Cellular cytotoxicity assessed by the 51Cr release assay

Journal of Immunological Methods, 90 (1986) 15-23

15

Elsevier JIM 03919

Cellular cytotoxicity assessed by the 51Cr release assay Biological interpretation of mathematical parameters S i m o n J. Bol *, H e n k J. R o s d o r f f , Cees P. R o n t e l t a p a n d L e o A. H e n n e n Rotterdam Radio-Therapeutic Institute, Rotterdam, and Radiobiological Institute TNO, Rijswijk, The Netherlands

(Received10 July 1985, accepted 10 January 1986)

This study deals with the interpretation of primary data of the 5aCr release assay for cellular cytotoxicity. In particular the dose-effect relationship between increasing numbers of lymphoid cells and the percentage of target cells killed has been considered. The number of target cells killed depends on the frequency and the activity of cytotoxic cells. These two parameters are often not distinguished from each other, which causes confusion and frequently results in vague descriptions of cytotoxicity data. Because in many cases not all cells in the target cell population can be lysed, we recommend the introduction of the plateau value for target cell kill. This maximum of target cell kill is a measure of the frequency of lysable target cells, but also depends on the cytotoxic cell activity. Description of the dose-effect curve by y = A ( 1 - e -kx) allows the simultaneous calculation of the maximum kill (A) and the frequency of cytotoxic cells (k) in the lymphoid cell population (x). Results are presented which indicate that A and k represent totally independent biological parameters the use of which permits a more objective description of cytotoxicity data. Key words: Cell-mediated cytotoxicity," 5~Cr release assay," Cytotoxic cell frequency and activity," Rat NK cells

Introduction

The 51Cr release assay is widely used to determine cell-mediated cytotoxicity (Brunner et al., 1968). The quantity of 51Cr released from labelled target cells in a certain period of time can be taken as a measure of the number of target cells lysed by cytotoxic cells. This simple measurement can thus be used to obtain qualitative information on whether cytotoxic ceils are present and whether target ceils are susceptible to lysis. However, problems arise when different lymphoid cell popula* Correspondence to: Simon J. Bol, Department of Clinical Haematology and Oncology, Royal Children's Hospital, Flemington Road, Parkville, Victoria 3052, Melbourne, Australia.

tions containing cytotoxic cells, and different target cell types a r e t o be compared quantitatively. Various investigators have described differences in the number of target cells killed in terms of high and low activity, efficiency or number of cytotoxic cells or high and low susceptibility to lysis of target cells. When no separate measures are used to distinguish between these different phenomena, this description of cytotoxicity data is still qualitative rather than quantitative. This problem has been noted by several authors (Henney, 1971; Miller and Dunkley, 1974; Thorn and Henney, 1976a; Zeijlemaker et al., 1977; Pross et al., 1981; Bloom and Korn, 1983; Callewaert et al., 1983; Krebs and Norrild, 1983). However, a unifying consensus has not been adopted and the use of many different parameters, lytic units and

0022-1759/86/$03.50 © 1986 ElsevierSciencePublishers B.V. (BiomedicalDivision)

16 complicated mathematical descriptions causes confusion. Therefore, many authors continue to present their data as percentage lysis of target cells without analysis of the dose-effect curves. In this study the dose-effect relationship between the number of lymphoid cells and the number of lysed target cells is considered. In principle, the dose-effect curve is characterised by two parameters: activity and frequency of cytotoxic cells within the lymphoid cell population. Here we propose that the activity and frequency should be considered as independent biological entities, which can be simultaneously determined from the dose-effect curve.

Definition of activity of cytotoxic cells using the lymphoid cell titration method When the number of 51Cr-labelled target cells is fixed (e.g., 10 4 cells per well in 96-well microtitre plates) and the number of lymphoid cells is increased, the point will be approached where there is a large excess of lymphocytes over target cells. Consequently, all target cells which are susceptible to lysis will be met by cytotoxic cells and lysed. When the target cell population contains cells which are not susceptible to lysis (heterogeneity), not all cells will be lysed even when lymphocytes are added in large excess (Trinchieri et al., 1973; Pross et al., 1981; Bloom and Korn, 1983). Thus, the maximum percentage of target cells killed is a measure of the frequency of target cells which are susceptible to lysis. In addition, this maximum percentage of target cells that can be killed supplies information on the efficiency of the interaction between cytotoxic cells and target cells. Activated lymphocytes may well recognise a wider range of cells in the heterogeneous target cell population. Thus, the maximum percentage of target cells that can be killed supplies information on the functional properties of target as well as cytotoxic cells. Definition of frequency of cytotoxic cells The dose-effect relationship between the number of lymphoid cells and the number of target cells lysed (amount of 51Cr release) can be analysed on the basis of the 'single hit' Poisson probability distribution (Henney, 1971; Miller and Dunkley,

