Mechanics and structure of titin oligomers explored with atomic force microscopy

Effects of CaCl2 on the structure of high-density lipoprotein and low-density lipoprotein isolated from rapidly salted separated egg yolk

According to previous research, adding CaCl2 to the salting solution improves the quality of salted separated egg yolk. To further understand the improvement mechanism of CaCl2, this paper investigated the effect of CaCl2 on the structure of high-density lipoprotein (HDL) and low-density lipoprotein (LDL) during the salting process. The results indicated that the addition of CaCl2 can affect the composition of HDL and LDL apolipoproteins, improving the orderliness of the HDL structure and the looseness of the LDL structure. It was discovered by atomic force microscopy (AFM) that adding CaCl2 to the salting solution can weaken the aggregation behavior of HDL. Simultaneously, the addition of CaCl2 decreased the relative content of intermolecular β-sheets in the secondary structure of HDL and LDL, influenced their tertiary conformation, and prevented HDL and LDL from participating in the formation of a three-dimensional gel structure by influencing their hydrogen bonds and hydrophobic interactions.

Structural and mechanical properties of folded protein hydrogels with embedded microbubbles

Globular folded proteins are powerful building blocks to create biomaterials with mechanical robustness and inherent biological functionality. Here we explore their potential as advanced drug delivery scaffolds, by embedding microbubbles (MBs) within a photo-activated, chemically cross-linked bovine serum albumin (BSA) protein network. Using a combination of circular dichroism (CD), rheology, small angle neutron scattering (SANS) and microscopy we determine the nanoscale and mesoscale structure and mechanics of this novel multi-composite system. Optical and confocal microscopy confirms the presence of MBs within the protein hydrogel, their reduced diffusion and their effective rupture using ultrasound, a requirement for burst drug release. CD confirms that the inclusion of MBs does not impact the proportion of folded proteins within the cross-linked protein network. Rheological characterisation demonstrates that the mechanics of the BSA hydrogels is reduced in the presence of MBs. Furthermore, SANS reveals that embedding MBs in the protein hydrogel network results in a smaller number of clusters that are larger in size (∼16.6% reduction in number of clusters, 17.4% increase in cluster size). Taken together, we show that MBs can be successfully embedded within a folded protein network and ruptured upon application of ultrasound. The fundamental insight into the impact of embedded MBs in protein scaffolds at the nanoscale and mesoscale is important in the development of future platforms for targeted and controlled drug delivery applications.

The N-terminus of obscurin is flexible in solution

The N-terminal half of the giant cytoskeletal protein obscurin is comprised of more than 50 Ig-like domains, arranged in tandem. Domains 18-51 are connected to each other through short 5-residue linkers, and this arrangement has been previously shown to form a semi-flexible rod in solution. Domains 1-18 generally have slightly longer ~7 residue interdomain linkers, and the multidomain structure and motion conferred by this kind of linker is understudied. Here, we use NMR, SAXS, and MD to show that these longer linkers are associated with significantly more domain/domain flexibility, with the resulting multidomain structure being moderately compact. Further examination of the relationship between interdomain flexibility and linker length shows there is a 5 residue "sweet spot" linker length that results in dual-domain systems being extended, and conversely that both longer or shorter linkers result in a less extended structure. This detailed knowledge of the obscurin N terminus structure and flexibility allowed for mathematical modeling of domains 1-18, which suggests that this region likely forms tangles if left alone in solution. Given how infrequently protein tangles occur in nature, and given the pathological outcomes that occur when tangles do arise, our data suggest that obscurin is likely either significantly scaffolded or else externally extended in the cell.

Nonspecific Amyloid Aggregation of Chicken Smooth-Muscle Titin: In Vitro Investigations

A giant multidomain protein of striated and smooth vertebrate muscles, titin, consists of tandems of immunoglobulin (Ig)- and fibronectin type III (FnIII)-like domains representing β-sandwiches, as well as of disordered segments. Chicken smooth muscles express several titin isoforms of ~500-1500 kDa. Using various structural-analysis methods, we investigated in vitro nonspecific amyloid aggregation of the high-molecular-weight isoform of chicken smooth-muscle titin (SMT_HMW, ~1500 kDa). As confirmed by X-ray diffraction analysis, under near-physiological conditions, the protein formed amorphous amyloid aggregates with a quaternary cross-β structure within a relatively short time (~60 min). As shown by circular dichroism and Fourier-transform infrared spectroscopy, the quaternary cross-β structure-unlike other amyloidogenic proteins-formed without changes in the SMT_HMW secondary structure. SMT_HMW aggregates partially disaggregated upon increasing the ionic strength above the physiological level. Based on the data obtained, it is not the complete protein but its particular domains/segments that are likely involved in the formation of intermolecular interactions during SMT_HMW amyloid aggregation. The discovered properties of titin position this protein as an object of interest for studying amyloid aggregation in vitro and expanding our views of the fundamentals of amyloidogenesis.

Nanosurgical Manipulation of Titin and Its M-Complex

Titin is a multifunctional filamentous protein anchored in the M-band, a hexagonally organized supramolecular lattice in the middle of the muscle sarcomere. Functionally, the M-band is a framework that cross-links myosin thick filaments, organizes associated proteins, and maintains sarcomeric symmetry via its structural and putative mechanical properties. Part of the M-band appears at the C-terminal end of isolated titin molecules in the form of a globular head, named here the “M-complex”, which also serves as the point of head-to-head attachment of titin. We used high-resolution atomic force microscopy and nanosurgical manipulation to investigate the topographical and internal structure and local mechanical properties of the M-complex and its associated titin molecules. We find that the M-complex is a stable structure that corresponds to the transverse unit of the M-band organized around the myosin thick filament. M-complexes may be interlinked into an M-complex array that reflects the local structural and mechanical status of the transversal M-band lattice. Local segments of titin and the M-complex could be nanosurgically manipulated to achieve extension and domain unfolding. Long threads could be pulled out of the M-complex, suggesting that it is a compact supramolecular reservoir of extensible filaments. Nanosurgery evoked an unexpected volume increment in the M-complex, which may be related to its function as a mechanical spacer. The M-complex thus displays both elastic and plastic properties which support the idea that the M-band may be involved in mechanical functions within the muscle sarcomere.

