Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes studied by the Sharma (IISc Bangalore) and Dogic (UCSB) Labs have in-plane fluid-like dynamics and out-of-plane bending elasticity, but their open edges and micron length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. First, we discuss how doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped minimal surfaces with complex edge structures. Theoretical modeling demonstrates that their formation is driven by increasing positive Gaussian modulus, which in turn is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to exotic topologically distinct structures, including shapes similar to catenoids, tri-noids, four-noids, and higher order structures. We then mathematically explore the mechanics of these catenoid-like structures subject to an external axial force and elucidate their intimate connection to two problems whose solutions date back to Euler: the shape of an area-minimizing soap film and the buckling of a slender rod under compression. A perturbation theory argument directly relates the tensions of membranes to the stability properties of minimal surfaces. We also investigate the effects of including a Gaussian curvature modulus, which, for small enough membranes, causes the axial force to diverge as the ring separation approaches its maximal value.

Alterations in sleep are hallmarks of the ageing process and emerges as risk factors for Alzheimer’s disease (AD). While the fine-tuned coalescence of sleep microstructure elements may influence age-related cognitive trajectories, its association with AD-related processes is not fully established. We investigated whether sleep arousals and the coupling of spindles and slow waves, key elements of sleep microstructure, are associated with early amyloid-beta (Aβ) brain burden, hallmark of AD neuropathology, and cognitive change at 2 years in 100 late-midlife healthy individuals. We first found that arousals interrupting sleep continuity were positively linked to Aβ burden, while, by contrast, the more prevalent arousals upholding sleep continuity were associated with lower Aβ burden and better cognition. We further found that young-like co-occurrence of spindles and slow-depolarisation slow waves is associated to lower burden of Aβ over the medial prefrontal cortex and is predictive of memory decline at 2-year follow-up. We provide empirical evidence that arousals are diverse and differently associated with early AD-related neuropathology and cognition. We further show the altered coupling of sleep microstructure elements that are key to its mnesic functions may contribute to poorer brain and cognitive trajectories. The presentation will end with preliminary data show that activity of the locus coeruleus, essential to sleep and showing some of the earliest signs of AD-related pathological processes, is associated with sleep quality. These preliminary findings are the first of a project ailed at link sleep and AD through the locus coeruleus.

The fusion of cell aggregates widely exists during biological processes such as development, tissue regeneration, and tumor invasion. Cellular spheroids (spherical cell aggregates) are commonly used to study this phenomenon. In previous studies, with approximated assumptions and measurements, researchers found that the fusion of two spheroids with some cell type is similar to the coalescence of two liquid droplets. However, with more accurate measurements focusing on the overall shape evolution in this process, we find that even in the previously-regarded liquid-like regime, the fusion process of spheroids can be very different from regular liquid coalescence. We conduct numerical simulations using both standard particulate models and vertex models with both Molecular Dynamics and Brownian Dynamics. The simulation results show that the difference between spheroids and regular liquid droplets is caused by the microscopic overdamped dynamics of each cell rather than the topological cell-cell interactions in the vertex model. Our research reveals the necessity of a new continuum theory for “liquid” with microscopically overdamped components, such as cellular and colloidal systems. Detailed analysis of our simulation results of different system sizes provides the basis for developing the new theory.