{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T13:53:55Z","timestamp":1770818035981,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T00:00:00Z","timestamp":1747612800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Eunice Kennedy Shriver National Institute of Child Health and Human Development","award":["R01HD110170"],"award-info":[{"award-number":["R01HD110170"]}]},{"name":"Thomas Harriot College of Arts and Sciences at East Carolina University and the East Carolina University Research and Economic Development Office","award":["R01HD110170"],"award-info":[{"award-number":["R01HD110170"]}]},{"name":"Fulbright Scholar-In-Residence Program, sponsored by the U.S. Department of State","award":["R01HD110170"],"award-info":[{"award-number":["R01HD110170"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Mammalian fertilization depends on sperm successfully navigating a spatially and chemically complex microenvironment in the female reproductive tract. This process is often conceptualized as a competitive race, but is better understood as a collective random search. Sperm within an ejaculate exhibit a diverse distribution of motility patterns, with some moving in relatively straight lines and others following tightly turning trajectories. Here, we present a two-state random walk model in which sperm switch from high-persistence-length to low-persistence-length motility modes. In reproductive biology, such a switch is often recognized as \u201chyperactivation\u201d. We study a circularly symmetric setup with sperm emerging at the center and searching a finite-area disk. We explore the implications of switching on search efficiency. The first proposed model describes an adaptive search strategy in which sperm achieve improved spatial coverage without cell-to-cell or environment-to-cell communication. The second model that we study adds a small amount of environment-to-cell communication. The models resemble macroscopic search-and-rescue tactics, but without organization or networked communication. Our findings provide a quantitative framework linking sperm motility patterns to efficient search strategies, offering insights into sperm physiology and the stochastic search dynamics of self-propelled particles.<\/jats:p>","DOI":"10.3390\/e27050539","type":"journal-article","created":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T11:54:26Z","timestamp":1747655666000},"page":"539","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Two-State Random Walk Model of Sperm Search on Confined Domains"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1987-3138","authenticated-orcid":false,"given":"Martin","family":"Bier","sequence":"first","affiliation":[{"name":"Department of Physics, East Carolina University, Greenville, NC 27858, USA"}]},{"given":"Maciej","family":"Majka","sequence":"additional","affiliation":[{"name":"Department of Physics, East Carolina University, Greenville, NC 27858, USA"}]},{"given":"Cameron","family":"Schmidt","sequence":"additional","affiliation":[{"name":"Department of Biology, East Carolina University, Greenville, NC 27858, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.cub.2013.02.007","article-title":"Rheotaxis guides mammalian sperm","volume":"23","author":"Miki","year":"2013","journal-title":"Curr. 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