Discrete dynamic model of the mammalian sperm acrosome reaction: the influence of acrosomal pH and biochemical heterogeneity

The acrosome reaction (AR) is an exocytotic process essential for mammalian fertilization. It involves diverse biochemical and physiological changes that culminate in the release of the acrosomal content to the extracellular medium as well as a reorganization of the plasma membrane (PM) that allows sperm to interact and fuse with the egg. In spite of many efforts, there are still important pending questions regarding the molecular mechanism regulating the AR. Particularly, the contribution of acrosomal alkalinization to AR triggering in physiological conditions is not well understood. Also, the dependence of the proportion of sperm capable of undergoing AR on the biochemical heterogeneity within a sperm population has not been studied. Here we present a discrete mathematical model for the human sperm AR, based on the biophysical and biochemical interactions among some of the main components of this complex exocytotic process. We show that this model can qualitatively reproduce diverse experimental results, and that it can be used to analyze how acrosomal pH (pHa) and cell heterogeneity regulate AR. Our results confirm that pHa increase can on its own trigger AR in a subpopulation of sperm, and furthermore, it indicates that this is a necessary step to trigger acrosomal exocytosis through progesterone, a known physiological inducer of AR. Most importantly, we show that the proportion of sperm undergoing AR is directly related to the detailed structure of the population biochemical heterogeneity.