A model of plasma membrane flow and cytosis regulation in growing pollen tubes

A model of cytosis regulation in growing pollen tubes is developed and simulations presented. The authors address the question on the minimal assumptions needed to describe the pattern of exocytosis and endocytosis reported recently by experimental biologists. Biological implications of the model are also treated. Concepts of flow and conservation of membrane material are used to pose an equation system, which describes the movement of plasma membrane in the tip of growing pollen tubes. After obtaining the central equations, relations describing the rates of endocytosis and exocytosis are proposed. Two cytosis receptors (for exocytosis and endocytosis), which have different recycling rates and activation times, suffice to describe a stable growing tube. Simulations show a very good spatial separation between endocytosis and exocytosis, in which separation is shown to depend strongly on exocytic vesicle delivery. In accordance to measurements, most vesicles in the clear zone are predicted to be endocytic. Membrane flow is essential to maintain cell polarity, and bi-directional flow seems to be a natural consequence of the proposed mechanism. For the first time, a model addressing plasma membrane flow and cytosis regulation were posed. Therefore, it represents a missing piece in an integrative model of pollen tube growth, in which cell wall mechanics, hydrodynamic fluxes and regulation mechanisms are combined.     

Theoretical model of reticulocyte to erythrocyte shape transformation

A theoretical model describing the kinetics of reticulocyte shape transformation was developed. The model considers the evolution of a simple cellular shape under transmembrane pressure difference, and proposes a four-parameter axisymmetric approximation of the cell surface. The mathematical analysis considers plasma membrane tension in the plane of bilayer leaflets, membrane spontaneous curvature and transmembrane transport of water. Cytoskeleton dilatational and shear rigidity, and the energetic barrier preventing the decrease of cell volume below a certain minimum are also incorporated. The set of adequate physical assumptions allowed for formulation of the equation for free energy of the investigated system. Computer simulations of cell shape changes, down to the state of free energy minimum, together with estimation of the time needed for the resulting transport of water, revealed a complex, three-phase picture of temporal alterations in cellular geometry with a wide spectrum of final results, and led to propose a standard model of reticulocyte-erythrocyte transformation. According to the model, both cell volume and surface undergo changes, and the work of the pressure, initially accumulated in the cytoskeleton, is consumed for local bending of the cell membrane. Further simulations with modified initial shape or parameters of the standard model show the trajectories of system evolution and help in better understanding the conditions for the erythro-, sphero-, ovalo-, stomato-, and leptoidal metamorphosis of maturing red blood cells. The stability of the final biconcave shape was also verified. Spherogenic modifications were discussed in the context of spherocytosis. Future development of the model was proposed.     

Interaction and fusion dynamics between cellular blebs

Membrane blebbing, as a mechanism for cells to regulate their internal pressure and membrane tension, is believed to play important roles in processes such as cell migration, spreading and apoptosis. However, the fundamental question of how different blebs interact with each other during their life cycles remains largely unclear. Here, we report a combined theoretical and experimental investigation to examine how the growth and retraction of a cellular bleb are influenced by neighboring blebs as well as the fusion dynamics between them. Specifically, a boundary integral model was developed to describe the shape evolution of cell membrane during the blebbing/retracting process. We showed that a drop in the intracellular pressure will be induced by the formation of a bleb whose retraction then restores the pressure level. Consequently, the volume that a second bleb can reach was predicted to heavily depend on its initial weakened size and the time lag with respect to the first bleb, all in quantitative agreement with our experimental observations. In addition, it was found that as the strength of membrane-cortex adhesion increases, the possible coalescence of two neighboring blebs changes from smooth fusion to abrupt coalescence and eventually to no fusion at all. Phase diagrams summarizing the dependence of such transition on key physical factors, such as the intracellular pressure and bleb separation, were also obtained.     

