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Human sperm accumulation near surfaces: a simulation study

  • D. J. SMITH (a1) (a2) (a3), E. A. GAFFNEY (a3) (a4), J. R. BLAKE (a1) (a3) and J. C. KIRKMAN-BROWN (a2) (a3)

A hybrid boundary integral/slender body algorithm for modelling flagellar cell motility is presented. The algorithm uses the boundary element method to represent the ‘wedge-shaped’ head of the human sperm cell and a slender body theory representation of the flagellum. The head morphology is specified carefully due to its significant effect on the force and torque balance and hence movement of the free-swimming cell. The technique is used to investigate the mechanisms for the accumulation of human spermatozoa near surfaces. Sperm swimming in an infinite fluid, and near a plane boundary, with prescribed planar and three-dimensional flagellar waveforms are simulated. Both planar and ‘elliptical helicoid’ beating cells are predicted to accumulate at distances of approximately 8.5–22 μm from surfaces, for flagellar beating with angular wavenumber of 3π to 4π. Planar beating cells with wavenumber of approximately 2.4π or greater are predicted to accumulate at a finite distance, while cells with wavenumber of approximately 2π or less are predicted to escape from the surface, likely due to the breakdown of the stable swimming configuration. In the stable swimming trajectory the cell has a small angle of inclination away from the surface, no greater than approximately 0.5°. The trapping effect need not depend on specialized non-planar components of the flagellar beat but rather is a consequence of force and torque balance and the physical effect of the image systems in a no-slip plane boundary. The effect is relatively weak, so that a cell initially one body length from the surface and inclined at an angle of 4°–6° towards the surface will not be trapped but will rather be deflected from the surface. Cells performing rolling motility, where the flagellum sweeps out a ‘conical envelope’, are predicted to align with the surface provided that they approach with sufficiently steep angle. However simulation of cells swimming against a surface in such a configuration is not possible in the present framework. Simulated human sperm cells performing a planar beat with inclination between the beat plane and the plane-of-flattening of the head were not predicted to glide along surfaces, as has been observed in mouse sperm. Instead, cells initially with the head approximately 1.5–3 μm from the surface were predicted to turn away and escape. The simulation model was also used to examine rolling motility due to elliptical helicoid flagellar beating. The head was found to rotate by approximately 240° over one beat cycle and due to the time-varying torques associated with the flagellar beat was found to exhibit ‘looping’ as has been observed in cells swimming against coverslips.

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J. P. Armitage & R. M. Macnab 1987 Unidirectional, intermittent rotation of the flagellum of rhodobacter sphaeroides. J. Bacteriol. 169 (2), 514518.

J. M. Baltz , D. F. Katz & R. A. Cone 1988 Mechanics of sperm–egg interaction at the zona pellucida. Biophys. J. 54, 643654.

J. R. Blake 1971 A note on the image system for a stokeslet in a no slip boundary. Proc. Camb. Phil. Soc. 70, 303310.

J. R. Blake & A. T. Chwang 1974 Fundamental singularities of viscous flow. Part 1. Image systems in the vicinity of a stationary no-slip boundary. J. Engng Math. 8, 2329.

C. J. Brokaw 1972 Computer simulation of flagellar movement I. Demonstration of stable bend propagation and bend initiation by a sliding filament model. Biophys. J. 12, 564586.

C. J. Brokaw 2002 Computer simulation of flagellar movement VII. Coordination of dynein by local curvature control can generate helical bending waves. Cell Motil. Cytoskel. 53, 102124.

A. T. Chwang & T. Y. Wu 1971 A note on the helical movement of micro-organisms. Proc. R. Soc. Lond. B 178 (1052), 327346.

A. T. Chwang & T. Y. Wu 1975 Hydrodynamics of the low-Reynolds-number flows. Part 2. The singularity method for Stokes flows. J. Fluid Mech. 67, 787815.

R. J. Clarke , O. E. Jensen , J. Billingham & P. M. Williams 2006 Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender-body analysis. Proc. R. Soc. A 462, 913933.

