Collective dynamics of sperm cells

Abstract

While only a single sperm may fertilize the egg, getting to the egg can be facilitated, and possibly enhanced, by sperm group dynamics. Examples range from the trains formed by wood mouse sperm to the bundles exhibited by echidna sperm. In addition, observations of wave-like patterns exhibited by ram semen are used to score prospective sample fertility for artificial insemination in agriculture. In this review, we discuss these experimental observations of collective dynamics, as well as describe recent mechanistic models that link the motion of individual sperm cells and their flagella to observed collective dynamics. Establishing this link in models involves negotiating the disparate time- and length scales involved, typically separated by a factor of 1000, to capture the dynamics at the greatest length scales affected by mechanisms at the shortest time scales. Finally, we provide some outlook on the subject, in particular, the open questions regarding how collective dynamics impacts fertility. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Keywords: biological fluid dynamics; collective dynamics; sperm motility.

Figure 1.

Schematic illustration depicting a mammalian sperm cell. Shown are the head and main components of the flagellum: connecting piece, mid-piece, principal piece and end piece. Also shown are the variations in the internal flagellar structure along the flagellum’s length. In particular, the mitochondrial sheath in the mid-piece, outer dense fibres in the mid- and principal pieces, and the fibrous sheath in the principal piece are shown. Present throughout most of the flagellum is the 9+2 axoneme comprised of 9 outer microtubule doublets, or pairs (dMT) and 2 single microtubles that make the central pair (CP). The end piece contains an arrangement of single microtubles (sMT). This figure is reproduced under Creative Commons BY-NC-ND 4.0, as well as with permission from the authors of [19].

Figure 2.

(a) Image of massal motility in ram semen. The scale bar is 200 μm. Reprinted figure with permission from [61] Copyright (2015) by the American Physical Society. (b) Image from simulations showing the clustering exhibited by synchronized sperm cells. This image is reproduced from [47] under Creative Commons BY 4.0. (c) Image from simulations showing the wave-like patterns that emerge when flagellar undulations change stochastically. This image is reproduced from [47] under Creative Commons BY 4.0.

Figure 3.

(a) Electronmicrograph showing the aggregates formed by deer mouse (P. maniculatus) sperm. This image is reproduced from [70] under Creative Commons BY 4.0. (b) Image showing fused opossum sperm. This image is reproduced from [71] under Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. (c) Echidna sperm bundle reproduced from [17] (Copyright (2007) by The University of Chicago). C, cement substance; Sp, sperm cells. The white scale bar is 10 μm.

Figure 4.

Simulated bundles from [82] of 10 flagella with (a) weak (forces only) and (b) strong (forces and aligning torques) connections at their apical ends. The bundles are shown at the times indicated, where T is the period of flagellar undulation. The bundle with strong connections readily moves along a straight path. (Online version in colour.)

Figure 5.

Images from a single simulation [82] of a strongly connected (spring forces and aligning torques) bundle of flagella that had its connections severed after 30 undulation periods. (a) After removing the connections, the group splits in two smaller groups. The bundles are shown at the times indicated, where T is the period of flagellar undulation. (b) At longer times, the larger group continues to split, while pairs continue to swim together. Here, the flagella are shown every 30 T. (Online version in colour.)