A multiscale sliding filament model of lymphatic muscle pumping

The lymphatics maintain fluid balance by returning interstitial fluid to veins via contraction/compression of vessel segments with check valves. Disruption of lymphatic pumping can result in a condition called lymphedema with interstitial fluid accumulation. Lymphedema treatments are often ineffective, which is partially attributable to insufficient understanding of specialized lymphatic muscle lining the vessels. This muscle exhibits cardiac-like phasic contractions and smooth muscle-like tonic contractions to generate and regulate flow. To understand the relationship between this sub-cellular contractile machinery and organ-level pumping, we have developed a multiscale computational model of phasic and tonic contractions in lymphatic muscle and coupled it to a lymphangion pumping model. Our model uses the sliding filament model (Huxley in Prog Biophys Biophys Chem 7:255-318, 1957) and its adaptation for smooth muscle (Mijailovich in Biophys J 79(5):2667-2681, 2000). Multiple structural arrangements of contractile components and viscoelastic elements were trialed but only one provided physiologic results. We then coupled this model with our previous lumped parameter model of the lymphangion to relate results to experiments. We show that the model produces similar pressure, diameter, and flow tracings to experiments on rat mesenteric lymphatics. This model provides the first estimates of lymphatic muscle contraction energetics and the ability to assess the potential effects of sub-cellular level phenomena such as calcium oscillations on lymphangion outflow. The maximum efficiency value predicted (40%) is at the upper end of estimates for other muscle types. Spontaneous calcium oscillations during diastole were found to increase outflow up to approximately 50% in the range of frequencies and amplitudes tested.

Stretching single titin molecules from failing human hearts reveals titin's role in blunting cardiac kinetic reserve

AIMS

Heart failure (HF) patients commonly experience symptoms primarily during elevated heart rates, as a result of physical activities or stress. A main determinant of diastolic passive tension, the elastic sarcomeric protein titin, has been shown to be associated with HF, with unresolved involvement regarding its role at different heart rates. To determine whether titin is playing a role in the heart rate (frequency-) dependent acceleration of relaxation (FDAR). W, we studied the FDAR responses in live human left ventricular cardiomyocytes and the corresponding titin-based passive tension (TPT) from failing and non-failing human hearts.

METHODS AND RESULTS

Using atomic force, we developed a novel single-molecule force spectroscopy approach to detect TPT based on the frequency-modulated cardiac cycle. Mean TPT reduced upon an increased heart rate in non-failing human hearts, while this reduction was significantly blunted in failing human hearts. These mechanical changes in the titin distal Ig domain significantly correlated with the frequency-dependent relaxation kinetics of human cardiomyocytes obtained from the corresponding hearts. Furthermore, the data suggested that the higher the TPT, the faster the cardiomyocytes relaxed, but the lower the potential of myocytes to speed up relaxation at a higher heart rate. Such poorer FDAR response was also associated with a lesser reduction or a bigger increase in TPT upon elevated heart rate.

CONCLUSIONS

Our study established a novel approach in detecting dynamic heart rate relevant tension changes physiologically on native titin domains. Using this approach, the data suggested that the regulation of kinetic reserve in cardiac relaxation and its pathological changes were associated with the intensity and dynamic changes of passive tension by titin.

Single-Molecule Force Spectroscopy on the N2A Element of Titin: Effects of Phosphorylation and CARP

Titin is a large filamentous protein that forms a sarcomeric myofilament with a molecular spring region that develops force in stretched sarcomeres. The molecular spring has a complex make-up that includes the N2A element. This element largely consists of a 104-residue unique sequence (N2A-Us) flanked by immunoglobulin domains (I80 and I81). The N2A element is of interest because it assembles a signalosome with CARP (Cardiac Ankyrin Repeat Protein) as an important component; CARP both interacts with the N2A-Us and I81 and is highly upregulated in response to mechanical stress. The mechanical properties of the N2A element were studied using single-molecule force spectroscopy, including how these properties are affected by CARP and phosphorylation. Three protein constructs were made that consisted of 0, 1, or 2 N2A-Us elements with flanking I80 and I81 domains and with specific handles at their ends for study by atomic force microscopy (AFM). The N2A-Us behaved as an entropic spring with a persistence length (Lp) of ∼0.35 nm and contour length (Lc) of ∼39 nm. CARP increased the Lp of the N2A-Us and the unfolding force of the Ig domains; force clamp experiments showed that CARP reduced the Ig domain unfolding kinetics. These findings suggest that CARP might function as a molecular chaperone that protects I81 from unfolding when mechanical stress is high. The N2A-Us was found to be a PKA substrate, and phosphorylation was blocked by CARP. Mass spectrometry revealed a PKA phosphosite (Ser-9895 in NP_001254479.2) located at the border between the N2A-Us and I81. AFM studies showed that phosphorylation affected neither the Lp of the N2A-Us nor the Ig domain unfolding force (Funfold). Simulating the force-sarcomere length relation of a single titin molecule containing all spring elements showed that the compliance of the N2A-Us only slightly reduces passive force (1.4%) with an additional small reduction by CARP (0.3%). Thus, it is improbable that the compliance of the N2A element has a mechanical function per se. Instead, it is likely that this compliance has local effects on binding of signaling molecules and that it contributes thereby to strain- and phosphorylation- dependent mechano-signaling.

The hierarchical emergence of worm-like chain behaviour from globular domain polymer chains

Biological organisms make use of hierarchically organised structures to modulate mechanical behaviour across multiple lengthscales, allowing microscopic objects to generate macroscopic effects. Within these structural hierarchies, the resultant physical behaviour of the entire system is determined not only by the intrinsic mechanical properties of constituent subunits, but also by their organisation in three-dimensional space. When these subunits are polyproteins, colloidal chains or other globular domain polymers, the Kratky-Porod model is often assumed for the individual subunits. Hence, it is implicitly asserted that the polymeric object has an intrinsic parameter, the persistence length, that defines its flexibility. However, the persistence lengths extracted from experiment vary, and are often relatively small. Through a series of simulations on polymer chains formed of globular subunits, we show that the persistence length itself is a hierarchical structural property, related not only to the intrinsic mechanical properties of the underlying monomeric subunits, but emerging due to the organisation of inhomogenous geometry along the polymer contour.

