Dependence of the nerve pulse generation threshold on the ability of forming an input signal based on the Hodgkin-Huxley model]

Different methods of definition of the threshold of the action potential (AP) generation were considered. It was established that the threshold defined as a difference between the critical value of the membrane depolarization and the resting potential was practically independent of the value and duration of an input signal which was given as a stepped function. It was shown that the critical values of the membrane depolarization could be defined by the point of bend, as well as by the point of maximum of the curve curvature on the frontal part of AP.     

Membrane reshaping by protein condensates

Proteins can organize into dynamic, functionally important assemblies on fluid membrane surfaces. Phase separation has emerged as an important mechanism for forming such protein assemblies on the membrane during cell signaling, endocytosis, and cytoskeleton regulation. Protein-protein phase separation thus adds novel fluid mosaics to the classical Singer and Nicolson model. Protein condensates formed in this process can modulate membrane morphologies. This is evident from recent reports of protein condensate-driven membrane reshaping in processes such as endocytosis, autophagosome formation, and protein storage vacuole morphogenesis in plants. Lateral phase separation (on the membrane surface) of peripheral curvature coupling proteins can modulate such membrane morphological transitions. Additionally, three-dimensional protein phase separation can result in droplets that through adhesion can affect membrane shape changes. How do these condensate-driven curvature generation mechanisms contrast with the classically recognized scaffolding and amphipathic helix insertion activities of specific membrane remodeling proteins? A salient feature of these condensate-driven membrane activities is that they depend upon both macroscopic features (such as interfacial energies of the condensate, membrane, and cytosol) as well as microscopic, molecular-level interactions (such as protein-lipid binding). This review highlights the current understanding of the mechanisms underlying curvature generation by protein condensates in various biological pathways.     

Mechanism of endophilin N-BAR domain-mediated membrane curvature

Endophilin-A1 is a BAR domain-containing protein enriched at synapses and is implicated in synaptic vesicle endocytosis. It binds to dynamin and synaptojanin via a C-terminal SH3 domain. We examine the mechanism by which the BAR domain and an N-terminal amphipathic helix, which folds upon membrane binding, work as a functional unit (the N-BAR domain) to promote dimerisation and membrane curvature generation. By electron paramagnetic resonance spectroscopy, we show that this amphipathic helix is peripherally bound in the plane of the membrane, with the midpoint of insertion aligned with the phosphate level of headgroups. This places the helix in an optimal position to effect membrane curvature generation. We solved the crystal structure of rat endophilin-A1 BAR domain and examined a distinctive insert protruding from the membrane interaction face. This insert is predicted to form an additional amphipathic helix and is important for curvature generation. Its presence defines an endophilin/nadrin subclass of BAR domains. We propose that N-BAR domains function as low-affinity dimers regulating binding partner recruitment to areas of high membrane curvature.     

Regulation of Membrane-Shape Transitions Induced by I-BAR Domains

I-BAR proteins are well-known actin-cytoskeleton adaptors and have been observed to be involved in the formation of plasma membrane protrusions (filopodia). I-BAR proteins contain an all-helical, crescent-shaped IRSp53-MIM domain (IMD) dimer that is believed to be able to couple with a membrane shape. This coupling could involve the sensing and even the generation of negative plasma membrane curvature. Indeed, the in vitro studies have shown that IMDs can induce inward tubulation of liposomes. While N-BAR domains, which generate positive membrane curvature, have received a considerable amount of attention from both theory and experiments, the mechanisms of curvature coupling through IMDs are comparatively less studied and understood. Here we used a membrane-shape stability assay developed recently in our lab to quantitatively characterize IMD-induced membrane-shape transitions. We determined a membrane-shape stability diagram for IMDs that reveals how membrane tension and protein density can comodulate the generation of IMD-induced membrane protrusions. From comparison to analytical theory, we determine three key parameters that characterize the curvature coupling of IMD. We find that the curvature generation capacity of IMDs is significantly stronger compared to that of endophilin, an N-BAR protein known to be involved in plasma membrane shape transitions. Contrary to N-BAR domains, where amphipathic helix insertion is known to promote its membrane curvature generation, for IMDs we find that amphipathic helices inhibit membrane shape transitions, consistent with the inverse curvature that IMDs generate. Importantly, in both of these types of BAR domains, electrostatic interactions affect membrane-binding capacity, but do not appear to affect the curvature generation capacity of the protein. These two types of BAR domain proteins show qualitatively similar membrane shape stability diagrams, suggesting an underlying ubiquitous mechanism by which peripheral proteins regulate membrane curvature.     

