Shape mode analysis exposes movement patterns in biology: flagella and flatworms as case studies

We illustrate shape mode analysis as a simple, yet powerful technique to concisely describe complex biological shapes and their dynamics. We characterize undulatory bending waves of beating flagella and reconstruct a limit cycle of flagellar oscillations, paying particular attention to the periodicity of angular data. As a second example, we analyze non-convex boundary outlines of gliding flatworms, which allows us to expose stereotypic body postures that can be related to two different locomotion mechanisms. Further, shape mode analysis based on principal component analysis allows to discriminate different flatworm species, despite large motion-associated shape variability. Thus, complex shape dynamics is characterized by a small number of shape scores that change in time. We present this method using descriptive examples, explaining abstract mathematics in a graphic way.Comment: 20 pages, 6 figures, accepted for publication in PLoS On

Ciliary contact interactions dominate surface scattering of swimming eukaryotes

Interactions between swimming cells and surfaces are essential to many microbiological processes, from bacterial biofilm formation to human fertilization. However, in spite of their fundamental importance, relatively little is known about the physical mechanisms that govern the scattering of flagellated or ciliated cells from solid surfaces. A more detailed understanding of these interactions promises not only new biological insights into structure and dynamics of flagella and cilia, but may also lead to new microfluidic techniques for controlling cell motility and microbial locomotion, with potential applications ranging from diagnostic tools to therapeutic protein synthesis and photosynthetic biofuel production. Due to fundamental differences in physiology and swimming strategies, it is an open question whether microfluidic transport and rectification schemes that have recently been demonstrated for pusher-type microswimmers such as bacteria and sperm cells, can be transferred to puller-type algae and other motile eukaryotes, as it is not known whether long-range hydrodynamic or short-range mechanical forces dominate the surface interactions of these microorganisms. Here, using high-speed microscopic imaging, we present direct experimental evidence that the surface scattering of both mammalian sperm cells and unicellular green algae is primarily governed by direct ciliary contact interactions. Building on this insight, we predict and verify experimentally the existence of optimal microfluidic ratchets that maximize rectification of initially uniform Chlamydomonas reinhardtii suspensions. Since mechano-elastic properties of cilia are conserved across eukaryotic species, we expect that our results apply to a wide range of swimming microorganisms.Comment: Preprint as accepted for publication in PNAS, for published journal version (open access) and Supporting Information see http://dx.doi.org/10.1073/pnas.121054811

Swimming by spinning: spinning-top type rotations regularize sperm swimming into persistently symmetric paths in 3D

Sperm modulate their flagellar symmetry to navigate through complex physico-chemical environments and achieve reproductive function. Yet it remains elusive how sperm swim forwards despite the inherent asymmetry of several components that constitutes the flagellar engine. Despite the critical importance of symmetry, or the lack of it, on sperm navigation and its physiological state, there is no methodology to date that can robustly detect the symmetry state of the beat in free-swimming sperm in 3D.How does symmetric progressive swimming emerge even for asymmetric beating, and how can beating (a)symmetry be inferred experimentally? Here, we numerically resolve the fluid mechanics of swimming around asymmetrically beating spermatozoa. This reveals that sperm spinning critically regularizes swimming into persistently symmetric paths in 3D, allowing sperm to swim forwards despite any imperfections on the beat. The sperm orientation in three-dimensions, and not the swimming path, can inform the symmetry state of the beat, eliminating the need of tracking the flagellum in 3D. We report a surprising correspondence between the movement of sperm and spinning-top experiments, indicating that the flagellum drives ''spinning-top'' type rotations during sperm swimming, and that this parallel is not a mere analogy. These results may prove essential in future studies on the role of (a)symmetry in spinning and swimming microorganisms and micro-robots, as body orientation detection has been vastly overlooked in favour of swimming path detection. Altogether, sperm rotation may provide a foolproof mechanism for forward propulsion and navigation in nature that would otherwise not be possible for flagella with broken symmetry

A dynamic basal complex modulates mammalian sperm movement

Centrioles are ancient organelles with a conserved architecture and their rigidity is thought to restrict microtubule sliding. Here authors show that, in mammalian sperm, the atypical distal centriole and its surrounding atypical pericentriolar matrix form a dynamic basal complex that facilitates a cascade of internal sliding deformations, coupling tail beating with asymmetric head kinking

Unlocking the Secrets of Multi-Flagellated Propulsion

In this work, unique high-speed imaging platforms and an array of theoretical analysis methods are used to thoroughly investigate eukaryotic multi-flagellated propulsion using Tritrichomonas foetus as a test case. Through experimental observations through our imaging system with superior resolution and capture rate exceeding that of previous studies, it was discovered for the first time that the T. foetus employs a strategy similar to that of the “run and tumble” strategies found in bacteria and Chlamydomonas; it has two distinct flagellar beating patterns that result in two different body swimming motions, linear and turning swimming. These two flagella patterns were then analyzed for the first time using two theoretical analysis methods that are often used to analyze uni-flagellated organisms; the Resistive Force Theory (RFT) and the Regularized Stokeslet Method (RSM). These theories were compared to uncover the more accurate method. Results showed that our modified-RFT model out-performed the RSM model. Due to these results, the quantitative analysis of the motion of each flagellum for both the swimming motions were carried out using the RFT method for the first time on a multi-flagellated cell, in both the 2-D and 3-D case. Digital Holographic Microscopy was used to produce the 3-D trajectory of the T.foetus for the first time. Through this method it was possible to for the first time, quantitatively analyze the thrust and energy contributions of each flagella in each direction. We find out that the turning motion dissipates approximately half as much energy as the linear swimming motion which leads to the belief that the motion is more energy efficient. The energy results coupled with the thrust results show the highly coordinated nature of multi-flagellated propulsion. Through this RFT model, it was observed that the propulsive force of the T.foetus is comparable to that of other eukaryotes with varying numbers of flagella like the sperm and Chlamydomonas, suggesting that higher thrust generation is not necessarily the goal of multi-flagellated propulsion, but these strategies result in greater maneuverability or sensing. Results from this study may serve as inspiration for biorobots due to the organism’s ideal size and finely controlled multi-flagellated propulsion

Physics of Microswimmers - Single Particle Motion and Collective Behavior

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.Comment: 54 pages, 59 figures, review article, Reports of Progress in Physics (to appear