Compartmentalized structure of the plasma membrane for receptor movements as revealed by a nanometer-level motion analysis

Movements of transferrin and alpha 2-macroglobulin receptor molecules in the plasma membrane of cultured normal rat kidney (NRK) fibroblastic cells were investigated by video-enhanced contrast optical microscopy with 1.8 nm spatial precision and 33 ms temporal resolution by labeling the receptors with the ligand-coated nanometer-sized colloidal gold particles. For both receptor species, most of the movement trajectories are of the confined diffusion type, within domains of approximately 0.25 microns2 (500-700 nm in diagonal length). Movement within the domains is random with a diffusion coefficient approximately 10(-9) cm2/s, which is consistent with that expected for free Brownian diffusion of proteins in the plasma membrane. The receptor molecules move from one domain to one of the adjacent domains at an average frequency of 0.034 s-1 (the residence time within a domain approximately 29 s), indicating that the plasma membrane is compartmentalized for diffusion of membrane receptors and that long- range diffusion is the result of successive intercompartmental jumps. The macroscopic diffusion coefficients for these two receptor molecules calculated on the basis of the compartment size and the intercompartmental jump rate are approximately 2.4 x 10(-11) cm2/s, which is consistent with those determined by averaging the long-term movements of many particles. Partial destruction of the cytoskeleton decreased the confined diffusion mode, increased the simple diffusion mode, and induced the directed diffusion (transport) mode. These results suggest that the boundaries between compartments are made of dynamically fluctuating membrane skeletons (membrane-skeleton fence model).     

Spatial Structure and Diffusive Dynamics from Single-Particle Trajectories Using Spline Analysis

Single-particle tracking of biomolecular probes has provided a wealth of information about intracellular trafficking and the dynamics of proteins and lipids in the cell membrane. Conventional mean-square displacement (MSD) analysis of single-particle trajectories often assumes that probes are moving in a uniform environment. However, the observed two-dimensional motion of probe particles is influenced by the local three-dimensional geometry of the cell membrane and intracellular structures, which are rarely flat at the submicron scale. This complex geometry can lead to spatially confined trajectories that are difficult to analyze and interpret using conventional two-dimensional MSD analysis. Here we present two methods to analyze spatially confined trajectories: spline-curve dynamics analysis, which extends conventional MSD analysis to measure diffusive motion in confined trajectories; and spline-curve spatial analysis, which measures spatial structures smaller than the limits of optical resolution. We show, using simulated random walks and experimental trajectories of quantum dot probes, that differences in measured two-dimensional diffusion coefficients do not always reflect differences in underlying diffusive dynamics, but can instead be due to differences in confinement geometries of cellular structures.     

A model for membrane patchiness: lateral diffusion in the presence of barriers and vesicle traffic

Patches (lateral heterogeneities) of cell surface membrane proteins and lipids have been imaged by a number of different microscopy techniques. This patchiness has been taken as evidence for the organization of membranes into domains whose composition differs from the average for the entire membrane. However, the mechanism and specificity of patch formation are not understood. Here we show how vesicle traffic to and from a cell surface membrane can create patches of molecules of the size observed experimentally. Our computer model takes into account lateral diffusion, barriers to lateral diffusion, and vesicle traffic to and from the plasma membrane. Neither barriers nor vesicle traffic alone create and maintain patches. Only the combination of these produces a dynamic but persistent patchiness of membrane proteins and lipids.     

Single-Molecule Imaging of the H-Ras Membrane-Anchor Reveals Domains in the Cytoplasmic Leaflet of the Cell Membrane

In the last decade evidence has accumulated that small domains of 50–700 nm in diameter are located in the exoplasmic leaflet of the plasma membrane. Most of these domains supposedly consist of specific sets of lipids and proteins, and are believed to coordinate signal transduction cascades. Whether similar domains are also present in the cytoplasmic leaflet of the plasma membrane is unclear so far. To investigate the presence of cytoplasmic leaflet domains, the H-Ras membrane-targeting sequence was fused to the C-terminus of the enhanced yellow fluorescent protein. Using single-molecule fluorescence microscopy, trajectories of individual molecules diffusing in the cytoplasmic leaflet of the plasma membrane were recorded. From these trajectories, the diffusion of individual membrane-anchored enhanced yellow fluorescent protein molecules was studied in live cells on timescales from 5 to 200 ms. The results show that the diffusion of 30–40% of the molecules is constrained in domains with a typical size of 200 nm. Neither breakdown of actin nor cholesterol extraction changed the domain characteristics significantly, indicating that the observed domains may not be related to the membrane domains identified so far.     