1974). It is described by the equation f=l-e

kx

(eq. 1)

where: x = number of lymphoid cells/well; f = the fraction of target cells lysed (maximum = 1); k = constant which depends on the composition of the lymphoid cell population tested. As outlined above, it is conceivable that in many cases not all target cells within a population can be lysed, depending on the properties of both the target cell and the cytotoxic cell. Therefore, equation 1 can be modified by introducing the asymptote, A, i.e., the maximum number or percentage of target cells that can be lysed:

Af = Y= A(1-e -kx)

(eq. 2)

where: Y = the absolute number of target cells killed or the percentage killed when A is expressed as maximum absolute numbers or maximum percentage, respectively. As described in detail by Miller and Dunkley (1974), the constant k is a relative measure of the frequency of cytotoxic cells in the lymphoid cell population.

Theoretical considerations for the comparative measurements of cytotoxic cell activity, A, and frequency, k If activity, A, and frequency, k, are independent parameters, their contribution to the final dose-effect curve can be analysed separately. In Fig. 1, two hypothetical lymphoid cell populations are compared which differ with respect to either the activity or the frequency of cytotoxic cells. The curves are described by Y = A(1 - e-kX). Figs. 1 A - D illustrate what can be expected when two different lymphoid cell preparations contain an identical frequency of cytotoxic cells, but differ with respect to the activity of the cytotoxic cells (i.e., identical k values but different A values). Thus the differences observed between the two curves are caused by differences in A only. Figs. 1A, B, C and D all show the same two curves, but plotted in different ways. It should be noted that when the A values are normalised (e.g., both set at 100) the two curves in each graph would be completely identical, because at any

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number" o f l y m p h o c y t e s / w e l l

Fig. 1. Theoretical curves of the relationship between the n u m b e r of lymphoid cells and the percentage of target cells killed. The curves are described by the exponential equation y=A(1-e-kX). A, B, C and D: solid line: A = 7 5 ; dotted line: A = 25; for both lines k is identically set at 5 x 10 -6. E, F, G and H: solid line: k = 5 x 10-6; dotted line: k = 1 x 10-6; for both lines A is identically set at 75. A and E: l o g - l i n e a r plot. B and F: l o g - l o g plot (Henney, 1971; Lafferty et al., 1974; Miller and Dunkley, 1974). The approximate linear part up to an x-value of about 3 x 1 0 4 lymphoid cells can be described by y = Akx. C and G: l i n e a r - l i n e a r plot (Henney, 1971; Lafferty et al., 1976; Warren et al., 1978; Warren, 1981). The tangent lines are described by y = Akx. D and H: linear - l o g survival plot (Pross et al., 1981).

x-value the two curves differ by a constant factor of 3 (75/25) along the Y-axis. A commonly applied method for evaluating differences in cytotoxicity among lymphoid cell preparations is the expression of data in lytic units (LU) (Cerottini and Brunner, 1971; Kay et al., 1977). One LU is defined as the number of lymphoid cells required to kill an arbitrarily prefixed percentage of target cells. Because this expression is based on the number of lymphoid cells, it is used as a measure of cytotoxic cell frequency. From the curves shown in Fig. 1A-D the problem

becomes clear. First, conclusions on comparisons between two lymphoid cell populations often depend on which part of the curve is considered. Second, since the differences between the curves can be due to differences in A values, different LU do not always represent different frequencies of cytotoxic cells. Figs. 1 E - H illustrate what can be expected when two lymphoid cell populations contain different frequencies of cytotoxic cells, but are identical with respect to the activity of the cytotoxic cells (i.e., different k values and identical A values). Thus, the differences observed between the two curves reflect only differences in k values. The k value is directly related to the LU. According to Poisson statistics, the number of lymphoid cells (xl), among which there will be 1 cytotoxic cell on the average, can be read at 63% kill in Figs. 1E, F, G or 37% survival in Fig. 1H (i.e., 63% and 37% of A, respectively). This x 1 is equal to 1/k.