R. Cortez 2001 The method of regularized stokeslets. SIAM J. Sci. Comput. 23 (4), 12041225.

R. Cortez , L. Fauci & A. Medovikov 2005 The method of regularized stokeslets in three dimensions: Analysis, validation and application to helical swimming. Phys. Fluids 17 (031504), 114.

J. Cosson , P. Huitorel & C. Gagnon 2003 How spermatozoa come to be confined to surfaces. Cell Motil. Cytoskel. 54, 5663.

R. G. Cox 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44, 791810.

R. H. Dillon , L. J. Fauci , C. Omoto & X. Yang 2007 Fluid dynamic models of flagellar and ciliary beating. Ann. N. Y. Acad. Sci. 1101, 494505.

R. D. Dresdner & D. F. Katz 1981 Relationships of mammalian sperm motility and morphology to hydrodynamic aspects of cell function. Biol. Reprod. 25, 920930.

R. D. Dresdner , D. F. Katz & S. A. Berger 1980 The propulsion by large amplitude waves of uniflagellar micro-organisms of finite length. J. Fluid Mech. 97, 591621.

E. Z. Drobnis , A. I. Yudin , G. N. Cherr & D. F. Katz 1988 Hamster sperm penetration of the zona pellucida: kinematic analysis and mechanical implications. Dev. Biol. 130 (1), 311323.

L. Fauci & A. McDonald 1995 Sperm motility in the presence of boundaries. Bull. Math. Biol. 57 (5), 679699.

G. R. Fulford , D. F. Katz & R. L. Powell 1998 Swimming of spermatozoa in a linear viscoelastic fluid. Biorheology 35 (4–5), 295309.

S. Gueron & K. Levit-Gurevich 2001 A three-dimensional model for ciliary motion based on the internal 9+2 structure. Proc. R. Soc. Lond. B 268, 599607.

S. Gueron & N. Liron 1992 Ciliary motion modeling, and dynamic multicilia interactions. Biophys. J. 63, 10451058.

S. Gueron & N. Liron 1993 Simulations of three-dimensional ciliary beats and cilia interactions. Biophys. J. 65, 499507.

G. J. Hancock 1953 The self-propulsion of microscopic organisms through liquids. Proc. R. Soc. B 217, 96121.

J. J. L. Higdon 1979 a A hydrodynamic analysis of flagellar propulsion. J. Fluid Mech. 90, 685711.

J. J. L. Higdon 1979 b The hydrodynamics of flagellar propulsion: helical waves. J. Fluid Mech. 94 (2), 331351.

M. Hines & J. J. Blum 1978 Bend propagation in flagella. I. Derivation of equations of motion and their simulation. Biophys. J. 23 (2), 4157.

M. Hines & J. J. Blum 1983 Three-dimensional mechanics of eukaryotic flagella. Biophys. J. 41, 6779.

S. Ishijima , S. Oshio & H. Mohri 1986 Flagellar movement of human spermatozoa. Gamete Res. 13, 185197.

R. E. Johnson 1980 An improved slender-body theory for Stokes flow. J. Fluid Mech. 99 (2), 411431.

R. E. Johnson & C. J. Brokaw 1979 A comparison between resistive-force theory and slender-body theory. Biophys. J. 25 (1), 113127.

D. F. Katz , J. R. Blake & S. L. Pavieri-Fontana 1975 On the movement of slender bodies near plane boundaries at low Reynolds number. J. Fluid Mech. 72 (3), 529540.

D. F. Katz , J. W. Overstreet , S. J. Samuels , P. W. Niswander , T. D. Bloom & E. L. Lewis 1986 Morphometric analysis of spermatozoa in the assessment of human male infertility. J. Androl. 7 (4), 203210.

M. Kinukawa , J. Ohmuro , S. A. Baba , S. Murashige , M. Okuno , M. Nagata & F. Aoki 2005 Analysis of flagellar bending in hamster spermatozoa: characterisation of an effective stroke. Biol. Reprod. 73 (6), 12691274.

