with the metal to he estimated than with species likely to cause interference, the method becomes extremelv selective. A similar technique has heeh, and is being, ripidly developed in biochemistry and medicine under the title saturation &alysis.3 Use is frequently made of the immune reaction. The analyte is regarded as an antigen and a suitable organism is provoked into producing an antibody which will combine with it. A preparation of the antibody can then be made and added in suhstoichiometric amounts to solutions of labelled antigen variously diluted with the samples for analysis and with
Experimental Results Silver ConTent/
Sample
C,d-'
C+K'
10-ag MOTHER LIQUOR
s t a n d a r d solutions of unlabelled antigen. T h e antigen-antihody complex is isolated in each case a n d its count r a t e measured. A calibration curve is constructed with t h e results from t h e standard solutions a n d t h e antigen content of t h e sample solurions read from it. T h e use of standard s o l ~ l t i o nt so obtain a mlihration graph is necessary because t h e reactions a r e not clear cut. Absolute standardization in technique in dealing with t h e samples a n d s t a n d a r d s is required. Determinations can h r carried out a t s u b - n a n o g r a m le\,els with sufficient a c curacy for clinical and biochemical research purposes. Experimenis The two simple experiments described here are suitable for undereraduate use. The first illustrates an inoreanic a~olicationof suhkiehiometrv, (the . ~ determination of the silver e o n i e k o f a ohotographic tilm,. I t can br convrnienrly used tusupplem~nrn mdm. chemical investigaliun of mmple destruction prucedurrs prevrouslg , ~ makes use of largely thesame appadescribed in this J ~ u r n a land ratus and materials. The second experiment illustrates a medical application of saturation analysis (the estimation of a hormone, the concentration of which is indicative of satisfactory placental function during pregnancy) and uses a commercially available kit of materials. In some institutions suitable samples of serum from females in late pregnancy may be available; otherwise i t may be necessaryto dilute an aliquot of one of the standard solutions provided in the kit, for use as the samples. One kit will allow ten students toeaehproduce acalibration graph and a duplicate analysis of a sample. ~
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~~
The Determination of Silver in Photographic Film Stripping film, as used in autoradiography, was taken as the sample for this experiment. A single plate, scored into 1-cm squares, provided sufficient samples for many experiments. Silver-ll0m (Radiochemical Centre code SES 1)was used in the form of aqueous silver nitrate a t a specific activity 1.4 Cilg. This was diluted with aqueous, inactive, mole I-' "carrier" silver nitrate to give a solution containing 5 X silver and -100 pCi of silver-ll0m I-'. A well-type scintillation counter was employed for determinations of radioactivity. Stripping film, 1cm2, was placed in a 10 ml conical flask together with 2 ml of a mixture of three parts perchhie acid to two parts nitric acid. The flask was covered t o prevent loss of spray, and heated to -80°C for 1hr, by which time the film was completely dissolved. The contents of the flask were diluted to 50 ml and 2 ml of this solution were added t o 2 ml tracer solution and 6 ml water, and extracted with mole I-'). Two 10 ml of a solution of dithizone in chloroform (5 X The oraeedure milliliters ofthe extract were taken for countine (C,). . was repeated without the sample (Ct). Results for eight samples, analyzed by four students, are given in the table. The count rates are corrected far background. The precision of the measurements was quite favorable for inexperienced students using the technique for the first time. Apart from the preparation of reagents. e the time taken for each . and from the s a m ~ l destruction, determination was only a few minutes. ~~
~
PRECIPITATE
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~
~~~
\
~
~
~
T h e Determination of Human Placental Lactogen (HPL) In Serum This experiment is conveniently performed using the H P L Immunoassay Kit (code IM68) of the Radiochemical Centre, Amersham.
Graphs of count rate of precipitate and mother liquor versus concentration of HPL. (Student 1. 0; Student 2. 0;Student 3, m).
.
Radioactivitv was measured with a well-tvoe . scintillation counter. The rmgenrc in nn HPI. lmmunoassay Kit were reconstituted folIow,ng the m n m h t u r r r ' s insrrucrions Six 15-mlconical crntritugc tubes were labelled 1-6, and their background count determined. Aliquots (50 p1) of the standard sera (1,3,6 and 10pg ml of HPL) from the kit were pipetted into tubes 1-4 and of the ser&under test into tubes 5 and 6. Iodinated P S I )HPL solution ( 5 W d was added to each tube. the contents mixed. rabbit anti-HPLserum (5Wull . . . added. and the #;tmtenumixed a&. After RO mm ethanol (2 ml) was a d d i d to each tube. theconrents m i x d s n d thenrentr~fugedfor5minnr 2OM rpm. The mother liquor was decanted into numbered, stoppered vials and the centrifuge tubes inverted to drain, on a filter paper, for 5 min. The centrifuge tubes and the stoppered vials were counted. Graphs of net count rate versus concentration of HPL were plotted for both precipitates and mother liquors, allowing the concentration in the serum under test t o be determined. Plots obtained by three students are shown. The experiment is best performed with a reasonably large group of students, when the effects of such parameters as differing experimental skill, order of addition of reagents, timing, and shape of tubes can be compared. Thus the plot obtained by student 3 shows the effect of reversing the order of addition of iodinated HPL and rabbit anti-HPLserum, in order toinvestigate the reversihility of the antigen-antibody formation.
Volume 54, Number 7, July 1977 1 453