Experimental evidence for the independence of A and k From this analysis of literature data on the dose-effect relationship between the number of lymphoid cells and the number of target cells killed it becomes clear that the introduction of the maximum kill value A as an independently defined biological parameter will be helpful in comparing cytotoxicity data. The validity of the proposed independency of A and k was studied by analysis of the cytotoxic effects of rat spleen cells. Since the cytotoxic cells in the spleen can be detected without prolonged specific stimulation they have been indicated as natural killer (NK) cells.

Materials and methods

Spleen cells Specific pathogen-flee female W A G / R I J rats of 6-10 weeks of age were used as spleen cell donors. Spleen cell suspensions were prepared in RPMI 1640 medium at a pH of 7.4 and an osmolality of 282 mOsm. The medium was supplemented with 10% v / v heat-inactivated FCS (Sero Med), 24 mM N a H C O 3, 20 mM Hepes buffer, an additional 2 mM glutamine, 1% v / v nonessential amino acids solution (Flow Lab), 100 U penicil-

18 lin/streptomycin (Gibco Bio-Cult) and 5 × 10 -5 M 2-mercaptoethanol. A suspension of single cells was obtained by pressing the spleen through a nylon sieve while adding medium. Cell aggregates were allowed to settle for 5 min after which they were removed. All procedures were carried out on melting ice. Activation of natural killer (NK) cells was performed by incubation of spleen cells at 37°C at a concentration of 5 × 1 0 6 cells/ml (National incubator, 5% CO 2 in air, fully humidified) (Reynolds and Herberman, 1981). Aliquots of 20 ml cell suspension were incubated in 75 cm 2 culture flasks (Costar) in the upright position. After incubation, the cells were washed once. Cells were not recounted and cell numbers used in the cytotoxicity tests were based on the counts before culture.

Rat natural killer cell leukaemia Natural killer cell leukaemias (RNK) occur spontaneously in F344 rats and are transplantable in syngeneic rats (Stromberg et al., 1983; Reynolds et al., 1984). Several R N K leukaemia lines were obtained through cooperation with Dr. C.W. Reynolds (NCI, Frederick, MD, U.S.A.). One cell line, R N K 16, was selected on the basis of high cytotoxic activity, stable cytotoxic properties in subsequent in vivo passages, and relatively rapid in vivo growth. Leukaemic spleen cells were obtained from F344 rats 25 days after i.p. injection of 1 × 10 6 R N K 16 cells. Before testing, the cell suspensions were depleted of dead cells and erythrocytes by density separation on metrizamide solution (1.085 g / c m 3, 20°C, 282 mOsm, pH 7.4).

Target tumour cell lines The Moloney virus-induced mouse YAC-1 and the Gross virus-induced rat W / F u - G 1 lymphoma cells were used as N K cell target tumours. In addition, the R-1,M rhabdomyosarcoma, developed and transplantable in W A G / R I J rats (Reinhold and DeBree, 1968; Hermens, 1980) and ConA-stimulated W A G / R I J and BN rat lymph node cells were used as target cells. The tumour cell lines were screened monthly for mycoplasma and were negative.

51Cr release assay The cytotoxic effects of spleen N K cells were determined using the 51Cr release assay. Assays were carried out in round bottomed 96-well microtitre plates (Greiner). From a starting spleen cell suspension of 20 × 1 0 6 cells/ml serial 1 / 3 dilutions were prepared and each cell dilution was tested in duplicate or triplicate (150 /d/well). Target cells were incubated in the presence of 51chromium (Amersham, U.K.) (100/~Ci/106 cells in 100 /~l) in phosphate-buffered saline supplemented with 10% FCS. After 1 h incubation at 37°C, the cells were washed three times (4 ml, 500 × g, 5 min) to remove excess 51Cr. Finally, the target cells were suspended at 105 cells/ml and 10 4 cells (100 /xl) were added to each well. Then the plates were centrifuged (100 × g, 2 min), incubated at 37°C for a fixed time, centrifuged again (200 × g, 5 min) and 100 /L1 of supernatant from each well was collected. The amount of 51Cr released from target cells into the supernatant was determined by use of a gamma counter. To determine the 51Cr spontaneously released from target cells, complete series of control incubations were carried out with heat-inactivated (48°C, 15 min) spleen cells. The maximum of 51Cr release was determined by lysis of the target cells in 5% saponin. The specific fractional 51Cr release was calculated by ( T - S ) / ( M - S) in which T, S and M represent the gamma counts in the supernatants of the test, spontaneous and maximum release group, respectively. The fractional standard deviation (SD) for the specific fractional 5aCr release was calculated on the basis of count statistics:

