Padmini Rangamani

Cell Shape and Negative Links in Regulatory Motifs Together Control Spatial Information Flow in Signaling Networks

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.

Decoding information in cell shape.

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.

Mechanisms controlling cell size and shape during isotropic cell spreading.

Cell motility is important for many developmental and physiological processes. Motility arises from interactions between physical forces at the cell surface membrane and the biochemical reactions that control the actin cytoskeleton. To computationally analyze how these factors interact, we built a three-dimensional stochastic model of the experimentally observed isotropic spreading phase of mammalian fibroblasts. The multiscale model is composed at the microscopic levels of three actin filament remodeling reactions that occur stochastically in space and time, and these reactions are regulated by the membrane forces due to membrane surface resistance (load) and bending energy. The macroscopic output of the model (isotropic spreading of the whole cell) occurs due to the movement of the leading edge, resulting solely from membrane force-constrained biochemical reactions. Numerical simulations indicate that our model qualitatively captures the experimentally observed isotropic cell-spreading behavior. The model predicts that increasing the capping protein concentration will lead to a proportional decrease in the spread radius of the cell. This prediction was experimentally confirmed with the use of Cytochalasin D, which caps growing actin filaments. Similarly, the predicted effect of actin monomer concentration was experimentally verified by using Latrunculin A. Parameter variation analyses indicate that membrane physical forces control cell shape during spreading, whereas the biochemical reactions underlying actin cytoskeleton dynamics control cell size (i.e., the rate of spreading). Thus, during cell spreading, a balance between the biochemical and biophysical properties determines the cell size and shape. These mechanistic insights can provide a format for understanding how force and chemical signals together modulate cellular regulatory networks to control cell motility.

Cell spreading as a hydrodynamic process

Many cell types have the ability to move themselves by crawling on extra-cellular matrices. Although cell motility is governed by actin and myosin filament assembly, the pattern of the movement follows the physical properties of the network ensemble average. The first step of motility, cell spreading on matrix substrates, involves a transition from round cells in suspension to polarized cells on substrates. Here we show that the spreading dynamics on 2D surfaces can be described as a hydrodynamic process. In particular, we show that the transition from isotropic spreading at early time to anisotropic spreading is reminiscent of the fingering instability observed in many spreading fluids. During cell spreading, the main driving force is the polymerization of actin filaments that push the membrane forward. From the equilibrium between the membrane force and the cytoskeleton, we derive a first order expression of the polymerization stress that reproduces the observed behavior. Our model also allows an interpretation of the effects of pharmacological agents altering the polymerization of actin. In particular we describe the influence of Cytochalasin D on the nucleation of the fingering instability.

Oscillatory phase separation in giant lipid vesicles induced by transmembrane osmotic differentials

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

Design principles for robust vesiculation in clathrin-mediated endocytosis

Significance Plasma membrane tension plays an important role in various biological processes. In particular, recent experimental studies have shown that membrane tension inhibits membrane budding processes like clathrin-mediated endocytosis. We have identified a mathematical relationship between the curvature-generating capability of the protein coat and membrane tension that can predict whether the coat alone is sufficient to produce closed buds. Additionally, we show that a combination of increased coat rigidity and applied force from actin polymerization can produce closed buds at high membrane tensions. These findings are general to any membrane-budding process, suggesting that biology has evolved to take advantage of a set of physical design principles to ensure robust vesicle formation across a range of organisms and mechanical environments. 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.

Protein-induced membrane curvature alters local membrane tension.

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.

Interaction between surface shape and intra-surface viscous flow on lipid membranes

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.

Membrane fission by protein crowding

Significance The division of membrane-bound compartments into smaller, separate volumes is essential to cells. The process of membrane fission is required for the separation of two membrane compartments. The prevailing view has been that to drive fission, proteins must contain specific structural features such as curved scaffolds and wedge-like membrane insertions. In contrast, this work demonstrates a more general mechanism, in which crowding among membrane-bound proteins drives fission. Like a compressed gas, collisions among crowded proteins generate pressure that can stretch, bend, and ultimately disrupt membrane surfaces, leading to fission. The discovery of this mechanism broadens our perspective on membrane fission by demonstrating how any protein, independent of its structure, can assist in this essential cellular process. Membrane fission, which facilitates compartmentalization of biological processes into discrete, membrane-bound volumes, is essential for cellular life. Proteins with specific structural features including constricting rings, helical scaffolds, and hydrophobic membrane insertions are thought to be the primary drivers of fission. In contrast, here we report a mechanism of fission that is independent of protein structure—steric pressure among membrane-bound proteins. In particular, random collisions among crowded proteins generate substantial pressure, which if unbalanced on the opposite membrane surface can dramatically increase membrane curvature, leading to fission. Using the endocytic protein epsin1 N-terminal homology domain (ENTH), previously thought to drive fission by hydrophobic insertion, our results show that membrane coverage correlates equally with fission regardless of the hydrophobicity of insertions. Specifically, combining FRET-based measurements of membrane coverage with multiple, independent measurements of membrane vesiculation revealed that fission became spontaneous as steric pressure increased. Further, fission efficiency remained equally potent when helices were replaced by synthetic membrane-binding motifs. These data challenge the view that hydrophobic insertions drive membrane fission, suggesting instead that the role of insertions is to anchor proteins strongly to membrane surfaces, amplifying steric pressure. In line with these conclusions, even green fluorescent protein (GFP) was able to drive fission efficiently when bound to the membrane at high coverage. Our conclusions are further strengthened by the finding that intrinsically disordered proteins, which have large hydrodynamic radii yet lack a defined structure, drove fission with substantially greater potency than smaller, structured proteins.

Signaling Network Triggers and Membrane Physical Properties Control the Actin Cytoskeleton-Driven Isotropic Phase of Cell Spreading

Cell spreading is regulated by signaling from the integrin receptors that activate intracellular signaling pathways to control actin filament regulatory proteins. We developed a hybrid model of whole-cell spreading in which we modeled the integrin signaling network as ordinary differential equations in multiple compartments, and cell spreading as a three-dimensional stochastic model. The computed activity of the signaling network, represented as time-dependent activity levels of the actin filament regulatory proteins, is used to drive the filament dynamics. We analyzed the hybrid model to understand the role of signaling during the isotropic phase of fibroblasts spreading on fibronectin-coated surfaces. Simulations showed that the isotropic phase of spreading depends on integrin signaling to initiate spreading but not to maintain the spreading dynamics. Simulations predicted that signal flow in the absence of Cdc42 or WASP would reduce the spreading rate but would not affect the shape evolution of the spreading cell. These predictions were verified experimentally. Computational analyses showed that the rate of spreading and the evolution of cell shape are largely controlled by the membrane surface load and membrane bending rigidity, and changing information flow through the integrin signaling network has little effect. Overall, the plasma membrane acts as a damper such that only ∼5% of the actin dynamics capability is needed for isotropic spreading. Thus, the biophysical properties of the plasma membrane can condense varying levels of signaling network activities into a single cohesive macroscopic cellular behavior.