Summary. Technical variation is a linear function of the incremental mean in the mixed lymphocyte reaction (MLR) and is independent of the immune status.
Aust. J, Exp. Biol. Med, Sci., 62 (Pt 6) 711-715 (1984)
Briej Communication:
THE RELATION BETWEEN TECHNICAL VARIATION AND THH MEAN IN THE MIXED L Y M P H ( X : Y T E REACTION IN I H E RAT by A. D. HIBBERD, J. E. WELLS*. P. A. WALKER* AND V. J. LINDSAY (From the Departments of Surgery and *Biostallstics. Christchurch Clinical School of Medicine, Christchurch, New Zealand.) (Accepted for publication August 3. 1984.) Summary. Technical variation is a linear function of the incremental mean in the mixed lymphocyte reaction (MLR) and is independent of the immune status of the responders and the gene dose of ihc stimulators. Logarithmic transformation of the absolute count 'control mean makes tecbnical variation independent of the mean. We recommend that this transformation be used before parametric analysis of the data. INTRODUCTION The MLR is important because it is used to match living-related renal donor and recipient (Kissmeyer-Nielsen. 1979), predict renal graft survival (Opelz and Terasaki. 1977) and measure disparity at (he B region of the rat major hislocompatibilily complex (D region in the human. 1 region in the mouse) (Antczak. Brown and Howard. 1979). If it can be done rapidly, it may become important in cadaveric renal transplantation (Fabre. 1982) because it will better predict graft survival than HI.A-DR matching alone (van Es and Balner. 1978). MLR counts vary considerably within one condition (Osa and Weksler. 1977) and between different conditions (Osoba and Falk. 1974). Several researchers have suggested that a logarithmic transformation of MLR counts be done before doing a parametric analysis of the data (Dei and Urbano. 1977; Farrant et al.. 1980) because it reduces Ihe heterogeneity of the technical variation across conditions (Farrant et al.. 1980). Yet they have not explained why such heterogeneity occurs nor why the logarithmic transformation worked. In this study we aimed to explore the relationship between technical variation and the mean in the MLR under a variety of conditions. MATERIALS AND METHODS
Rat colony We used AS2 (RTI') for responders. AS (RT1») or (AS X AS2)Fi hybrids for allogeneic stimulators and AS2 for autologous stimulators. TTie strains AS and AS2 differ at ihe RTI locus and at least three olher minor hislocompaiibility loci (Heslop. 1968), These strains. originally derived from a colony in the University of Otago. Dunedin. are now inbred in the Animal Research Laboratory of this School. They were 3-6 months old. MLR We used a mieroculture technique for rat lymphocyte transformation described by Lindsay and .Allardyce (1979). In brief, lymphoid cells from peripheral blood were prepared bv centrifugation on a gradient of Ficoll-Urografin. Stimulators were prepared by irradiating the lymphoid cells at 2.000 rad with a superficial X-ray machine (RT 100. Phillips. Germany). Responders or stimulators were plated out in quintuples at 200.000 cells per well on flat Abbreviations used In this paper: MLR. mixed lymphocyte reaction: s. sample standard
deviation.
