Pan-tissue scaling of stiffness versus fibrillar collagen reflects contractility-driven strain that inhibits fibril degradation.

Polymer network properties such as stiffness often exhibit characteristic power laws in polymer density and other parameters. However, it remains unclear whether diverse animal tissues, composed of many distinct polymers, exhibit such scaling. Here, we examined many diverse tissues from adult mouse and embryonic chick to determine if stiffness ( E tissue ) follows a power law in relation to the most abundant animal protein, Collagen-I, even with molecular perturbations. We quantified fibrillar collagen in intact tissue by second harmonic generation (SHG) imaging and from tissue extracts by mass spectrometry (MS), and collagenase-mediated decreases were also tracked. Pan-tissue power laws for tissue stiffness versus Collagen-I levels measured by SHG or MS exhibit sub-linear scaling that aligns with results from cellularized gels of Collagen-I but not acellular gels. Inhibition of cellular myosin-II based contraction fits the scaling, and combination with inhibitors of matrix metalloproteinases (MMPs) show collagenase activity is strain - not stress- suppressed in tissues, consistent with past studies of gels and fibrils. Beating embryonic hearts and tendons, which differ in both collagen levels and stiffness by >1000-fold, similarly suppressed collagenases at physiological strains of ∼5%, with fiber-orientation regulating degradation. Scaling of E tissue based on 'use-it-or-lose-it' kinetics provides insight into scaling of organ size, microgravity effects, and regeneration processes while suggesting contractility-driven therapeutics.

Substrate stiffness-modulated registry phase correlations in cardiomyocytes map structural order to coherent beating.

Recent experiments show that both striation, an indication of the structural registry in muscle fibres, as well as the contractile strains produced by beating cardiac muscle cells can be optimized by substrate stiffness. Here we show theoretically how the substrate rigidity dependence of the registry data can be mapped onto that of the strain measurements. We express the elasticity-mediated structural registry as a phase-order parameter using a statistical physics approach that takes the noise and disorder inherent in biological systems into account. By assuming that structurally registered myofibrils also tend to beat in phase, we explain the observed dependence of both striation and strain measurements of cardiomyocytes on substrate stiffness in a unified manner. The agreement of our ideas with experiment suggests that the correlated beating of heart cells may be limited by the structural order of the myofibrils, which in turn is regulated by their elastic environment.

Optimal matrix rigidity for stress fiber polarization in stem cells.

The shape and differentiation of human mesenchymal stem cells is especially sensitive to the rigidity of their environment; the physical mechanisms involved are unknown. A theoretical model and experiments demonstrate here that the polarization/alignment of stress-fibers within stem cells is a non-monotonic function of matrix rigidity. We treat the cell as an active elastic inclusion in a surrounding matrix whose polarizability, unlike dead matter, depends on the feedback of cellular forces that develop in response to matrix stresses. The theory correctly predicts the monotonic increase of the cellular forces with the matrix rigidity and the alignment of stress-fibers parallel to the long axis of cells. We show that the anisotropy of this alignment depends non-monotonically on matrix rigidity and demonstrate it experimentally by quantifying the orientational distribution of stress-fibers in stem cells. These findings offer a first physical insight for the dependence of stem cell differentiation on tissue elasticity.

Cell shape, spreading symmetry and the polarization of stress-fibers in cells.

The active regulation of cellular forces during cell adhesion plays an important role in the determination of cell size, shape and internal structure. While on flat, homogeneous and isotropic substrates some cells spread isotropically, others spread anisotropically and assume elongated structures. In addition, in their native environment as well as in vitro experiments, the cell shape and spreading asymmetry can be modulated by the local distribution of adhesive molecules and topography of the environment. We present a simple elastic model, and experiments on stem cells to explain the variation of cell size with the matrix rigidity. In addition, we predict the experimental consequences of two mechanisms of acto-myosin polarization and focus here on the effect of the cell spreading asymmetry on the regulation of the stress-fiber alignment in the cytoskeleton. We show that when cell spreading is sufficiently asymmetric the alignment of acto-myosin forces in the cell increases monotonically with the matrix rigidity; however, in general this alignment is non-monotonic as shown previously. These results highlight the importance of the symmetry characteristics of cell spreading in the regulation of cytoskeleton structure and suggest a mechanism by which different cell types may acquire different morphologies and internal structures in different mechanical environments.

Cys shotgun labeling of macrophages adhering to and engulfing Ig-opsonized cells.

A method is being developed to study cytoskeletal reorganization in cell adhesion processes. The initial model process is adhesion and phagocytosis of beads or red blood cells by macrophages. Live cell labeling with Cys reactive fluorophores is performed before and during phagocytosis with different color labeling dyes. Since Cys is a relatively hydrophobic amino acid, its differential exposure and labeling in principle reflects changes in tertiary or quaternary structure of specific proteins. Similar studies conducted on red blood cells under fluid shear conditions showed that specific domains in spectrin undergo extensible unfolding within sheared cells. The initial work here with macrophages also suggests some structural changes in phagocytosis although the proteins and specific sites have yet to be identified.

