Rigid-Body Rotation Versus Transverse Bending Wave Swimming of Magnetically-Functionalized Sperm Cells

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 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 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.

I. INTRODUCTION

There is an increasing need for wireless autonomous microrobots that can perform important tasks such as sensing, diagnosis [1], [2], locomotion, actuation [3], and localized drug delivery [4]. A challenge with these active systems is the bulk fabrication of stimuli-responsive biocompatible materials at the micro scale; loading with concentrated doses of drugs and swimming efficiently at low Reynolds number (Re) hydrodynamics. One solution for the fabrication of such systems is a biohybrid approach, in which synthetic and biological components are self-assembled through electrostatic interactions into biohybrid microrobots with novel properties. In this framework, motile or immotile cells are integrated with inorganic components, that are developed by synthesis or microfabrication. Propulsive thrust can be directly produced by motile organisms [5] or by external magnetic fields [6]. In these biohybrid active systems, the inorganic component can provide additional functions (e.g., magnetic moment for wireless actuation [6], photothermal therapy [7], and contrast agents for noninvasive localization [8], [9]) that cannot be incorporated to the organisms through genetic engineering. The use of immotile organisms as elements for the propagation of mechanical waves makes the biohybrid microrobots less sensitive to chemical and biological conditions (e.g., pH, nutritional levels, temperature, lifetime of the cells) in the environment. Although maximum robustness to biological conditions can be obtained from the integration of immotile cells and inorganic components (Fig. 1(a)), the variation between the produced samples is significant, in terms of geometry, elasticity [10], and magnetization [11], for two key reasons. First, there is a variation of stiffness of the flagella influenced by the level of adenosine triphosphate (ATP), Mg, and other molecular levels inside the cell [17]. This leads to an intrinsic variation of bending stiffness. Second, the membrane composition affects the surface charge, thereby changing the particle-membrane electrostatic interactions. Particularly, in spermatozoa, the membrane charge varies with the maturation state of the cell. This property leads to a variation of particle load on the flagella, also influencing the stiffness of the biohybrid microrobot. The cell membrane potential shows a significant difference between samples, leading to sporadically attached nanoparticles along the flagellum (Fig. 1(b)).