Actin protofilament orientation at the erythrocyte membrane

Complementary mesoscale dynamics of spectrin and acto-myosin shape membrane territories during mechanoresponse

The spectrin-based membrane skeleton is a major component of the cell cortex. While expressed by all metazoans, its dynamic interactions with the other cortex components, including the plasma membrane or the acto-myosin cytoskeleton, are poorly understood. Here, we investigate how spectrin re-organizes spatially and dynamically under the membrane during changes in cell mechanics. We find spectrin and acto-myosin to be spatially distinct but cooperating during mechanical challenges, such as cell adhesion and contraction, or compression, stretch and osmolarity fluctuations, creating a cohesive cortex supporting the plasma membrane. Actin territories control protrusions and contractile structures while spectrin territories concentrate in retractile zones and low-actin density/inter-contractile regions, acting as a fence that organize membrane trafficking events. We unveil here the existence of a dynamic interplay between acto-myosin and spectrin necessary to support a mesoscale organization of the lipid bilayer into spatially-confined cortical territories during cell mechanoresponse.

Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

We establish that the Fourier modes of the magnetization serve as the dynamical eigenmodes for the two-dimensional Ising model at the critical temperature with local spin-exchange moves, i.e., Kawasaki dynamics. We obtain the dynamical scaling properties for these modes and use them to calculate the time evolution of two dynamical quantities for the system, namely, the autocorrelation function and the mean-square deviation of the line magnetizations. At intermediate times 1≲t≲L^{z_{c}}, where z_{c}=4-η=15/4 is the dynamical critical exponent of the model, we find that the line magnetization undergoes anomalous diffusion. Following our recent work on anomalous diffusion in spin models, we demonstrate that the generalized Langevin equation with a memory kernel consistently describes the anomalous diffusion, verifying the corresponding fluctuation-dissipation theorem with the calculation of the force autocorrelation function.

Feisty filaments: actin dynamics in the red blood cell membrane skeleton

PURPOSE OF REVIEW

This article discusses recent advances and unsolved questions in our understanding of actin filament organization and dynamics in the red blood cell (RBC) membrane skeleton, a two-dimensional quasi-hexagonal network consisting of (α1β1)2-spectrin tetramers interconnecting short actin filament-based junctional complexes.

RECENT FINDINGS

In contrast to the long-held view that RBC actin filaments are static structures that do not exchange subunits with the cytosol, RBC actin filaments are dynamic structures that undergo subunit exchange and turnover, as evidenced by monomer incorporation experiments with rhodamine-actin and filament disruption experiments with actin-targeting drugs. The malaria-causing parasite, Plasmodium falciparum, co-opts RBC actin dynamics to construct aberrantly branched actin filament networks. Even though RBC actin filaments are dynamic, RBC actin filament lengths are highly uniform (∼37 nm). RBC actin filament lengths are thought to be stabilized by the capping proteins, tropomodulin-1 and αβ-adducin, as well as the side-binding protein tropomyosin, present in an equimolar combination of two isoforms, TM5b (Tpm1.9) and TM5NM1 (Tpm3.1).

SUMMARY

New evidence indicates that RBC actin filaments are not simply passive cytolinkers, but rather dynamic structures whose assembly and disassembly play important roles in RBC membrane function.

Anatomy of the red cell membrane skeleton: unanswered questions

The red cell membrane skeleton is a pseudohexagonal meshwork of spectrin, actin, protein 4.1R, ankyrin, and actin-associated proteins that laminates the inner membrane surface and attaches to the overlying lipid bilayer via band 3-containing multiprotein complexes at the ankyrin- and actin-binding ends of spectrin. The membrane skeleton strengthens the lipid bilayer and endows the membrane with the durability and flexibility to survive in the circulation. In the 36 years since the first primitive model of the red cell skeleton was proposed, many additional proteins have been discovered, and their structures and interactions have been defined. However, almost nothing is known of the skeleton's physiology, and myriad questions about its structure remain, including questions concerning the structure of spectrin in situ, the way spectrin and other proteins bind to actin, how the membrane is assembled, the dynamics of the skeleton when the membrane is deformed or perturbed by parasites, the role lipids play, and variations in membrane structure in unique regions like lipid rafts. This knowledge is important because the red cell membrane skeleton is the model for spectrin-based membrane skeletons in all cells, and because defects in the red cell membrane skeleton underlie multiple hemolytic anemias.