Computational Estimates of Membrane Flow and Tension Gradient in Motile Cells

All parts of motile cells, including the plasma membrane, have to translocate in the direction of locomotion. Both directed intracellular membrane transport coupled with polarized endo- and exocytosis and fluid flow in the plane of the plasma membrane can contribute to this overall plasma membrane translocation. It remains unclear how strong a force is required to generate this flow. We numerically solve Stokes equations for the viscous membrane flow across a flat plasma membrane surface in the presence of transmembrane proteins attached to the cytoskeleton and find the membrane tension gradient associated with this flow. This gradient is sensitive to the size and density of the transmembrane proteins attached to the cytoskeleton and can become significant enough to slow down cell movement. We estimate the influence of intracellular membrane transport and actin growth and contraction on the tension gradient, and discuss possible ‘tank tread’ flow at ventral and dorsal surfaces.     

Role of ion channels during cell division

Ion channels are transmembrane proteins whose canonical function is the transport of ions across the plasma membrane to regulate cell membrane potential and play an essential role in neural communication, nerve conduction, and muscle contraction. However, over the last few years, non-canonical functions have been identified for many channels, having active roles in phagocytosis, invasiveness, proliferation, among others. The participation of some channels in cell proliferation has raised the question of whether they may play an active role in mitosis. There are several reports showing the participation of channels during interphase, however, the direct participation of ion channels in mitosis has received less attention. In this article, we summarize the current evidence on the participation of ion channels in mitosis. We also summarize some tools that would allow the study of ion channels and cell cycle regulatory molecules in individual cells during mitosis.     

Membrane Reserves and Hypotonic Cell Swelling

To accommodate expanding volume (V) during hyposmotic swelling, animal cells change their shape and increase surface area (SA) by drawing extra membrane from surface and intracellular reserves. The relative contributions of these processes, sources and extent of membrane reserves are not well defined. In this study, the SA and V of single substrate-attached A549, 16HBE14o⁻, CHO and NIH 3T3 cells were evaluated by reconstructing cell three-dimensional topology based on conventional light microscopic images acquired simultaneously from two perpendicular directions. The size of SA reserves was determined by swelling cells in extreme 98% hypotonic (∼6 mOsm) solution until membrane rupture; all cell types examined demonstrated surprisingly large membrane reserves and could increase their SA 3.6 ± 0.2-fold and V 10.7 ± 1.5-fold. Blocking exocytosis (by N-ethylmaleimide or 10°C) reduced SA and V increases of A549 cells to 1.7 ± 0.3-fold and 4.4 ± 0.9-fold, respectively. Interestingly, blocking exocytosis did not affect SA and V changes during moderate swelling in 50% hypotonicity. Thus, mammalian cells accommodate moderate (<2-fold) V increases mainly by shape changes and by drawing membrane from preexisting surface reserves, while significant endomembrane insertion is observed only during extreme swelling. Large membrane reserves may provide a simple mechanism to maintain membrane tension below the lytic level during various cellular processes or acute mechanical perturbations and may explain the difficulty in activating mechanogated channels in mammalian cells. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Endocytosis and exocytosis protect cells against severe membrane tension variations

The ability of cells to regulate their shape and volume is critical for many cell functions. How endocytosis and exocytosis, as important ways of membrane trafficking, affect cellular volume regulation is still unclear. Here, we develop a theoretical framework to study the dynamics of cell volume, endocytosis, and exocytosis in response to osmotic shocks and mechanical loadings. This model can not only explain observed dynamics of endocytosis and exocytosis during osmotic shocks but also predict the dynamics of endocytosis and exocytosis during cell compressions. We find that a hypotonic shock stimulates exocytosis, while a hypertonic shock stimulates endocytosis; and exocytosis in turn allows cells to have a dramatic change in cell volume but a small change in membrane tension during hyposmotic swelling, protecting cells from rupture under high tension. In addition, we find that cell compressions with various loading speeds induce three distinct dynamic modes of endocytosis and exocytosis. Finally, we show that increasing endocytosis and exocytosis rates reduce the changes in cell volume and membrane tension under fast cell compression, whereas they enhance the changes in cell volume and membrane tension under slow cell compression. Together, our findings reveal critical roles of endocytosis and exocytosis in regulating cell volume and membrane tension.     