~[rC~S/(T-S)]2+ [ MCff+S / ( M -

S)] 2

Mathematical analysis of dose-effect curves The dependence of the number of killed target cells on the number of lymphoid cells has been analysed with the exponential model y = A ( 1 - e -kx) This description results in saturation at the level A for larger values of x. Computer fitting of the experimental data to this model was performed

19

using the method of maximum likelihood as follows. Let the data consist of a sample of observations extracted from a parent distribution which determines the probability of making any particular observation. Further, the parent parameters /3o = (A0, k0) of the function under consideration are such that the actual relationship between y and x is given by y = y ( x ; £ ) = s(x; Ao, ko)

(eq. 3)

For any given value of x = xj, one can calculate the probability Pi for making the observed measurement y, assuming a Gaussian distribution with a standard deviation oi for the observation about the actual value y(xi):

[ '{y yx;,121

exp - 7

(eq. 4)

o,

The probability P for making the observed set of m measurements of the values of Yi is the product of these probabilities, for short

£)=y,-y(x,; £). exp - ~

°i

square fit. The method applied to fit the non-linear model is based upon a modified LevenbergMarquardt algorithm. X2 can be considered to be the appropriate measure of the goodness of fit.

Results

Activation of cytotoxicity of rat spleen cells The cytotoxic effect of rat spleen N K cells was tested by measuring the 51Cr release from labelled N K susceptible YAC-1 or W / F u - G 1 tumour cells in a 3 h assay. The cytotoxic effect, expressed as percentage lysed target cells, can be increased by overnight (18 h) incubation at 37°C in the presence of adherent cells (Reynolds and Herberman, 1981). To investigate whether this increase is caused by an increase in cytotoxic cell frequency (recruitment of pre-NK cells) or an increase in efficiency (activity as defined in this study), dose-effect curves of 'fresh' and 'activated' spleen cells were compared and analysed. Fig. 2 shows the result of two typical experiments in which the cytotoxicity before and after 37°C incubation (day 0 and day 1) were compared. It is observed that the A values are significantly different, but that the k values are similar. This indicates that the frequency of N K cells is similar at day 0 and day 1 (similar k), but that the

(eq. 5) The method of maximum likelihood consists of making the assumption that the observed set of measurements is more likely to have come from the actual parent distribution of equation 3 than from any other similar distribution with different parameters and, therefore, that equation 5 is the maximum probability. The best estimate for the parameters fl are therefore the values which maximise the probability of equation 5 which is equivalent to minimising the weighted sum of squares of deviations, X2, in the exponential.

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activated

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The optimum fit to the data is the fit which produces the smallest sum of squares or the least-

Fig. 2. Cytotoxic activity of rat spleen cells before (fresh, dotted line) and after 18 h incubation at 37°C (activated, solid line). The left and fight hand panels represent the results of two typical experiments which differ with respect to cytotoxic cell frequency, k, and maximum target cell kill, A. The curves represent the computed best fit of y = A(1--eTkX).

20

independent parameters. The correlation between k and A values determined in 19 independent experiments is shown in Fig. 3. The k values range from 1.1 to 2 . 4 × 1 0 6 ( m e a n + S D : 1.7+ 0.5) and A values range from 8 to 55% (30 + 15). The correlation coefficient r = 0.10. This indicates that there is no significant correlation between k and A.

