Single-particle tracking: effects of corrals.

Structural proteins of the membrane skeleton are thought to form "corrals" at the membrane surface, and these corrals may restrict lateral diffusion of membrane proteins. Recent experimental developments in single-particle tracking and laser trapping make it possible to examine the corral model in detail. Techniques to interpret these experiments are presented. First, escape times for a diffusing particle in a corral are obtained from Monte Carlo calculations and analytical solutions for various corral sizes, shapes, and escape probabilities, and reduced to a common curve. Second, the identification of corrals in tracking experiments is considered. The simplest way to identify corrals is by sight. If the walls are impermeable enough, a trajectory fills the corral before the diffusing particle escapes. The fraction of distinct sites visited before escape is calculated for corrals of various sizes, shapes, and escape probabilities, and reduced to a common curve. This fraction is also a measure of the probability that the diffusing species will react with another species in the corral before escaping. Finally, the effect of the sampling interval on the measurement of the short-range diffusion coefficient is examined.     

Regulation Mechanism of the Lateral Diffusion of Band 3 in Erythrocyte Membranes by the Membrane Skeleton

Mechanisms that regulate the movement of a membrane spanning protein band 3 in erythrocyte ghosts were investigated at the level of a single or small groups of molecules using single particle tracking with an enhanced time resolution (0.22 ms). Two-thirds of band 3 undergo macroscopic diffusion: a band 3 molecule is temporarily corralled in a mesh of 110 nm in diameter, and hops to an adjacent mesh an average of every 350 ms. The rest (one-third) of band 3 exhibited oscillatory motion similar to that of spectrin, suggesting that these band 3 molecules are bound to spectrin. When the membrane skeletal network was dragged and deformed/translated using optical tweezers, band 3 molecules that were undergoing hop diffusion were displaced toward the same direction as the skeleton. Mild trypsin treatment of ghosts, which cleaves off the cytoplasmic portion of band 3 without affecting spectrin, actin, and protein 4.1, increased the intercompartmental hop rate of band 3 by a factor of 6, whereas it did not change the corral size and the microscopic diffusion rate within a corral. These results indicate that the cytoplasmic portion of band 3 collides with the membrane skeleton, which causes temporal confinement of band 3 inside a mesh of the membrane skeleton.     

A Dynamic Corral Model of Receptor Trafficking at a Synapse

The postsynaptic density (PSD) is a cytoskeletal specialization within the postsynaptic membrane of a neuron that helps to concentrate and organize neurotransmitter receptors at a chemical synapse. The total number of receptors within the PSD, which is a major factor in determining the physiological strength or weight of a synapse, fluctuates due to the surface diffusion of receptors into and out of the PSD, and the interactions of receptors with scaffolding proteins and cytoskeletal elements within the PSD. In this article, we present a stochastic model of protein receptor trafficking at the PSD that takes into account these various processes. The PSD is treated as a stochastically gated corral, which contributes a source of extrinsic or environmental noise that supplements the intrinsic noise arising from small receptor numbers. Using a combination of stochastic analysis and Monte Carlo simulations, we determine the time-dependent variation in the mean and variance of synaptic receptor numbers for a variety of initial conditions that simulate fluorescence recovery after photobleaching experiments, and indicate how such data might be used to infer certain properties of the PSD.     

The brush border cytoskeleton is not static: in vivo turnover of proteins

The shape and stability of intestinal epithelial cell microvilli are maintained by a cytoskeletal core composed of a bundle of actin filaments with several associated proteins. The core filaments are intimately associated with the overlying plasma membrane, in which there occur rapid turnover of proteins and constant incorporation of new membrane. Previous work has shown that starvation or inhibition of protein synthesis results in modulation of microvillar length, which indicates that there may be cytoskeletal protein turnover. We demonstrate herein, by means of in vivo pulse labeling with radioactive amino acids, that turnover of brush border cytoskeletal proteins occurs in mature absorptive cells. Turnover of cytoskeletal proteins appears to be quite slow relative to membrane protein turnover, which suggests that the turnover of these two microvillar compartments is not coupled. We thus conclude that cytoskeletal protein turnover may be a factor used to maintain normal length and stability of microvilli and that the cytoskeleton cannot be considered a static structure.     

