Significance of Poisson distribution theory in analysing the interaction between human spermatozoa and zona-free hamster oocytes

Abstract

Summary. The value of Poisson distribution theory in describing and predicting the nature of sperm\p=n-\egg interaction in vitro has been investigated using an interspecific i n\ x=r eq-\ vitro fertilization system, incorporating zona-free hamster oocytes and human spermatozoa. The frequency distribution of polyspermic oocyte penetrations in 72 experiments exhibited good agreement with the Poisson distribution at all levels of fertilization, indicating that each oocyte must be of equal penetrability and that there can be no block to polyspermy in this interspecific system. Poisson distribution theory also accurately described the relationship between oocyte penetration and sperm motility in 50 out of 54 separate experiments spread across 10 serial dilution curves. For each dilution series the shape of the fitted curve was fixed but its location along the x\ x=r eq-\ axis varied from donor to donor. The fixed nature of the relationship between sperm motility and egg penetration enables the results of such in-vitro fertilization experiments to be corrected for the number of motile spermatozoa in the incubation media. On the basis of these findings a protocol is described for assessing the results of the zona-free hamster oocyte penetration assay, which involves analysis of the degree of polyspermy followed by the application of Poisson distribution theory to correct the results to a standard concentration of motile spermatozoa. Changes in the penetrating ability of human spermatozoa after vasectomy and characterization of the degree of inter-ejaculate variation in penetrating potential are two clinical examples of such analyses given in the text. The statistical methods described in this paper should also be of general relevance to the study of fertilization mechanisms, in providing a rationale by which to analyse the quantitative nature of sperm\p=n-\egg interaction in vitro.

Application of Poisson distribution theory to the zona-free hamster oocyte penetration test to assess sperm function of men with asthenozoospermia

“…Furthermore, analysis of the in-vitro penetration data using the Poisson model described by Aitken & Elton (1984) has emphasized that the impaired penetration rates observed with these asthenozoospermic patients is not simply a consequence of the reduced numbers of motile sperm¬ atozoa because when the results were corrected to a constant concentration of motile cells, there were still differences between the asthenozoospermic patients and the normal fertile controls. Although no assessments of the quality of sperm movement were made in this study we have previously shown that the movement characteristics exhibited by human spermatozoa have little impact on the aspects of sperm function measured by the penetration test (Aitken et al, 1983a(Aitken et al, , 1985.…”

“…Our previous study (Aitken & Elton, 1984) ( -rm) where r = the ratio of the theoretical concentration of motile spermatozoa to the observed concentration in the assay. In the present study this formula was used to correct each result obtained with the hamster oocyte assay to that which would have been observed at a fixed motile sperm concentration of 5 106/ml.…”

“…A statistical procedure for making these assessments has been devised using maximum likelihood methods (Fisher, 1963), the full details of which will be reported separately. In essence, the procedure recog¬ nizes that within any group of patients the value of varies from individual to individual and even between repeated samples from the same individual (Aitken & Elton, 1984 (Winer, 1971) which gives a variety of positively skewed shapes and has two parameters characterizing the mean value and standard deviation. These can be estimated by maximum likelihood methods and different groups can be compared using 2 tests with two degrees of freedom to test for significant differences in these parameters.…”

“…We have described the significance of Poisson distribution theory in analysing the quantitative interaction between zona-free hamster oocytes and human spermatozoa (Aitken & Elton, 1984). One of the consequences of this relationship was that equations could be constructed for correcting the outcome of the penetration test for differences in the concentration of motile spermatozoa in the incubation medium.…”

Significance of intracellular calcium and cyclic adenosine 3',5'-monophosphate in the mechanisms by which prostaglandins influence human sperm function

“…The assay was performed using a total sperm concentration of 10 106 spermatozoa/ml and the results were subsequently adjusted for a standard concentration of 5 106 motile spermatozoa/ml. This correction was based upon the formula described by Aitken & Elton (1984) + was assessed by monitoring the fluorescence signal emitted by the Ca2+ chelating agent, Quin-2, as described by Tsien, Pozzan & Rink (1982). The spermatozoa were washed 3 times with Medium BWW, and finally resuspended at a total sperm concentration of 20 106/ml.…”