The spermatid plasma membrane comes of age

Spermiogenesis affords a unique opportunity to examine the formation of plasma membrane domains. Recent attempts to chart the life cycles of well-characterized integral plasma membrane proteins during spermiogenesis have suggested that spermatids are at least as adept as epithelial cells or neurons at establishing their plasma membrane domains. They appear to expand upon the standard recipe involving concurrent domain-specific protein targeting and diffusion barriers by using a combination of intracellular storage within the secretory pathway, developmentally-regulated delivery to provisional plasma membrane domains, large-scale redistributions of diffusion barriers and integral plasma membrane proteins, and the shedding of an entire plasma membrane domain.     

Self diffusion of water in frog muscle.

Self diffusion of cell water has been measured at diffusion times ranging form 0.3 ms to 2.4 s for three muscle types of Rana pipiens, using various magnetic field gradient nuclear magnetic resonance methods. Intracellular diffusion coefficients and membrane permeabilities are calculated with the aid of previous theoretical results for regularly spaced permeable planar barriers. The intracellular diffusion coefficient is 1.6 x 10-5 cm2/s, in approximate agreement with other literature values for skeletal muscles. The outer membrane permeabilities are estimated at 0.01 cm/s for two of the muscle types, and much higher for the other one.     

Tethered polymer-supported planar lipid bilayers for reconstitution of integral membrane proteins: silane-polyethyleneglycol-lipid as a cushion and covalent linker

There is increasing interest in supported membranes as models of biological membranes and as a physiological matrix for studying the structure and function of membrane proteins and receptors. A common problem of protein-lipid bilayers that are directly supported on a hydrophilic substrate is nonphysiological interactions of integral membrane proteins with the solid support to the extent that they will not diffuse in the plane of the membrane. To alleviate some of these problems we have developed a new tethered polymer-supported planar lipid bilayer system, which permitted us to reconstitute integral membrane proteins in a laterally mobile form. We have supported lipid bilayers on a newly designed polyethyleneglycol cushion, which provided a soft support and, for increased stability, covalent linkage of the membranes to the supporting quartz or glass substrates. The formation and morphology of the bilayers were followed by total internal reflection and epifluorescence microscopy, and the lateral diffusion of the lipids and proteins in the bilayer was monitored by fluorescence recovery after photobleaching. Uniform bilayers with high lateral lipid diffusion coefficients (0.8-1.2 x 10(-8) cm(2)/s) were observed when the polymer concentration was kept slightly below the mushroom-to-brush transition. Cytochrome b(5) and annexin V were used as first test proteins in this system. When reconstituted in supported bilayers that were directly supported on quartz, both proteins were largely immobile with mobile fractions < 25%. However, two populations of laterally mobile proteins were observed in the polymer-supported bilayers. Approximately 25% of cytochrome b(5) diffused with a diffusion coefficient of approximately 1 x 10(-8) cm(2)/s, and 50-60% diffused with a diffusion coefficient of approximately 2 x 10(-10) cm(2)/s. Similarly, one-third of annexin V diffused with a diffusion coefficient of approximately 3 x 10(-9) cm(2)/s, and two-thirds diffused with a diffusion coefficient of approximately 4 x 10(-10) cm(2)/s. A model for the interaction of these proteins with the underlying polymer is discussed.     

Translational diffusion of individual class II MHC membrane proteins in cells

Single-molecule epifluorescence microscopy was used to observe the translational motion of GPI-linked and native I-E(k) class II MHC membrane proteins in the plasma membrane of CHO cells. The purpose of the study was to look for deviations from Brownian diffusion that might arise from barriers to this motion. Detergent extraction had suggested that these proteins may be confined to lipid microdomains in the plasma membrane. The individual I-E(k) proteins were visualized with a Cy5-labeled peptide that binds to a specific extracytoplasmic site common to both proteins. Single-molecule trajectories were used to compute a radial distribution of displacements, yielding average diffusion coefficients equal to 0.22 (GPI-linked I-E(k)) and 0.18 microm(2)/s (native I-E(k)). The relative diffusion of pairs of proteins was also studied for intermolecular separations in the range 0.3-1.0 microm, to distinguish between free diffusion of a protein molecule and diffusion of proteins restricted to a rapidly diffusing small domain. Both analyses show that motion is predominantly Brownian. This study finds no strong evidence for significant confinement of either GPI-linked or native I-E(k) in the plasma membrane of CHO cells.     