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A. D. HIBBERD, J. E. WELLS, P. A. WALKER AND V. J. LINDSAY
bottom microtitre plates (Sterilin, Middlesex, U.K.) in Eagle's minimal essential medium. After incubation at 37° in humidified air with 10% CO2 for 5 days, 0 4 /*Ci tritiated thymidine {activity 5 Ci/mol) was added, the cells were harvested on glass fibre discs (Skatron A. A., Liebyen. Norway) and ihe radioactivity of each disc counted on a scintillation counter (Beckman LS-250 Liquid Scintillation Counter). Statistics We divided the blood for the responders Into iwo (A,B) and, similarly, the blood for the allogeneic stimulators (Cx, Dx, where x denotes irradiation). Each was processed independently of the others. We combined each responder with each allogeneic stimulator on the plate and thus formed 4 sels of cells: A 4* Cx. + Dx, B + Cx and B + Dx. Because each set was done in quintuples, we obtained 20 absolute counls for one experiment. From a group of AS2 rats we obtained another aliquot of blood which was divided into tWG, similarly processed, and irradiated to form autologous stimulators (Ex, Fx). From 4 sets of cells, namely, A + Ex, A + Fx. B + Ex and B -|- Fx, we obtained 20 autologous control counts. The mean of each control set was subtracted from each of the corresponding absolute counts to obtain the incremental counts. Technical variation was measured in two ways. TTie first, called SoTtnii, was the standard deviation of all 20 incremental counts and so included variation from all steps in the method, both splitting of blood aliquots and plating out. The second, called Swuhin. was the standard deviation obtained from the pooled estimate of the variation within each of the 4 sets of quintuples, and so measures only the variation due to plating out cells. For each e.xperiment, technical variation about the absolute mean is identical to technical variation about the incremental mean, because these two means differ by a constant which is the control mean. Experimental design It is shown In Table I. We studied the relationship between standard deviation and incremental mean under four different conditions: with normal AS2 rats (group one): with AS2 rats sensitized by 1 (ml) of AS blood intraperitoneally 3 days before assay (group two (a)) or 15 days before assay (group two (b)) and with normal AS2 rats whos/* responders were stimulated by (AS X AS2)Fi lymphocytes (group ihree). For each experiment in the three groups we calculated s^TBrmi, Swi.hm, the absolute mean (mean of the absolute counts'), the incremental mean (mean of the incremental counts) and the control mean (mean of the autologous control counts) and the mean of the ratio (absolute count/control mean).
TABLE 1 The rat strains providing lymphocytes for reapondcr.t and stimulators in the MLR and the treatment of the rat providing the responders.
Group
Trc.itment of Number of rat providing e.\periments responders
1 2 (a) 2 (h) 3
26 4 .
4 11
^ Denotes irradiation.
Nil AS blood 3 days before MLR AS blood 15 davs before MLR Nil
Mixed Lymphocyte Reaction Absolute Count Control Count Responder Stimulator Responder Stimulator A.S2 AS2
ASx
AS2 AS2
AS2
ASx
AS2
AS:
ASN
f A S X A S 2 ) F , , AS2
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TECHNICAL VARIATION IN THE MLR
RESULTS The standard deviation, S(,Y.«II, is a linear function of the incremcnial mean (r = -89) and a linear function of the absoluic mean (r — -93). The other standard devialion, Swubio, is also a linear function ol' the incremental mean (r — -85) and a linear function of the absolute mean (r - 91). ligiirc I shows ihe relationship between S.Mi.i. and ihc incremental mean. Working with the ratio of the absolute count to the control mean did not remove the linearity of the rcIationNhip between the slandard deviation and the mean (Fig. 2). We then worked with the logarithm of this ratio of the absolute count lo the control mean (Fig- 3). A comparison of Fig. 3 with Fig. 2 or Fig. 1 shows how- this logarithmic transformation completely removes the relationship between standard deviation and the mean. Because the ratio of the absolute count to the tonlrol mean is always positive, every value may be transformed in contraiit to the logarithmic transformation of incremental counts.
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1000 2000 3000 4000 5000 6000 7000 8000 900C INCREMENTAL MEAN
Fis. 1. It shows the relationship between standard devialion (within) and incremental mean. DISCUSSION Under a variety of experimental conditions the technical variation of the MLR \^a^ found to be a linear function of the incremental mean. This relationship applies to mixtures of L-uIturtd allogeneic lymphocytes irrespective of the immune stattis of the responders or the gene dose of the stimulators. The effect of this relationship is thai high mean values are estimated less precisely rhan low mean values whether ihe incremenUil means or ratios (absolute count/ control mean) are used.
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A. D. HIBBERD, J. E. WELLS. P. A. WALKER AND V. J. LINDSAY 7—,
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