Distinct mechanical properties in homologous spectrin-like repeats of utrophin

Patients with Duchenne muscular dystrophy (DMD) lack the protein dystrophin, which is a critical molecular component of the dystrophin-glycoprotein complex (DGC). Dystrophin is hypothesized to function as a molecular shock absorber that mechanically stabilizes the sarcolemma of striated muscle through interaction with the cortical actin cytoskeleton via its N-terminal half and with the transmembrane protein β-dystroglycan via its C-terminal region. Utrophin is a fetal homologue of dystrophin that can subserve many dystrophin functions and is therefore under active investigation as a dystrophin replacement therapy for DMD. Here, we report the first mechanical characterization of utrophin using atomic force microscopy (AFM). Our data indicate that the mechanical properties of spectrin-like repeats in utrophin are more in line with the PEVK and Ig-like repeats of titin rather than those reported for repeats in spectrin or dystrophin. Moreover, we measured markedly different unfolding characteristics for spectrin repeats within the N-terminal actin-binding half of utrophin compared to those in the C-terminal dystroglycan-binding half, even though they exhibit identical thermal denaturation profiles. Our results demonstrate dramatic differences in the mechanical properties of structurally homologous utrophin constructs and suggest that utrophin may function as a stiff elastic element in series with titin at the myotendinous junction.

Obscurin is a semi-flexible molecule in solution

Obscurin, a giant modular cytoskeletal protein, is comprised mostly of tandem immunoglobulin-like (Ig-like) domains. This architecture allows obscurin to connect distal targets within the cell. The linkers connecting the Ig domains are usually short (3-4 residues). The physical effect arising from these short linkers is not known; such linkers may lead to a stiff elongated molecule or, conversely, may lead to a more compact and dynamic structure. In an effort to better understand how linkers affect obscurin flexibility, and to better understand the physical underpinnings of this flexibility, here we study the structure and dynamics of four representative sets of dual obscurin Ig domains using experimental and computational techniques. We find in all cases tested that tandem obscurin Ig domains interact at the poles of each domain and tend to stay relatively extended in solution. NMR, SAXS, and MD simulations reveal that while tandem domains are elongated, they also bend and flex significantly. By applying this behavior to a simplified model, it becomes apparent obscurin can link targets more than 200 nm away. However, as targets get further apart, obscurin begins acting as a spring and requires progressively more energy to further elongate.

AFM Imaging Reveals Multiple Conformational States of ADAMTS13

Background

ADAMTS13 (A disintegrin and metalloprotease with a thrombospondin type 1 motif 13) cleaves Von Willebrand factor (VWF) to regulate its size, thereby preventing aberrant platelet aggregation and thrombus. Deficiency of ADAMTS13 caused by either genetic mutations or by inhibitory autoantibodies against ADAMTS13 leads to thrombotic thrombocytopenic purpura (TTP). Recently, ADAMTS13 was reported to adopt a “closed” conformation with lower activity and an “open” one resulting from the engagements of VWF D4-CK domains or antibodies to the distal domains of ADAMTS13, or mutations in its spacer domain. These engagements or mutations increase ADAMTS13 activity by ~ 2.5-fold. However, it is less known whether the conformation of ADAMTS13 is dynamic or stable.

Results

Wild type ADAMTS13 (WT-ADAMTS13) and the gain-of-function variant (GOF-ADAMTS13) with five mutations (R568K / F592Y / R660K / Y661F / Y665F) in spacer domain were imaged by atomic force microscopy (AFM) at pH 6 and pH 7.5. The data revealed that at both pH 6 and pH 7.5, WT-ADAMTS13 adopted two distinct conformational states (state I and state II), while an additional state (state III) was observed in GOF-ADAMTS13. In the present study, we propose that state I is the “closed” conformation, state III is the “open” one, and state II is an intermediate one. Comparing to pH 7.5, the percentages of state II of WT-ADAMTS13 and state III of GOF-ADAMTS13 increased at pH 6, with the decrease in the state I for WT-ADAMTS13 and state I and state II for GOF-ADAMTS13, suggesting lower pH extended the conformation of ADAMTS13.

Conclusion

Both WT- and GOF-ADAMTS13 exist multiple conformational states and lower pH might alter the tertiary structure and/or disrupt the intra-domain interactions, increasing the flexibility of ADAMTS13 molecules.

Electronic supplementary material

The online version of this article (10.1186/s13036-018-0102-y) contains supplementary material, which is available to authorized users.

Injectable dynamic covalent hydrogels of boronic acid polymers cross-linked by bioactive plant-derived polyphenols

We report here the development of hydrogels formed at physiological conditions using PEG (polyethylene glycol) based polymers modified with boronic acids (BAs) as backbones and the plant derived polyphenols ellagic acid (EA), epigallocatechin gallate (EGCG), tannic acid (TA), nordihydroguaiaretic acid (NDGA), rutin trihydrate (RT), rosmarinic acid (RA) and carminic acid (CA) as linkers. Rheological frequency sweep and single molecule force spectroscopy (SMFS) experiments show that hydrogels linked with EGCG and TA are mechanically stiff, arising from the dynamic covalent bond formed by the polyphenol linker and boronic acid functionalized polymer. Stability tests of the hydrogels in physiological conditions revealed that gels linked with EA, EGCG, and TA are stable. We furthermore showed that EA- and EGCG-linked hydrogels can be formed via in situ gelation in pH 7.4 buffer, and provide long-term steady state release of bioactive EA. In vitro experiments showed that EA-linked hydrogel significantly reduced the viability of CAL-27 human oral cancer cells via gradual release of EA.

Structural characteristics and membrane interactions of tandem α-synuclein oligomers

Pre-fibrillar oligomers of α-synuclein are thought to be pathogenic molecules leading to neurotoxicity associated with Parkinson’s disease and other neurodegenerative disorders. However, small oligomers are difficult to isolate for study. To gain better insight into the properties of small α-synuclein oligomers, we investigated engineered oligomers of specific size (dimers, tetramers, and octamers) linked head-to-tail in tandem, comparing the behavior of the oligomers to monomeric α-synuclein. All oligomeric constructs remained largely disordered in solution, as determined from dynamic light scattering and size-exclusion chromatography. Electron microscopy revealed that each construct could aggregate to form fibrils similar to those formed by monomeric α-synuclein. The interactions with large unilamellar vesicles (LUVs) composed of negatively-charged lipids differed depending on size, with smaller oligomers forming more extensive helical structure as determined by CD spectroscopy. Monitoring the influx of a fluorescence bleaching agent into vesicles showed that larger oligomers were somewhat more effective at degrading vesicular integrity and inducing membrane permeabilization.

