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Statistical aspects of cell motility determinations with a modified chemotaxis assembly for multiwell filter assays
Journal o f Immunological Methods. 46 (1981) 251--258 Elsevier/North-Holland Biomedical Press
251
STATISTICAL ASPECTS OF CELL MOTILITY DETERMINATIONS WITH A MODIFIED CHEMOTAXIS ASSEMBLY FOR MULTIWELL FILTER ASSAYS
LARS-GORAN AXELSSON *, GORAN NILSSON ** and BENGT BJORKSTI~N ,.1 * Departments o f Biomedical Research and * * Applied Mathematics. Pharmacia AB. Uppsala. Sweden
(Received 13 February 1981, accepted 15 June 1981)
A multiple chamber assembly for determination of neutrophil migration consisting of disposable lower plastic chambers and an easily cleaned and inert upper chamber made of stainless steel was constructed and used in experimental work. Using results of chemotaxis determinations in the assembly and a statistical model, the consequences of various ways to present cell migration data are discussed. With any method for multiple measurements of chemotaxis of cells from a given sample, there are occasional extreme results ('outliers') deviating considerably from other determinations. We show that the medians of chemotaxis determinations performed in triplicate are less influenced by such outliers than the mean values. The risk of an outlier affecting the median value was in our assembly about 0.2%, compared with a 10% chance of influencing the mean value.
INTRODUCTION
In 1962, Boyden described an in vitro micropore filter technique for measuring cell migration. This represented a major improvement over previous methods for analyzing cell migration. Various modifications of the filter technique have since been described to overcome some of the technical difficulties and to improve precision and accuracy. As well as the latter, some recent modifications have addressed various technical problems, e.g., detachment from various types of filters (Harvath et al., 1980; Keller et al., 1980), handling of chambers (Maroni et al., 1972; Addison and Babbage, 1976; Snyderman and Pike, 1976; Swanson, 1977; Falk et al., 1980), and the influence of gravity (Park, 1980). In our experience some of the major problems with reproducibility arise from the fact that the Boyden chambers have to be meticulously cleaned before re-use. When the chemotactic chambers are repeatedly washed and
1 Correspondence to B. BjSrkst~n, Department of Experimental Allergy Reserach, Pharmacia AB, Box 17, S-751 03 Uppsala 1, Sweden. 0022-1759/81/0000--0000/$02.50 © 1981 Elsevier/North-Holland Biomedical Press
252 various detergents used, small cracks develop to which cells may adhere. Any remaining chemokinetic substances or detergents may also markedly influence results. To avoid these problems, we have constructed a multiple chamber assembly, consisting of a disposable lower plastic chamber and an inert, easily cleaned upper chamber made of stainless steel. However, even under carefully standardized conditions multiple tests of the same sample occasionally yield individual results differing considerably from each other. Such extreme results or 'outliers' may significantly influence the mean value of the determinations. A simple model was designed to demonstrate, from a statistical point of view, the consequences of various ways of presenting cell migration data, with particular regard to the occurrence of outliers. MATERIAL AND METHODS
Leukocyte preparation Blood from the cubital vein of healthy staff members was collected in Venoject tubes (Terumo, T o k y o , Japan) with 143 U.S.P. units sodium heparin per 10 ml blood. Dextran 500 (Pharmacia Fine Chemicals, Uppsala, Sweden) was added to give a final concentration of 1%. The erythrocytes were allowed to sediment for a b o u t 30 min in room temperature. The polymorphonuclear neutrophil (PMN) rich supernatant fluid was collected and contaminating erythrocytes were eliminated by hypotonic lysis with distilled water. After 15 sec 1.5 M NaC1 was added to restore isotonic conditions. The PMNs were then washed twice and resuspended in Gey's buffer, pH 7.2, at a concentration of 3 × 106 PMN/ml. Viability was 97% as estimated b y trypan blue exclusion. Chemotaxis assembly The assembly consists of a 100 mm × 35 mm × 250 mm support of plexiglass with 10 holes 6 mm × ~35 mm, each in 4 rows, and a stainless steel 18/8 plate (100 mm × 10 mm × 250 mm) with 40 holes corresponding to those in the plexiglass support (Fig. 1). Plastic microcentrifuge tubes, Beckman Microfuge tube, ETH 26, LKB, Stockholm, Sweden, were placed in the support. Micropore filters were placed on t o p of the tubes and secured with the stainless steel plate, which was held in place with 3 position pins and 3 screws. The position of the holes in the steel plate n o w corresponded to the tubes attached to the support. A detail of the assembly demonstrating an individual chamber is shown in Fig. 2. Chemotaxis assay The microtubes were filled either with 400 ~1 Gey's buffer to measure random migration, or with 10% activated serum in Gey's buffer to measure stimulated migration. The activated serum was obtained b y incubating
253
Fig. 1. Assembly for multiwell filter assays.