Septin Dynamics Are Essential for Exocytosis

Septins are a family of 14 cytoskeletal proteins that dynamically form hetero-oligomers and organize membrane microdomains for protein complexes. The previously reported interactions with SNARE proteins suggested the involvement of septins in exocytosis. However, the contradictory results of up- or down-regulation of septin-5 in various cells and mouse models or septin-4 in mice suggested either an inhibitory or a stimulatory role for these septins in exocytosis. The involvement of the ubiquitously expressed septin-2 or general septin polymerization in exocytosis has not been explored to date. Here, by nano-LC with tandem MS and immunoblot analyses of the septin-2 interactome in mouse brain, we identified not only SNARE proteins but also Munc-18-1 (stabilizes assembled SNARE complexes), N-ethylmaleimide-sensitive factor (NSF) (disassembles SNARE complexes after each membrane fusion event), and the chaperones Hsc70 and synucleins (maintain functional conformation of SNARE proteins after complex disassembly). Importantly, α-soluble NSF attachment protein (SNAP), the adaptor protein that mediates NSF binding to the SNARE complex, did not interact with septin-2, indicating that septins undergo reorganization during each exocytosis cycle. Partial depletion of septin-2 by siRNA or impairment of septin dynamics by forchlorfenuron inhibited constitutive and stimulated exocytosis of secreted and transmembrane proteins in various cell types. Forchlorfenuron impaired the interaction between SNAP-25 and its chaperone Hsc70, decreasing SNAP-25 levels in cultured neuroendocrine cells, and inhibited both spontaneous and stimulated acetylcholine secretion in mouse motor neurons. The results demonstrate a stimulatory role of septin-2 and the dynamic reorganization of septin oligomers in exocytosis.     

Distinct apical and basolateral membrane requirements for stretch-induced membrane traffic at the apical surface of bladder umbrella cells

Epithelial cells respond to mechanical stimuli by increasing exocytosis, endocytosis, and ion transport, but how these processes are initiated and coordinated and the mechanotransduction pathways involved are not well understood. We observed that in response to a dynamic mechanical environment, increased apical membrane tension, but not pressure, stimulated apical membrane exocytosis and ion transport in bladder umbrella cells. The exocytic response was independent of temperature but required the cytoskeleton and the activity of a nonselective cation channel and the epithelial sodium channel. The subsequent increase in basolateral membrane tension had the opposite effect and triggered the compensatory endocytosis of added apical membrane, which was modulated by opening of basolateral K⁺ channels. Our results indicate that during the dynamic processes of bladder filling and voiding apical membrane dynamics depend on sequential and coordinated mechanotransduction events at both membrane domains of the umbrella cell.     

Model for calcium dependent oscillatory growth in pollen tubes

Experiments have shown that pollen tubes grow in an oscillatory mode, the mechanism of which is poorly understood. We propose a theoretical growth model of pollen tubes exhibiting such oscillatory behaviour. The pollen tube and the surrounding medium are represented by two immiscible fluids separated by an interface. The physical variables are pressure, surface tension, density and viscosity, which depend on relevant biological quantities, namely calcium concentration and thickness of the cell wall. The essential features generally believed to control oscillating growth are included in the model, namely a turgor pressure, a viscous cell wall which yields under pressure, stretch-activated calcium channels which transport calcium ions into the cytoplasm and an exocytosis rate dependent on the cytosolic calcium concentration in the apex of the cell. We find that a calcium dependent vesicle recycling mechanism is necessary to obtain an oscillating growth rate in our model. We study the variation in the frequency of the growth rate by changing the extracellular calcium concentration and the density of ion channels in the membrane. We compare the predictions of our model with experimental data on the frequency of oscillation versus growth speed, calcium concentration and density of calcium channels.     

Turgor pressure, membrane tension and the control of exocytosis in higher plants

Both turgor pressure and differences in membrane tension are capable of providing an energy input into exocytosis, the process of fusion of Golgi vesicles with the cell membrane in plants. It is shown that the contribution of turgor pressure is much larger than that of membrane tension, so that the exocytotic process is not likely on thermodynamic grounds to be reversible unless another source of energy is made available. However, recycling of membrane material as flattened, empty vesicles is energetically possible and is likely to be favoured when the magnitude of membrane tension in the cell membrane is low. Thus the outward flows of membrane and cell wall material are in principle linked to turgor, whereas membrane tension influences the inward flow of membrane material.     

