Wave propagation in microtubule-based bio-nano-architected networks: A lesson from nature

Microtubules, bio-polymeric hollow tubes forming entangled radial networks from the nucleus to the cell membrane, are considered the main part of the cytoskeleton providing mechanical stiffness, organization and shape for the cytoplasm of the eukaryotic cells and playing substantial roles in some cellular processes such as mechanotransduction, cell division, intercellular transports, internal organization of the cell components, etc. In all of the mentioned functions, the network structure of the microtubules has the main responsibility proving the importance of more in-depth studies of their mechanical properties. This paper addresses the elastic wave propagation in various two-dimensional microtubule-based bio-nano-architected periodic networks to analyze their dynamic characteristics for possible further utilizations. The study starts with selecting a proper beam model for a single microtubule, as proved by previous experiments, and continues with creating ten widely used periodic structures, namely square, triangle, triangle-square, triangle-diamond, negative Poisson's ratio, semi-honeycomb, star-honeycomb, zig-zag, hexagram, and Sierpinski triangle, thereof. To obtain the dispersion curves, finite element models are developed for both individual and networked microtubules, and the phononic band structures are calculated based on Bloch's theorem. The results reveal the possibility of designing bandgaps in specific ranges for the low- and high-frequency bio-filter applications depending on the topologies of the selected unit cells as well as the considered periodicities. This application helps researchers control the ways to absorb some unwanted or hazardous vibrations using architected periodic structures and, thanks to the higher biocompatibility resulted from their biomaterial origin, the networks can be applied in next-generation nano-biomechanical instruments such as implantable biosensors.