fresh pooled human serum with heat aggregated human IgG. The microtubes were covered b y filters with 3.0 pm pore size (Millipore S.A., Molsheim, France). The pre-warmed (37°C) steel plate was placed over the support and secured. The holes in the plate were filled with 200 pl of the cell suspension. The assembly was then incubated at 37°C for 60 min in humidified air with 5% CO2. After incubation, the metal plate was removed. Since the filters had a larger contact area to the steel plate than to the microtubes, they usually stuck to the plate and were easily removed. They were then fixed, stained with hematoxylin, cleared with xylene and
~'~ [~'~'~-- steelplate • filter |
!
~
tube tube support
Fig. 2. Detail of an individual chamber in the multiwell assembly.
254
m o u n t e d on glass slides (Wilkinson, 1974). Migration was estimated by the leading front method (Zigmond and Hirsch, 1973). Results were expressed as mean distance in pm for 5 fields per filter. The modified assembly was used in routine work for measuring random migration and chemotaxis. Of the migration experiments performed, 212 chemotaxis experiments were done in triplicate filters. These data were analyzed statistically. Reproducibility within single experiments was evaluated by simultaneously testing random migration and chemotactic responsiveness of cells from one donor in 20 filters. Statistical methods There is always some variation when multiple measurements of the same sample are done. Sometimes a single result is so widely separated from the others as to suggest that it is from a different population. Such extreme values are designated 'outliers'. The occurrence of outliers may seriously impair the precision of a method. It is thus important to minimize the influence of such outliers in the final presentation of the test results. To demonstrate the consequences of various ways of presenting chemotaxis data a simple statistical model was designed. In this model the correct value in the experiment was assumed to be 100 pm and the probability of obtaining that value assumed to be 0.8. Further the probability of 10% deviation
TABLE 1 Probability o f distribution o f individual results and estimates w h e n test results are given as m e a n or m e d i a n values o f 2, 3 o r 5 filters. The 'true' value was assumed to be 100.
Value
Individual result
Mean o f 2
Mean o f 3
Median o f 3
Mean o f 5
Median o f 5
90 92 93.3 94 95 96 96.7 98 100 102 103.3 104 105 106 106.7 108 110
0.1
0.01
0.001
0.028
0.00001 0.00040
0.00856
0.024 0.00645 0.16 0.05280 0.195 0.8
0.66
0.560
0.944
0.22410 0.43248 0.22410
0.98288
0.195 0.05280 0.16 0.00645 0.024 0.1
0.01
0.001
0.028
O.O0040 0.00001
0.00856
255
o f the measured value from the true value, i.e., measurements of 90 and 110 ~m, was assumed to be 0.1 for each. Deviations of 10% or more were considered outliers. With these assumptions, the distribution of estimates obtained by performing duplicate, triplicate or quintiplicate assays and presenting data as the median or the mean are shown in Table 1. It will be seen t h a t taking the median rather than the mean values gives a higher probability for presenting a result equal to 100, i.e., the true value, but also implies a slightly higher risk for an extreme deviation from 100. Moderate deviations of the mean values are c o m m o n . The proportion of outliers m a y be estimated by performing a large number of measurements on the same sample, plotting the results and decide which results are to be considered as outlying. An example of this is shown in Fig. 3. However, usually only a few replicates of a large number of different samples are done, e.g., triplicate filters from m a n y different experiments. In such cases the outliers cannot be identified from a histogram of all the observations, since t h e y are from m a n y different populations.
tO0
A
B
•
90 80 •..