Is lipid translocation involved during endo- and exocytosis?

Stimulation of the aminophospholipid translocase, responsible for the transport of phosphatidylserine and phosphatidylethanolamine from the outer to the inner leaflet of the plasma membrane, provokes endocytic-like vesicles in erythrocytes and stimulates endocytosis in K562 cells. In this article arguments are given which support the idea that the active transport of lipids could be the driving force involved in membrane folding during the early step of endocytosis. The model is sustained by experiments on shape changes of pure lipid vesicles triggered by a change in the proportion of inner and outer lipids. It is shown that the formation of microvesicles with a diameter of 100-200 nm caused by the translocation of plasma membrane lipids implies a surface tension in the whole membrane. It is likely that cytoskeleton proteins and inner organelles prevent a real cell from undergoing overall shape changes of the type seen with giant unilamellar vesicles. Another hypothesis put forward in this article is the possible implication of the phospholipid 'scramblase' during exocytosis which could favor the unfolding of microvesicles.     

Pay attention to membrane tension: Mechanobiology of the cell surface

The cell surface is a mechanobiological unit that encompasses the plasma membrane, its interacting proteins, and the complex underlying cytoskeleton. Recently, attention has been directed to the mechanics of the plasma membrane, and in particular membrane tension, which has been linked to diverse cellular processes such as cell migration and membrane trafficking. However, how tension across the plasma membrane is regulated and propagated is still not completely understood. Here, we review recent efforts to study the interplay between membrane tension and the cytoskeletal machinery and how they control cell form and function. We focus on factors that have been proposed to affect the propagation of membrane tension and as such could determine whether it can act as a global or local regulator of cell behavior. Finally, we discuss the limitations of the available tool kit as new approaches that reveal its dynamics in cells are needed to decipher how membrane tension regulates diverse cellular processes.     

The possible influence of osmotic poration on cell membrane water permeability

It has been hypothesized that pores in the plasma membrane form under conditions of rapid water efflux, allowing extracellular ice to grow into the cytoplasm under conditions of rapid freezing. When cells with intracellular ice are thawed slowly, the transmembrane ice crystal expands through recrystallization causing the cell to lyse. One of the implications of this hypothesis is that osmotic pores will provide an alternative route for water movement under conditions of osmotically induced flow. We show that the plasma membrane water permeability of a fibroblast cell changes as a function of the osmotic pressure gradient that is used to drive water movement. It is further shown that cell volume is more important than the magnitude of water flux in causing this departure from a uniform water permeability. We suggest that these data provide evidence of a transient route for water movement across cell membranes.     

Specificity of the Transport of Lipid II by FtsW in Escherichia coli

Synthesis of biogenic membranes requires transbilayer movement of lipid-linked sugar molecules. This biological process, which is fundamental in prokaryotic cells, remains as yet not clearly understood. In order to obtain insights into the molecular basis of its mode of action, we analyzed the structure-function relationship between Lipid II, the important building block of the bacterial cell wall, and its inner membrane-localized transporter FtsW. Here, we show that the predicted transmembrane helix 4 of Escherichia coli FtsW (this protein consists of 10 predicted transmembrane segments) is required for the transport activity of the protein. We have identified two charged residues (Arg¹⁴⁵ and Lys¹⁵³) within this segment that are specifically involved in the flipping of Lipid II. Mutating these two amino acids to uncharged ones affected the transport activity of FtsW. This was consistent with loss of in vivo activity of the mutants, as manifested by their inability to complement a temperature-sensitive strain of FtsW. The transport activity of FtsW could be inhibited with a Lipid II variant having an additional size of 420 Da. Reducing the size of this analog by about 274 Da resulted in the resumption of the transport activity of FtsW. This suggests that the integral membrane protein FtsW forms a size-restricted porelike structure, which accommodates Lipid II during transport across the bacterial cytoplasmic membrane.     