A three-dimensional random network model of the cytoskeleton and its role in mechanotransduction and nucleus deformation

We have developed a three-dimensional random network model of the intracellular actin cytoskeleton and have used it to study the role of the cytoskeleton in mechanotransduction and nucleus deformation. We use the model to predict the deformation of the nucleus when mechanical stresses applied on the plasma membrane are propagated through the random cytoskeletal network to the nucleus membrane. We found that our results agree with previous experiments utilizing micropipette pulling. Therefore, we propose that stress propagation through the random cytoskeletal network can be a mechanism to effect nucleus deformation, without invoking any biochemical signaling activity. Using our model, we also predict how nucleus strain and its relative displacement within the cytosol vary with varying concentrations of actin filaments and actin-binding proteins. We find that nucleus strain varies in a sigmoidal manner with actin filament concentration, while there exists an optimal concentration of actin-binding proteins that maximize nucleus displacement. We provide a theoretical analysis for these nonlinearities in terms of the connectivity of the random cytoskeletal network. Finally, we discuss laser ablation experiments that can be performed to validate these results in order to advance our understanding of the role of the cytoskeleton in mechanotransduction.     

Erythroid anion transporter assembly is mediated by a developmentally regulated recruitment onto a preassembled membrane cytoskeleton

Analysis of the expression and assembly of the anion transporter by metabolic pulse-chase and steady-state protein and RNA measurements reveals that the extent of association of band 3 with the membrane cytoskeleton varies during chicken embryonic development. Pulse-chase studies have indicated that band 3 polypeptides do not associate with the membrane cytoskeleton until they have been transported to the plasma membrane. At this time, band 3 polypeptides are slowly recruited, over a period of hours, onto a preassembled membrane cytoskeletal network and the extent of this cytoskeletal assembly is developmentally regulated. Only 3% of the band 3 polypeptides are cytoskeletal-associated in 4-d erythroid cells vs. 93% in 10-d erythroid cells and 36% in 15-d erythroid cells. This observed variation appears to be regulated primarily at the level of recruitment onto the membrane cytoskeleton rather than by different transport kinetics to the membrane or differential turnover of the soluble and insoluble polypeptides and is not dependent upon the lineage or stage of differentiation of the erythroid cells. Steady-state protein and RNA analyses indicate that the low levels of cytoskeletal band 3 very early in development most likely result from limiting amounts of ankyrin and protein 4.1, the membrane cytoskeletal binding sites for band 3. As embryonic development proceeds, ankyrin and protein 4.1 levels increase with a concurrent rise in the level of cytoskeletal band 3 until, on day 10 of development, virtually all of the band 3 polypeptides are cytoskeletal bound. After day 10, the levels of total and cytoskeletal band 3 decline, whereas ankyrin and protein 4.1 continue to accumulate until day 18, indicating that the cytoskeletal association of band 3 is not regulated solely by the availability of membrane cytoskeletal binding sites at later stages of development. Thus, multiple mechanisms appear to regulate the recruitment of band 3 onto the erythroid membrane cytoskeleton during chicken embryonic development.     

Clustered diffusion of integrins

We discuss the diffusion of clusters of integrins (and other similar membrane proteins) on a cell membrane with a cortical cytoskeleton. We argue that protein clusters—in contrast with normal oligomers, which are forced to pass through cytoskeletal barriers all at once—should be treated essentially as many-legged random walkers that can pass through a cytoskeletal barrier by putting one leg at a time through the fence. We present the mathematics that should describe the phenomenon, which result in a two-parameter model of diffusion that should apply to any cluster size. We also perform and discuss numerical simulations of the effect in the erythrocyte model system.     

Diffusion in a Fluid Membrane with a Flexible Cortical Cytoskeleton

We calculate the influence of a flexible network of long-chain proteins, which is anchored to a fluid membrane, on protein diffusion in this membrane. This is a model for the cortical cytoskeleton and the lipid bilayer of the red blood cell, which we apply to predict the influence of the cytoskeleton on the diffusion coefficient of a mobile band 3 protein. Using the pressure field that the cytoskeleton exerts on the membrane, from the steric repulsion between the diffusing protein and the cytoskeletal filaments, we define a potential landscape for the diffusion within the bilayer. We study the changes to the diffusion coefficient on removal of one type of anchor proteins, e.g., in several hemolytic anemias, as well as for isotropic and anisotropic stretching of the cytoskeleton. We predict an overall increase of the diffusion for a smaller number of anchor proteins and increased diffusion for anisotropic stretching in the direction of the stretch, because of the decrease in the spatial frequency as well as in the height of the potential barriers.     

