SPERM SWIMMING THEORY STANDS THE TEST OF TIME

Abstract

When sperm cells are released, they have a simple objective: find the egg and do it fast. Benjamin Friedrich is a physicist who is fascinated by the relationship between the sperm's beating flagellum and the path it takes. ‘How you get from the beat of the tail to the swimming path is pure physics of hydrodynamic forces,’ says Friedrich. Friedrich explains that James Gray and G. J. Hancock proposed a theory of sperm motility, known as resistive force theory, which could predict a sperm's speed in The Journal of Experimental Biology in 1955. However, no one had successfully tested the theory by comparing it with an extensive data set and there had been some debate about the reliability of Gray's simple approach. Working with Frank Jülicher at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, Friedrich realised that he and his collaborators, biologists Ingmar Riedel-Kruse and Jonathon Howard, were collecting the ideal data on sperm swimming to test the 50-year-old theory (p. 1226).Filming bull sperm swimming in circles at 250 frames s−1 through a phase contrast microscope, Riedel-Kruse accurately measured the position of the beating flagellum and sperm head within less than 1 μm. ‘Of course this cannot be done accurately by hand,’ explains Friedrich, so Riedel-Kruse developed accurate computer algorithms to determine the position of the flagellum.With 1 million datapoints for the flagellum's position in hand, it was time for Friedrich to begin testing the theory. Knowing the position of the flagellum and its instantaneous speed, Friedrich plugged these values into Gray and Hancock's theory to calculate the way in which the sperm head wiggled as it moved along its circular path. Amazingly, Friedrich's calculations agreed remarkably well with the movies: his calculated sperm movements were identical to the sperm's movements in the movies.Having used the theory to calculate the sperm's trajectory, Friedrich was also able to calculate a key parameter in Gray and Hancock's equations called the drag anisotropy ratio. According to Friedrich, whenever we move we push against something solid, like the earth, but sperm swimming in fluids have nothing solid to push against, so they have to rely on an imbalance between the friction forces that the flagellum experiences as it moves sideways and forward. The ratio of the two friction coefficients is the drag anisotropy factor and it must be greater than 1 for the sperm to move forward. Comparing his calculations with the movies of swimming sperm, Friedrich found that the perpendicular friction coefficient is 80% higher than the parallel friction coefficient, giving him a drag anisotropy factor of 1.8. Using this value, he was then able to calculate the radius of curvature of the sperm's circular path and found that it agreed perfectly with the movies. Gray and Hancock's theory had stood the test of time remarkably well.Friedrich says, ‘It is exciting that we can use physics to better understand biological questions. Of course sometimes physicists are ignorant of the nice details of a study and there can be clashes between the two cultures, but it is well worth the joint efforts of biologists and physicists to find out how biological phenomena work.’