Trains, tails and loops of partially adsorbed semi-flexible filaments

Polymer adsorption is a fundamental problem in statistical mechanics that has direct relevance to diverse disciplines ranging from biological lubrication to stability of colloidal suspensions. We combine experiments with computer simulations to investigate depletion induced adsorption of semi-flexible polymers onto a hard-wall. Three dimensional filament configurations of partially adsorbed F-actin polymers are visualized with total internal reflection fluorescence microscopy. This information is used to determine the location of the adsorption/desorption transition and extract the statistics of trains, tails and loops of partially adsorbed filament configurations. In contrast to long flexible filaments which primarily desorb by the formation of loops, the desorption of stiff, finite-sized filaments is largely driven by fluctuating filament tails. Simulations quantitatively reproduce our experimental data and allow us to extract universal laws that explain scaling of the adsorption-desorption transition with relevant microscopic parameters. Our results demonstrate how the adhesion strength, filament stiffness, length, as well as the configurational space accessible to the desorbed filament can be used to design the characteristics of filament adsorption and thus engineer properties of composite biopolymeric materials.

Organization of FtsZ filaments in the bacterial division ring measured from polarized fluorescence microscopy

Cytokinesis in bacteria is accomplished by a ring-shaped cell-division complex (the Z-ring). The primary component of the Z-ring is FtsZ, a filamentous tubulin homolog that serves as a scaffold for the recruitment of other cell-division-related proteins. FtsZ forms filaments and bundles. In the cell, it has been suggested that FtsZ filaments form the arcs of the ring and are aligned in the cell-circumferential direction. Using polarized fluorescence microscopy in live Escherichia coli cells, we measure the structural organization of FtsZ filaments in the Z-ring. The data suggest a disordered organization: a substantial portion of FtsZ filaments are aligned in the cell-axis direction. FtsZ organization in the Z-ring also appears to depend on the bacterial species. Taken together, the unique arrangement of FtsZ suggests novel unexplored mechanisms in bacterial cell division.

The human erythrocyte plasma membrane: a Rosetta Stone for decoding membrane-cytoskeleton structure

The mammalian erythrocyte, or red blood cell (RBC), is a unique experiment of nature: a cell with no intracellular organelles, nucleus or transcellular cytoskeleton, and a plasma membrane with uniform structure across its entire surface. By virtue of these specialized properties, the RBC membrane has provided a template for discovery of the fundamental actin filament network machine of the membrane skeleton, now known to confer mechanical resilience, anchor membrane proteins, and organize membrane domains in all cells. This chapter provides a historical perspective and critical analysis of the biochemistry, structure, and physiological functions of this actin filament network in RBCs. The core units of this network are nodes of ~35-37 nm-long actin filaments, interconnected by long strands of (α1β1)₂-spectrin tetramers, forming a 2D isotropic lattice with quasi-hexagonal symmetry. Actin filament length and stability is critical for network formation, relying upon filament capping at both ends: tropomodulin-1 at pointed ends and αβ-adducin at barbed ends. Tropomodulin-1 capping is essential for precise filament lengths, and is enhanced by tropomyosin, which binds along the short actin filaments. αβ-adducin capping recruits spectrins to sites near barbed ends, promoting network formation. Accessory proteins, 4.1R and dematin, also promote spectrin binding to actin and, with αβ-adducin, link to membrane proteins, targeting actin nodes to the membrane. Dissection of the molecular organization within the RBC membrane skeleton is one of the paramount achievements of cell biological research in the past century. Future studies will reveal the structure and dynamics of actin filament capping, mechanisms of precise length regulation, and spectrin-actin lattice symmetry.