Stiffening of Red Blood Cells Induced by Cytoskeleton Disorders: A Joint Theory-Experiment Study

The functions and elasticities of the cell are largely related to the structures of the cytoskeletons underlying the lipid bilayer. Among various cell types, the red blood cell (RBC) possesses a relatively simple cytoskeletal structure. Underneath the membrane, the RBC cytoskeleton takes the form of a two-dimensional triangular network, consisting of nodes of actins (and other proteins) and edges of spectrins. Recent experiments focusing on the malaria-infected RBCs (iRBCs) show that there is a correlation between the elongation of spectrins in the cytoskeletal network and the stiffening of the iRBCs. Here we rationalize the correlation between these two observations by combining the wormlike chain model for single spectrins and the effective medium theory for the network elasticity. We specifically focus on how the disorders in the cytoskeletal network affect its macroscopic elasticity. Analytical and numerical solutions from our model reveal that the stiffness of the membrane increases with increasing end-to-end distances of spectrins, but has a nonmonotonic dependence on the variance of the end-to-end distance distributions. These predictions are verified quantitatively by our atomic force microscopy and micropipette aspiration measurements of iRBCs. The model may, from a molecular level, provide guidelines for future identification of new treatment methods for RBC-related diseases, such as malaria infection.     

Switching of membrane organelles between cytoskeletal transport systems is determined by regulation of the microtubule-based transport

Intracellular transport of membrane organelles occurs along microtubules (MTs) and actin filaments (AFs). Although transport along each type of the cytoskeletal tracks is well characterized, the switching between the two types of transport is poorly understood because it cannot be observed directly in living cells. To gain insight into the regulation of the switching of membrane organelles between the two major transport systems, we developed a novel approach that combines live cell imaging with computational modeling. Using this approach, we measured the parameters that determine how fast membrane organelles switch back and forth between MTs and AFs (the switching rate constants) and compared these parameters during different signaling states. We show that regulation involves a major change in a single parameter: the transferring rate from AFs onto MTs. This result suggests that MT transport is the defining factor whose regulation determines the choice of the cytoskeletal tracks during the transport of membrane organelles.     

Simulation of integrin-cytoskeletal interactions in migrating fibroblasts.

Cell migration is a dynamic phenomenon requiring a physical interaction between the internal cell motile machinery and the external substratum in which adhesion receptors, such as integrins, serve as the transmembrane link. To analyze quantitatively this interaction, we apply a modified Brownian dynamics algorithm to simulate cytoskeleton-mediated transport of integrin on the dorsal surfaces of migrating fibroblasts. Previously, we experimentally demonstrated that integrin is transported in an intermittent fashion, with directed excursions interspersed by diffusive periods, preferentially toward the cell edge where the integrin is likely used in the formation of nascent adhesions. Integrins containing mutations in the cytoskeleton-binding region of the cytoplasmic domain display statistically different degrees of directed transport, indicating that this phenomenon is dependent on cytoskeletal associations. In the present work, we develop a computer algorithm generating simulated integrin transport trajectories, given estimates for the rate constants defining coupling (kc) and uncoupling (ku) of integrin with cytoskeletal components. Other parameters supplied to the program, the diffusion coefficient (D) for integrin in the membrane and the instantaneous velocity (vi) of the integrin/cytoskeleton complex, have been measured independently in our experimental system. By comparing the simulated trajectories with those obtained experimentally, we are able to estimate the coupling and uncoupling rate constants for the interaction of integrin with cytoskeletal elements in vivo. We find that integrin couples with cytoskeletal elements at a rate approximately 10 times slower than its rate of uncoupling (kc = 0.3 s-1, ku = 3 s-1). Comparison of these rate constants with an equivalent rate constant for diffusion, k+ = 0.4 s-1, indicates that the coupling interaction is likely a diffusion-limited process, as is typically expected for membrane processes. We further show by calculation that directed transport is necessary for integrin to traverse the length of an extending lamellipod to its leading edge; diffusion alone is not sufficiently fast to supply adhesion receptors to points of new cell/substratum contact.     

A Highlights from MBoC Selection: Single-molecule analysis of diffusion and trapping of STIM1 and Orai1 at endoplasmic reticulum–plasma membrane junctions