Interaction of the Hydrophobic Tip of an Atomic Force Microscope with Oligopeptides Immobilized Using Short and Long Tethers

We report an investigation of the adhesive force generated between the hydrophobic tip of an atomic force microscope (AFM) and surfaces presenting oligopeptides immobilized using either short (∼1 nm) or long (∼60 nm) tethers. Specifically, we used either sulfosuccinimidyl-4-(N-maleimidomethyl)cyclohexane-1-carboxylate (SSMCC) or 10 kDa polyethylene glycol (PEG) end-functionalized with maleimide and N-hydroxysuccinimide groups to immobilize helical oligomers of β-amino acids (β-peptides) to mixed monolayers presenting tetraethylene glycol (EG4) and amine-terminated EG4 (EG4N) groups. When SSMCC was used to immobilize the β-peptides, we measured the adhesive interaction between the AFM tip and surface to rupture through a single event with magnitude consistent with the interaction of a single β-peptide with the AFM tip. Surprisingly, this occurred even when, on average, multiple β-peptides were located within the interaction area between the AFM tip and surface. In contrast, when using the long 10 kDa PEG tether, we observed the magnitude of the adhesive interaction as well as the dynamics of the rupture events to unmask the presence of the multiple β-peptides within the interaction area. To provide insight into these observations, we formulated a simple mechanical model of the interaction of the AFM tip with the immobilized β-peptides and used the model to demonstrate that adhesion measurements performed using short tethers (but not long tethers) are dominated by the interaction of single β-peptides because (i) the mechanical properties of the short tether are highly nonlinear, thus causing one β-peptide to dominate the adhesion force at the point of rupture, and (ii) the AFM cantilever is mechanically unstable following the rupture of the adhesive interaction with a single β-peptide. Overall, our study reveals that short tethers offer the basis of an approach that facilitates measurement of adhesive interactions with single molecules presented at surfaces.

Diverse metastable structures formed by small oligomers of α-synuclein probed by force spectroscopy

Oligomeric aggregates are widely suspected as toxic agents in diseases caused by protein aggregation, yet they remain poorly characterized, partly because they are challenging to isolate from a heterogeneous mixture of species. We developed an assay for characterizing structure, stability, and kinetics of individual oligomers at high resolution and sensitivity using single-molecule force spectroscopy, and applied it to observe the formation of transient structured aggregates within single oligomers of α-synuclein, an intrinsically-disordered protein linked to Parkinson's disease. Measurements of the molecular extension as the proteins unfolded under tension in optical tweezers revealed that even small oligomers could form numerous metastable structures, with a surprisingly broad range of sizes. Comparing the structures formed in monomers, dimers and tetramers, we found that the average mechanical stability increased with oligomer size. Most structures formed within a minute, with size-dependent rates. These results provide a new window onto the complex α-synuclein aggregation landscape, characterizing the microscopic structural heterogeneity and kinetics of different pathways.

Cross-species mechanical fingerprinting of cardiac myosin binding protein-C

Cardiac myosin binding protein-C (cMyBP-C) is a member of the immunoglobulin (Ig) superfamily of proteins and consists of 8 Ig- and 3 fibronectin III (FNIII)-like domains along with a unique regulatory sequence referred to as the MyBP-C motif or M-domain. We previously used atomic force microscopy to investigate the mechanical properties of murine cMyBP-C expressed using a baculovirus/insect cell expression system. Here, we investigate whether the mechanical properties of cMyBP-C are conserved across species by using atomic force microscopy to manipulate recombinant human cMyBP-C and native cMyBP-C purified from bovine heart. Force versus extension data obtained in velocity-clamp experiments showed that the mechanical response of the human recombinant protein was remarkably similar to that of the bovine native cMyBP-C. Ig/Fn-like domain unfolding events occurred in a hierarchical fashion across a threefold range of forces starting at relatively low forces of ~50 pN and ending with the unfolding of the highest stability domains at ~180 pN. Force-extension traces were also frequently marked by the appearance of anomalous force drops suggestive of additional mechanical complexity such as structural coupling among domains. Both recombinant and native cMyBP-C exhibited a prominent segment ~100 nm-long that could be stretched by forces <50 pN before the unfolding of Ig- and FN-like domains. Combined with our previous observations of mouse cMyBP-C, these results establish that although the response of cMyBP-C to mechanical load displays a complex pattern, it is highly conserved across species.

Low-force transitions in single titin molecules reflect a memory of contractile history

Titin is a giant elastomeric muscle protein that has been suggested to function as a sensor of sarcomeric stress and strain, but the mechanisms by which it does so are unresolved. To gain insight into its mechanosensory function we manipulated single titin molecules with high-resolution optical tweezers. Discrete, step-wise transitions, with rates faster than canonical Ig domain unfolding occurred during stretch at forces as low as 5 pN. Multiple mechanisms and molecular regions (PEVK, proximal tandem-Ig, N2A) are likely to be involved. The pattern of transitions is sensitive to the history of contractile events. Monte-Carlo simulations of our experimental results predicted that structural transitions begin before the complete extension of the PEVK domain. High-resolution atomic force microscopy (AFM) supported this prediction. Addition of glutamate-rich PEVK domain fragments competitively inhibited the viscoelastic response in both single titin molecules and muscle fibers, indicating that PEVK domain interactions contribute significantly to sarcomere mechanics. Thus, under non-equilibrium conditions across the physiological force range, titin extends by a complex pattern of history-dependent discrete conformational transitions, which, by dynamically exposing ligand-binding sites, could set the stage for the biochemical sensing of the mechanical status of the sarcomere.