70
~" ._c
3o
60
m
so
_-2O o
~to: 4O 30 20
tO
'V' -"
!
:
"U
"0.8
"0.4
-0.2
0.0
,-...., 0.8) Dea|atlees free the l e d l a n en a le|erlekefe scale rfn~ 0.2
0.4
0.6
Fig. 3. Results of two migration experiments (A and B) in which random migration (squares) and chemotaxis towards 10% activated serum (circles) were done in 20 microwells. The stippled bars to the left show median values -+ S.D. of the median. The bars to the right represent mean values -+ S.D. Fig. 4. Distribution of the deviation from the median in 212 triplicate filters in a semilogarithmic scale.
256
By constructing a histogram o f the deviations from the median for each experiment a rough estimate o f the proportion o f outliers may be obtained. The estimate is obtained by dividing the number o f outlying deviations in such histograms by the total number of observations. By this m e t h o d the true proportion of outliers will be slightly underestimated, since occasional triplicates will contain two or three outliers in the same direction. An example of this model is shown in Fig. 4. The precision of a mean value is usually given as the standard deviation. There is no similar simple relationship between the standard deviation of the median and the standard deviation o f the individual observation. To estimate the standard deviation of the median of, e.g., triplicate filters, several consecutive triplicates from the same sample m a y be used. This was done by regarding the first 18 filters in each experiment presented in Fig. 3 as 6 triplicate determinations. RESULTS
In Fig. 3 the results are shown of two experiments in which random migration and chemotaxis towards 10% activated serum were measured in 20 filters with cells from the same sample. In the chemotaxis assays migration was considerably larger into respectively 1 and 2 of the 20 filters. These 3 values were considered as outliers from the respective samples. By regarding the first 18 filters in each experiment as 6 triplicate determinations, the standard deviation o f the medians could be calculated. As shown in the figure the standard deviations of the means and o f the medians were similar in 3 o f the 4 determinations. The distribution o f the 424 deviations from the medians of the 212 chemotaxis determinations done in triplicate is shown in Fig. 4 in which the deviations of the extreme values from the medians for each triplicate are shown after logarithmic transformation (ln). If deviations below --0.4 and above +0.4 on the logarithmic scale, i.e., below 67% and above 149% of the median on a linear scale, are considered as outliers, the estimated risk of low outliers was 2.2% and o f high outliers 1.1%. Thus the risk of at least one outlier in a triplicate was about 10%. This means t h a t in 10% of the triplicates the mean values would have been influenced by an outlier. The risk t h a t the median value for the triplicates was an outlier, i.e., t h a t 2 or 3 o f the filters in a certain triplicate represented outliers in the same direction, was calculated to about 0.2% (3 X 0.02 : . 0.98 + 3 X 0.012 • 0.98 + 0.023 + 0.013). DISCUSSION
The assembly has been used for 1 year in our laboratory and has been f o u n d easy to handle. The chemotaxis assays were usually done in triplicate and the results were expressed as the median distance traveled by the leading
257 front cells. In this w a y we avoided the error introduced by extreme results occasionally obtained in a single chamber. Obviously the best w a y to obtain reliable data would be to perform all experiments of neutrophil migration in many filters simultaneously, since any extreme and conceivably 'false' results would be easily identified as shown in Fig. 3. However, this would considerably limit the number of experiments that could be performed on a single day. Thus a balance b e t w e e n confidence and practicality must be reached. When determinations are done with a limited number o f filters for each experiment, the median values are less influenced b y outliers than the mean values. For determinations done in triplicate filters the risk for falsely high or low values caused b y outliers was estimated to be only a b o u t 0.2% provided the results were expressed as median values, compared with a risk of almost 10% if the mean values were used. The corresponding figure for analysis of 5 filters would, according to the model, be smaller. Thus to routinely express the results as the median value rather than the mean appears preferable. It should, however, be pointed o u t that when the median value is influenced by outliers, the resulting error is greater than when mean values are used. From a practical point o f view, occasional (0.2%) large errors are usually easily recognized and thus o f less consequence than more c o m m o n l y obtained (10%) 'moderate' errors seen with the mean values. No exact proportions o f outliers in the migrations assays can of course be given since this is influenced b y many factors in various laboratories and b y the definition o f outliers. However, even very careful standardization of methods does not eliminate the risk of occasional extreme results. Depending on the t y p e of study and the desired precision the minimum number o f filters can be calculated in the individual laboratories performing the tests. Possible explanations for occasional outliers include heterogeneity of individual filters and technical errors, e.g., in counting cells, filling chambers or when determining the distance traveled b y leading front cells. Other errors, e.g., those caused b y cleaning and handling chemotactic chambers, are minimized b y the use o f disposable lower chambers and the use o f an inert stainless steel plate upper chamber. Another advantage of a technical nature is the possibility of running up to 40 individual chambers simultaneously in one assembly. The weight o f the steel block and the elasticity of the microtube brims produces a tight connection between upper and lower chambers and filter, minimizing leakage. In our experience this modified Boyden chamber assembly is useful for various investigations of cell migration. REFERENCES
Addison, J.E. and J.W. Babbage, 1976, J. Immunol. Methods 10, 385. Boyden, S., 1962, J. Exp. Med. 115,453. Falk, W., R.H. Goodwife, Jr. and E.J. Leonard, 1980, J. Immunol. Methods 33, 239.
