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  1. Free, publicly-accessible full text available April 1, 2023
  2. YAP/TAZ is a master regulator of mechanotransduction whose functions rely on translocation from the cytoplasm to the nucleus in response to diverse physical cues. Substrate stiffness, substrate dimensionality, and cell shape are all input signals for YAP/TAZ, and through this pathway, regulate critical cellular functions and tissue homeostasis. Yet, the relative contributions of each biophysical signal and the mechanisms by which they synergistically regulate YAP/TAZ in realistic tissue microenvironments that provide multiplexed input signals remain unclear. For example, in simple two-dimensional culture, YAP/TAZ nuclear localization correlates strongly with substrate stiffness, while in three-dimensional (3D) environments, YAP/TAZ translocation can increase withmore »stiffness, decrease with stiffness, or remain unchanged. Here, we develop a spatial model of YAP/TAZ translocation to enable quantitative analysis of the relationships between substrate stiffness, substrate dimensionality, and cell shape. Our model couples cytosolic stiffness to nuclear mechanics to replicate existing experimental trends, and extends beyond current data to predict that increasing substrate activation area through changes in culture dimensionality, while conserving cell volume, forces distinct shape changes that result in nonlinear effect on YAP/TAZ nuclear localization. Moreover, differences in substrate activation area versus total membrane area can account for counterintuitive trends in YAP/TAZ nuclear localization in 3D culture. Based on this multiscale investigation of the different system features of YAP/TAZ nuclear translocation, we predict that how a cell reads its environment is a complex information transfer function of multiple mechanical and biochemical factors. These predictions reveal a few design principles of cellular and tissue engineering for YAP/TAZ mechanotransduction.

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  3. Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of the membrane. Experiments have shown that lipid flow in the plane of the membrane is closely coupled with the diffusion of proteins. Thus, there is a need for a comprehensive framework that accounts for the interplay between these processes. Here, we present a theory for the coupled in-plane viscous flow of lipids, diffusion of transmembrane proteins and elastic deformation of lipid bilayers. Themore »proteins in the membrane are modelled such that they influence membrane bending by inducing a spontaneous curvature. We formulate the free energy of the membrane with a Helfrich-like curvature elastic energy density function modified to account for the chemical potential energy of proteins. We derive the conservation laws and equations of motion for this system. Finally, we present results from dimensional analysis and numerical simulations and demonstrate the effect of coupled transport processes in governing the dynamics of membrane bending and protein diffusion.« less
  4. Membrane bending is a ubiquitous cellular process that is required for membrane traffic, cell motility, organelle biogenesis, and cell division. Proteins that bind to membranes using specific structural features, such as wedge-like amphipathic helices and crescent-shaped scaffolds, are thought to be the primary drivers of membrane bending. However, many membrane-binding proteins have substantial regions of intrinsic disorder which lack a stable three-dimensional structure. Interestingly, many of these disordered domains have recently been found to form networks stabilized by weak, multivalent contacts, leading to assembly of protein liquid phases on membrane surfaces. Here we ask how membrane-associated protein liquids impact membranemore »curvature. We find that protein phase separation on the surfaces of synthetic and cell-derived membrane vesicles creates a substantial compressive stress in the plane of the membrane. This stress drives the membrane to bend inward, creating protein-lined membrane tubules. A simple mechanical model of this process accurately predicts the experimentally measured relationship between the rigidity of the membrane and the diameter of the membrane tubules. Discovery of this mechanism, which may be relevant to a broad range of cellular protrusions, illustrates that membrane remodeling is not exclusive to structured scaffolds but can also be driven by the rapidly emerging class of liquid-like protein networks that assemble at membranes.

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  5. Jędrzejewska-Szmek, Joanna (Ed.)
  6. Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein–protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work, here, we focus on the role of explicit aggregation of proteins on themore »surface of the membrane in the presence of membrane bending and diffusion. We develop a comprehensive framework that includes lipid flow, membrane bending, the entropy of protein distribution, along with an explicit aggregation potential and derive the governing equations for the coupled system. We compare this framework to the Cahn–Hillard formalism to predict the regimes in which the proteins form patterns on the membrane. We demonstrate the utility of this model using numerical simulations to predict how aggregation and diffusion, when coupled with curvature generation, can alter the landscape of membrane–protein interactions.« less
  7. In the highly dynamic metabolic landscape of a neuron, mitochondrial membrane architectures can provide critical insight into the unique energy balance of the cell. Current theoretical calculations of functional outputs like ATP and heat often represent mitochondria as idealized geometries and therefore can miscalculate the metabolic fluxes. To analyze mitochondrial morphology in neurons of mouse cerebellum neuropil, 3D tracings of complete synaptic and axonal mitochondria were constructed using a database of serial TEM tomographyimages and converted to watertight meshes with minimal distortion of the original microscopy volumes with agranularity of 1.6 nanometer isotropic voxels. The resulting in silico representations weremore »subsequently quantified by differential geometry methods in terms of the mean and Gaussian curvatures, surface areas, volumes, and membrane motifs, all of which can alter the metabolic output of the organelle. Finally, we identify structural motifs that are present across this population of mitochondria; observations which may contribute to future modeling studies of mitochondrial physiology and metabolism in neurons.« less
  8. Abstract

    Membrane nanotubes are dynamic structures that may connect cells over long distances. Nanotubes are typically thin cylindrical tubes, but they may occasionally have a beaded architecture along the tube. In this paper, we study the role of membrane mechanics in governing the architecture of these tubes and show that the formation of bead-like structures along the nanotubes can result from local heterogeneities in the membrane either due to protein aggregation or due to membrane composition. We present numerical results that predict how membrane properties, protein density, and local tension compete to create a phase space that governs the morphologymore »of a nanotube. We also find that there exists a discontinuity in the energy that impedes two beads from fusing. These results suggest that the membrane-protein interaction, membrane composition, and membrane tension closely govern the tube radius, number of beads, and the bead morphology.

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