The role of cell size and shape in controlling local intracellular signaling reactions, and how this spatial information originates and is propagated, is not well understood. We have used partial differential equations to model the flow of spatial information from the beta-adrenergic receptor to MAPK1,2 through the cAMP/PKA/B-Raf/MAPK1,2 network in neurons using real geometries. The numerical simulations indicated that cell shape controls the dynamics of local biochemical activity of signal-modulated negative regulators, such as phosphodiesterases and protein phosphatases within regulatory loops to determine the size of microdomains of activated signaling components. The model prediction that negative regulators control the flow of spatial information to downstream components was verified experimentally in rat hippocampal slices. These results suggest a mechanism by which cellular geometry, the presence of regulatory loops with negative regulators, and key reaction rates all together control spatial information transfer and microdomain characteristics within cells.

SUMMARY Shape is an indicator of cell health. But how is the information in shape decoded? We hypothesize that decoding occurs by modulation of signaling through changes in plasma membrane curvature. Using analytical approaches and numerical simulations, we studied how elongation of cell shape affects plasma membrane signaling. Mathematical analyses reveal transient accumulation of activated receptors at regions of higher curvature with increasing cell eccentricity. This distribution of activated receptors is periodic, following the Mathieu function, and it arises from local imbalance between reaction and diffusion of soluble ligands and receptors in the plane of the membrane. Numerical simulations show that transient microdomains of activated receptors amplify signals to downstream protein kinases. For growth factor receptor pathways, increasing cell eccentricity elevates the levels of activated cytoplasmic Src and nuclear MAPK1,2. These predictions were experimentally validated by changing cellular eccentricity, showing that shape is a locus of retrievable information storage in cells.

Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation, and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this article, we show that the partial differential equations arising from classical elastic model of lipid membranes, which account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, cannot be solved for nonaxisymmetric geometries using straightforward numerical techniques; instead, a viscous-elastic formulation is necessary to fully describe the system. Therefore, we develop a viscous-elastic model for inhomogeneous membranes of the Helfrich type. Using the newly available viscous-elastic model, we find that the lipids flow to accommodate changes in membrane curvature during protein adsorption. We show that, at the end of protein adsorption process, the system sustains a residual local tension to balance the difference between the actual mean curvature and the imposed spontaneous curvature. We also show that this change in membrane tension can have a functional impact such as altered response to pulling forces in the presence of proteins.

The theory of intra-surface viscous flow on lipid bilayers is developed by combining the equations for flow on a curved surface with those that describe the elastic resistance of the bilayer to flexure. The model is derived directly from balance laws and augments an alternative formulation based on a variational principle. Conditions holding along an edge of the membrane are emphasized and the coupling between flow and membrane shape is simulated numerically.

A critical step in cellular-trafficking pathways is the budding of membranes by protein coats, which recent experiments have demonstrated can be inhibited by elevated membrane tension. The robustness of processes like clathrin-mediated endocytosis (CME) across a diverse range of organisms and mechanical environments suggests that the protein machinery in this process has evolved to take advantage of some set of physical design principles to ensure robust vesiculation against opposing forces like membrane tension. Using a theoretical model for membrane mechanics and membrane protein interaction, we have systematically investigated the influence of membrane rigidity, curvature induced by the protein coat, area covered by the protein coat, membrane tension, and force from actin polymerization on bud formation. Under low tension, the membrane smoothly evolves from a flat to budded morphology as the coat area or spontaneous curvature increases, whereas the membrane remains essentially flat at high tensions. At intermediate, physiologically relevant, tensions, the membrane undergoes a "snap-through instability" in which small changes in the coat area, spontaneous curvature or membrane tension cause the membrane to "snap" from an open, U-shape to a closed bud. This instability can be smoothed out by increasing the bending rigidity of the coat, allowing for successful budding at higher membrane tensions. Additionally, applied force from actin polymerization can bypass the instability by inducing a smooth transition from an open to a closed bud. Finally, a combination of increased coat rigidity and force from actin polymerization enables robust vesiculation even at high membrane tensions. membrane tension | clathrin-mediated endocytosis | membrane modeling C lathrin-mediated endocytosis (CME), an essential cellular process in eukaryotes, is an archetypal example of a membrane-deformation process that takes as input multiple variables, such as membrane bending, tension, protein-induced spontaneous curvature, and actin-mediated forces, and generates vesicular morphologies as its output (1). Although more than 60 different protein species act in a coordinated manner during CME (2), we can distill this process into a series of mechanochemical events where a feedback between the biochemistry of the protein machinery and the mechanics of the plasma membrane and the actin cytoskeleton control endocytic patch topology and morphology (3, 4).In Fig. 1, we outline the main steps that lead to bud formation. Despite the complexity of CME, a variety of experimental approaches have served to identify the governing principles of bud formation in CME. We have identified a few key features from recent experiments that govern bud formation and have summarized the main results below.i) Protein-induced spontaneous curvature: a critical step in CME is the assembly of a multicomponent protein coat that clusters cargo and bends the membrane into a budded morphology. Clathrin assembles into a lattice-like cage on the membrane with the assistance...