Harvath, L., W. Falk and E.J. Leonard, 1980, J. Immunol. Methods 37, 39.
258 Keller, H., J.H. Wissler, B. Damerau, M.W. Hess and H. Cottier, 1980, J. Immunol. Methods 36, 41. Maroni, E.S., D.N.K. Symon and P.C. Wilkinson, 1972, J. Reprod. Fertil. 28,359. Park, B.H., 1980, Experientia 36,473. Snyderman, R. and M.C~ Pike, 1976, in: In Vitro Methods in Cell Mediated and Tumor Immunity, eds. B.R. Bloom and J.R. David (Academic Press, New York) p. 651. Swanson, M.J., 1977, J. Immunol. Methods 16,385. Wilkinson, P.C., 1974, Chemotaxis and Inflammation (Churchill-Livingstone, Edinburgh) p. 168. Zigmond, S.H. and J.G. Hirsch, 1973, J. Exp. Med. 137,187.
251
STATISTICAL ASPECTS OF CELL MOTILITY DETERMINATIONS WITH A MODIFIED CHEMOTAXIS ASSEMBLY FOR MULTIWELL FILTER ASSAYS
LARS-GORAN AXELSSON *, GORAN NILSSON ** and BENGT BJORKSTI~N ,.1 * Departments o f Biomedical Research and * * Applied Mathematics. Pharmacia AB. Uppsala. Sweden
(Received 13 February 1981, accepted 15 June 1981)
A multiple chamber assembly for determination of neutrophil migration consisting of disposable lower plastic chambers and an easily cleaned and inert upper chamber made of stainless steel was constructed and used in experimental work. Using results of chemotaxis determinations in the assembly and a statistical model, the consequences of various ways to present cell migration data are discussed. With any method for multiple measurements of chemotaxis of cells from a given sample, there are occasional extreme results ('outliers') deviating considerably from other determinations. We show that the medians of chemotaxis determinations performed in triplicate are less influenced by such outliers than the mean values. The risk of an outlier affecting the median value was in our assembly about 0.2%, compared with a 10% chance of influencing the mean value.