Barriers to diffusion of plasma membrane proteins form early during guinea pig spermiogenesis.

The plasma membrane of the mature guinea pig sperm is segregated into at least four domains of different composition. Previous studies have shown that some proteins localized within these domains are free to diffuse laterally, suggesting that barriers to protein diffusion are responsible for maintaining the nonuniform distribution of at least some surface proteins in mature sperm. The different membrane domains appear sequentially during sperm morphogenesis in the testis and during later passage through the epididymis. To determine when diffusion barriers become functional during sperm development, we examined the diffusion of two proteins that are expressed on the cell surface of developing spermatids and become segregated to different plasma membrane domains during the course of spermiogenesis. Both proteins exhibited rapid lateral diffusion throughout spermiogenesis, even after they become localized to specific regions of the surface membrane. These results suggest that barriers to membrane diffusion form concomitantly with membrane domains during spermiogenesis.     

Lateral diffusion of small compounds in human stratum corneum and model lipid bilayer systems.

An image-based technique of fluorescence recovery after photobleaching (video-FRAP) was used to measure the lateral diffusion coefficients of a series of nine fluorescent probes in two model lipid bilayer systems, dimyristoylphosphatidylcholine (DMPC) and DMPC/cholesterol (40 mol%), as well as in human stratum corneum-extracted lipids. The probes were all lipophilic, varied in molecular weight from 223 to 854 Da, and were chosen to characterize the lateral diffusion of small compounds in these bilayer systems. A clear molecular weight dependence of the lateral diffusion coefficients in DMPC bilayers was observed. Values ranged from 6.72 x 10(-8) to 16.2 x 10(-8) cm2/s, with the smaller probes diffusing faster than the larger ones. Measurements in DMPC/cholesterol bilayers, which represent the most thorough characterization of small-solute diffusion in this system, exhibited a similar molecular weight dependence, although the diffusion coefficients were lower, ranging from 1.62 x 10(-8) to 5.60 x 10(-8) cm2/s. Lateral diffusion measurements in stratum corneum-extracted lipids, which represent a novel examination of diffusion in this unique lipid system, also exhibited a molecular weight dependence, with values ranging from 0.306 x 10(-8) to 2.34 x 10(-8) cm2/s. Literature data showed that these strong molecular weight dependencies extend to even smaller compounds than those examined in this study. A two-parameter empirical expression is presented that describes the lateral diffusion coefficient in terms of the solute's molecular weight and captures the size dependence over the range examined. This study illustrates the degree to which small-molecule lateral diffusion in stratum corneum-extracted lipids can be represented by diffusion in DMPC and DMPC/cholesterol bilayer systems, and may lead to a better understanding of small-solute transport across human stratum corneum.     

Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy). Effects of calcium-induced differentiation in cultured epithelial cells.

The movements of E-cadherin, epidermal growth factor receptor, and transferrin receptor in the plasma membrane of a cultured mouse keratinocyte cell line were studied using both single particle tracking (SPT; nanovid microscopy) and fluorescence photobleaching recovery (FPR). In the SPT technique, the receptor molecules are labeled with 40 nm-phi colloidal gold particles, and their movements are followed by video-enhanced differential interference contrast microscopy at a temporal resolution of 33 ms and at a nanometer-level spatial precision. The trajectories of the receptor molecules obtained by SPT were analyzed by developing a method that is based on the plot of the mean-square displacement against time. Four characteristic types of motion were observed: (a) stationary mode, in which the microscopic diffusion coefficient is less than 4.6 x 10(-12) cm2/s; (b) simple Brownian diffusion mode; (c) directed diffusion mode, in which unidirectional movements are superimposed on random motion; and (d) confined diffusion mode, in which particles undergoing Brownian diffusion (microscopic diffusion coefficient between 4.6 x 10(-12) and 1 x 10(-9) cm2/s) are confined within a limited area, probably by the membrane-associated cytoskeleton network. Comparison of these data obtained by SPT with those obtained by FPR suggests that the plasma membrane is compartmentalized into many small domains 300-600 nm in diameter (0.04-0.24 microns2 in area), in which receptor molecules are confined in the time scale of 3-30 s, and that the long-range diffusion observed by FPR can occur by successive movements of the receptors to adjacent compartments. Calcium-induced differentiation decreases the sum of the percentages of molecules in the directed diffusion and the stationary modes outside of the cell-cell contact regions on the cell surface (which is proposed to be the percentage of E-cadherin bound to the cytoskeleton/membrane-skeleton), from approximately 60% to 8% (low- and high-calcium mediums, respectively).     