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Fig. 3. Correlation between cytotoxic cell frequency, k, and maximum target cell kill, A. The A and k values of the dose-effect curves from 19 independent experiments were obtained by the computed best fits of y = A ( 1 - e kx).

activity of N K cells is increased on day 1 (increased A). These results suggest that k and A represent i

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Target cell specificity of rat N K cells Whether a N K cell can recognise and kill all cells in a certain target cell population will be expressed in the height of the maximum percentage kill of target cells, A. Furthermore, if there are different types of N K cells with different specificities for different target cells, the frequencies (k) of these N K cells are likely to be different. Fig. 4 shows the cytotoxic effect of spleen cells, activated by 18 h incubation at 37°C, on four different target cells. The plateau values (A) of the percentage killed target cells are different for the various target cell types, whereas the k values are similar, indicating that the frequencies of N K cells lysing the different target cells are similar. This suggests that all four target cell types are recognised by one type of N K cell, but that each target cell population contains a different proportion of lysable cells.

~o--

........

, 107

spleen c e l l s / w e l l

Fig. 4. Cytotoxic effect of activated spleen cells on different types of target cells. YAC-I: xenogeneic lymphoma; R-l, M: syngeneic non-immunogenic rhabdomyosarcoma; BN LN: allogeneic lectin stimulated lymph node cells from BN rats; WAG LN: syngeneic lectin simulated lymph node cells. The curves represent the computed best fits of y = A(1 - e - J ' x ) .

The influence of assay time on A and k The duration of the assay will determine the number of recognitive interactions and the degree of recycling of the cytotoxic cells. If recycling takes place, the k value represents an apparent frequency measure. The value of A will also depend on the duration of the assay, since the release of 51Cr from damaged target cells is time dependent (MacDonald, 1975; Thorn and Henney, 1976b; Lees et al., 1977; MacDonald et al., 1978). Figs. 5 and 6 show the effect of the assay time on the dose-effect curves. Spleen cells, activated by 18 h incubation at 37°C, were tested for their cytotoxicity against YAC-1 cells. Parallel tests were performed and groups were harvested at 1, 2, 3, 4, 5, 6 and 10 h. Up to 3 h the A value increases. Beyond 3 h of assay the A value remains unchanged. The k value, however, continues to in-

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0• | 104

.......

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I0 s 37°(: a c t i v a t e d spleen

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Fig. 5. Effect of assay time on the dose-effect curve. Activated spleen cells were tested for cytotoxic effects in 1, 2, 3, 4, 5, 6 and 10 h assays. For clarity only the dose-effect curves obtained in the 1, 2, 5 and 10 h assays are shown. The A and k values of all the curves are shown in Fig. 6. The curves represent the computed best fits of y = A(1- e-kX). crease with time. These effects are illustrated in Fig. 6 in which A a n d k values are p l o t t e d as a f u n c t i o n of the a s s a y time.

Effects of experimental change in NK cell frequency T o o b t a i n final evidence that c y t o t o x i c cell frequency, k, a n d activity, A, can be d e t e r m i n e d

.15 70.

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Fig. 7. Cytotoxic cell frequency, k (dotted line), and maximum target cell kill, A (solid line), in cell suspensions containing varying concentrations of cytotoxic cells. The frequency of F344 rat leukemic NK cells (RNK-16) was experimentally varied by dilution in BN rat spleen cells. The k and A values were obtained from dose-effect curves fitted by y = A(1e kx).

i n d e p e n d e n t l y , the frequency of N K cells in spleen cell suspensions was varied experimentally. T o this p u r p o s e spleen cells f r o m rats b e a r i n g the N K l e u k a e m i a R N K 16 were used ( R e y n o l d s et al., 1984) to assure a high initial frequency of N K cells. To o b t a i n starting cell suspensions with different N K cell frequencies, R N K 16 spleen cells were d i l u t e d in spleen cells f r o m BN rats, which c o n t a i n very low frequencies of N K cells. F r o m these starting cell suspensions r o u t i n e serial dilutions in m e d i u m were p r e p a r e d , which were tested in the 5tCr release assay using Y A C - 1 as target cells. Fig. 7 shows the A a n d k values c a l c u l a t e d f r o m the dose-effect curves of R N K 16 of which the frequency was c h a n g e d to ½, ¼ a n d ½ in c o m p a r i s o n to the original frequency. T h e analysis shows that the A values of the different curves are similar, b u t that there is a difference of a factor of 2 a m o n g the k values. This indicates that the k values can be used as a m e a s u r e of c y t o t o x i c cell frequency, i n d e p e n d e n t l y of the A value.

