Their leader, Kenta Ishimoto<\/a> of the Research Institute for Mathematical Sciences, worked with colleagues Cl\u00e9ment Moreau<\/a> and Kento Yasuda<\/a> to pin down the trick: a property they call odd elasticity, measured by a new \u201codd elastic modulus.\u201d<\/p>\n Sperm tails and physics<\/p>\n At our scale a swimmer throws water backward and glides forward in balance. Shrink the scene a thousand times and inertia vanishes, leaving syrup thick drag called low Reynolds number flow. <\/p>\n One flick of a tiny flagellum usually stalls before it starts, so the cell must wiggle in a non reciprocal pattern that never repeats in reverse.<\/p>\n Newton\u2019s equal and opposite law assumes forces act in isolated pairs without added energy. <\/p>\n But sperm<\/a> tails aren\u2019t passive springs, they\u2019re powered by molecular motors that constantly inject energy into the system. That disrupts the clean symmetry Newton envisioned.<\/p>\n What the team actually measured<\/p>\n Ishimoto\u2019s group used high speed video of human sperm and the green alga Chlamydomonas<\/a>, both of which swim with whip-like flagella. <\/p>\n They tracked the tail\u2019s position over time and mapped those shapes into a two dimensional coordinate system known as \u201cshape space.\u201d These patterns form stable loops, called limit cycles, that repeat every beat\u00a0\u00a0<\/p>\n To link movement to internal forces, the researchers created an elastic matrix for the flagellum. The off-diagonal parts of this matrix, normally ignored in passive systems, revealed long-range, non reciprocal forces within the tail. <\/p>\n These are captured in the odd elastic modulus, a measure of how the tail deforms without a mirrored pushback\u00a0\u00a0<\/p>\n Sperm tail elasticity explained<\/p>\n In sperm tails, a single localized bend sends tension through the entire tail. But instead of balancing out, these forces add energy that moves the next bend forward. The result is a traveling wave, one that moves without causing an equal push in the opposite direction\u00a0\u00a0<\/p>\n The study shows that the tail\u2019s odd elasticity directly controls the wave\u2019s speed and efficiency. This isn\u2019t just theoretical. <\/p>\n As the odd modulus increases, so does the propulsion velocity. That finding aligns with observed beat frequencies<\/a> in human sperm, which can cycle at about 20 times per second.<\/p>\n How the math changes the game<\/p>\n In classical mechanics, elastic materials deform and then recover, storing energy like springs. Odd elasticity breaks this loop. Work done in one stroke isn\u2019t recouped in the next, it drives the system forward. <\/p>\n Near the tail\u2019s steady-state motion, the team found that the standard, symmetric (even) part of the modulus essentially vanished. Only the odd part mattered\u00a0\u00a0<\/p>\n This behavior stays consistent even when randomness is added. The researchers tested what happens when the tail\u2019s beat fluctuates. Surprisingly, the sperm<\/a> still swam efficiently. That suggests that the linear odd modulus governs swimming stability in noisy or sticky environments\u00a0\u00a0<\/p>\n Algae, robots, and medicine<\/p>\n Chlamydomonas cells move with two flagella that beat in asymmetrical strokes. Even with these different mechanics, the model held. <\/p>\n That points to a shared strategy in many swimming cells: generate odd elasticity and let the non-reciprocal forces do the work\u00a0\u00a0<\/p>\n This insight could be used in soft robotics. Imagine tiny bots navigating the bloodstream or crawling through mud, not with motors, but by waving internal fibers tuned with odd modulus dynamics. The model gives a playbook for how to build them.<\/p>\n Why sperm tails matter<\/p>\n Newton\u2019s third law still works, just not in systems that continually absorb and expend energy. What sperm<\/a> demonstrate is that when you\u2019re far from equilibrium, you don\u2019t have to obey force symmetry anymore. Cells that swim, flap, or twist with internal motors all bypass this constraint\u00a0\u00a0<\/p>\n The paper also shows that you can blend fluid and solid mechanics into a single, unified theory. <\/p>\n The tail\u2019s odd elasticity doesn\u2019t just describe motion, it connects elasticity, internal energy, and hydrodynamics into one model that can apply to many other living systems\u00a0\u00a0<\/p>\n How cells tune their elasticity on the fly is still unclear. Sperm likely adjust their stiffness in response to chemical signals<\/a> during the journey to the egg. Mapping how molecular motors distribute themselves could help decode this control system.<\/p>\n Another big question is how viscosity affects swimming. Sperm can face cervical mucus thousands of times thicker than water. <\/p>\n This model hints that tuning the odd modulus helps sperm compensate for the extra drag, but measuring it in live tissue remains a challenge.<\/p>\n Nature doesn\u2019t break physical laws, it rewrites the assumptions they rely on. In the micro world, sperm swim not by brute force, but by flexing internal springs in asymmetric ways that push without pushback. And that\u2019s how they get ahead.<\/p>\n The study is published in PRX Life<\/a>.<\/p>\n \u2014\u2013<\/p>\n Like what you read? Subscribe to our newsletter<\/a> for engaging articles, exclusive content, and the latest updates.\u00a0<\/p>\n Check us out on EarthSnap<\/a>, a free app brought to you by Eric Ralls<\/a> and Earth.com.<\/p>\n \u2014\u2013<\/p>\n","protected":false},"excerpt":{"rendered":"Human sperm are famously good swimmers, yet the physics of their motion has puzzled scientists for decades. Thick…\n","protected":false},"author":3,"featured_media":145682,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25],"tags":[492,159,67,132,68],"class_list":{"0":"post-145681","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-physics","9":"tag-science","10":"tag-united-states","11":"tag-unitedstates","12":"tag-us"},"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@us\/115028408574523882","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts\/145681","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/comments?post=145681"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts\/145681\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/media\/145682"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/media?parent=145681"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/categories?post=145681"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/tags?post=145681"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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