Reviewing mathematical models of sperm signaling networks.

Dave Garbers' work significantly contributed to our understanding of sperm's regulated motility, capacitation, and the acrosome reaction. These key sperm functions involve complex multistep signaling pathways engaging numerous finely orchestrated elements. Despite significant progress, many parameters and interactions among these elements remain elusive. Mathematical modeling emerges as a potent tool to study sperm physiology, providing a framework to integrate experimental results and capture functional dynamics considering biochemical, biophysical, and cellular elements. Depending on research objectives, different modeling strategies, broadly categorized into continuous and discrete approaches, reveal valuable insights into cell function. These models allow the exploration of hypotheses regarding molecules, conditions, and pathways, whenever they become challenging to evaluate experimentally. This review presents an overview of current theoretical and experimental efforts to understand sperm motility regulation, capacitation, and the acrosome reaction. We discuss the strengths and weaknesses of different modeling strategies and highlight key findings and unresolved questions. Notable discoveries include the importance of specific ion channels, the role of intracellular molecular heterogeneity in capacitation and the acrosome reaction, and the impact of pH changes on acrosomal exocytosis. Ultimately, this review underscores the crucial importance of mathematical frameworks in advancing our understanding of sperm physiology and guiding future experimental investigations.