Interactions of Thellungiella salsuginea dehydrins TsDHN-1 and TsDHN-2 with membranes at cold and ambient temperatures-surface morphology and single-molecule force measurements show phase separation, and reveal tertiary and quaternary associations

Dehydrins (group 2 late embryogenesis abundant proteins) are intrinsically-disordered proteins that are expressed in plants experiencing extreme environmental conditions such as drought or low temperature. Their roles include stabilizing cellular proteins and membranes, and sequestering metal ions. Here, we investigate the membrane interactions of the acidic dehydrin TsDHN-1 and the basic dehydrin TsDHN-2 derived from the crucifer Thellungiella salsuginea that thrives in the Canadian sub-Arctic. We show using compression studies with a Langmuir-Blodgett trough that both dehydrins can stabilize lipid monolayers with a lipid composition mimicking the composition of the plant outer mitochondrial membrane, which had previously been shown to induce ordered secondary structures (disorder-to-order transitions) in the proteins. Ellipsometry of the monolayers during compression showed an increase in monolayer thickness upon introducing TsDHN-1 (acidic) at 4°C and TsDHN-2 (basic) at room temperature. Atomic force microscopy of supported lipid bilayers showed temperature-dependent phase transitions and domain formation induced by the proteins. These results support the conjecture that acidic dehydrins interact with and potentially stabilize plant outer mitochondrial membranes in conditions of cold stress. Single-molecule force spectroscopy of both proteins pulled from supported lipid bilayers indicated the induced formation of tertiary conformations in both proteins, and potentially a dimeric association for TsDHN-2.

Spontaneous dimerization of titin protein Z1Z2 domains induces strong nanomechanical anchoring

Muscle elasticity strongly relies on the mechanical anchoring of the giant protein titin to both the sarcomere M-band and the Z-disk. Such strong attachment ensures the reversible dynamics of the stretching-relaxing cycles determining the muscle passive elasticity. Similarly, the design of biomaterials with enhanced elastic function requires experimental strategies able to secure the constituent molecules to avoid mechanical failure. Here we show that an engineered titin-mimicking protein is able to spontaneously dimerize in solution. Our observations reveal that the titin Z1Z2 domains are key to induce dimerization over a long-range distance in proteins that would otherwise remain in their monomeric form. Using single molecule force spectroscopy, we measure the threshold force that triggers the noncovalent transition from protein dimer to monomer, occurring at ∼700 piconewtons. Such extremely high mechanical stability is likely to be a natural protective mechanism that guarantees muscle integrity. We propose a simple molecular model to understand the force-induced dimer-to-monomer transition based on the geometric distribution of forces occurring within a dimeric protein under mechanical tension.

Evidence that αC region is origin of low modulus, high extensibility, and strain stiffening in fibrin fibers

Fibrin fibers form the structural scaffold of blood clots and perform the mechanical task of stemming blood flow. Several decades of investigation of fibrin fiber networks using macroscopic techniques have revealed remarkable mechanical properties. More recently, the microscopic origins of fibrin's mechanics have been probed through direct measurements on single fibrin fibers and individual fibrinogen molecules. Using a nanomanipulation system, we investigated the mechanical properties of individual fibrin fibers. The fibers were stretched with the atomic force microscope, and stress-versus-strain data was collected for fibers formed with and without ligation by the activated transglutaminase factor XIII (FXIIIa). We observed that ligation with FXIIIa nearly doubled the stiffness of the fibers. The stress-versus-strain behavior indicates that fibrin fibers exhibit properties similar to other elastomeric biopolymers. We propose a mechanical model that fits our observed force extension data, is consistent with the results of the ligation data, and suggests that the large observed extensibility in fibrin fibers is mediated by the natively unfolded regions of the molecule. Although some models attribute fibrin's force-versus-extension behavior to unfolding of structured regions within the monomer, our analysis argues that these models are inconsistent with the measured extensibility and elastic modulus.

Combined atomic force microscopy and fluorescence microscopy

The atomic force microscope (AFM) is a high-resolution scanning-probe instrument which has become an important tool for cellular and molecular biophysics in recent years, but lacks the time resolution and functional specificities offered by fluorescence microscopic techniques. The advantages of both methods may be exploited by combining and synchronizing them. In this paper, the biological applications of AFM, fluorescence, and their combinations are briefly reviewed, and the assembly and utilization of a spatially and temporally synchronized AFM and total internal reflection fluorescence microscope are described. The application of the method is demonstrated on a fluorescently labeled cell culture.

Molecular origin of strain softening in cross-linked F-actin networks

Two types of measurement are presented that relate molecular events to macroscopic behavior of F-actin networks. First, shear modulus is measured by oscillating an embedded microbead. Second, a microbead is translated at constant rate and transitions in the resisting force are observed. The loading rate dependence of the force at the transitions is similar to that of the molecular unbinding force, suggesting that they share a common origin. Reversibility tests of shear modulus provide further evidence that strain softening of F-actin networks is caused by force-induced rupture of cross-links.

Roles of titin in the structure and elasticity of the sarcomere

The giant protein titin is thought to play major roles in the assembly and function of muscle sarcomeres. Structural details, such as widths of Z- and M-lines and periodicities in the thick filaments, correlate with the substructure in the respective regions of the titin molecule. Sarcomere rest length, its operating range of lengths, and passive elastic properties are also directly controlled by the properties of titin. Here we review some recent titin data and discuss its implications for sarcomere architecture and elasticity.

Comparative biomechanics of thick filaments and thin filaments with functional consequences for muscle contraction

The scaffold of striated muscle is predominantly comprised of myosin and actin polymers known as thick filaments and thin filaments, respectively. The roles these filaments play in muscle contraction are well known, but the extent to which variations in filament mechanical properties influence muscle function is not fully understood. Here we review information on the material properties of thick filaments, thin filaments, and their primary constituents; we also discuss ways in which mechanical properties of filaments impact muscle performance.

Structure-function relations of the giant elastic protein titin in striated and smooth muscle cells

The striated muscle sarcomere contains, in addition to thin and thick filaments, a third myofilament comprised of titin. The extensible region of titin spans the I-band region of the sarcomere and develops passive force in stretched sarcomeres. This force positions the A-bands in the middle of the sarcomere, maintains sarcomere length homogeneity and, importantly, is responsible for myocardial passive tension that determines diastolic filling. Recent work suggests that smooth muscle expresses a truncated titin isoform with a short extensible region that is predicted to develop high passive force levels. Several mechanisms for tuning the titin-based passive tension have been discovered that involve alternative splicing as well as posttranslational modification, mechanisms that are at play both during normal muscle function as well as during disease.