A membrane bending model of outer hair cell electromotility

We propose a new mechanism for outer hair cell electromotility based on electrically induced localized changes in the curvature of the plasma membrane (flexoelectricity). Electromechanical coupling in the cell's lateral wall is modeled in terms of linear constitutive equations for a flexoelectric membrane and then extended to nonlinear coupling based on the Langevin function. The Langevin function, which describes the fraction of dipoles aligned with an applied electric field, is shown to be capable of predicting the electromotility voltage displacement function. We calculate the electrical and mechanical contributions to the force balance and show that the model is consistent with experimentally measured values for electromechanical properties. The model rationalizes several experimental observations associated with outer hair cell electromotility and provides for constant surface area of the plasma membrane. The model accounts for the isometric force generated by the cell and explains the observation that the disruption of spectrin by diamide reduces force generation in the cell. We discuss the relation of this mechanism to other proposed models of outer hair cell electromotility. Our analysis suggests that rotation of membrane dipoles and the accompanying mechanical deformation may be the molecular mechanism of electromotility.     

The novel protein kinase C isoforms -delta and -epsilon modulate caerulein-induced zymogen activation in pancreatic acinar cells

Isoforms of protein kinase C (PKC) have been shown to modulate some cellular responses such as pathological secretion and generation of inflammatory mediators during acute pancreatitis (AP). We propose that PKC also participates in premature zymogen activation within the pancreatic acinar cell, a key event in the initiation of AP. This hypothesis was examined in in vivo and cellular models of caerulein-induced AP using PKC activators and inhibitors. Phorbol ester, 12-O-tetradecanoylphorbol-13-acetate (TPA, 200 nM), a known activator of PKC, enhanced zymogen activation at both 0.1 nM and 100 nM caerulein, concentrations which mimic physiological and supraphysiological effects of the hormone cholecystokinin, respectively, in preparations of pancreatic acinar cells. Isoform-specific PKC inhibitors for PKC-delta and PKC-epsilon reduced supraphysiological caerulein-induced zymogen activation. Using a cell-free reconstitution system, we showed that inhibition of PKC-delta and -epsilon, reduced zymogen activation in both zymogen granule-enriched and microsomal fractions. In dispersed acinar cells, 100 nM caerulein stimulation caused PKC-delta and -epsilon isoform translocation to microsomal membranes using cell fractionation and immunoblot analysis. PKC translocation was confirmed with in vivo studies and immunofluorescence microscopy in pancreatic tissues from rats treated with or without 100 nM caerulein. PKC-epsilon redistributed from an apical to a supranuclear region following caerulein administration. The signal for PKC-epsilon overlapped with granule membrane protein, GRAMP-92, an endosomal/lysosomal marker, in a supranuclear region where zymogen activation takes place. These results indicate that PKC-delta and -epsilon isoforms translocate to specific acinar cell compartments and modulate zymogen activation.     