Giant lipid vesicles are closed compartments consisting of semi-permeable shells, which isolate femto- to pico-liter quantities of aqueous core from the bulk. Although water permeates readily across vesicular walls, passive permeation of solutes is hindered. In this study, we show that, when subject to a hypotonic bath, giant vesicles consisting of phase separating lipid mixtures undergo osmotic relaxation exhibiting damped oscillations in phase behavior, which is synchronized with swell–burst lytic cycles: in the swelled state, osmotic pressure and elevated membrane tension due to the influx of water promote domain formation. During bursting, solute leakage through transient pores relaxes the pressure and tension, replacing the domain texture by a uniform one. This isothermal phase transition—resulting from a well-coordinated sequence of mechanochemical events—suggests a complex emergent behavior allowing synthetic vesicles produced from simple components, namely, water, osmolytes, and lipids to sense and regulate their micro-environment.DOI: http://dx.doi.org/10.7554/eLife.03695.001

A critical step in cellular-trafficking pathways is the budding of membranes by protein coats, which recent experiments have demonstrated can be inhibited by elevated membrane tension. The robustness of processes like clathrin-mediated endocytosis (CME) across a diverse range of organisms and mechanical environments suggests that the protein machinery in this process has evolved to take advantage of some set of physical design principles to ensure robust vesiculation against opposing forces like membrane tension. Using a theoretical model for membrane mechanics and membrane protein interaction, we have systematically investigated the influence of membrane rigidity, curvature induced by the protein coat, area covered by the protein coat, membrane tension, and force from actin polymerization on bud formation. Under low tension, the membrane smoothly evolves from a flat to budded morphology as the coat area or spontaneous curvature increases, whereas the membrane remains essentially flat at high tensions. At intermediate, physiologically relevant, tensions, the membrane undergoes a "snap-through instability" in which small changes in the coat area, spontaneous curvature or membrane tension cause the membrane to "snap" from an open, U-shape to a closed bud. This instability can be smoothed out by increasing the bending rigidity of the coat, allowing for successful budding at higher membrane tensions. Additionally, applied force from actin polymerization can bypass the instability by inducing a smooth transition from an open to a closed bud. Finally, a combination of increased coat rigidity and force from actin polymerization enables robust vesiculation even at high membrane tensions. membrane tension | clathrin-mediated endocytosis | membrane modeling C lathrin-mediated endocytosis (CME), an essential cellular process in eukaryotes, is an archetypal example of a membrane-deformation process that takes as input multiple variables, such as membrane bending, tension, protein-induced spontaneous curvature, and actin-mediated forces, and generates vesicular morphologies as its output (1). Although more than 60 different protein species act in a coordinated manner during CME (2), we can distill this process into a series of mechanochemical events where a feedback between the biochemistry of the protein machinery and the mechanics of the plasma membrane and the actin cytoskeleton control endocytic patch topology and morphology (3, 4).In Fig. 1, we outline the main steps that lead to bud formation. Despite the complexity of CME, a variety of experimental approaches have served to identify the governing principles of bud formation in CME. We have identified a few key features from recent experiments that govern bud formation and have summarized the main results below.i) Protein-induced spontaneous curvature: a critical step in CME is the assembly of a multicomponent protein coat that clusters cargo and bends the membrane into a budded morphology. Clathrin assembles into a lattice-like cage on the membrane with the assistance...

The 2019 novel coronavirus, SARS-CoV-2, is an emerging pathogen of critical significance to international public health. Knowledge of the interplay between molecular-scale virus-receptor interactions, single-cell viral replication, intracellular-scale viral transport, and emergent tissue-scale viral propagation is limited. Moreover, little is known about immune system-virus-tissue interactions and how these can result in low-level (asymptomatic) infections in some cases and acute respiratory distress syndrome (ARDS) in others, particularly with respect to presentation in different age groups or pre-existing inflammatory risk factors like diabetes. A critical question for treatment and protection is why it appears that the severity of infection may correlate with the initial level of virus exposure. Given the nonlinear interactions within and among each of these processes, multiscale simulation models can shed light on the emergent dynamics that lead to divergent outcomes, identify actionable "choke points" for pharmacologic interactions, screen potential therapies, and identify potential biomarkers that differentiate response dynamics. Given the complexity of the problem and the acute need for an actionable model to guide therapy discovery and optimization, we introduce a prototype of a multiscale model of SARS-CoV-2 dynamics in lung and intestinal tissue that will be iteratively refined. The first prototype model was built and shared internationally as open source code and interactive, cloud-hosted executables in under 12 hours. In a sustained community effort, this model will integrate data and expertise across virology, immunology, mathematical biology, quantitative systems physiology, cloud and high performance computing, and other domains to accelerate our response to this critical threat to international health.