Analysis of chemotaxis when the fraction of responsive cells is small--application to mammalian sperm guidance.

The detection of chemotaxis-related changes in the swimming behavior of mammalian spermatozoa in a spatial chemoattractant gradient has hitherto been an intractable problem. The difficulty is that the fraction of responsive cells in the sperm population is very small and that the large majority of the cells, though non-responsive, are motile too. Assessment of the chemotactic effects in a spatial gradient is also very sensitive to the quality of sperm tracking. To overcome these difficulties we propose a new approach, based on the analysis of the distribution of instantaneous directionality angles made by spermatozoa in a spatial gradient versus a no-gradient control. Although the use of this parameter does not allow identification of individual responding cells, it is a reliable measure of directionality, independent of errors in cell tracking caused by cell collisions, track crossings, and track splitting. The analysis identifies bias in the swimming direction of a population relative to the gradient direction. It involves statistical chi2 tests of the very large sample of measured angles, where the critical chi2 values are adjusted to the sample size by the bootstrapping procedure. The combination of the newly measured parameter and the special analysis provides a highly sensitive method for the detection of a chemotactic response, even a very small one.