Magnetic nanoparticles can be electrostatically assembled around sperm cells to form biohybrid micro robots. These biohybrid microrobots possess sufficient magnetic material to potentially allow for pulse-echo localization and wireless actuation. Alternatively, magnetic excitation of these nanoparticles can be used for localization based on Faraday's law of induction using a detection coil. Here, we investigate the influence of the electrostatic attraction between positively charged nanoparticles and negatively charged sperm cells on the activation of the nanoparticles during nonlinear differential magnetometry and wireless magnetic actuation. Activation of clusters of free nanoparticles and nanoparticles bound to the body of sperm cells is achieved by a combination of a high- frequency alternating field and a pulsating static field. The nonlinear response in both cases indicates that constraining the nanoparticles is likely to yield significant decreases in the magnetometry sensitivity. While the attachment of particles to the cells enables wireless actuation (rolling locomotion), the rate of change of the magnetization of the nanoparticles decreases one order of magnitude compared to free nanoparticles

Cell membrane potential affects the electrostatic self-assembly of magnetizable nanoparticles around the flagellum of sperm cells, leading to the formation of biohybrid microrobots (i.e., IRONSperm) with various bending stiffness. Here we explain the influence of bull sperm cell membrane potential on the formation of two types of IRONSperm samples that are produced by electrostatic self-assembly. The first type is a proximal-coated soft body with nanoparticles concentrated on the head to maintain high flexibility of the flagellum and create a passively propagating transverse bending wave under the influence of an external rotating magnetic field. The second type is a rigid-body with nanoparticles approximately uniformly distributed along the length to provide arbitrary geometry that maintains a constant chiral shape and propel by rotation about its long axis. We present a magneto-elastohydrodynamic model to predict the swimming speed at low Reynolds number for rigid IRONSperm with arbitrary shapes, and show that decreasing the bending stiffness allows the model to capture the behavior of its soft counterpart. While the response of a rigid chiral IRONSperm is distinguished by a greater swimming speed with a smooth decay with frequency, the benefit of a soft flagellum in certain scenarios would present a much smaller range of frequencies for wireless actuation.