10i 0

,

0

, h , , , q l ,, . . . .

• ,

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. . . .

,

10 assay time

. . . .

15

Discussion

0

(h)

Fig. 6. The values of k (dotted line) and A (solid line) of the dose effect curves shown in Fig. 5 plotted as a function of the assay time.

Cytotoxic cell frequency (k) and plateau kill (,4) are independent parameters T h e m a i n conclusion f r o m the d a t a p r e s e n t e d here is that k a n d A are i n d e p e n d e n t p a r a m e t e r s .

22

For example, as shown in Fig. 3, there is no correlation between k and A. Moreover, during prolonged assays k continues to increase, whereas A, after an initial increase, remains constant (Fig. 5) and a deliberate change in cytotoxic cell frequency changes the value of k, but not of A (Fig. 6). The value of k thus represents a relative measure of the frequency of cytotoxic cells and is not dependent on the frequency or properties of target cells used. As shown in Fig. 2 activation of speen cells results in an increase in the maximum percentage of target cells killed (A). This increase in A can be easily misinterpreted. Seemingly, after activation, the same number of cytotoxic cells lyse more target cells which could lead to the conclusion that activation results in recycling of cytotoxic cells. In fact, the dose-effect curve represents the chance process for the interaction between increasing numbers of cytotoxic cells and residual, non-lysed target cells. The frequency of lysis-susceptible target cells (i.e., the height of the plateau, A) does not affect the shape of the probability distribution. Consequently, assessment of the frequency of cytotoxic cells (k) is not dependent on the frequency of lysable cells in the target cell population.

Lytic units (LU) are directly related to k The comparison of different dose-effect curves on the basis of LU is generally restricted to parallel curves with identical plateau (maximum kill) values (Pross et al., 1981). In this respect the independence of k and A is of practical significance. When A is regarded as a separate biological parameter, it is permissible to normalise the curves with respect to A (determination of A will be necessary). This normalisation of A values will allow an easy comparison of the shapes of the curves. In the majority of cases the shapes will be similar (parallel curves). Then, LU can be defined as the number of lymphoid cells (x) needed to kill a number (or percentage) of target cells which represents 50% (or any percentage) of the A value. The relationship between LU and k is evident: the number of lymphoid cells, x, at y = 50% of A is given by in 2 / k and x at y = 63% of A is given by 1/k. As shown in Fig. 6 the value of k can be

increased by recycling of cytotoxic cells. When comparing different lymphoid cell populations, determination of complete dose-effect curves at different assay times will be necesssary to distinguish between differences in recycling capacity or frequency of cytotoxic cells.

Biological significance of A The interpretation of A is complex since the maximum kill of target cells can reflect properties of target cells as well as of cytotoxic cells. However, in experiments where target cells or cytotoxic cells are treated before testing (e.g., activation of cytotoxic cells), changes in A can, in principle, be ascribed to changes in the properties of the treated cell type. The results depicted in Fig. 2 can thus be interpreted as activation of the cytotoxic cells involved. A further implication of the maximum target cell kill is that a proportion of the cells in the population cannot be recognised or lysed by the cytotoxic cells tested. This could indicate that several additional cytotoxic cells with different specificities are needed to eradicate the total target cell population. The results of Fig. 4, showing identical k values, but different A values for different target cells could be interpreted as specificity of the N K cells involved. Whether the residual cells of the populations could be attacked by other types of N K cells or that antigen specific CTL are necessary remains to be established. Literature interpretations of k and related constants Although the asymptote (A) of target cell kill and constants related to k have been introduced in mathematical equations by a number of authors, these parameters have not been considered to be independent. Trinchieri et al. (1973) used the Von Krogh equation to calculate a constant which is related to the k value used here, i.e., a measure of the frequency of cytotoxic cells. However, those authors used this constant as a measure of 'efficiency' of different cytotoxic cells. Lafferty et al. (1976), Warren et al. (1978) and Warren (1981) have used the initial slope of the dose-effect curve as a measure of cytotoxicity (Fig. 1C and G). The value of Akx was indicated as 'cytotoxic potency' (Lafferty et al., 1974) and no distinction was made whether changes in this value are due to changes