The 'metabolon,' CD47, and the 'phagocytic synapse': molecular co-localization and species divergence.

CD47 is a widely expressed integral membrane protein, found also on red blood cells where it reportedly has a key role in inhibiting phagocytic clearance of RBC by signaling within a multi-molecular 'phagocytic synapse'. Calreticulin is postulated to be on the RBC surface and stimulate phagocytosis, whereupon CD47 on the RBC binds SIRPalpha on the phagocyte and signals a block against phagocytosis. While studies of mouse suggest such an inhibitory role for CD47, CD47 seems to have distinct interactions in human RBC--particularly within a 'metabolon' complex of CD47, Rh proteins, and several other proteins. We have assessed the relative density, co-clustering, and mobility of some of the implicated proteins on human RBC versus murine RBC (hu-RBC and mu-RBC, respectively), and we find a few major differences. While RBC from both species express similar densities of CD47 and SIRPalpha interactions are measurably modest, the interactions prove species-specific. While RBC from both species also have detectable calreticulin, fresh hu-RBC are found to have 10-100-fold more calreticulin binding sites on their surface. Imaging of clusters of SIRPalpha-CD47 on both species of RBC show that RhD does co-localize with CD47 on hu-RBC, but neither calreticulin nor Glycophorin-A appear enriched in the metabolon complexes. Furthermore, mouse-cells alone tend to aggregate due to cross-bridging by SIRPalpha complexes, showing accumulation of CD47 in the adhesion zone, which is consistent with a high mobility of CD47 unique to mu-RBC.

Elongation and fluctuations of semiflexible polymers in a nematic solvent.

We directly visualize single polymers with persistence lengths l(p), ranging from 0.05 to 16 microm, dissolved in the nematic phase of rodlike fd virus. Polymers with a sufficiently large persistence length undergo a coil-rod transition at the isotropic-nematic transition of the background solvent. We quantitatively analyze the transverse fluctuations of the semiflexible polymers and show that at long wavelengths they are driven by the fluctuating nematic background. We extract the Odijk deflection length and the elastic constant of the background nematic phase from the data.

Effect of bilayer thickness on membrane bending rigidity.

The bending rigidity k(c) of bilayer vesicles self-assembled from amphiphilic diblock copolymers has been measured using single- and dual-micropipet techniques. These copolymers are nearly a factor of 5 greater in hydrophobic membrane thickness d than their lipid counterparts and an order of magnitude larger in molecular weight M(n). The macromolecular structure of these amphiphiles lends insight into and extends relationships for traditional surfactant behavior. We find the scaling of k(c) with thickness to be nearly quadratic, in good agreement with existing theories for bilayer membranes. The results here are key to understanding and designing soft interfaces such as biomembrane mimetics.

Electromechanical limits of polymersomes.

Self-assembled membranes of amphiphilic diblock copolymers enable comparisons of cohesiveness with lipid membranes over the range of hydrophobic thicknesses d = 3-15 nm. At zero mechanical tension the breakdown potential V(c) for polymersomes with d = 15 nm is 9 V, compared to 1 V for liposomes with d = 3 nm. Nonetheless, electromechanical stresses at breakdown universally exhibit a V(c)(2) dependence, and membrane capacitance shows the expected strong d dependence, conforming to simple thermodynamic models. The viscous nature of the diblock membranes is apparent in the protracted postporation dynamics.

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.

New insights into red cell network structure, elasticity, and spectrin unfolding--a current review.

The red cell membrane's well-recognized ability to withstand the stresses of circulation clearly has its origins in various levels of spectrin-actin network structure. We highlight recently obtained insights into this sub-structure and also briefly explain the implications to membrane components that interact with the network. Novel insights into the resilience of this cytoskeleton are being provided by experiments that range from atomic force microscopy (AFM) tests of single, unfoldable spectrin chains to micropatterned photobleaching of a pipette-deformed network. Continued progress in atomic level structure determinations of non-erythroid spectrin and related repeats are further complemented by theoretical efforts--computational approaches most notably--that have begun to correlate molecular scale aspects of structure with micro-mechanical measures. All of this recent activity in the biophysics of red cell structure-function challenges and refines some of the most basic tenets in cell membrane response.

Preparation, stability, and in vitro performance of vesicles made with diblock copolymers.