Targeting signals and subunit interactions in coated vesicle adaptor complexes

There are two clathrin-coated vesicle adaptor complexes in the cell, one associated with the plasma membrane and one associated with the TGN. The subunit composition of the plasma membrane adaptor complex is alpha-adaptin, beta-adaptin, AP50, and AP17; while that of the TGN adaptor complex is gamma-adaptin, beta'-adaptin, AP47, and AP19. To search for adaptor targeting signals, we have constructed chimeras between alpha-adaptin and gamma-adaptin within their NH2-terminal domains. We have identified stretches of sequence in the two proteins between amino acids approximately 130 and 330-350 that are essential for targeting. Immunoprecipitation reveals that this region determines whether a construct coassemblies with AP50 and AP17, or with AP47 and AP19. These observations suggest that these other subunits may play an important role in targeting. In contrast, beta- and beta'-adaptins are clearly not involved in this event. Chimeras between the alpha- and gamma-adaptin COOH-terminal domains reveal the presence of a second targeting signal. We have further investigated the interactions between the adaptor subunits using the yeast two-hybrid system. Interactions can be detected between the beta/beta'-adaptins and the alpha/gamma- adaptins, between the beta/beta'-adaptins and the AP50/AP47 subunits, between alpha-adaptin and AP17, and between gamma-adaptin and AP19. These results indicate that the adaptor subunits act in concert to target the complex to the appropriate membrane.     

Increased vesicle endocytosis due to an increase in the plasma membrane phosphatidylserine concentration.

Endocytosis vesiculation consists of local membrane invaginations, continuously generated on the plasma membrane surface of living cells. This vesiculation process was found to be activated in vivo by the generation of a transmembrane surface area asymmetry in the plasma membrane bilayer, after enhancement of transbilayer phospholipid translocation. The observed enhancement was shown to be in good quantitative agreement with a theoretical model of elastic equilibrium describing stabilization of 100-nm vesicles in response to phospholipid redistribution. Very rapid dynamic vesiculation and direct re-fusion of the vesicles, both dependent on the phospholipid translocation activity, were found on a time scale of seconds. Both vesiculation and re-fusion were shown to result in a steady-state population of internal vesicles at long time points. The plasma membrane appears to be a dynamic structure, oscillating between two distinct curvature states, the 10 microns-1 "vesicle" and the 0.1 micron-1 "plasma membrane" curvature states. This dynamic behavior is discussed in terms of an elastic control of the membranes curvature state by the phospholipid translocation activity.     

Lateral redistribution of transmembrane proteins and liquid-ordered domains in lipid membranes with inhomogeneous curvature

A number of processes in living cells are accompanied by significant changes of the geometric curvature of lipid membranes. In turn, heterogeneity of the lateral curvature can lead to spatial redistribution of membrane components, most important of which are transmembrane proteins and liquid-ordered lipid-protein domains. These components have a so-called hydrophobic mismatch: the length of the transmembrane domain of the protein, or the thickness of the bilayer of the domain differ from the thickness of the surrounding membrane. In this work we consider redistribution of membrane components with hydrophobic mismatch in membranes with non-uniform geometric curvature. Dependence of the components’ energy on the curvature is calculated in terms of theory of elasticity of liquid crystals adapted to lipid membranes. According to the calculations, transmembrane proteins prefer regions of the membrane with zero curvature. Liquid-ordered domains having a size of a few nm distribute mainly into regions of the membrane with small negative curvature appearing in the cell plasma membrane in the process of endocytosis. The distribution of domains of a large radius is determined by a decrease of their perimeter upon bending; these domains distribute into membrane regions with relatively large curvature.     

Erythrocyte shape simulation by numerical optimization

In a recent paper we examined the morphology of erythrocytes in terms of the mean mean curvature (MMC) of their cell membranes. A computer simulation of these shapes based on the different geometries showed that the MMC increased from the sphero-stomatocyte to the spheroechinocyte via the discocyte. In this work we extend this analysis by using a numerical optimization method based on importance sampling and the principle of adiabatic cooling. The erythrocyte membrane is treated as a single closed fluid lamina exhibiting viscoelastic characteristics. The energy function of the lamina includes the following terms: (i) Curvature-elastic energy terms which depend on both local and global curvature. (ii) A term describing the compression elasticity of the lamina. (iii) A term which depends on the volume of the cell and which is related to the osmotic pressure across the membrane. In the simulation the cell is assumed to have axial symmetry and it can therefore be described by a finite set of conic sections. So far we have been able to obtain an energy minimum corresponding to a discocyte shape using a sphere as the initial configuration. Our results therefore imply that the well-known sequence of erythrocyte shapes could solely be governed by the above mentioned properties of an ideal fluid forming a closed singly connected lamina.     