INTRODUCTION
In 1962, Boyden described an in vitro micropore filter technique for measuring cell migration. This represented a major improvement over previous methods for analyzing cell migration. Various modifications of the filter technique have since been described to overcome some of the technical difficulties and to improve precision and accuracy. As well as the latter, some recent modifications have addressed various technical problems, e.g., detachment from various types of filters (Harvath et al., 1980; Keller et al., 1980), handling of chambers (Maroni et al., 1972; Addison and Babbage, 1976; Snyderman and Pike, 1976; Swanson, 1977; Falk et al., 1980), and the influence of gravity (Park, 1980). In our experience some of the major problems with reproducibility arise from the fact that the Boyden chambers have to be meticulously cleaned before re-use. When the chemotactic chambers are repeatedly washed and
1 Correspondence to B. BjSrkst~n, Department of Experimental Allergy Reserach, Pharmacia AB, Box 17, S-751 03 Uppsala 1, Sweden. 0022-1759/81/0000--0000/$02.50 © 1981 Elsevier/North-Holland Biomedical Press
252 various detergents used, small cracks develop to which cells may adhere. Any remaining chemokinetic substances or detergents may also markedly influence results. To avoid these problems, we have constructed a multiple chamber assembly, consisting of a disposable lower plastic chamber and an inert, easily cleaned upper chamber made of stainless steel. However, even under carefully standardized conditions multiple tests of the same sample occasionally yield individual results differing considerably from each other. Such extreme results or 'outliers' may significantly influence the mean value of the determinations. A simple model was designed to demonstrate, from a statistical point of view, the consequences of various ways of presenting cell migration data, with particular regard to the occurrence of outliers. MATERIAL AND METHODS
Leukocyte preparation Blood from the cubital vein of healthy staff members was collected in Venoject tubes (Terumo, T o k y o , Japan) with 143 U.S.P. units sodium heparin per 10 ml blood. Dextran 500 (Pharmacia Fine Chemicals, Uppsala, Sweden) was added to give a final concentration of 1%. The erythrocytes were allowed to sediment for a b o u t 30 min in room temperature. The polymorphonuclear neutrophil (PMN) rich supernatant fluid was collected and contaminating erythrocytes were eliminated by hypotonic lysis with distilled water. After 15 sec 1.5 M NaC1 was added to restore isotonic conditions. The PMNs were then washed twice and resuspended in Gey's buffer, pH 7.2, at a concentration of 3 × 106 PMN/ml. Viability was 97% as estimated b y trypan blue exclusion. Chemotaxis assembly The assembly consists of a 100 mm × 35 mm × 250 mm support of plexiglass with 10 holes 6 mm × ~35 mm, each in 4 rows, and a stainless steel 18/8 plate (100 mm × 10 mm × 250 mm) with 40 holes corresponding to those in the plexiglass support (Fig. 1). Plastic microcentrifuge tubes, Beckman Microfuge tube, ETH 26, LKB, Stockholm, Sweden, were placed in the support. Micropore filters were placed on t o p of the tubes and secured with the stainless steel plate, which was held in place with 3 position pins and 3 screws. The position of the holes in the steel plate n o w corresponded to the tubes attached to the support. A detail of the assembly demonstrating an individual chamber is shown in Fig. 2. Chemotaxis assay The microtubes were filled either with 400 ~1 Gey's buffer to measure random migration, or with 10% activated serum in Gey's buffer to measure stimulated migration. The activated serum was obtained b y incubating
253
Fig. 1. Assembly for multiwell filter assays.
fresh pooled human serum with heat aggregated human IgG. The microtubes were covered b y filters with 3.0 pm pore size (Millipore S.A., Molsheim, France). The pre-warmed (37°C) steel plate was placed over the support and secured. The holes in the plate were filled with 200 pl of the cell suspension. The assembly was then incubated at 37°C for 60 min in humidified air with 5% CO2. After incubation, the metal plate was removed. Since the filters had a larger contact area to the steel plate than to the microtubes, they usually stuck to the plate and were easily removed. They were then fixed, stained with hematoxylin, cleared with xylene and
~'~ [~'~'~-- steelplate • filter |
!
~
tube tube support
Fig. 2. Detail of an individual chamber in the multiwell assembly.
254
m o u n t e d on glass slides (Wilkinson, 1974). Migration was estimated by the leading front method (Zigmond and Hirsch, 1973). Results were expressed as mean distance in pm for 5 fields per filter. The modified assembly was used in routine work for measuring random migration and chemotaxis. Of the migration experiments performed, 212 chemotaxis experiments were done in triplicate filters. These data were analyzed statistically. Reproducibility within single experiments was evaluated by simultaneously testing random migration and chemotactic responsiveness of cells from one donor in 20 filters. Statistical methods There is always some variation when multiple measurements of the same sample are done. Sometimes a single result is so widely separated from the others as to suggest that it is from a different population. Such extreme values are designated 'outliers'. The occurrence of outliers may seriously impair the precision of a method. It is thus important to minimize the influence of such outliers in the final presentation of the test results. To demonstrate the consequences of various ways of presenting chemotaxis data a simple statistical model was designed. In this model the correct value in the experiment was assumed to be 100 pm and the probability of obtaining that value assumed to be 0.8. Further the probability of 10% deviation
TABLE 1 Probability o f distribution o f individual results and estimates w h e n test results are given as m e a n or m e d i a n values o f 2, 3 o r 5 filters. The 'true' value was assumed to be 100.