Dynamic light scattering and atomic force microscopy imaging on fragments of beta-connectin from human cardiac muscle

In order to investigate the protein folding-unfolding process, dynamic light scattering (DLS) and atomic force microscopy (AFM) imaging were used to study two fragments of the muscle cardiac protein beta-connectin, also known as titin. Both fragments belong to the I band of the sarcomer, and they are composed of four domains from I(27) to I(30) (tetramer) and eight domains from I(27) to I(34) (octamer). DLS measurements provide the size of both fragments as a function of temperature from 20 up to 86 degrees C, and show a thermal denaturation due to temperature increase. AFM imaging of both fragments in the native state reveals a homogeneous and uniform distribution of comparable structures. The DLS and AFM techniques turn out to be complementary for size measurements of the fragments and fragment aggregates. An unexpected result is that the octamer folds into a smaller structure than the tetramer and the unfolded octamer is also smaller than the unfolded tetramer. This feature seems related to the significance of the hydrophobic interactions between domains of the fragment. The longer the fragment, the more easily the hydrophobic parts of the domains interact with each other. The fragment aggregation behavior, in particular conditions, is also revealed by both DLS and AFM as a process that is parallel to the folding-unfolding transition.

A regular pattern of Ig super-motifs defines segmental flexibility as the elastic mechanism of the titin chain

Myofibril elasticity, critical to muscle function, is dictated by the intrasarcomeric filament titin, which acts as a molecular spring. To date, the molecular events underlying the mechanics of the folded titin chain remain largely unknown. We have elucidated the crystal structure of the 6-Ig fragment I65-I70 from the elastic I-band fraction of titin and validated its conformation in solution using small angle x-ray scattering. The long-range properties of the chain have been visualized by electron microscopy on a 19-Ig fragment and modeled for the full skeletal tandem. Results show that conserved Ig-Ig transition motifs generate high-order in the structure of the filament, where conformationally stiff segments interspersed with pliant hinges form a regular pattern of dynamic super-motifs leading to segmental flexibility in the chain. Pliant hinges support molecular shape rearrangements that dominate chain behavior at moderate stretch, whereas stiffer segments predictably oppose high stretch forces upon full chain extension. There, librational entropy can be expected to act as an energy barrier to prevent Ig unfolding while, instead, triggering the unraveling of flanking springs formed by proline, glutamate, valine, and lysine (PEVK) sequences. We propose a mechanistic model based on freely jointed rigid segments that rationalizes the response to stretch of titin Ig-tandems according to molecular features.

Poly-Ig tandems from I-band titin share extended domain arrangements irrespective of the distinct features of their modular constituents

The cellular function of the giant protein titin in striated muscle is a major focus of scientific attention. Particularly, its role in passive mechanics has been extensively investigated. In strong contrast, the structural details of this filament are very poorly understood. To date, only a handful of atomic models from single domain components have become available and data on poly-constructs are limited to scarce SAXS analyses. In this study, we examine the molecular parameters of poly-Ig tandems from I-band titin relevant to muscle elasticity. We revisit conservation patterns in domain and linker sequences of I-band modules and interpret these in the light of available atomic structures of Ig domains from muscle proteins. The emphasis is placed on features expected to affect inter-domain arrangements. We examine the overall conformation of a 6Ig fragment, I65-I70, from the skeletal I-band of soleus titin using SAXS and electron microscopy approaches. The possible effect of highly conserved glutamate groups at the linkers as well as the ionic strength of the medium on the overall molecular parameters of this sample is investigated. Our findings indicate that poly-Ig tandems from I-band titin tend to adopt extended arrangements with low or moderate intrinsic flexibility, independently of the specific features of linkers or component Ig domains across constitutively- and differentially-expressed tandems. Linkers do not appear to operate as free hinges so that lateral association of Ig domains must occur infrequently in samples in solution, even that inter-domain sequences of 4-5 residues length would well accommodate such geometry. It can be expected that this principle is generally applicable to all Ig-tandems from I-band titin.

Can the passive elasticity of muscle be explained directly from the mechanics of individual titin molecules?

Recent progress in understanding the role of titin/connectin in muscle elasticity has been heavily based on results from single molecule mechanical experiments. The shape of force-extension curves from such data is similar to curves from muscle fibres and it has been tempting to assume that muscle elasticity can be extrapolated directly from the single molecule data. In this paper we discuss some of the factors that act on titin in the sarcomere that are likely to preclude such a direct extrapolation.

The mechanical fingerprint of a parallel polyprotein dimer

We use the GCN4 oligomerization domain to engineer a covalently linked parallel polyprotein dimer based on the well-studied I27 domain of titin. We use single molecule atomic force microscopy techniques to stretch single polyprotein fibers and verify their mechanical properties. We find that the engineered polyprotein dimers extend in perfect register, doubling the unfolding force and halving the persistence length while keeping the contour length increase unchanged. These experiments directly confirm the mechanical scaling laws proposed for parallel bundles of modular proteins.

Mechanical manipulation of Alzheimer’s amyloid β1–42 fibrils

The 39- to 42-residue-long amyloid beta-peptide (Abeta-peptide) forms filamentous structures in the neuritic plaques found in the neuropil of Alzheimer's disease patients. The assembly and deposition of Abeta-fibrils is one of the most important factors in the pathogenesis of this neurodegenerative disease. Although the structural analysis of amyloid fibrils is difficult, single-molecule methods may provide unique insights into their characteristics. In the present work, we explored the nanomechanical properties of amyloid fibrils formed from the full-length, most neurotoxic Abeta1-42 peptide, by manipulating individual fibrils with an atomic force microscope. We show that Abeta-subunit sheets can be mechanically unzipped from the fibril surface with constant forces in a reversible transition. The fundamental unzipping force (approximately 23 pN) was significantly lower than that observed earlier for fibrils formed from the Abeta1-40 peptide (approximately 33 pN), suggesting that the presence of the two extra residues (Ile and Ala) at the peptide's C-terminus result in a mechanical destabilization of the fibril. Deviations from the constant force transition may arise as a result of geometrical constraints within the fibril caused by its left-handed helical structure. The nanomechanical fingerprint of the Abeta1-42 is further influenced by the structural dynamics of intrafibrillar interactions.