Nanomechanics of multiple units in the erythrocyte membrane skeletal network

Erythrocytes undergo deformations when they transport O₂ and CO₂ across the membrane, yet the 3D nanomechanics of the skeletal network remains poorly understood. Expanding from our previous single isolated unit, we now simulate networks consisting of 1–10 concentric rings of repeating units in equibiaxial deformation. The networks are organized with (1) a 3D model for a single unit, (2) a wrap-around mode between Sp and actin protofilament in the intra-unit interaction, and (3) a random inter-unit connectivity. These assumptions permit efficient five-degrees-of-freedom (5DOF) simulations when up to 30 pN of radial forces are applied to the boundary spectrin (Sp) and the center and other units are analyzed. As 6 Sp balance their tensions, hexagonal units become irregular. While actin protofilaments remain tangent to the network, their yaw (Φ) angles change drastically with addition of neighboring units or an Sp unfolding. It is anticipated that during deformation, transmembrane complexes associated with the network move laterally through the lipid bilayer and increase the diffusion of molecules across the membrane. When protofilament/Sp sweeps under the lipid bilayer, they mix up the submembrane concentration gradient. Thus, the nanomechanics of actin protofilaments and Sp may enhance the transport of molecules during erythrocyte deformation.

Spectrin folding versus unfolding reactions and RBC membrane stiffness

Spectrin (Sp), a key component of the erythrocyte membrane, is routinely stretched to near its fully folded contour length during cell deformations. Such dynamic loading may induce domain unfolding as suggested by recent experiments. Herein we develop a model to describe the folding/unfolding of spectrin during equilibrium or nonequilibrium extensions. In both cases, our model indicates that there exists a critical extension beyond which unfolding occurs. We further deploy this model, together with a three-dimensional model of the junctional complex in the erythrocyte membrane, to explore the effect of Sp unfolding on the membrane's mechanical properties, and on the thermal fluctuation of membrane-attached beads. At large deformations our results show a distinctive strain-induced unstiffening behavior, manifested in the slow decrease of the shear modulus, and accompanied by an increase in bead fluctuation. Bead fluctuation is also found to be influenced by mode switching, a phenomenon predicted by our three-dimensional model. The amount of stiffness reduction, however, is modest compared with that reported in experiments. A possible explanation for the discrepancy is the occurrence of spectrin head-to-head disassociation which is also included within our modeling framework and used to analyze bead motion as observed via experiment.

A hybrid model for erythrocyte membrane: a single unit of protein network coupled with lipid bilayer

To investigate the nanomechanics of the erythrocyte membrane we developed a hybrid model that couples the actin-spectrin network to the lipid bilayer. This model features a Fourier space Brownian dynamics model of the bilayer, a Brownian dynamics model of the actin protofilament, and a modified wormlike-chain model of the spectrin (including a cable-dynamics model to predict the oscillation in tension). This model enables us to predict the nanomechanics of single or multiple units of the protein network, the lipid bilayer, and the effect of their interactions. The present work is focused on the attitude of the actin protofilament at the equilibrium states coupled with the elevations of the lipid bilayer through their primary linkage at the suspension complex in deformations. Two different actin-spectrin junctions are considered at the junctional complex. With a point-attachment junction, large pitch angles and bifurcation of yaw angles are predicted. Thermal fluctuations at bifurcation may lead to mode-switching, which may affect the network and the physiological performance of the membrane. In contrast, with a wrap-around junction, pitch angles remain small, and the occurrence of bifurcation is greatly reduced. These simulations suggest the importance of three-dimensional molecular junctions and the lipid bilayer/protein network coupling on cell membrane mechanics.

Application of fluorescence polarization microscopy to measure fluorophore orientation in the outer hair cell plasma membrane

The biophysical properties and organization of cell membranes regulate many membrane-based processes, including electromotility in outer hair cells (OHCs) of the cochlea. Studies of the membrane environment can be carried out by measuring the orientation of membrane-bound fluorophores using fluorescence polarization microscopy (FPM). Due to the cylindrical shape of OHCs, existing FPM theory developed for spherical cells is not applicable. We develop a new method for analyzing FPM data suitable for the quasi-cylindrical OHC. We present the theory for this model, as well as a study of the orientation of the fluorescent probe pyridinium, 4-[2-[6-(dioctylamino)-2-naphthalenyl]ethenyl]-1-(3-sulfopropyl) (di-8-ANEPPS) in the OHC membrane. Our results indicate that the absorption transition dipole moment of di-8-ANEPPS orients symmetrically about the membrane normal at 27 deg with respect to the plane of the membrane. The observed agreement between theoretical predictions and experimental measurements establishes the applicability of FPM to study OHC plasma membrane properties.