A metabolic osmotic model of human erythrocytes

A metabolic osmotic model of red blood cells is presented which takes into account the main reaction steps of glycolysis and the passive and active fluxes of ions across the cell membrane. Cellular energy metabolism and osmotic behaviour are linked by the ATP consumption for the active transport of cations as well as by the osmotic action of the glycolytic intermediate 2,3-diphosphoglycerate (2,3-DPG). The model is based on a system of differential equations describing the metabolic reactions and transport processes. Further, two algebraic conditions for the osmotic equilibrium and the electroneutrality of the cell are considered. Using realistic system parameters the model allows the calculation of a great number of dependent variables, among them the cell volume, the concentrations of metabolites and ions and the transmembrane potential. Only stationary states are considered.The parameter dependence of important model variables is characterized by control coefficients. The main results are: (a) The volume of erythrocytes is mainly determined by the permeabilities of the leak fluxes of cations, the content of hemoglobin and the activity of the hexokinase-phosphofructokinase system of glycolysis; (b) Changes of volume affect the glycolytic rate mainly by changing the concentration of ATP which is a regulator of glycolysis; (c) A change in the membrane area may affect the other cell properties only if it is connected with variations of the number of active and leak sites of the membrane.     

植物细胞生物碱跨膜传递模型研究(II)-膜电位影响下的饱和特性模型

在中性生物碱饱和特性模型的基础上,引入膜电位的影响,考虑生物碱阳离子通量对总生物碱扩散通量的影响,从而导出膜电位影响的饱和特性模型。将模型在特定参数下积分,对实验结果进行数值模拟,结果表明,所建模型可很好描述各种生物碱（高ｐＫａ值和低ｐＫａ值生物碱）的跨膜传递过程,为建立描述生物碱跨膜传递过程的普适性模型提供了理论基础     

Cell Blebbing and Membrane Area Homeostasis in Spreading and Retracting Cells

Cells remodel their plasma membrane and cytoskeleton during numerous physiological processes, including spreading and motility. Morphological changes require the cell to adjust its membrane tension on different timescales. While it is known that endo- and exocytosis regulate the cell membrane area in a timescale of 1 h, faster processes, such as abrupt cell detachment, require faster regulation of the plasma membrane tension. In this article, we demonstrate that cell blebbing plays a critical role in the global mechanical homeostasis of the cell through regulation of membrane tension. Abrupt cell detachment leads to pronounced blebbing (which slow detachment does not), and blebbing decreases with time in a dynamin-dependent fashion. Cells only start spreading after a lag period whose duration depends on the cell's blebbing activity. Our model quantitatively reproduces the monotonic decay of the blebbing activity and accounts for the lag phase in the spreading of blebbing cells.     

Novel splice variants of amphiphysin I are expressed in retina

The MscL channel is a mechanosensitive channel which is gated by membrane stress or tension. Here, we describe a series of simulations which apply simulated mechanical stress to a molecular model of the MscL channel using two methods - direct force application to the transmembrane segments, and anisotropic pressure coupling. In the latter simulations, pressures less than that equivalent to a bilayer tension of 12 dyn/cm did not cause the channel to open, while pressures in excess of this value resulted in the channel opening. These results are in approximate agreement with experimental findings.     

A General Model for the Dynamics of the Cell Volume

The conservation of the cell volume within values compatible with the overall cell functions represents an ubiquitous property, shared by cells comprising the whole biological world. Water transport across membranes constitutes the main process associated to the dynamics of the cell volume, its chronic and acute regulations therefore represent crucial aspects of cell homeostasis. In spite of the biological diversity, the dynamics of the cell volume exhibits common basic features in the diverse types of cells. The purpose of this study is to show that there is a general model capable to describe the basic aspects of the dynamics of the cell volume. It is demonstrated here that the steady states of this model represent asymptotically stable configurations. As illustrations, several cases of non-polarized (i.e., symmetrical) and polarized (e.g., epithelial) cells performing water transport are shown here to represent particular cases of the general model. From a biological perspective, the existence of a general model for the dynamics of the cell volume reveals that, in spite of physiological and morphological peculiarities, there is a basic common design of the membrane transport processes. In view of its stability properties, this basic design may represent an ancestral property that has proven to be successful regarding the overall homeostatic properties of cells.