Mechanotransduction involving multimodular proteins: converting force into biochemical signals

Cells can sense and transduce a broad range of mechanical forces into distinct sets of biochemical signals that ultimately regulate cellular processes, including adhesion, proliferation, differentiation, and apoptosis. Deciphering at the nanoscale the design principles by which sensory elements are integrated into structural protein motifs whose conformations can be switched mechanically is crucial to understand the process of transduction of force into biochemical signals that are then integrated to regulate mechanoresponsive pathways. While the major focus in the search for mechanosensory units has been on membrane proteins such as ion channels, integrins, and associated cytoplasmic complexes, a multimodular design of tandem repeats of various structural motifs is ubiquitously found among extracellular matrix proteins, as well as cell adhesion molecules, and among many intracellular players that physically link transmembrane proteins to the contractile cytoskeleton. Single-molecule studies have revealed an unexpected richness of mechanosensory motifs, including force-regulated conformational changes of loop-exposed molecular recognition sites, intermediate states in the unraveling pathway that might either expose cryptic binding or phosphorylation sites, or regions that display enzymatic activity only when unmasked by force. Insights into mechanochemical signal conversion principles will also affect various technological fields, from biotechnology to tissue engineering and drug development.

Spatially and temporally synchronized atomic force and total internal reflection fluorescence microscopy for imaging and manipulating cells and biomolecules

The atomic force microscope is a high-resolution scanning-probe instrument which has become an important tool for cellular and molecular biophysics in recent years but lacks the time resolution and functional specificities offered by fluorescence microscopic techniques. To exploit the advantages of both methods, here we developed a spatially and temporally synchronized total internal reflection fluorescence and atomic force microscope system. The instrument, which we hereby call STIRF-AFM, is a stage-scanning device in which the mechanical and optical axes are coaligned to achieve spatial synchrony. At each point of the scan the sample topography (atomic force microscope) and fluorescence (photon count or intensity) information are simultaneously recorded. The tool was tested and validated on various cellular (monolayer cells in which actin filaments and intermediate filaments were fluorescently labeled) and biomolecular (actin filaments and titin molecules) systems. We demonstrate that with the technique, correlated sample topography and fluorescence images can be recorded, soft biomolecular systems can be mechanically manipulated in a targeted fashion, and the fluorescence of mechanically stretched titin can be followed with high temporal resolution.

Nanomechanical properties of desmin intermediate filaments

Desmin intermediate filaments play important role in the mechanical integrity and elasticity of muscle cells. The mechanisms of how desmin contributes to cellular mechanics are little understood. Here, we explored the nanomechanics of desmin by manipulating individual filaments with atomic force microscopy. In complex, hierarchical force responses we identified recurring features which likely correspond to distinct properties and structural transitions related to desmin's extensibility and elasticity. The most frequently observed feature is an initial unbinding transition that corresponds to the removal of approximately 45-nm-long coiled-coil dimers from the filament surface with 20-60 pN forces in usually two discrete steps. In tethers longer than 60 nm we most often observed force plateaus studded with bumps spaced approximately 16 nm apart, which are likely caused by a combination of protofilament unzipping, dimer-dimer sliding and coiled-coil-domain unfolding events. At high stresses and strains non-linear, entropic elasticity was dominant, and sometimes repetitive sawtooth force transitions were seen which might arise because of slippage within the desmin protofilament. A model is proposed in which mechanical yielding is caused by coiled-coil domain unfolding and dimer-dimer sliding/slippage, and strain hardening by the entropic elasticity of partially unfolded protofilaments.

Adhesive modular proteins occur in the extracellular mucilage of the motile, pennate diatom Phaeodactylum tricornutum

This Letter reports on adhesive modular proteins recorded by atomic force microscopy on live cells from the extracellular mucilage secreted from, and deposited around, the motile form of the pennate diatom Phaeodactylum tricornutum. This is the first report of modular proteins and their supramolecular assemblies, called adhesive nanofibers (ANFs), to be found on diatoms that use adhesives not only for substratum adhesion, but as a conduit for cell motility. The permanent adhesive pads secreted by Toxarium undulatum, a sessile centric diatom, were previously shown to possess ANFs with a modular protein backbone. Our results reported here suggest that modular proteins may be an important component of diatom adhesives in general, and that diatoms utilize the tensile strength, toughness, and flexibility of ANFs for multiple functions. Significantly, the genome of P. tricornutum has recently been sequenced; this will allow directed searches of the genome to be made for genes with modular protein homologs, and subsequent detailed studies of their molecular structure and function.

Diatom adhesive mucilage contains distinct supramolecular assemblies of a single modular protein

A previous study used atomic force microscopy saw-tooth retraction curves to characterize the adhesive mucilage pads of the diatom Toxarium undulatum. The major mucilage component consisted of adhesive nanofibers (ANFs) made up of modular proteins arranged into cohesive units, each containing a set number of modular proteins aligned in parallel. This study shows that T. undulatum adhesive mucilage is a biocomposite containing four additional adhesive components, including single modular proteins that are likely to be the structural units from which the ANFs are assembled. Two further distinct supramolecular assemblies were observed to coexist with ANFs (ANFs II and III), along with a continuum of single modular proteins through oligomers made up of varying numbers of modular proteins arranged in parallel. All components of the adhesive biocomposite produce a characteristic force spectrum with the same interpeak distance (35.3 +/- 0.3 (mean +/- SE) nm), suggesting they are derived from discrete supramolecular assemblies of the same modular protein, but they are distinguishable from one another based on the rupture force, persistence length, and interpeak force measured from their saw-tooth curves.

Nanomechanical force measurements of gliadin protein interactions

The strength and nature of interactions between monomeric gliadin proteins involving alpha-alpha, omega-omega, and alpha-omega interactions in 0.01M acetic acid, and the effect of urea has been investigated. It was shown by means of nanomechanical force measurements that the stretching events in the separation curve after adhesive phenomena originated from proteins. These stretching events displayed different responses of the alpha- and omega-gliadins to urea. While 2M urea caused the more globular alpha-gliadins to unfold, the beta-turn-rich omega-gliadins remained fairly stable even in 8M urea. This suggests different roles for gliadins in the formation of dough; while the omega-gliadins are still in a compact structure being responsible for the viscous flow, the alpha-gliadins have already started to participate in forming the network in dough.