Structural insights into yeast septin organization from polarized fluorescence microscopy

Septins are polymerizing GTPases that function in cortical organization and cell division. In Saccharomyces cerevisiae they localize at the isthmus between the mother and the daughter cells, where they undergo a transition from a non-dynamic hourglass-shaped assembly to two separate rings, at the onset of cytokinesis. Septins form filaments as pure protein and in vivo, but the filament organization within the hourglass and ring structures is controversial. Here, we use polarized fluorescence microscopy of orientationally constrained green fluorescent protein to determine septin filament organization and dynamics in living yeast. We found that the hourglass is made of filaments aligned along the yeast bud neck. During the transition from hourglass to rings the filaments rotate through 90 degrees in the membrane plane and become circumferential. These data resolve a long-standing controversy in the field and provide strong evidence that septins have a mechanical function in cell division.

3-D nanomechanics of an erythrocyte junctional complex in equibiaxial and anisotropic deformations

The erythrocyte membrane skeleton deforms constantly in circulation, but the mechanics of a junctional complex (JC) in the network is poorly understood. We previously proposed a 3-D mechanical model for a JC (Sung, L. A., and C. Vera. Protofilament and hexagon: A three-dimensional mechanical model for the junctional complex in the erythrocyte membrane skeleton. Ann Biomed Eng 31:1314-1326, 2003) and now developed a mathematical model to compute its equilibrium by dynamic relaxation. We simulated deformations of a single unit in the network to predict the tension of 6 alphabeta spectrin (Sp) (top, middle, and bottom pairs), and the attitude of the actin protofilament [pitch (theta), yaw (phi) and roll (psi) angles]. In equibiaxial deformation, 6 Sp would not begin their first round of "single domain unfolding in cluster" until the extension ratio (lambda) reach approximately 3.6, beyond the maximal sustainable lambda of approximately 2.67. Before Sp unfolds, the protofilament would gradually raise its pointed end away from the membrane, while phi and psi remain almost unchanged. In anisotropic deformation, protofilaments would remain tangent but swing and roll drastically at least once between lambda(i) = 1.0 and approximately 2.8, in a deformation angle- and lambda(i)-dependent fashion. This newly predicted nanomechanics in response to deformations may reveal functional roles previous unseen for a JC, and molecules associated with it, during erythrocyte circulation.

Topographical pattern dynamics in passive adhesion of cell membranes

Strong adhesion of highly active cells often nucleates focal adhesions, synapses, and related structures. Red cells lack such complex adhesion systems and are also nonmotile, but they are shown here to dynamically evolve complex spatial patterns beyond an electrostatic threshold for strong adhesion. Spreading of the cell onto a dense, homogeneous poly-L-lysine surface appears complete in <1 s with occasional blisters that form and dissipate on a similar timescale; distinct rippled or stippled patterns in fluorescently labeled membrane components emerge later, however, on timescales more typical of long-range lipid diffusion (approximately minutes). Within the contact zone, the anionic fluorescent lipid fluorescein phosphoethanolamine is seen to rearrange, forming worm-like rippled or stippled domains of <500 nm that prove independent of whether the cell is intact and sustaining a tension or ruptured. Lipid patterns are accompanied by visible perturbations in Band 3 distribution and weaker perturbations in membrane skeleton actin. Pressing down on the membrane quenches the lipid patterns, revealing a clear topographical basis for pattern formation. Counterion screening and membrane fluctuations likely contribute, but the results primarily highlight the fact that even in adhesion of a passive red cell, regions of strong contact slowly evolve to become interspersed with regions where the membrane is more distant from the surface.

Deformation-enhanced fluctuations in the red cell skeleton with theoretical relations to elasticity, connectivity, and spectrin unfolding

To assess local elasticity in the red cell's spectrin-actin network, nano-particles were tethered to actin nodes and their constrained thermal motions were tracked. Cells were both immobilized and controllably deformed by aspiration into a micropipette. Since the network is well-appreciated as soft, thermal fluctuations even in an unstressed portion of network were expected to be many tens of nanometers based on simple equipartition ideas. Real-time particle tracking indeed reveals such root-mean-squared motions for 40-nm fluorescent beads either tethered to actin directly within a cell ghost or connected to actin from outside a cell via glycophorin. Moreover, the elastically constrained displacements are significant on the scale of the network's internodal distance of approximately 60-80 nm. Surprisingly, along the aspirated projection-where the network is axially extended by as much as twofold or more-fluctuations in the axial direction are increased by almost twofold relative to motions in the unstressed network. The molecular basis for such strain softening is discussed broadly in terms of force-driven transitions. Specific considerations are given to 1) protein dissociations that reduce network connectivity, and 2) unfolding kinetics of a localized few of the red cell's approximately 10(7) spectrin repeats.