Vesicles made completely from diblock copolymers-polymersomes-can be stably prepared by a wide range of techniques common to liposomes. Processes such as film rehydration, sonication, and extrusion can generate many-micron giants as well as monodisperse, approximately 100 nm vesicles of PEO-PEE (polyethyleneoxide-polyethylethylene) or PEO-PBD (polyethyleneoxide-polybutadiene). These thick-walled vesicles of polymer can encapsulate macromolecules just as liposomes can but, unlike many pure liposome systems, these polymersomes exhibit no in-surface thermal transitions and a subpopulation even survive autoclaving. Suspension in blood plasma has no immediate ill-effect on vesicle stability, and neither adhesion nor stimulation of phagocytes are apparent when giant polymersomes are held in direct, protracted contact. Proliferating cells, in addition, are unaffected when cultured for an extended time with an excess of polymersomes. The effects are consistent with the steric stabilization that PEG-lipid can impart to liposomes, but the present single-component polymersomes are far more stable mechanically and are not limited by PEG-driven micellization. The results potentiate a broad new class of technologically useful, polymer-based vesicles.

Forced unfolding modulated by disulfide bonds in the Ig domains of a cell adhesion molecule.

Cell adhesion molecules (CAMs) mediate cell attachment and stress transfer through extracellular domains. Here we forcibly unfold the Ig domains of a prototypical Ig superfamily CAM that contains intradomain disulfide bonds. The Ig domains of all such CAMs have conformations homologous to cadherin extracellular domains, titin Ig-type domains, and fibronectin type-III (FNIII) domains. Atomic force microscopy has been used to extend the five Ig domains of Mel-CAM (melanoma CAM)--a protein that is overexpressed in metastatic melanomas--under conditions where the disulfide bonds were either left intact or disrupted through reduction. Under physiological conditions where intradomain disulfide bonds are intact, partial unfolding was observed at forces far smaller than those reported previously for either titin's Ig-type domains or tenascin's FNIII domains. This partial unfolding under low force may be an important mechanism for imparting elasticity to cell-cell contacts, as well as a regulatory mechanism for adhesive interactions. Under reducing conditions, Mel-CAM's Ig domains were found to fully unfold through a partially folded state and at slightly higher forces. The results suggest that, in divergent evolution of all such domains, stabilization imparted by disulfide bonds relaxes requirements for strong, noncovalent, folded-state interactions.

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.

Direct measures of large, anisotropic strains in deformation of the erythrocyte cytoskeleton.

The erythrocyte's spectrin-actin membrane skeleton is directly shown to be capable of sustaining large, anisotropic strains. Photobleaching of an approximately 1-micrometer stripe in rhodamine phalloidin-labeled actin appears stable up to at least 37 degrees C, and is used to demonstrate large in-surface stretching during elastic deformation of the skeleton. Principal extension or stretch ratios of at least approximately 200% and contractions down to approximately 40%, both referenced to an essentially undistorted cell, are visually demonstrated in micropipette-imposed deformation. Such anisotropic straining is seen to be consistent at a qualitative level with now classic analyses (Evans. 1973. Biophys. J. 13:941-954) and is generally nonhomogeneous though axisymmetric down to the submicron scale. Local, direct measurements of stretching prove quantitatively consistent (within approximately 10%) with integrated estimates that are based simply on a measured relative density distribution of actin. The measurements are also in close agreement with direct computation of mean spectrin chain extension in full statistical mechanical simulations of a coarse-grained network held in a micropipette. Finally, as a cell thermally fragments near approximately 48 degrees C, the patterned photobleaching demonstrates a destructuring of the surface network in a process that is more readily attributable to transitions in spectrin than in F-actin.

Actin protofilament orientation at the erythrocyte membrane.

The short actin filaments in the erythrocyte's membrane skeleton are shown to be largely oriented tangent to the lipid bilayer. Actin "proto"-filaments have previously been described as junctional centers intertriangulated by spectrin; however, the protofilaments may simultaneously serve as pinning centers between the network and the overlying bilayer. The latter function now seems of particular importance because near-normal network assembly has been reported with transgenic mouse sphero-erythrocytes that lack the primary linkage protein Band 3. To assess possible physical constraints on actin protofilaments in intact membranes, fluorescence polarization microscopy (FPM) has been used to study rhodamine phalloidin-labeled red cell ghosts. A basis for interpreting FPM images of cells is provided by FPM applied to isolated actin filaments. These are labeled with the same rhodamine probes and imaged at various orientations with respect to the polarizers, including filament orientations perpendicular to the image plane. High aperture and fluorophore conjugation effects are found to be minimal, enabling development of a simple, semi-empirical model which indicates that protofilaments are generally within approximately 20 degrees of the membrane tangent plane.

Polymersomes: tough vesicles made from diblock copolymers.

Vesicles were made from amphiphilic diblock copolymers and characterized by micromanipulation. The average molecular weight of the specific polymer studied, polyethyleneoxide-polyethylethylene (EO40-EE37), is several times greater than that of typical phospholipids in natural membranes. Both the membrane bending and area expansion moduli of electroformed polymersomes (polymer-based liposomes) fell within the range of lipid membrane measurements, but the giant polymersomes proved to be almost an order of magnitude tougher and sustained far greater areal strain before rupture. The polymersome membrane was also at least 10 times less permeable to water than common phospholipid bilayers. The results suggest a new class of synthetic thin-shelled capsules based on block copolymer chemistry.