Biomechanics of Neutrophil Tethers.

Leukocytes, including neutrophils, which are propelled by blood flow, can roll on inflamed endothelium using transient bonds between selectins and their ligands, and integrins and their ligands. When such receptor-ligand bonds last long enough, the leukocyte microvilli become extended and eventually form thin, 20 m long tethers. Tether formation can be observed in blood vessels in vivo and in microfluidic flow chambers. Tethers can also be extracted using micropipette aspiration, biomembrane force probe, optical trap, or atomic force microscopy approaches. Here, we review the biomechanical properties of leukocyte tethers as gleaned from such measurements and discuss the advantages and disadvantages of each approach. We also review and discuss viscoelastic models that describe the dependence of tether formation on time, force, rate of loading, and cell activation. We close by emphasizing the need to combine experimental observations with quantitative models and computer simulations to understand how tether formation is affected by membrane tension, membrane reservoir, and interactions of the membrane with the cytoskeleton.

Geometric principles of second messenger dynamics in dendritic spines.

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity.

Coherent Motion of Monolayer Sheets under Confinement and Its Pathological Implications.

Coherent angular rotation of epithelial cells is thought to contribute to many vital physiological processes including tissue morphogenesis and glandular formation. However, factors regulating this motion, and the implications of this motion if perturbed, remain incompletely understood. In the current study, we address these questions using a cell-center based model in which cells are polarized, motile, and interact with the neighboring cells via harmonic forces. We demonstrate that, a simple evolution rule in which the polarization of any cell tends to orient with its velocity vector can induce coherent motion in geometrically confined environments. In addition to recapitulating coherent rotational motion observed in experiments, our results also show the presence of radial movements and tissue behavior that can vary between solid-like and fluid-like. We show that the pattern of coherent motion is dictated by the combination of different physical parameters including number density, cell motility, system size, bulk cell stiffness and stiffness of cell-cell adhesions. We further observe that perturbations in the form of cell division can induce a reversal in the direction of motion when cell division occurs synchronously. Moreover, when the confinement is removed, we see that the existing coherent motion leads to cell scattering, with bulk cell stiffness and stiffness of cell-cell contacts dictating the invasion pattern. In summary, our study provides an in-depth understanding of the origin of coherent rotation in confined tissues, and extracts useful insights into the influence of various physical parameters on the pattern of such movements.