Following endoplasmic reticulum (ER) Ca²⁺ depletion, STIM1 and Orai1 complexes assemble autonomously at ER–plasma membrane (PM) junctions to trigger store-operated Ca²⁺ influx. One hypothesis to explain this process is a diffusion trap in which activated STIM1 diffusing in the ER becomes trapped at junctions through interactions with the PM, and STIM1 then traps Orai1 in the PM through binding of its calcium release-activated calcium activation domain. We tested this model by analyzing STIM1 and Orai1 diffusion using single-particle tracking, photoactivation of protein ensembles, and Monte Carlo simulations. In resting cells, STIM1 diffusion is Brownian, while Orai1 is slightly subdiffusive. After store depletion, both proteins slow to the same speeds, consistent with complex formation, and are confined to a corral similar in size to ER–PM junctions. While the escape probability at high STIM:Orai expression ratios is <1%, it is significantly increased by reducing the affinity of STIM1 for Orai1 or by expressing the two proteins at comparable levels. Our results provide direct evidence that STIM-Orai complexes are trapped by their physical connections across the junctional gap, but also reveal that the complexes are surprisingly dynamic, suggesting that readily reversible binding reactions generate free STIM1 and Orai1, which engage in constant diffusional exchange with extrajunctional pools.     

Mechanics and control of the cytoskeleton in Amoeba proteus.

Many models of the cytoskeletal motility of Amoeba proteus can be formulated in terms of the theory of reactive interpenetrating flow (Dembo and Harlow, 1986). We have devised numerical methodology for testing such models against the phenomenon of steady axisymmetric fountain flow. The simplest workable scheme revealed by such tests (the minimal model) is the main preoccupation of this study. All parameters of the minimal model are determined from available data. Using these parameters the model quantitatively accounts for the self assembly of the cytoskeleton of A. proteus: for the formation and detailed morphology of the endoplasmic channel, the ectoplasmic tube, the uropod, the plasma gel sheet, and the hyaline cap. The model accounts for the kinematics of the cytoskeleton: the detailed velocity field of the forward flow of the endoplasm, the contraction of the ectoplasmic tube, and the inversion of the flow in the fountain zone. The model also gives a satisfactory account of measurements of pressure gradients, measurements of heat dissipation, and measurements of the output of useful work by amoeba. Finally, the model suggests a very promising (but still hypothetical) continuum formulation of the free boundary problem of amoeboid motion. by balancing normal forces on the plasma membrane as closely as possible, the minimal model is able to predict the turgor pressure and surface tension of A. proteus. Several dynamical factors are crucial to the success of the minimal model and are likely to be general features of cytoskeletal mechanics and control in amoeboid cells. These are: a constitutive law for the viscosity of the contractile network that includes an automatic process of gelation as the network density gets large; a very vigorous cycle of network polymerization and depolymerization (in the case of A. proteus, the time constant for this reaction is approximately 12 s); control of network contractility by a diffusible factor (probably calcium ion); and control of the adhesive interaction between the cytoskeleton and the inner surface of the plasma membrane.     

MreB-Dependent Organization of the E.?coli Cytoplasmic Membrane Controls Membrane Protein Diffusion

The functional organization of prokaryotic cell membranes, which is essential for many cellular processes, has been challenging to analyze due to the small size and nonflat geometry of bacterial cells. Here, we use single-molecule fluorescence microscopy and three-dimensional quantitative analyses in live Escherichia coli to demonstrate that its cytoplasmic membrane contains microdomains with distinct physical properties. We show that the stability of these microdomains depends on the integrity of the MreB cytoskeletal network underneath the membrane. We explore how the interplay between cytoskeleton and membrane affects trans-membrane protein (TMP) diffusion and reveal that the mobility of the TMPs tested is subdiffusive, most likely caused by confinement of TMP mobility by the submembranous MreB network. Our findings demonstrate that the dynamic architecture of prokaryotic cell membranes is controlled by the MreB cytoskeleton and regulates the mobility of TMPs.     

The chondrocyte cytoskeleton in mature articular cartilage: structure and distribution of actin, tubulin, and vimentin filaments.

We investigated the structure of the chondrocyte cytoskeleton in intact tissue sections of mature bovine articular cartilage using confocal fluorescence microscopy complemented by protein extraction and immunoblotting analysis. Actin microfilaments were present inside the cell membrane as a predominantly cortical structure. Vimentin and tubulin spanned the cytoplasm from cell to nuclear membrane, the vimentin network appearing finer compared to tubulin. These cytoskeletal structures were present in chondrocytes from all depth zones of the articular cartilage. However, staining intensity varied from zone to zone, usually showing more intense staining for the filament systems at the articular surface compared to the deeper zones. These results obtained on fluorescently labeled sections were also corroborated by protein contents extracted and observed by immunoblotting. The observed cytoskeletal structures are compatible with some of the proposed cellular functions of these systems and support possible microenvironmental regulation of the cytoskeleton, including that due to physical forces from load-bearing, which are known to vary through the depth layers of articular cartilage.     