Reversible changes of extracellular pH during action potential generation in a higher plant Cucurbita pepo

A pH-sensitive electrode was applied to measure activity of H⁺ ions in the medium surrounding excitable cells of pumpkin (Cucurbita pepo L.) seedlings during cooling-induced generation of action potential (AP). Reversible alkalization shifts were found to occur synchronously with AP, which could be due to the influx of H⁺ ions from external medium into excitable cells. Ethacrynic acid (an anion channel blocker) reduced the AP amplitude but had no effect on the transient alkalization of the medium. An inhibitor of plasma membrane H⁺-ATPase, N,N’-dicyclohexylcarbodiimide suppressed both the AP amplitude and the extent of alkalization. In experiments with plasma membrane vesicles, the hydrolytic H⁺-ATPase activity was subjected to inhibition by Ca²⁺ concentrations in the range characteristic of cytosolic changes during AP generation. The addition of a calcium channel blocker verapamil and a chelating agent EGTA to inhibit Ca²⁺ influx from the medium eliminated the AP spike and diminished reversible alkalization of the external solution. An inhibitor of protein kinase, H-7 alleviated the inhibitory effect of Ca²⁺ on hydrolytic H⁺-ATPase activity in plasma membrane vesicles and suppressed the reversible alkalization of the medium during AP generation. The results provide evidence that the depolarization phase of AP is associated not only with activation of chloride channels and Cl^? efflux but also with temporary suppression of plasma membrane H⁺-ATPase manifested as H⁺ influx. The Ca²⁺-induced inhibition of the plasma membrane H⁺-ATPase is supposedly mediated by protein kinases.     

Nonlinear sorting, curvature generation, and crowding of endophilin N-BAR on tubular membranes

The curvature of biological membranes is controlled by membrane-bound proteins. For example, during endocytosis, the sorting of membrane components, vesicle budding, and fission from the plasma membrane are mediated by adaptor and accessory proteins. Endophilin is a peripherally binding membrane protein that functions as an endocytic accessory protein. Endophilin's membrane tubulation capacity is well known. However, to understand the thermodynamic and mechanical aspects of endophilin function, experimental measurements need to be compared to quantitative theoretical models. We present measurements of curvature sorting and curvature generation of the endophilin A1 N-BAR domain on tubular membranes pulled from giant unilamellar vesicles. At low concentration, endophilin functions primarily as a membrane curvature sensor; at high concentrations, it also generates curvature. We determine the spontaneous curvature induced by endophilin and observe sigmoidal curvature/composition coupling isotherms that saturate at high membrane tensions and protein solution concentrations. The observation of saturation is supported by a strong dependence of lateral diffusion coefficients on protein density on the tether membrane. We develop a nonlinear curvature/composition coupling model that captures our experimental observations. Our model predicts a curvature-induced phase transition among two states with varying protein density and membrane curvature. This transition could act as a switch during endocytosis.     

Lipid-Composition-Mediated Forces Can Stabilize Tubular Assemblies of I-BAR Proteins

Collective action by inverse-Bin/Amphiphysin/Rvs (I-BAR) domains drive micron-scale membrane remodeling. The macroscopic curvature sensing and generation behavior of I-BAR domains is well characterized, and computational models have suggested various mechanisms on simplified membrane systems, but there remain missing connections between the complex environment of the cell and the models proposed thus far. Here, we show a connection between the role of protein curvature and lipid clustering in the relaxation of large membrane deformations. When we include phosphatidylinositol 4,5-bisphosphate-like lipids that preferentially interact with the charged ends of an I-BAR domain, we find clustering of phosphatidylinositol 4,5-bisphosphate-like lipids that induce a directional membrane-mediated interaction between membrane-bound I-BAR domains. Lipid clusters mediate I-BAR domain interactions and cause I-BAR domain aggregates that would not arise through membrane fluctuation-based or curvature-based interactions. Inside of membrane protrusions, lipid cluster-mediated interaction draws long side-by-side aggregates together, resulting in more cylindrical protrusions as opposed to bulbous, irregularly shaped protrusions.     

