From flagellar undulations to collective motion: predicting the dynamics of sperm suspensions

Abstract

Swimming cells and microorganisms are as diverse in their collective dynamics as they are in their individual shapes and propulsion mechanisms. Even for sperm cells, which have a stereotyped shape consisting of a cell body connected to a flexible flagellum, a wide range of collective dynamics is observed spanning from the formation of tightly packed groups to the display of larger-scale, turbulence-like motion. Using a detailed mathematical model that resolves flagellum dynamics, we perform simulations of sperm suspensions containing up to 1000 cells and explore the connection between individual and collective dynamics. We find that depending on the level of variation in individual dynamics from one swimmer to another, the sperm exhibit either a strong tendency to aggregate, or the suspension exhibits large-scale swirling. Hydrodynamic interactions govern the formation and evolution of both states. In addition, a quantitative analysis of the states reveals that the flows generated at the time scale of flagellum undulations contribute significantly to the overall energy in the surrounding fluid, highlighting the importance of resolving these flows.

Traveling concentration pulses of bacteria in a generalized Keller–Segel model

“…Collective motion of biological and artificial microswimmers shows a broad range of interesting phenomena as demonstrated in several review articles [1][2][3][4][5]. The formation of various patterns and clustering have been investigated both experimentally and theoretically in systems of bacteria [6][7][8][9][10][11][12][13], of eukaryotic cells such as Dictyostelium discoideum or human sperm [14][15][16][17][18][19][20][21][22], as well as in suspensions of active colloids [4,[23][24][25][26][27][28][29][30][31][32]. In this article we study the collective behavior of a bacterial population, which in the concentration field of a chemoattractant forms a traveling solitary pulse.…”

Pairwise hydrodynamic interactions of synchronized spermatozoa

“…Such studies range from examining the motion of individual swimmers in non-trivial background flows to their behavior in confined geometries [9][10][11][12][13][14]. However, there have been comparatively few theoretical studies that have considered the collective behaviors of multiple spermatozoa, recent examples being the large-scale numerical simulations of Schoeller and Keaveny [15], Yang et al [16], with notable additional work pertaining to swimming in two dimensions, though there remains significant scope for investigating the complex near-field interactions of swimmers in detail. The latter investigations include classical two-dimensional swimming sheet models, introduced in the classical study of Taylor [17] and used later by Fauci and McDonald [13] to study the interactions of model spermatozoa via the immersed boundary method with two-dimensional hydrodynamics.…”

Cellular geometry controls the efficiency of motile sperm aggregates

“…In a rare number of systems, sperm form cooperative groups, or aggregates [2][3][4][5]; this unique behavior is believed to improve the swimming performance of the cells involved, compared to individual cells, and therefore the chances of successful fertilization [4]. Yet, in vitro studies have shown inconsistent results [5] and the underlying physics of the associations remains elusive [6][7][8].…”