Value
Individual result
Mean o f 2
Mean o f 3
Median o f 3
Mean o f 5
Median o f 5
90 92 93.3 94 95 96 96.7 98 100 102 103.3 104 105 106 106.7 108 110
0.1
0.01
0.001
0.028
0.00001 0.00040
0.00856
0.024 0.00645 0.16 0.05280 0.195 0.8
0.66
0.560
0.944
0.22410 0.43248 0.22410
0.98288
0.195 0.05280 0.16 0.00645 0.024 0.1
0.01
0.001
0.028
O.O0040 0.00001
0.00856
255
o f the measured value from the true value, i.e., measurements of 90 and 110 ~m, was assumed to be 0.1 for each. Deviations of 10% or more were considered outliers. With these assumptions, the distribution of estimates obtained by performing duplicate, triplicate or quintiplicate assays and presenting data as the median or the mean are shown in Table 1. It will be seen t h a t taking the median rather than the mean values gives a higher probability for presenting a result equal to 100, i.e., the true value, but also implies a slightly higher risk for an extreme deviation from 100. Moderate deviations of the mean values are c o m m o n . The proportion of outliers m a y be estimated by performing a large number of measurements on the same sample, plotting the results and decide which results are to be considered as outlying. An example of this is shown in Fig. 3. However, usually only a few replicates of a large number of different samples are done, e.g., triplicate filters from m a n y different experiments. In such cases the outliers cannot be identified from a histogram of all the observations, since t h e y are from m a n y different populations.
tO0
A
B
•
90 80 •..
70
~" ._c
3o
60
m
so
_-2O o
~to: 4O 30 20
tO
'V' -"
!
:
"U
"0.8
"0.4
-0.2
0.0
,-...., 0.8) Dea|atlees free the l e d l a n en a le|erlekefe scale rfn~ 0.2
0.4
0.6
Fig. 3. Results of two migration experiments (A and B) in which random migration (squares) and chemotaxis towards 10% activated serum (circles) were done in 20 microwells. The stippled bars to the left show median values -+ S.D. of the median. The bars to the right represent mean values -+ S.D. Fig. 4. Distribution of the deviation from the median in 212 triplicate filters in a semilogarithmic scale.
256
By constructing a histogram o f the deviations from the median for each experiment a rough estimate o f the proportion o f outliers may be obtained. The estimate is obtained by dividing the number o f outlying deviations in such histograms by the total number of observations. By this m e t h o d the true proportion of outliers will be slightly underestimated, since occasional triplicates will contain two or three outliers in the same direction. An example of this model is shown in Fig. 4. The precision of a mean value is usually given as the standard deviation. There is no similar simple relationship between the standard deviation of the median and the standard deviation o f the individual observation. To estimate the standard deviation of the median of, e.g., triplicate filters, several consecutive triplicates from the same sample m a y be used. This was done by regarding the first 18 filters in each experiment presented in Fig. 3 as 6 triplicate determinations. RESULTS
In Fig. 3 the results are shown of two experiments in which random migration and chemotaxis towards 10% activated serum were measured in 20 filters with cells from the same sample. In the chemotaxis assays migration was considerably larger into respectively 1 and 2 of the 20 filters. These 3 values were considered as outliers from the respective samples. By regarding the first 18 filters in each experiment as 6 triplicate determinations, the standard deviation o f the medians could be calculated. As shown in the figure the standard deviations of the means and o f the medians were similar in 3 o f the 4 determinations. The distribution o f the 424 deviations from the medians of the 212 chemotaxis determinations done in triplicate is shown in Fig. 4 in which the deviations of the extreme values from the medians for each triplicate are shown after logarithmic transformation (ln). If deviations below --0.4 and above +0.4 on the logarithmic scale, i.e., below 67% and above 149% of the median on a linear scale, are considered as outliers, the estimated risk of low outliers was 2.2% and o f high outliers 1.1%. Thus the risk of at least one outlier in a triplicate was about 10%. This means t h a t in 10% of the triplicates the mean values would have been influenced by an outlier. The risk t h a t the median value for the triplicates was an outlier, i.e., t h a t 2 or 3 o f the filters in a certain triplicate represented outliers in the same direction, was calculated to about 0.2% (3 X 0.02 : . 0.98 + 3 X 0.012 • 0.98 + 0.023 + 0.013). DISCUSSION