Inactivation of plasmalemma conductance in alkaline zones of <Emphasis Type="Italic">Chara corallina</Emphasis> after generation of action potential

A microelectrode study with Chara corallina cells has shown that post-excitation changes of membrane potential and plasmalemma resistance, induced by the action potential (AP) generation, differ substantially for cell areas producing zones of high and low external pH. In cell regions producing alkaline zones, the AP generation was followed by post-excitation hyperpolarization by about 50 mV, concomitant with four- to eightfold increase in plasmalemma resistance and a considerable drop of pericellular pH. In the acidic areas the post-excitation hyperpolarization was weak or absent, and the membrane resistance showed no significant increase within 1–2 min after AP. The membrane excitation in the acidic zones was accompanied by a noticeable pH increase near the cell surface, indicative of the inhibition of plasma membrane H⁺ pump. The results suggest that the high local conductance of the plasmalemma is closely related to alkaline zone formation and the depolarized state of illuminated cell under resting conditions. Excitation-induced changes of membrane potential and pH in the cell vicinity were fully reversible, with the recovery period of ∼15 min at a photon flux density of ∼100 μE/(m² s). At shorter intervals between excitatory stimuli, differential membrane properties of nonuniform regions turned smoothed and could be overlooked. It is concluded that the origin of alkaline zones in illuminated Chara cells cannot be ascribed to hypothetical operation of H⁺/HCO₃⁻ symport or OH⁻/HCO₃⁻ antiport.     

Computational biology in the study of cardiac ion channels and cell electrophysiology

The cardiac cell is a complex biological system where various processes interact to generate electrical excitation (the action potential, AP) and contraction. During AP generation, membrane ion channels interact nonlinearly with dynamically changing ionic concentrations and varying transmembrane voltage, and are subject to regulatory processes. In recent years, a large body of knowledge has accumulated on the molecular structure of cardiac ion channels, their function, and their modification by genetic mutations that are associated with cardiac arrhythmias and sudden death. However, ion channels are typically studied in isolation (in expression systems or isolated membrane patches), away from the physiological environment of the cell where they interact to generate the AP. A major challenge remains the integration of ion-channel properties into the functioning, complex and highly interactive cell system, with the objective to relate molecular-level processes and their modification by disease to whole-cell function and clinical phenotype. In this article we describe how computational biology can be used to achieve such integration. We explain how mathematical (Markov) models of ion-channel kinetics are incorporated into integrated models of cardiac cells to compute the AP. We provide examples of mathematical (computer) simulations of physiological and pathological phenomena, including AP adaptation to changes in heart rate, genetic mutations in SCN5A and HERG genes that are associated with fatal cardiac arrhythmias, and effects of the CaMKII regulatory pathway and beta-adrenergic cascade on the cell electrophysiological function.     

Morphogenesis in Volvox: analysis of critical variables.

Inversion, the process by which Volvox embryos turn inside out, was analyzed by a combination of geometrical and experimental techniques. It was shown that simple geometric figures are adequate to represent cell shapes during inversion and that cell volumes remain constant as cell shapes change and the embryo inverts. The first stage of inversion, phialopore opening, results from the release of compressive forces as the embryo withdraws from its surrounding vesicle during a two-stage contraction of each cell around its radial axis. Premature phialopore opening occurs when withdrawal of the embryo from the vesicle is elicited artificially by exposure to either calcium ionophore or hypertonic solutions. The major event of inversion, generation of negative curvature, requires both microtubule-driven elongation of cells (to produce a classical "flask" shape) and cytochalasin-sensitive active migration of cytoplasmic bridges to the outermost ends of flask cells. Colchicine, cyclic GMP and isobutyl methyl xanthine (individually) block both normal elongation and bridge migration; cytochalasin D blocks bridge migration selectively. Flask cell formation and bridge migration are adequate to account for the negative curvature observed. An asymmetric bending of flask cell stalks along the ring of maximum curvature accounts for the fact that the embryo is not constricted in a "purse-string" fashion as negative curvature is generated. Inversion of the posterior hemisphere involves an elastic snap-through resulting from a combination of compressive stresses generated by inversion of the anterior hemisphere and the circumferential restraint imposed by cells at the equator. We conclude that the observed changes in cell shape and the migration of cytoplasmic bridges are the result of an ordered process of membrane-cytoskeletal interactions, and both necessary and sufficient to account for the morphogenetic process of inversion in Volvox.     