Tumor necrosis factor and immune interferon act in concert to slow the lateral diffusion of proteins and lipids in human endothelial cell membranes

Vascular endothelial surface-related activities may depend on the lateral mobility of specific cell surface macromolecules. Previous studies have shown that cytokines induce changes in the morphology and surface antigen composition of vascular endothelial cells in vitro and at sites of immune and inflammatory reactions in vivo. The effects of cytokines on membrane dynamic properties have not been examined. In the present study, we have used fluorescence photobleaching recovery (FPR) to quantify the effects of the cytokines tumor necrosis factor (TNF) and immune interferon (IFN-gamma) on the lateral mobilities of class I major histocompatibility complex protein, of an abundant 96,000 Mr mesenchymal cell surface glycoprotein (gp96), and of a phospholipid probe in cultured human endothelial cell (HEC) membranes. Class I protein and gp96 were directly labeled with fluorescein-conjugated monoclonal antibodies; plasma membrane lipid mobility was examined with the phospholipid analogue fluorescein phosphatidylethanolamine (Fl-PE). In untreated, confluent HEC monolayers, diffusion coefficients were 30 x 10(-10) cm2 s-1 for class I protein, 14 x 10(-10) cm2 s-1 for gp96, and 80 x 10(-10) cm2 s-1 for Fl-PE. Fractional mobilities were greater than 80% for each probe. Cultures treated at visual confluence for 3-4 d with either 100 U/ml TNF or 200 U/ml IFN-gamma did not exhibit significant changes in protein or lipid mobilities despite significant changes in cell morphology and membrane antigen composition. In HEC cultures treated concomitantly with TNF and IFN-gamma, however, diffusion coefficients decreased by 71-79% for class I protein, 29-55% for gp96, and 23-38% for Fl-PE. Fractional mobilities were unchanged. By immunoperoxidase transmission electron microscopy, plasma membranes of untreated and cytokine-treated HEC were flat and stained uniformly for class I antigen. "Line" FPR measurements on doubly treated HEC demonstrated isotropic diffusion of class I protein, gp96, and Fl-PE. Finally, although TNF and IFN-gamma retarded the growth of HEC cultures and disrupted the organization of cell monolayers, the slow diffusion rates of gp96 and Fl-PE in confluent doubly treated monolayers were not reproduced in sparse or subconfluent untreated monolayers. We conclude that the slowing of protein and lipid diffusion induced by the combination of TNF and IFN-gamma is not due to plasma membrane corrugations, to anisotropic diffusion barriers, or to decreased numbers of cell-cell contacts.(ABSTRACT TRUNCATED AT 400 WORDS)     

Multiple domains of occludin are involved in the regulation of paracellular permeability

Tight junctions form selective paracellular diffusion barriers that regulate the diffusion of solutes across epithelia and constitute intramembrane diffusion barriers that prevent the intermixing of apical and basolateral lipids in the extracytoplasmic leaflet of the plasma membrane. In MDCK cells, previous expression experiments demonstrated that occludin, a tight junction protein with four transmembrane domains, is critically involved in both of these tight junction functions and that its COOH-terminal cytoplasmic domain is of functional importance. By expressing mutant and chimeric occludin that exert a dominant negative effect on selective paracellular diffusion, we now demonstrate that the extracytoplasmic domains and at least one of the transmembrane domains are also critically involved in selective paracellular permeability. Multiple domains of occludin are thus important for the regulation of paracellular permeability. Expression of chimeras containing at least one transmembrane domain of occludin also resulted in an enhanced intracellular accumulation of claudin-4, another transmembrane protein of tight junctions, suggesting that the two proteins may cooperate in the regulation of paracellular permeability.     