Elastic thickness compressibilty of the red cell membrane

We have used an ultrasensitive force probe and optical interferometry to examine the thickness compressibility of the red cell membrane in situ. Pushed into the centers of washed-white red cell ghosts lying on a coverglass, the height of the microsphere-probe tip relative to its closest approach on the adjacent glass surface revealed the apparent material thickness, which began at approximately 90 nm per membrane upon detection of contact (force approximately 1-2 pN). With further impingement, the apparent thickness per membrane diminished over a soft compliant regime that spanned approximately 40 nm and stiffened on approach to approximately 50 nm under forces of approximately 100 pN. The same force-thickness response was obtained on recompression after retraction of the probe, which demonstrated elastic recoverability. Scaled by circumferences of the microspheres, the forces yielded energies of compression per area which exhibited an inverse distance dependence resembling that expected for flexible polymers. Attributed to the spectrin component of the membrane cytoskeleton, the energy density only reached one thermal energy unit (k(B)T) per spectrin tetramer near maximum compression. Hence, we hypothesized that the soft compliant regime probed in the experiments represented the compressibility of the outer region of spectrin loops and that the stiff regime < 50 nm was the response of a compact mesh of spectrin backed by a hardcore structure. To evaluate this hypothesis, we used a random flight theory for the entropic elasticity of polymer loops to model the spectrin network. We also examined the possibility that additional steric repulsion and apparent thickening could arise from membrane thermal-bending excitations. Fixing the energy scale to k(B)T/spectrin tetramer, the combined elastic response of a network of ideal polymer loops plus the membrane steric interaction correlated well with the measured dependence of energy density on distance for a statistical segment length of approximately 5 nm for spectrin (i.e., free chain end-to-end length of approximately 29 nm) and a hardcore limit of approximately 30 nm for underlying structure.

Actin protofilament orientation in deformation of the erythrocyte membrane skeleton

The red cell's spectrin-actin network is known to sustain local states of shear, dilation, and condensation, and yet the short actin filaments are found to maintain membrane-tangent and near-random azimuthal orientations. When calibrated with polarization results for single actin filaments, imaging of micropipette-deformed red cell ghosts has allowed an assessment of actin orientations and possible reorientations in the network. At the hemispherical cap of the aspirated projection, where the network can be dilated severalfold, filaments have the same membrane-tangent orientation as on a relatively unstrained portion of membrane. Likewise, over the length of the network projection pulled into the micropipette, where the network is strongly sheared in axial extension and circumferential contraction, actin maintains its tangent orientation and is only very weakly aligned with network extension. Similar results are found for the integral membrane protein Band 3. Allowing for thermal fluctuations, we deduce a bound for the effective coupling constant, alpha, between network shear and azimuthal orientation of the protofilament. The finding that alpha must be about an order of magnitude or more below its tight-coupling value illustrates how nanostructural kinematics can decouple from more macroscopic responses. Monte Carlo simulations of spectrin-actin networks at approximately 10-nm resolution further support this conclusion and substantiate an image of protofilaments as elements of a high-temperature spin glass.

New insights into erythrocyte membrane organization and microelasticity

The erythrocyte membrane's ability to withstand the stresses of circulation has its origins in various levels of structural organization. Central to this membrane's structure-function relationships is a quasi-two-dimensional meshwork of spectrin-actin-protein 4.1 that imparts a resilence to the overlying plasma membrane. New insights into the nonlinear microelasticity of this substructure are being provided by experiments that range from elegant atomic force microscopy tests of single spectrin chains to patterned photobleaching of the micropipette-deformed network. Breakthroughs in atomic level structure determinations are further complemented by emerging biophysical studies of transgenically engineered mice lacking specific erythrocyte membrane proteins. Recent theoretical efforts (computational approaches most notably) also have begun to correlate molecular scale aspects of structure with mechanical measures. All of this recent activity in the biophysics of erythrocyte structure-function is certain to challenge and refine some of the most basic tenets in cell membrane structure-function.