The Vesicle Trafficking Protein Sar1 Lowers Lipid Membrane Rigidity

The sculpting of membranes into dynamic, curved shapes is central to intracellular cargo trafficking. Though the generation of membrane curvature during trafficking necessarily involves both lipids and membrane-associated proteins, current mechanistic views focus primarily on the formation of rigid cages and curved scaffolds by protein assemblies. Here we report on a different mechanism for the control of membrane deformation, unrelated to the imposition of predefined curvature, involving modulation of membrane material properties: Sar1, a GTPase that regulates vesicle trafficking from the endoplasmic reticulum, lowers the rigidity of the lipid bilayer membrane to which it binds. In vitro assays in which optically trapped microspheres create controlled membrane deformations revealed a monotonic decline in bending modulus as a function of Sar1 concentration, down to nearly zero rigidity, indicating a dramatic lowering of the energetic cost of curvature generation. This is the first demonstration that a vesicle trafficking protein lowers the rigidity of its target membrane, leading to a new conceptual framework for vesicle biogenesis.     

Cell motility: the integrating role of the plasma membrane

The plasma membrane is of central importance in the motility process. It defines the boundary separating the intracellular and extracellular environments, and mediates the interactions between a motile cell and its environment. Furthermore, the membrane serves as a dynamic platform for localization of various components which actively participate in all aspects of the motility process, including force generation, adhesion, signaling, and regulation. Membrane transport between internal membranes and the plasma membrane, and in particular polarized membrane transport, facilitates continuous reorganization of the plasma membrane and is thought to be involved in maintaining polarity and recycling of essential components in some motile cell types. Beyond its biochemical composition, the mechanical characteristics of the plasma membrane and, in particular, membrane tension are of central importance in cell motility; membrane tension affects the rates of all the processes which involve membrane deformation including edge extension, endocytosis, and exocytosis. Most importantly, the mechanical characteristics of the membrane and its biochemical composition are tightly intertwined; membrane tension and local curvature are largely determined by the biochemical composition of the membrane and the biochemical reactions taking place; at the same time, curvature and tension affect the localization of components and reaction rates. This review focuses on this dynamic interplay and the feedbacks between the biochemical and biophysical characteristics of the membrane and their effects on cell movement. New insight on these will be crucial for understanding the motility process.     

Curvature of double-membrane organelles generated by changes in membrane size and composition

Transient double-membrane organelles are key players in cellular processes such as autophagy, reproduction, and viral infection. These organelles are formed by the bending and closure of flat, double-membrane sheets. Proteins are believed to be important in these morphological transitions but the underlying mechanism of curvature generation is poorly understood. Here, we describe a novel mechanism for this curvature generation which depends primarily on three membrane properties: the lateral size of the double-membrane sheets, the molecular composition of their highly curved rims, and a possible asymmetry between the two flat faces of the sheets. This mechanism is evolutionary advantageous since it does not require active processes and is readily available even when resources within the cell are restricted as during starvation, which can induce autophagy and sporulation. We identify pathways for protein-assisted regulation of curvature generation, organelle size, direction of bending, and morphology. Our theory also provides a mechanism for the stabilization of large double-membrane sheet-like structures found in the endoplasmic reticulum and in the Golgi cisternae.