3D-printed micrometer-scale wireless magnetic cilia with metachronal programmability

Biological cilia play essential roles in self-propulsion, food capture, and cell transportation by performing coordinated metachronal motions. Experimental studies to emulate the biological cilia metachronal coordination are challenging at the micrometer length scale because of current limitations in fabrication methods and materials. We report on the creation of wirelessly actuated magnetic artificial cilia with biocompatibility and metachronal programmability at the micrometer length scale. Each cilium is fabricated by direct laser printing a silk fibroin hydrogel beam affixed to a hard magnetic FePt Janus microparticle. The 3D-printed cilia show stable actuation performance, high temperature resistance, and high mechanical endurance. Programmable metachronal coordination can be achieved by programming the orientation of the identically magnetized FePt Janus microparticles, which enables the generation of versatile microfluidic patterns. Our platform offers an unprecedented solution to create bioinspired microcilia for programmable microfluidic systems, biomedical engineering, and biocompatible implants.

(C) In-plane (x-y) rotation of a FePt-JMP under a rotating magnetic field B (2 mT) at 0.5 Hz. The FePt-JMP aligns its magnetization direction with the external field, resulting in in-plane rotation, which leads to its orientation.

Supplementary Note 1. Mechanics for the nonreciprocal motion and the definition of the swept area of the F-MAC
Nonreciprocal motion indicates that there is a difference in the swept area by the cilia during their two beating strokes (i.e. effective/power stroke and recovery stroke). In terms of a 2D whip-like motion, the swept area difference derives from the bending difference of the cilia during the two beating strokes. For an active cilium as shown in ref. 20, the bending difference is resulted from the encoded magnetic profile of the cilia themselves. While, in our case, the bending difference is attributed to the passive silk fibroin appendages (the so-called SF flag), which is observed experimentally and confirmed numerically (Fig 5 and Fig. S13). The mechanics underlying this difference is simply because much larger hydrodynamic drag forces exert on the SF flag during the elastic stroke than during the magnetic stroke. This is due to the much faster moving speed of the SF flag during the elastic stroke than during the magnetic stroke as observed and carefully analyzed experimentally and confirmed numerically (Fig 5 and Fig. S13). According to the drag equation , (S1) where is the hydrodynamic drag force exerted on the SF flag, is the mass density of the fluid, is the flow velocity relative to the SF flag, is the drag coefficient, and A is the reference area; a larger moving speed results in a larger hydrodynamic drag on the SF flag. And according to the cantilever beam deflection equation is the induced deflection of the SF flag, L is the height of the SF flag, E is the Young's modulus of the SF flag, and I is the area moment of inertia of cross section of the SF flag; the larger hydrodynamic drag leads to a larger bending deformation of the SF flag. In summary, a lager moving speed of the SF flag contributes to a larger bending deformation, and thus a nonreciprocal motion is induced. More detailed mathematical model of the driving forces for the nonreciprocal motion can be found in the description of the numerical simulations in the Materials and Methods section.
The swept area of a 2D whip-like motion represents the area of the ciliary trajectories projected onto the motion plane (in our case, the xy plane) during one beating cycle, which is commonly used by the cilia community (refs. 1, 2, 18, 20, 30, 62 and 66). We also employed this definition to define the swept area of our cilia. However, in our case where our F-MAC have a 3D geometry, the swept area have two components: (1) the area swept by the cilia body (the Janus particles attached with the SF beams), which is projected onto the xy plane; during one beating cycle, the swept area of elastic and magnetic strokes cancels out and no net swept area is induced; (2) the area swept by the SF appendage, i.e. the SF flag, which is projected onto both the xz and yz planes as the flag undergoes a 3D trajectory. The former induces no net swept area because of the reciprocal motion, while the latter results in a net swept area as observed experimentally and confirmed numerically.
Movie S2. Fabrication process of a cilium with a flag-shaped additional structure. Movie S10. Fluid transporting capability of a single F-MAC under a uniform rotating magnetic field of 6 mT at 5 Hz. Note that the particle tracking videos have a frame rate of 5 fps since they are extracted from the original videos (which have a frame rate of 50 fps) with a 10-frame interval to show more clearly the trajectories of the moving tracer particles.

Movie
Movie S11. F-MAC motion under a uniform rotating magnetic field of 6 mT at 100 Hz. The video shows that the beating frequency of the F-MAC is the same as the actuation frequency, meaning no stepping-out of the MAC motion.
Movie S12. Fluid transporting capability of metachronal F-MAC arrays under a uniform rotating magnetic field of 6 mT at 5 Hz. Note that the particle tracking videos have a frame rate of 5 fps since they are extracted from the original videos (which have a frame rate of 50 fps) with a 10frame interval to show more clearly the trajectories of the moving tracer particles.
Movie S13. Circulating and mixing flows generated by a circular metachronal F-MAC array under a uniform rotating magnetic field of 6 mT at 5 Hz.