Mammalian Sperm Motility: Observation and Theory

Mammalian spermatozoa motility is a subject of growing importance because of rising human infertility and the possibility of improving animal breeding. We highlight opportunities for fluid and continuum dynamics to provide novel insights concerning the mechanics of these specialized cells, especially during their remarkable journey to the egg. The biological structure of the motile sperm appendage, the flagellum, is described and placed in the context of the mechanics underlying the migration of mammalian sperm through the numerous environments of the female reproductive tract. This process demands certain specific changes to flagellar movement and motility for which further mechanical insight would be valuable, although this requires improved modeling capabilities, particularly to increase our understanding of sperm progression in vivo. We summarize current theoretical studies, highlighting the synergistic combination of imaging and theory in exploring sperm motility, and discuss the challenges for future observational and theoretical studies in understanding the underlying mechanics.\ud Acronyms and Definitions\ud Acrosome: the cap of the sperm head containing enzymes allowing penetration of the zona pellucida via the acrosome reaction\ud Adenosine triphosphate (ATP): the currency unit of chemical energy transfer in living cells\ud Axoneme: a phylogenetically conserved structure within the eukaryotic flagellum consisting of a ring of nine microtubule doublets and a central pair, frequently referred to as 9 + 2\ud Bending moment density: the moment per unit length associated with flagellar bending; it can be divided into a hydrodynamic moment, an elastic moment (from the flagellar bending stiffness), an active moment (generated by dyneins exerting forces between adjacent microtubule doublets), and a passive moment resisting shear\ud Capacitation: the physiological state of a sperm required for fertilization, which is accompanied by the motility patterns associated with hyperactivation, characterized in saline by high-amplitude asymmetric beating\ud Central pair: a pair of microtubules along the length of the axoneme, symmetrically and slightly offset from the axoneme centerline\ud Cumulus oophorus: the outer vestment of the mammalian egg consisting of hundreds of cells radiating out from the egg embedded within a non-Newtonian hyaluronic acid gel\ud Dynein: a molecular motor within the axoneme, attached between adjacent microtubule doublets, that exerts a shearing force to induce axonemal bending\ud Flagellum: a motile cellular appendage that drives the swimming of sperm and other cells; this article focuses on the eukaryotic flagellum\ud Microtubule doublet: a pair of proteinaceous filament structures running the length of the axoneme; dyneins drive their bending, which induces flagellar motion\ud Mid-piece: the region of a sperm flagellum with a mitochondrial sheath, where ATP is generated\ud Oocyte: the egg\ud Outer dense fibers and fibrous sheath: accessory structures reinforcing the mammalian sperm flagellum; the combined axoneme and accessory structures are referred to as 9+9+2\ud Resistive-force theory: an approximation for the local drag of a slender filament element in Stokes flow (or a viscoelastic generalization thereof)\ud Rheotaxis: directed motility in response to the influence of fluid flow\ud Shear: in the context of the flagellum, the relative movement of adjacent microtubule doublets\ud Slender-body theory: an improved approximation for the local drag on a slender filament element in Stokes flow (or a viscoelastic generalization thereof)\ud Zona pellucida: a tough glycoprotein coat between the human egg and the cumulus oophorus, which a sperm must penetrate for successful fertilizatio

Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration

Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum–fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape—no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems

Calculations of the Local Density of States for some Simple Systems

A recently proposed convolution technique for the calculation of local density of states is described more thouroughly and new results of its application are presented. For separable systems the exposed method allows to construct the ldos for a higher dimensionality out of lower dimensional parts. Some practical and theoretical aspects of this approach are also discussed.Comment: 5 pages, 3 figure

Intergalactic HeII absorption towards QSO 1157+3143

We report the discovery of a further line of sight allowing detection of HeII Ly alpha absorption by the intergalactic medium. A HST/STIS survey of 32 bright z ~ 3 quasars selected from the Hamburg Quasar Surveys yielded one detection toward QSO 1157+3143 (z ~ 3, B ~ 17). A 10 orbit follow-up spectrum reveals a UV spectrum significantly supressed by two intervening Lyman limit systems at z=2.77 and 2.94, but with the continuum flux recovering sufficiently shortward of ~ 1700 A to allow study of the HeII absorption spectrum in the redshift range 2.75 < z < 2.97. The absorption is characterized by alternating voids and dense filament structures seen in both HeII and HI. Attempts to model the HeII opacity in terms of HI Ly alpha forest absorption are not successful in the voids, suggesting that HeII reionization is not complete between z=2.77 and 2.97 or that an optically thin Lyman limit system with z ~ 0.3 is responsible for the additional opacity.Comment: 6 pages, 4 figures, accepted by A&

EVALUATION OF PREHOSPITAL BLOOD PRODUCTS TO ATTENUATE ACUTE COAGULOPATHY OF TRAUMA IN A MODEL OF SEVERE INJURY AND SHOCK IN ANESTHETIZED PIGS

This material is licensed under the terms of the Open Government Licence except where otherwise statedUK Ministry of Defence

R.A.Fisher, design theory, and the Indian connection

Design Theory, a branch of mathematics, was born out of the experimental statistics research of the population geneticist R. A. Fisher and of Indian mathematical statisticians in the 1930s. The field combines elements of combinatorics, finite projective geometries, Latin squares, and a variety of further mathematical structures, brought together in surprising ways. This essay will present these structures and ideas as well as how the field came together, in itself an interesting story.Comment: 11 pages, 3 figure

Inclusive quasi-elastic electron-nucleus scattering

This article presents a review of the field of inclusive quasi-elastic electron-nucleus scattering. It discusses the approach used to measure the data and includes a compilation of data available in numerical form. The theoretical approaches used to interpret the data are presented. A number of results obtained from the comparison between experiment and calculation are then reviewed. The analogies and differences to other fields of physics exploiting quasi-elastic scattering from composite systems are pointed out.Comment: Accepted for publication in Reviews of Modern Physic

Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions

We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of non-interacting fermions, and apply it to harmonically confined systems of up to N=1000 fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calculation of the density of single-particle states from Green's functions in the energy domain. In contrast to the Thomas-Fermi (local density) approximation, the exact profiles under harmonic confinement show negative local pressure in the tails and a prominent shell structure which may become accessible to observation in magnetically trapped gases of fermionic alkali atoms.Comment: 8 pages, 3 figures, accepted for publication in Phys. Rev. Let