Diffusion barriers in ram and boar sperm plasma membranes: directionality of lipid diffusion across the posterior ring

The plasma membrane of mammalian spermatozoa, like that of other differentiated cells, is compartmentalized into discrete regions or domains that are biochemically and functionally distinct from one another. Physical structures within the membrane, such as the posterior ring at the juncture of the sperm head and tail, have long been thought to act as diffusion barriers to help segregate important molecules required for fertilization within specific domains and to regulate migration of molecules between domains. In this investigation, we used a quantitative photobleaching technique (video-FRAP) to assess the efficacy of the posterior ring as a barrier to exchange of lipids between the postacrosomal and midpiece plasma membranes. A lipid reporter probe (1,1'-diduodecyl-3,3,3', 3'-tetramethylindocarbocyanine; DiIC(12)) was incorporated into the plasma membrane of live ram and boar spermatozoa, and the directionality of its diffusion across the posterior ring was measured by line-profile analysis. Results showed that DiIC(12) was able to traverse the posterior ring from the direction of the postacrosomal plasma membrane and to diffuse onto the midpiece plasma membrane. These results suggest that the posterior ring is not an immutable barrier to lipid exchange in mature spermatozoa and that there are other mechanisms for maintaining in-plane lipid asymmetry, such as differential phase behavior and interaction with the submembranous cytoskeleton.     

Lipid polarity and sorting in epithelial cells

Apical and basolateral membrane domains of epithelial cell plasma membranes possess unique lipid compositions. The tight junction, the structure separating the two domains, forms a diffusion barrier for membrane components and thereby prevents intermixing of the two sets of lipids. The barrier apparently resides in the outer, exoplasmic leaflet of the plasma membrane bilayer. First data are now available on the generation of these differences in Madin-Darby canine kidney (MDCK) cells, grown on filter supports. Experiments in which fluorescent precursors of apical lipids were introduced into the cell have demonstrated that upon biosynthesis apical lipids are sorted from basolateral lipids in an intracellular compartment. In this paper we present a model for the sorting process, the central point of which is that the two sets of lipids laterally segregate into microdomains that bud to form vesicles delivering the lipids to the apical and the basolateral plasma membrane domains, respectively.     

Single-molecule anisotropy imaging

A novel method, single-molecule anisotropy imaging, has been employed to simultaneously study lateral and rotational diffusion of fluorescence-labeled lipids on supported phospholipid membranes. In a fluid membrane composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, in which the rotational diffusion time is on the order of the excited-state lifetime of the fluorophore rhodamine, a rotational diffusion constant, D(rot) = 7 x 10(7) rad(2)/s, was determined. The lateral diffusion constant, measured by direct analysis of single-molecule trajectories, was D(lat) = 3.5 x 10(-8) cm(2)/s. As predicted from the free-volume model for diffusion, the results exhibit a significantly enhanced mobility on the nanosecond time scale. For membranes of DPPC lipids in the L(beta) gel phase, the slow rotational mobility permitted the direct observation of the rotation of individual molecules characterized by D(rot) = 1.2 rad(2)/s. The latter data were evaluated by a mean square angular displacement analysis. The technique developed here should prove itself profitable for imaging of conformational motions of individual proteins on the time scale of milliseconds to seconds.     

Effect of cell substratum on lateral mobility of lipids in the plasma membrane of vascular endothelial cells

Bovine vascular endothelial cells can be maintained in a highly differentiated state in vitro, either by the addition of fibroblast growth factor (FGF) to the culture medium or by plating the cells on extracellular matrix (ECM)-coated dishes. Under these conditions the cells proliferate actively and at confluence form a tightly packed monolayer composed of nonoverlapping polarized cells. A fluorescence recovery after photobleaching method was used to determine the lateral mobility coefficient D of the lipophilic fluorescent probe, 5N-(hexadecanoyl)-aminofluorescein (HEDAF), in the basal and apical plasma membranes of endothelial cells under various culture conditions (cells on glass coverslips in the presence or absence of FGF, or cells plated on ECM in the exponential growth phase or at confluence). A heterogeneous distribution of lateral diffusion coefficients D was found in a given cell population. Nevertheless, for the basal membrane, a "mean" D value close to 2.0 x 10(-9) cm2/s was found for all the culture conditions. The "mean" D value of HEDAF in the apical pole was slightly higher when sparse cells were exposed to FGF (D = 2.2 x 10(-9) cm2/s) and was further enhanced when cells were growing or confluent on ECM-coated coverslips (D = 2.7 x 10(-9) cm2/s). On the other hand, when the cells were maintained in the absence of FGF on glass coverslips, similar "mean" D values were found in both cell poles (D = 2.0 x 10(-9) cm2/s). These results show that lateral mobility of lipids in endothelial plasmalemma varies in response to external factors such as FGF and the ECM.     

