Microfabricated tissue gauges to measure and manipulate forces from 3D microtissues

Physical forces generated by cells drive morphologic changes during development and can feedback to regulate cellular phenotypes. Because these phenomena typically occur within a 3-dimensional (3D) matrix in vivo, we used microelectromechanical systems (MEMS) technology to generate arrays of microtissues consisting of cells encapsulated within 3D micropatterned matrices. Microcantilevers were used to simultaneously constrain the remodeling of a collagen gel and to report forces generated during this process. By concurrently measuring forces and observing matrix remodeling at cellular length scales, we report an initial correlation and later decoupling between cellular contractile forces and changes in tissue morphology. Independently varying the mechanical stiffness of the cantilevers and collagen matrix revealed that cellular forces increased with boundary or matrix rigidity whereas levels of cytoskeletal and extracellular matrix (ECM) proteins correlated with levels of mechanical stress. By mapping these relationships between cellular and matrix mechanics, cellular forces, and protein expression onto a bio-chemo-mechanical model of microtissue contractility, we demonstrate how intratissue gradients of mechanical stress can emerge from collective cellular contractility and finally, how such gradients can be used to engineer protein composition and organization within a 3D tissue. Together, these findings highlight a complex and dynamic relationship between cellular forces, ECM remodeling, and cellular phenotype and describe a system to study and apply this relationship within engineered 3D microtissues.

Swimming direction reversal of flagella through ciliary motion of mastigonemes.

Bio-inspired designs can provide an answer to engineering problems such as swimming strategies at the micron or nano-scale. Scientists are now designing artificial micro-swimmers that can mimic flagella-powered swimming of micro-organisms. In an application such as lab-on-a-chip in which micro-object manipulation in small flow geometries could be achieved by micro-swimmers, control of the swimming direction becomes an important aspect for retrieval and control of the micro-swimmer. A bio-inspired approach for swimming direction reversal (a flagellum bearing mastigonemes) can be used to design such a system and is being explored in the present work. We analyze the system using a computational framework in which the equations of solid mechanics and fluid dynamics are solved simultaneously. The fluid dynamics of Stokes flow is represented by a 2D Stokeslets approach while the solid mechanics behavior is realized using Euler-Bernoulli beam elements. The working principle of a flagellum bearing mastigonemes can be broken up into two parts: (1) the contribution of the base flagellum and (2) the contribution of mastigonemes, which act like cilia. These contributions are counteractive, and the net motion (velocity and direction) is a superposition of the two. In the present work, we also perform a dimensional analysis to understand the underlying physics associated with the system parameters such as the height of the mastigonemes, the number of mastigonemes, the flagellar wave length and amplitude, the flagellum length, and mastigonemes rigidity. Our results provide fundamental physical insight on the swimming of a flagellum with mastigonemes, and it provides guidelines for the design of artificial flagellar systems.

A coordination-based approach to elasticity of floppy and stiff random networks

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network $\delta z$; a floppy network has $\delta z<0$, while a stiff network has $\delta z>0$. Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of non-affine displacements, and the network stiffening as a function of $\delta z$, derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks.

Optimal displacement mechanisms beneath shallow foundations on linear-elastic perfectly plastic soil

An energy method for a linear-elastic perfectly plastic method utilising the von Mises yield criterion with associated flow developed in 2013 by McMahon and co-workers is used to compare the ellipsoidal cavity-expansion mechanism, from the same work, and the displacement fields of other research by Levin, in 1995, and Osman and Bolton, in 2005, which utilise the Hill and Prandtl mechanisms respectively. The energy method was also used with a mechanism produced by performing a linear-elastic finite-element analysis in Abaqus. At small values of settlement and soil rigidity the elastic mechanism provides the lowest upper-bound solution, and matches well with finite-element analysis results published in the literature. At typical footing working loads and settlements the cavity-expansion mechanism produces a more optimal solution than the displacement fields within the Hill and Prandtl mechanisms, and also matches well with the published finite-element analysis results in this range. Beyond these loads, at greater footing settlements, or soil rigidity, the Prandtl mechanism is shown to be the most appropriate.