Mechanical Unfolding of TNfn3: The Unfolding Pathway of a fnIII Domain Probed by Protein Engineering, AFM and MD Simulation

Protein engineering Phi-value analysis combined with single molecule atomic force microscopy (AFM) was used to probe the molecular basis for the mechanical stability of TNfn3, the third fibronectin type III domain from human tenascin. This approach has been adopted previously to solve the forced unfolding pathway of a titin immunoglobulin domain, TI I27. TNfn3 and TI I27 are members of different protein superfamilies and have no sequence identity but they have the same beta-sandwich structure consisting of two antiparallel beta-sheets. TNfn3, however, unfolds at significantly lower forces than TI I27. We compare the response of these proteins to mechanical force. Mutational analysis shows that, as is the case with TI I27, TNfn3 unfolds via a force-stabilised intermediate. The key event in forced unfolding in TI I27 is largely the breaking of hydrogen bonds and hydrophobic interactions between the A' and G-strands. The mechanical Phi-value analysis and molecular dynamics simulations reported here reveal that significantly more of the TNfn3 molecule contributes to its resistance to force. Both AFM experimental data and molecular dynamics simulations suggest that the rate-limiting step of TNfn3 forced unfolding reflects a transition from the extended early intermediate to an aligned intermediate state. As well as losses of interactions of the A and G-strands and associated loops there are rearrangements throughout the core. As was the case for TI I27, the forced unfolding pathway of TNfn3 is different from that observed in denaturant studies in the absence of force.

Hierarchical extensibility in the PEVK domain of skeletal-muscle titin

Titin is the main determinant of passive muscle force. Physiological extension of titin derives largely from its PEVK (Pro-Glu-Val-Lys) domain, which has a different length in different muscle types. Here we characterized the elasticity of the full-length, human soleus PEVK domain by mechanically manipulating its contiguous, recombinant subdomain segments: an N-terminal (PEVKI), a middle (PEVKII), and a C-terminal (PEVKIII) one third. Measurement of the apparent persistence lengths revealed a hierarchical arrangement according to local flexibility: the N-terminal PEVKI is the most rigid and the C-terminal PEVKIII is the most flexible segment within the domain. Immunoelectron microscopy supported the hierarchical extensibility within the PEVK domain. The effective persistence lengths decreased as a function of ionic strength, as predicted by the Odijk-Skolnick-Fixman model of polyelectrolyte chains. The ionic strength dependence of persistence length was similar in all segments, indicating that the residual differences in the elasticity of the segments derive from nonelectrostatic mechanisms.

Visualizing and manipulating individual protein molecules

Single-molecule imaging and manipulation techniques have evolved in the past decade from mere jaw-dropping attractions to essential laboratory tools. By applying single-molecule methods important insights otherwise unavailable have been obtained on various biomolecular systems. Constantly improving single-molecule imaging techniques keep expanding the scale of the explorable spatial detail, thereby providing possible solutions to getting around the debilitating diffraction limit present in physiological-condition structural investigations. In some areas, such as motor protein studies, single-molecule methods have become part of the routine and essential research toolkit. Entire research fields, such as single-molecule force spectroscopy, have been born. In the present review single-molecule visualization and manipulation methods are reviewed with a focus on proteins. Relevant signals and prominent applications are discussed along with experimental examples and recent important results. Finally, the perspectives of the single-molecule field are explored.

Reversible Mechanical Unzipping of Amyloid β-Fibrils

Amyloid fibrils are self-associating filamentous structures, the deposition of which is considered to be one of the most important factors in the pathogenesis of Alzheimer's disease and various other disorders. Here we used single molecule manipulation methods to explore the mechanics and structural dynamics of amyloid fibrils. In mechanically manipulated amyloid fibrils, formed from either amyloid beta (Abeta) peptides 1-40 or 25-35, beta-sheets behave as elastic structures that can be "unzipped" from the fibril with constant forces. The unzipping forces were different for Abeta1-40 and Abeta25-35. Unzipping was fully reversible across a wide range of stretch rates provided that coupling, via the beta-sheet, between bound and dissociated states was maintained. The rapid, cooperative zipping together of beta-sheets could be an important mechanism behind the self-assembly of amyloid fibrils. The repetitive force patterns contribute to a mechanical fingerprint that could be utilized in the characterization of different amyloid fibrils.

Diastolic left ventricular function Experimental study of the early filling period using the Voigt model

BACKGROUND

The left ventricular (LV) diastolic function is usually described by the diastolic part of the LV pressure-volume relationship (PVR). The mathematical analysis of the PVR provides parameters of diastolic LV as well as myocardial function. Up to now, all approaches assume the myocardium as a passive elastic medium. This implies that each increase in LV volume is associated with a corresponding increase in LV pressure. Obviously this does not agree with actual PVR's during the LV early filling phase, where a decrease of pressure (due to relaxation) can be observed. Therefore, we analysed the LV diastolic PVR using the Voigt model to provide a better understanding of the concomitant processes of relaxation and filling especially during the early diastole.

METHODS AND RESULTS

LV volumes and pressures were measured in an experimental study (6 pigs) using biplane cineangiography (100 frames/s) and simultaneous pressure measurements (catheter tip manometer). LV volumes were determined from all cine frames of total cardiac cycles. Instantaneous (beat to beat) changes in duration (Deltat(f)) of the LV filling period were achieved by atrial stimulation and by releasing post-extrasystolic beats. A total of 26 PVR's with different Deltat(f) were evaluated. According to the Voigt model the compliance (product of the resting volume V(0) and the elastic coefficients) of the total muscle fibre (V(0).K(tot)) and of the serial elastic element (V(0).K(se)) were calculated (average: V(0).K(tot) = 3.43 ml/ mmHg; V(0).K(se) = 5.07 ml/mmHg; n = 26). The interindividual differences between the compliances were in some individuals significant (V(0).K(tot): p < 5% in 6 of 15 Wilcoxon tests ; V(0).K(se): p < 5% in 3 of 15 Wilcoxon tests) but the intraindividual range of these parameters (due to different Deltat(f)) were in some cases as pronounced as the interindividual differences.

CONCLUSIONS

As in 22 of 26 measurements V(0).K(tot) is less than V(0).K(se) it must be concluded that the early diastolic PVR cannot be described by passive elasticity and the laws of elastomechanics only. These inconsistencies can be explained by the early diastolic LV suction (untwisting) as well as by recent findings regarding the titin filament. Both mechanisms augment LV diastolic filling even in unfavourable working conditions (shortened filling) such as exercise.

Virus shapes and buckling transitions in spherical shells

We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one-parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl-von Kármán number gamma=YR(2)/kappa, where Y is the two-dimensional Young's modulus of the protein shell, kappa is its bending rigidity, and R is the mean virus radius. The shape can be parametrized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large gamma, 10(3)<gamma<10(8), and find results applicable to icosahedral shapes of large vesicles studied with freeze fracture and electron microscopy.