Ultracentrifugal analysis of the junction complexes of the red cell membrane cytoskeletal network: application to hereditary spherocytosis and metabolically depleted cells

A method has been developed for the assessment of the number of spectrin dimer units associated with each actin protofilament junction, in the membrane cytoskeletal network (i.e. the degree of branching) of the red cell. Ghosts are first exposed to elevated temperature at low ionic strength to dissociate some 65% of the spectrin tetramers (that link the network junctions) into dimers, without causing their release from the actin filaments. Non-ionic detergent is then added to solubilize the membrane itself with its intrinsic proteins, so as to liberate the cytoskeletal material, and the mixture is immediately examined in the analytical ultracentrifuge. The predominant components observed are isolated junctions (20 S), free spectrin dimers and the residual undissociated cytoskeletal material, with very minor components, probably corresponding to multiple junctions, linked by spectrin tetramers. The junction boundary is homogeneous within the accuracy of measurement and is taken to correspond to a complex containing six spectrin dimers, known to predominate in situ. About 17% of the total network is liberated in this form and 12% as free spectrin dimers. In hereditary spherocytosis both the size of the junction complex (as reflected by its sedimentation coefficient) and the proportion of the complex and of free spectrin liberated are indistinguishable from normal values. We conclude that the reported deficit of spectrin in hereditary spherocytosis is not reflected by a lower degree of branching of the network, and, if the membrane area is not correspondingly reduced, this must mean that the junctions are more widely spaced and the spectrin tetramers therefore more extended. In metabolically depleted cells, in which the cytoskeletal proteins are known to be extensively dephosphorylated, there is no change in the sedimentation pattern and thus no detectable loss of spectrin from the junctions or weakening in the cohesion of the cytoskeletal network.     

Modelling the evolution and spread of HIV immune escape mutants

During infection with human immunodeficiency virus (HIV), immune pressure from cytotoxic T-lymphocytes (CTLs) selects for viral mutants that confer escape from CTL recognition. These escape variants can be transmitted between individuals where, depending upon their cost to viral fitness and the CTL responses made by the recipient, they may revert. The rates of within-host evolution and their concordant impact upon the rate of spread of escape mutants at the population level are uncertain. Here we present a mathematical model of within-host evolution of escape mutants, transmission of these variants between hosts and subsequent reversion in new hosts. The model is an extension of the well-known SI model of disease transmission and includes three further parameters that describe host immunogenetic heterogeneity and rates of within host viral evolution. We use the model to explain why some escape mutants appear to have stable prevalence whilst others are spreading through the population. Further, we use it to compare diverse datasets on CTL escape, highlighting where different sources agree or disagree on within-host evolutionary rates. The several dozen CTL epitopes we survey from HIV-1 gag, RT and nef reveal a relatively sedate rate of evolution with average rates of escape measured in years and reversion in decades. For many epitopes in HIV, occasional rapid within-host evolution is not reflected in fast evolution at the population level.     

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.     

Cytoskeleton association and virion incorporation of the human immunodeficiency virus type 1 Vif protein.

The human immunodeficiency virus type 1 (HIV-1) Vif protein has an important role in the regulation of virus infectivity. This function of Vif is cell type specific, and virions produced in the absence of Vif in restrictive cells have greatly reduced infectivity. We show here that the intracellular localization of Vif is dependent on the presence of the intermediate filament vimentin. Fractionation of acutely infected T cells or transiently transfected HeLa cells demonstrates the existence of a soluble and a cytoskeletal form and to a lesser extent the presence of a detergent-extractable form of Vif. Confocal microscopy suggests that in HeLa cells, Vif is predominantly present in the cytoplasm and closely colocalizes with the intermediate filament vimentin. Treatment of cells with drugs affecting the structure of vimentin filaments affect the localization of Vif accordingly, indicating a close association of Vif with this cytoskeletal component. The association of Vif with vimentin can cause the collapse of the intermediate filament network into a perinuclear aggregate. In contrast, analysis of Vif in vimentin-negative cells reveals significant staining of the nucleus and the nuclear membrane in addition to diffuse cytoplasmic staining. In addition to the association of Vif with intermediate filaments, analyses of virion preparations demonstrate that Vif is incorporated into virus particles. In sucrose density gradients, Vif cosediments with capsid proteins even after detergent treatment of virus preparations, suggesting that Vif is associated with the inner core of HIV particles. We propose a model in which Vif has a crucial function as a virion component either by regulating virus maturation or following virus entry into a host cell possibly involving an interaction with the cellular cytoskeletal network.