Bacteria-inspired Robotic Propulsion from Bundling of Soft Helical Filaments at Low Reynolds Number

The bundling of flagella is known to create a "run" phase, where the bacteria moves in a nearly straight line rather than making changes in direction. Historically, mechanical explanations for the bundling phenomenon intrigued many researchers, and significant advances were made in physical models and experimental methods. Contributing to the field of research, we present a bacteria-inspired centimeter-scale soft robotic hardware platform and a computational framework for a physically plausible simulation model of the multi-flagellated robot under low Reynolds number (~0.1). The fluid-structure interaction simulation couples the Discrete Elastic Rods algorithm with the method of Regularized Stokeslet Segments. Contact between two flagella is handled by a penalty-based method. We present a comparison between our experimental and simulation results and verify that the simulation tool can capture the essential physics of this problem. Preliminary findings on robustness to buckling provided by the bundling phenomenon and the efficiency of a multi-flagellated soft robot are compared with the single-flagellated counterparts. Observations were made on the coupling between geometry and elasticity, which manifests itself in the propulsion of the robot by nonlinear dependency on the rotational speed of the flagella.Comment: Supplementary Video: https://youtu.be/qevN1NovCZ

How Sperm Beat and Swim: From Filament Deformation to Activity

Understanding the dynamics of microbiological swimmers is a key element on the way to discovering biological mechanisms, to develop new sophisticated bio-mimetic technologies, e.g., artificial microswimmers, and to design novel microfluidic devices, e.g., for diagnosis applications. In this work, we focus on the dynamics of microswimmers with a slender flexible body, for which the spermatozoon is one of the best biological representatives. The overarching theme of our investigation is the relation between elasticity and dynamics of semiflexible filaments, their hydrodynamic interactions and active motion. We first study the dynamics of one, two and three sedimenting filaments in a viscous fluid. The dynamics of a settling filament is simpler than that of the beating flagellum because it is dominated only by the passive elastic restoring force. It allows a fundamental understanding of the dynamics generated by the competition of elastic and hydrodynamic forces. At the same time, the settling dynamics is of technological importance as it may suggest, e.g., new purification techniques. We find that the settling plane of an isolated semi-flexible filament is not always stable. When the external field is strong enough, the system encounters two (subsequent) dynamical transitions that break the planarity and chirality of the filament shape. New stationary settling shapes are found that correspond to drift and helical trajectories. Investigations with more filaments show that the settling dynamics may be much more rich than expected already at fields generated by modern centrifuges. Sperm cells are composed of a mostly spherical head and a whip-like appendage called flagellum. The flagellum has an oscillatory movement that sustains a traveling wave from the head to the tail. The motion of the flagellum provides the thrust needed to propel the spermatozoon and generates a complex flow field. As an essential step toward understanding the hydrodynamic cooperation between spermatozoa, we analyze high-speed experimental recording of pinned human sperm (in collaboration with researchers at the research center CAESAR, Bonn) and develop a minimal model of realistic beating. We infer the flagellum internal forces and, in the future, the generated flow field. It turns out that the model needs not to be complex and not to explicitly account for the observed left-right asymmetries in the rotational motion around the pinning point. The simulation closely reproduces the flagellum tracks recorded by high-speed video-microscopy, and the appropriate parameters are, thus, estimated directly from the experimental recordings. This is a new approach to extract also forces from the observed data in addition to the kinematics, as done by other established techniques. The inspection of high-speed recording of human spermatozoa also leads us to suggest a novel mechanism to control the swimming direction of spermatozoa via higher harmonic components of the beating frequency. The proposed mechanisms explain the usual circular trajectories by a shape anisotropy, a curved flagellum or a bent midpiece. Although it may look puzzling at first that higher beating frequency break a spatial symmetry, we show that a simple model can explain the observed behavior and match simulations with experiments. The beating pattern is not due to a predefined sinusoidal pacemaker, as used in the previous model. Instead, it is believed that the molecular motors distributed along the flagellum reach a self-organized state that generates the required force-pattern. Different models have been proposed to explain how the beating pattern is generated by a feedback system between molecular forces and flagellum shapes; however, explicit simulations lead to unexpected buckling instabilities. Thus, we present a simple mathematical (and later computational) model that is not bounded to a specific biomechanical hypothesis on the traits of the molecular motors. The resulting model highlights the difference between different feedback responses that couple the axoneme shape to the molecular motors forces. Among the possible models, we choose the model with the smoothest and the most regular behavior as we expect that, because of the variability of the biological environment and of the resilience of spermatozoa in the most disparate conditions, any representative model of active beating should not display ill-defined behaviors. The model is applied to the fascinating and contemporary investigation of the active response of the beating pattern to controlled perturbations. By numerical integration of the model, we quantify how the beating pattern (amplitude, frequency and wave vector) is affected by the medium viscosity and we show that it is possible to entrain the beating frequency to an external periodic force as generated in experimental setup or by other, surrounding, spermatozoa. This top-down approach provides a simple reference model that allows both investigation of small scale details and investigation of large cooperative assemblies of swimmers