Increased diffusional mobility of CFTR at the plasma membrane after deletion of its C-terminal PDZ binding motif

The cystic fibrosis transmembrane conductance regulator (CFTR) protein is a cAMP-regulated Cl- channel expressed at the apical plasma membrane. It has been proposed that the C-terminal PDZ binding motif of CFTR is required for its apical membrane targeting and that PDZ-domain interactions may tether CFTR to the actin cytoskeleton via soluble proteins including EBP50/NHERF1 and ezrin. We measured the diffusional mobility of human CFTR in the plasma membrane of Madin-Darby canine kidney cells by photobleaching of green fluorescent protein (GFP)-CFTR chimeras. After bleaching by a focused laser beam, GFP-CFTR fluorescence in the bleached membrane region recovered to approximately 90% of its initial level, indicating that nearly all of the CFTR was mobile. The GFP-CFTR diffusion coefficient (D) was 0.99 +/- 0.09 x 10(-10) cm2/s at 37 degrees C, similar to that of other membrane proteins. GFP-CFTR diffusion was not altered by protein kinase A or C activators but was blocked by paraformaldehyde and filipin. CFTR mutants lacking functional PDZ-binding domains (GFPCFTR-DeltaTRL and GFP-CFTR-DeltaTRA) were also mobile with D significantly increased by approximately 60% compared with GFP-CFTR. However, GFP-CFTR, GFP-CFTR-Delta TRL, and GFP-CFTR-DeltaTRA had similar mobilities (D approximately 12 x 10(-10) cm2/s) at the endoplasmic reticulum in brefeldin A-treated cells. Agents that modulate the actin cytoskeleton (cytochalasin D and jasplakinolide) altered the plasma membrane mobility of CFTR but not CFTR- DeltaTRL. EBP50 (NHERF1), a PDZ domain-containing protein that interacts with the C terminus of CFTR, diffused freely in the cytoplasm with a diffusion coefficient of 0.9 +/- 0.1 x 10(-7) cm2/s. EBP50 diffusion increased by approximately 2-fold after deletion of its ezrin-binding domain. These results indicate that wild-type CFTR is not tethered statically at the plasma membrane but that its diffusion is dependent on PDZ-domain interactions and an intact actin skeleton. PDZ-domain interactions of CFTR are thus dynamic and occur on a time scale of seconds or faster.     

Plasma membrane diffusion of G protein-coupled receptor oligomers

G protein-coupled receptors are known to form homo-and heteromers at the plasma membrane, but the molecular properties of these oligomers are relatively unknown. Here, we show a method that allows the diffusion of G protein-coupled receptors oligomers in the plasma membrane to be monitored in single cells by combining Bimolecular Fluorescence Complementation and Fluorescence Correlation Spectroscopy. With this approach we have measured, for the first time, the membrane diffusional characteristics of adenosine A(1) and A(2A) receptor homo-and heterodimers in Chinese Hamster Ovary cells. Interestingly, both homodimers display similar diffusion co-efficients (D) when expressed in living cells (D=5.0 and 4.8x10(-9) cm(2)/s, respectively) but the heterodimer formed by these receptors exhibit a significantly faster plasma membrane diffusion co-efficent (D=5.6x10(-9) cm(2)/s) when compared to the adenosine A(1) receptor tagged with the full-length yellow fluorescent protein (D=4.0x10(-9) cm(2)/s). Overall, these results demonstrate differences in plasma membrane diffusion between adenosine receptor homo-and heterodimers, providing new insights into the molecular plasticity of G protein-coupled receptor oligomerization.