migration, migration inhibition, phagocytosis assays
The description of the movement of cells has two basic techniques, one using a micropore filter and the other, the "under agarose" method. Descriptions of these methods can be found in Maderazo and Ward, 1986. The basic quantities involve describing the movement (chemotaxis), chemoattraction, chemokinesis, and the inhibition of these quantities. The work in this area is by nature computational as even the parameters of movement and the nature (randomness or purposeful) needs to be described in some way. The following papers deal with the many different approaches to these related problems: Fenton and Taylor, 1975; De Halleux and Deckus, 1975; Watanuki and Haga, 1977; Weese et al., 1978; McDaniel et al., 1978; Moss et al., 1979; Turner, 1979; Axelsson, et al., 1981; Repo et al., 1981; Lauffenburger and Zigmond, 1981; Fordham et al., 1982; Hamblin et al., 1982; Rhodes, 1982; Stickle et al., 1984; Minkin, et al., 1985; Pedersen, et al., 1988; Buettner et al.,1989; Jensen and Kharazmi, 1991 (using image analysis); Haddox et al., 1991; Azzara, et al., 1992; and Haddox et al., 1994. Assays of phagocytosis of many of these same cells is described in MacFarlane and Herzberg, 1984 and Saad et al., 1985.
Limiting dilution assays date from early bacteriology in the late 19th century, when a source material was diluted until either 1 or no bacteria were present. It was used as a method of purification of a bacterial sample. In immunology, this class of assays can be used in a very quantitative way, both to quantify the frequency of particular cell types in a sample and to identify the number of different cells responsible for an observed event. Analysis of the results is generally assumed to follow Poisson statistics, and that approach is standardized through the analysis of graphs on semilogarithmic paper. A monograph on the subject is Lefkovits and Waldmann, 1979, and many reviews, such as Fazekas de St. Groth, 1982, are readily available.
When many small aliquots of cells are drawn from the same source, and there is a rare cell type in that source. The number of the rare cells in the wells will follow a Poisson distribution (which approximates a binomial distribution in this case). In that way, the expected number of aliquots containing 0, 1, 2, and more cells of the rare type is known, and depends on the frequency of this rare type. From the Poisson distribution, the fraction of aliquots with n of the rare cells should be approximately
where is the average number of rare cells per aliquot. Put into microwells, the probability that an aliquot contains no rare cells (is "unresponsive" in most assays) at each dilution is
.With each dilution this average number of rare cells in the cultures is reduced. Taking the natural (base e) logarithm of the expression for P(0), we find that
(10)
As a result, the negative logarithm of the fraction of nonresponsive wells is an estimate for at each dilution. Also, as a dilution should not change the fraction of rare to other cells in the well, just reduce the overall number of cells, the average number of rare cells per well should be
(11)
or
) is proportional to the number of cells in a dilution. This is illustrated in Figure 9.
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