23

in A or k. Pross et al. (1981) compared the exponential equation used here, and the Von Krogh equation. They described the k-related constants representing a measure of cytotoxic cell frequency being related to LUs. But thereafter, these constants were indicated as measures of target cell susceptibility to lysis. Furthermore, Pross et al. (1981) set the condition that: 'A values should be the same in order for data from different lymphocyte preparations to be comparable'. In fact, this condition makes the introduction of A unnecessary, because when the dose-effect curves have identical asymptotes, any method of analysis will give similar ratios of cytotoxic parameters (LU, k, Von Krogh constant) between different lymphoid cell suspensions. Only recently, Bloom and Korn (1983) used the normalisation of the asymptote of target cell kill. They used different A values for the comparison of results from different experiments (i.e., testing lymphoid cell populations from different donors) and, within one experiment, different A values for different target cell types. Doing so, only the k-related constants were used to compare the frequencies of cytotoxic cells in the fractions after separation.

Conclusion

The present data show that the A value for target cell kill is a biological interpretable parameter independent of the k value for cytotoxic cell frequency. The determination of both parameters is required to obtain a meaningful description of cell mediated cytotoxicity.

Acknowledgements

The work was supported by the Queen Wilhelmina Fund of the Dutch National Cancer League.

Dr. J.J. Broerse is gratefully acknowledged for supplying the computer facilities.

References Bloom, E.T. and E.L. Korn, 1983, J. Immunol. Methods 58, 323. Brunner, K.T., J. Mauel, J.C. Cerottini and B. Chapuis, 1968, Immunology 14, 181. Callewaert, D.M., J. Geneyea, N.H. Mahle, S. Dayner, C. Korzeniewski and S. Schult, 1983, Scand. J. Immunol. 17, 479. Cerottini, J.C. and K.T. Brunner, 1971, in: In Vitro Methods in Cell-Mediated Immunity, eds. B.R. Bloom and P.R. Glade (Academic Press, New York) p. 369. Henney, C.S., 1971, J. Immunol. 107, 1558. Hermens, A.F., 1980, Br. J. Cancer 41 (suppl. IV), 245. Kay, H.D., G.D. Bonnard, W.H. West and R.B. Herberman, 1977, J. Immunol. 118, 2058. Krebs, H.J. and B. Norrild, 1983, Scand. J. Immunol. 17, 123. Lafferty, K.J., I.S. Misko and M.A. Cooley, 1974, Nature 249, 275. Lafferty, K.J., A. Bootes, G. Dart and D.W. Talmage, 1976, Transplantation 22, 138. Lees, R.K., H.R. MacDonald and N.R. Sinclair, 1977, J. Immunol. Methods 16, 233. MacDonald, H.R., 1975, Eur. J. Immunol. 5, 251. MacDonald, H.R., R.K. Lees and R.L. Howell, 1978, Transpl. Proc. 10, 339. Miller, R.G. and M. Dunkley, 1974, Cell Immunol. 14, 284. Pross, H.F., M.G. Baines, P. Rubin, P. Shragge and M.S. Patterson, 1981, J. Clin. Immunol. 1, 51, Reinhold, H.S. and C. DeBree, 1968, Eur. J. Cancer 4, 376. Reynolds C.W. and R.B. Herberman, 1981, J. Immunol. 126, 1581. Reynolds, C.W., E.W. Bere and J.M. Ward, 1984, J. Immunol. 132, 534. Stromberg, P.C., J.L. Rojko, L.M. Vogtsberger, C. Cheney and R. Berman, 1983, J. Natl. Cancer Inst. 71, 173. Thorn, R.M. and C.S. Henney, 1976a, J. Immunol. 117, 2213. Thorn, R.M. and C.S. Henney, 1976b, Nature 262, 75. Trinchieri, G., M. DeMarchi, W. Mayr, M. Savi and R. Ceppellini, 1973, Transpl. Proc. 5, 1631. Warren, H.S., 1981, Scand. J. Immunol. 14, 71. Warren, H.S., J.A. Woolnough and K.J. Lafferty, 1978, Aust. J. Exp. Biol. Med. Sci. 56, 247. Zeijlemaker, W.P., R.H.J. Van Oers, R.E.Y. De Goede and P.T.A. Schellekens, 1977, J. Immunol. 119, 1507.