E. Lauga 2007 Propulsion in a viscoelastic fluid. Phys. Fluids 19, 083104.

E. Lauga , W. R. DiLuzio , G. M. Whitesides & H. A. Stone 2006 Swimming in circles: motion of bacteria near solid boundaries. Biophys. J. 90 (2), 400412.

M. J. Lighthill 1976 Flagellar hydrodynamics. The Jon von Neumann lecture. SIAM Rev. 18 (2), 161230.

M. J. Lighthill 1996 aHelical distributions of stokeslets. J. Engng Math. 30 (1–2), 3578.

M. J. Lighthill 1996 bReinterpreting the basic theorem of flagellar hydrodynamics. J. Engng Math. 30 (1–2), 2534.

N. Liron 2001 The LGL (Lighthill–Gueron–Liron) Theorem–historical perspective and critique. Math. Methods Appl. Sci. 24, 15331540.

N. Liron & S. Mochon 1976 The discrete-cilia approach to propulsion of ciliated micro-organisms. J. Fluid Mech. 75, 593607.

K. E. Machin 1963 The control and synchronisation of flagellar movement. Proc. R. Soc. Lond. B 158 (970), 88104.

M. E. O'Neill & K. Stewartson 1967 On the slow motion of a sphere parallel to a nearby wall. J. Fluid Mech. 27, 705724.

O. Pironneau & D. F. Katz 1974 Optimal swimming of flagellated micro-organisms. J. Fluid Mech. 66, 391415.

C. Pozrikidis 2002 A Practical Guide to Boundary-Element Methods with the Software Library BEMLIB. Chapman and Hall/CRC.

M. Ramia , D. L. Tullock & N. Phan-Thien 1993 The role of hydrodynamic interaction in the locomotion of microorganisms. Biophys. J. 65, 755778.

R. Rikmenspoel 1965 The tail movement of bull spermatozoa. Observations and model calculations. Biophys. J. 5, 365392.

L. Rothschild 1963 Non-random distribution of bull spermatozoa in a drop of sperm suspension. Nature 198 (12211222).

W. B. Russel , E. J. Hinch , L. G. Leal & G. Tieffenbruck 1977 Rods falling near a vertical wall. J. Fluid Mech. 83 (2), 273287.

J. S. Shen , P. Y. Tam , W. J. Shack & T. J. Lardner 1975 Large amplitude motion of self-propelling slender filaments at low Reynolds numbers. J. Biomech. 8, 229236.

D. J. Smith , J. R. Blake & E. A. Gaffney 2008 Fluid mechanics of nodal flow due to embryonic primary cilia. J. R. Soc. Interface 5, 567573.

D. J. Smith , E. A. Gaffney & J. R. Blake 2007 Discrete cilia modelling with singularity distributions: application to the embryonic node and the airway surface liquid. Bull. Math. Biol. 69 (5), 14771510.

G. I. Taylor 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. Ser. A 209, 447461.

G. I. Taylor 1952 The action of waving cylindrical tails in propelling microscopic organisms. Proc. R. Soc. Lond. Ser. A 211 (1105), 225239.

G. G. Vernon & D. M. Woolley 1999 Three dimensional motion of avian spermatozoa. Cell Motil. Cytoskel. 42, 149161.

M. A. S. Vigeant , R. M. Ford , M. Wagner & L. K. Tamm 2002 Reversible and irreversible adhesion of motile escherichia coli cells analyzed by total internal reflection aqueous fluorescence microscopy. Appl. Environ. Microbiol. 68 (6), 27942801.

H. Winet , G. S. Bernstein & J. Head 1984 Observations on the response of human spermatozoa to gravity, boundaries and fluid shear. Reproduction 70, 511523.

D. P. Wolf , L. Blasco , M. A. Khan & M. Litt 1977 Human cervical mucus. I. Rheologic characteristics. Fertil. Steril. 28 (1), 4146.

D. M. Woolley 1977 Evidence for ‘twisted plane’ undulations in golden hamster sperm tails. J. Cell Biol. 75, 851865.

D. M. Woolley 2003 Motility of spermatozoa at surfaces. Reproduction 126, 259270.

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