Chemically-mediated communication in self-oscillating, biomimetic cilia

Abstract

A single biological cilium can sense minute chemical variations and transmit this information to neighboring cilia to produce a global response to the local change. Herein, we undertake the first computational study of self-oscillating, artificial cilia and show that this system can ''communicate'' to undergo a biomimetic, collective response to small-scale chemical changes. The cilia are formed from chemo-responsive gels undergoing the oscillatory Belousov-Zhabotinsky (BZ) reaction. The activator for the reaction, u, is generated within these BZ cilia and diffuses between the neighboring gels. We find that the spatial arrangement of the BZ cilia affects the local distribution of u, which in turn affects the dynamic behavior of the system. Consequently, two closely spaced cilia bend away from each other and the chemo-mechanical traveling waves within the gels propagate top down. By increasing the inter-cilia spacing, we dramatically alter the behavior of the system and uncover a distinctive form of chemotaxis: the tethered gels bend towards higher concentrations of u and hence, towards each other. This chemotaxis is particularly pronounced in an array of five cilia, where we observe a ''bunching'' of the cilia towards the highest concentration in u, accompanied by the synchronization of the chemomechanical waves. We also show that the cilial oscillations can be controlled remotely and noninvasively by light. By selectively illuminating certain cilia, we could ''play'' the array like a keyboard, causing a rhythmic variation in the heights of the gels. These attributes could be exploited in a range of microfluidic applications, where the controllable communication among the BZ cilia and selfoscillating surface topology can be harnessed to transport microscopic objects within the devices.

Chemo-responsive, self-oscillating gels that undergo biomimetic communication

“…As we show below, whether it is the pulsations of a single cilium or the collective bending of multiple cilia, these filaments not only sense, but also move in response to the local gradients in u. 66 In effect, these artificial cilia mimic the ability of biological species to direct their motion along chemical concentration gradients.…”

“…66 Hence, we could capture the interplay between the pulsations of the cilia and the dispersion of u, where the motion of the cilia affects the distribution of u, which in turn affects the movement of the cilia.…”

“…In the simulations presented below, the dimensionless velocity of the gel's expansion/contraction is approximately 0.1, which corresponds to approximately v = 8 mm s À1 using the scaling provided below. 66 If hydrodynamic effects were taken into account, one would expect the characteristic velocities created in the fluid by the cilia motion to be of the same order of magnitude as this v, which in turn would correspond to a low Reynolds numbers of 66 Re B 10 À2 (assuming the viscosity of the solution equals that of water and taking the length of the cilium, 1.3 mm (see below), to be the characteristic length scale). The hydrodynamic forces acting from the fluid on the gel surface would be negligibly small due to the low ratio of viscous to elastic forces; this ratio, the relevant capillary number 86 can be estimated as 66 Ca B 6 Â 10 À11 , where the bulk modulus of the NIPAAm gel is taken to be 10 5 Pa, 87 and again the length of a cilium is taken as the characteristic length scale.…”

“…66 The details of these model modifications are given in Section 4 below, followed by the results of computer simulations on the communication among the multiple BZ gel samples that are either attached to a substrate, freely slide along a substrate, or suspended in solution. Before presenting the results of these computer simulations, we first review current experimental advance for solution-mediated communication among multiple BZ gels.…”

“…90,91 In our BZ cilium, each element acts as an oscillator, and the intrinsic frequency of this oscillator depends on the boundary values of u in the outer fluid and neighboring elements. (The intrinsic frequency 66 of a small region of the gel refers to the frequency of the oscillations that an isolated gel of the same size would exhibit if it were placed in a fluid with the same value of u.) For u top = 0.0, the fixed end of the gel has the highest intrinsic frequency and hence, the traveling waves propagate bottom-up.…”