Trapped by a skeleton--the maintenance of epithelial membrane domains

Dynamics of pinned membranes with application to protein diffusion on the surface of red blood cells

We present a theoretical treatment and simulation algorithm for the dynamics of Helfrich elastic membrane surfaces in the presence of general harmonic perturbations and hydrodynamic coupling to the surrounding solvent. In the limit of localized and strong interactions, this harmonic model can be used to pin the membrane to intracellular/intercellular structures. We consider the case of pinning to the cytoskeleton and use such a model to estimate the macroscopic diffusion constant for band 3 protein on the surface of human erythrocytes. Comparison to experimental results suggests that thermal undulations of the membrane surface should play a significant role in protein mobility on the red blood cell.

Regulation of protein mobility via thermal membrane undulations

The in-plane diffusivelike motion of membrane bound proteins on the surface of cells is considered. We suggest, on the basis of theoretical arguments and simulation, that thermally excited undulations of the lipid bilayer may serve as a mechanism for proteins to hop between adjacent regions on the cell surface separated by barriers composed of internal cellular structure (e.g., the cytoskeleton). We specifically investigate the mobility of band 3 dimer on the surface of red blood cells where the spectrin cytoskeletal meshwork defines a series of "corrals" on the cell surface known to hinder protein motion. Previous models of this system have postulated that the cytoskeleton must deform to allow passage of membrane bound proteins out of these corral regions and have ignored fluctuations of the bilayer. Our model provides a complementary mechanism and we posit that the mobility of real proteins in real cells is likely the result of several mechanisms acting in parallel.

Lateral diffusion of membrane proteins in the presence of static and dynamic corrals: suggestions for appropriate observables

We consider the possibility of inferring the nature of cytoskeletal interaction with transmembrane proteins via optical experiments such as single-particle tracking (SPT) and near-field scanning optical microscopy (NSOM). In particular, we demonstrate that it may be possible to differentiate between static and dynamic barriers to diffusion by examining the time-dependent variance and higher moments of protein population inside cytoskeletal "corrals." Simulations modeling Band 3 diffusion on the surface of erythrocytes provide a concrete demonstration that these statistical tools might prove useful in the study of biological systems.

Regulation of protein mobility in cell membranes: a dynamic corral model

We analyze a two-state stochastic corral model for regulation of protein diffusion in a cell membrane. This model could mimic control of protein transport in the membrane by the cytoskeleton. The dynamic corral acts as a gate which when open permits an otherwise trapped protein to escape to a neighboring corral in the cytoskeletal network. We solve for the escape rate over a wide range of parameters of the model, and compare these results with Monte Carlo simulations. Upon introducing measured values of the model parameters for Band 3 in erythrocyte membranes, we are able to estimate the value for one unknown parameter, the average rate at which the corral closes. The ratio of calculated closing rate to measured opening rate is roughly 100:1, consistent with a gating mechanism whereby protein mobility is regulated by dissociation and reassociation of segments of the cytoskeletal network.

The cell biology of blastocyst development

Preimplantation development encompasses the "free"-living period of mammalian embryogenesis, which culminates in the formation of a fluid-filled structure, the blastocyst. Cavitation (blastocyst formation) is accompanied by the expression of a novel set of gene products that contribute directly to the attainment of cell polarity with the trophectoderm, which is both the first epithelium of development and the outer cell layer encircling the inner cell mass of the blastocyst. Several of these gene products have been identified and include the tight junction (ZO-1), Na/K-ATPase (alpha and beta subunits), uvomorulin, gap junction (connexin43), and growth factors such as transforming growth factor-alpha (TGF-alpha) and epidermal growth factor (EGF). This review will examine the role(s) of each of these gene products during the onset and progression of blastocyst formation. The trophectodermal tight junctional permeability seal regulates the leakage of blastocoel fluid and also assists in the maintenance of a polarized Na/K-ATPase distribution to the basolateral plasma membrane domain of the mural trophectoderm. The polarized distribution of the Na/K-ATPase plays an integral role in the establishment of a trans-trophectoderm Na+ gradient, which drives the osmotic accumulation of water across the epithelium into the nascent blastocoelic cavity. The cell adhesion provided by uvomorulin is necessary for the establishment of the tight junctional seal, as well as the maintenance of the polarized Na/K-ATPase distribution. Growth factors such as TGF-alpha and EGF stimulate an increase in the rate of blastocoel expansion, which could, in part, be mediated by secondary messengers that result in an increase in Na/K-ATPase activity. Insight into the mechanism of cavitation has, therefore, directly linked blastocyst formation to trophectoderm cell differentiation, which arises through fundamental cell biological processes that are directly involved in the attainment of epithelial cell polarity.

The membrane skeleton of erythrocytes. A percolation model

The spectrin network on the cytoplasmic surface of the erythrocyte membrane is modeled as a triangular lattice of spectrin tetramers. This network obstructs lateral diffusion of proteins and provides mechanical reinforcement to the membrane. These effects are treated in a systematic and unified manner in terms of a percolation model. The diffusion coefficient is obtained as a function of the fraction of normal spectrin tetramers for both static and fluctuating barriers. The elasticity of the network is calculated as a function of the fraction of normal spectrin and the ratio of bending to stretching energies. For static barriers, elasticity and lateral diffusion are incompatible: if a network is connected enough to be elastic, it is connected enough to block long-range lateral diffusion. The elasticity and the force required for mechanical breakdown go to zero at the percolation threshold; experimental evidence suggests the existence of a stability threshold at or near the percolation threshold. The model is qualitatively applicable to other cells with membrane skeletons, such as epithelial cells, in which localization of membrane proteins is essential to differentiation.

The membrane skeleton of erythrocytes: models of its effect on lateral diffusion

The membrane skeleton, a network of structural proteins attached to the cytoplasmic surface of the plasma membrane, hinders lateral diffusion of integral proteins. 2. In some types of cells, such as epithelial cells and nerve cells, the obstruction of lateral diffusion by the membrane skeleton is one of the mechanisms by which proteins are localized to domains on the cell surface. 3. The effect of the membrane skeleton on lateral diffusion may involve steric hindrance, transient binding or both. Three pictures of the effect are reviewed, the discrete barrier model, the continuous barrier model and the transient binding model. 4. Experiments to distinguish the models are discussed.