The assembly has been used for 1 year in our laboratory and has been f o u n d easy to handle. The chemotaxis assays were usually done in triplicate and the results were expressed as the median distance traveled by the leading
257 front cells. In this w a y we avoided the error introduced by extreme results occasionally obtained in a single chamber. Obviously the best w a y to obtain reliable data would be to perform all experiments of neutrophil migration in many filters simultaneously, since any extreme and conceivably 'false' results would be easily identified as shown in Fig. 3. However, this would considerably limit the number of experiments that could be performed on a single day. Thus a balance b e t w e e n confidence and practicality must be reached. When determinations are done with a limited number o f filters for each experiment, the median values are less influenced b y outliers than the mean values. For determinations done in triplicate filters the risk for falsely high or low values caused b y outliers was estimated to be only a b o u t 0.2% provided the results were expressed as median values, compared with a risk of almost 10% if the mean values were used. The corresponding figure for analysis of 5 filters would, according to the model, be smaller. Thus to routinely express the results as the median value rather than the mean appears preferable. It should, however, be pointed o u t that when the median value is influenced by outliers, the resulting error is greater than when mean values are used. From a practical point o f view, occasional (0.2%) large errors are usually easily recognized and thus o f less consequence than more c o m m o n l y obtained (10%) 'moderate' errors seen with the mean values. No exact proportions o f outliers in the migrations assays can of course be given since this is influenced b y many factors in various laboratories and b y the definition o f outliers. However, even very careful standardization of methods does not eliminate the risk of occasional extreme results. Depending on the t y p e of study and the desired precision the minimum number o f filters can be calculated in the individual laboratories performing the tests. Possible explanations for occasional outliers include heterogeneity of individual filters and technical errors, e.g., in counting cells, filling chambers or when determining the distance traveled b y leading front cells. Other errors, e.g., those caused b y cleaning and handling chemotactic chambers, are minimized b y the use o f disposable lower chambers and the use o f an inert stainless steel plate upper chamber. Another advantage of a technical nature is the possibility of running up to 40 individual chambers simultaneously in one assembly. The weight o f the steel block and the elasticity of the microtube brims produces a tight connection between upper and lower chambers and filter, minimizing leakage. In our experience this modified Boyden chamber assembly is useful for various investigations of cell migration. REFERENCES
Addison, J.E. and J.W. Babbage, 1976, J. Immunol. Methods 10, 385. Boyden, S., 1962, J. Exp. Med. 115,453. Falk, W., R.H. Goodwife, Jr. and E.J. Leonard, 1980, J. Immunol. Methods 33, 239.
Harvath, L., W. Falk and E.J. Leonard, 1980, J. Immunol. Methods 37, 39.
258 Keller, H., J.H. Wissler, B. Damerau, M.W. Hess and H. Cottier, 1980, J. Immunol. Methods 36, 41. Maroni, E.S., D.N.K. Symon and P.C. Wilkinson, 1972, J. Reprod. Fertil. 28,359. Park, B.H., 1980, Experientia 36,473. Snyderman, R. and M.C~ Pike, 1976, in: In Vitro Methods in Cell Mediated and Tumor Immunity, eds. B.R. Bloom and J.R. David (Academic Press, New York) p. 651. Swanson, M.J., 1977, J. Immunol. Methods 16,385. Wilkinson, P.C., 1974, Chemotaxis and Inflammation (Churchill-Livingstone, Edinburgh) p. 168. Zigmond, S.H. and J.G. Hirsch, 1973, J. Exp. Med. 137,187.