Cryo-EM structures of cardiac thin filaments reveal the 3D architecture of troponin.

Troponin is an essential component of striated muscle and it regulates the sliding of actomyosin system in a calcium-dependent manner. Despite its importance, the structure of troponin has been elusive due to its high structural heterogeneity. In this study, we analyzed the 3D structures of murine cardiac thin filaments using a cryo-electron microscope equipped with a Volta phase plate (VPP). Contrast enhancement by a VPP enabled us to reconstruct the entire repeat of the thin filament. We determined the orientation of troponin relative to F-actin and tropomyosin, and characterized the interactions between troponin and tropomyosin. This study provides a structural basis for understanding the molecular mechanism of actomyosin system.

Molecular integration of the anti-tropomyosin compound ATM-3507 into the coiled coil overlap region of the cancer-associated Tpm3.1.

Tropomyosins (Tpm) determine the functional capacity of actin filaments in an isoform-specific manner. The primary isoform in cancer cells is Tpm3.1 and compounds that target Tpm3.1 show promising results as anti-cancer agents both in vivo and in vitro. We have determined the molecular mechanism of interaction of the lead compound ATM-3507 with Tpm3.1-containing actin filaments. When present during co-polymerization of Tpm3.1 with actin, 3H-ATM-3507 is incorporated into the filaments and saturates at approximately one molecule per Tpm3.1 dimer and with an apparent binding affinity of approximately 2 µM. In contrast, 3H-ATM-3507 is poorly incorporated into preformed Tpm3.1/actin co-polymers. CD spectroscopy and thermal melts using Tpm3.1 peptides containing the C-terminus, the N-terminus, and a combination of the two forming the overlap junction at the interface of adjacent Tpm3.1 dimers, show that ATM-3507 shifts the melting temperature of the C-terminus and the overlap junction, but not the N-terminus. Molecular dynamic simulation (MDS) analysis predicts that ATM-3507 integrates into the 4-helix coiled coil overlap junction and in doing so, likely changes the lateral movement of Tpm3.1 across the actin surface resulting in an alteration of filament interactions with actin binding proteins and myosin motors, consistent with the cellular impact of ATM-3507.

High-speed AFM reveals subsecond dynamics of cardiac thin filaments upon Ca2+ activation and heavy meromyosin binding.

High-speed atomic force microscopy (HS-AFM) can be used to study dynamic processes with real-time imaging of molecules within 1- to 5-nm spatial resolution. In the current study, we evaluated the 3-state model of activation of cardiac thin filaments (cTFs) isolated as a complex and deposited on a mica-supported lipid bilayer. We studied this complex for dynamic conformational changes 1) at low and high [Ca2+] (pCa 9.0 and 4.5), and 2) upon myosin binding to the cTF in the nucleotide-free state or in the presence of ATP. HS-AFM was used to directly visualize the tropomyosin-troponin complex and Ca2+-induced tropomyosin movements accompanied by structural transitions of actin monomers within cTFs. Our data show that cTFs at relaxing or activating conditions are not ultimately in a blocked or activated state, respectively, but rather the combination of states with a prevalence that is dependent on the [Ca2+] and the presence of weakly or strongly bound myosin. The weakly and strongly bound myosin induce similar changes in the structure of cTFs as confirmed by the local dynamical displacement of individual tropomyosin strands in the center of a regulatory unit of cTF at the relaxed and activation conditions. The displacement of tropomyosin at the relaxed conditions had never been visualized directly and explains the ability of myosin binding to TF at the relaxed conditions. Based on the ratios of nonactivated and activated segments within cTFs, we proposed a mechanism of tropomyosin switching from different states that includes both weakly and strongly bound myosin.

Tropomyosin Structure, Function, and Interactions: A Dynamic Regulator.

Tropomyosin is the archetypal-coiled coil, yet studies of its structure and function have proven it to be a dynamic regulator of actin filament function in muscle and non-muscle cells. Here we review aspects of its structure that deviate from canonical leucine zipper coiled coils that allow tropomyosin to bind to actin, regulate myosin, and interact directly and indirectly with actin-binding proteins. Four genes encode tropomyosins in vertebrates, with additional diversity that results from alternate promoters and alternatively spliced exons. At the same time that periodic motifs for binding actin and regulating myosin are conserved, isoform-specific domains allow for specific interaction with myosins and actin filament regulatory proteins, including troponin. Tropomyosin can be viewed as a universal regulator of the actin cytoskeleton that specifies actin filaments for cellular and intracellular functions.

Cryo-EM Structure Determination Using Segmented Helical Image Reconstruction.

Treating helices as single-particle-like segments followed by helical image reconstruction has become the method of choice for high-resolution structure determination of well-ordered helical viruses as well as flexible filaments. In this review, we will illustrate how the combination of latest hardware developments with optimized image processing routines have led to a series of near-atomic resolution structures of helical assemblies. Originally, the treatment of helices as a sequence of segments followed by Fourier-Bessel reconstruction revealed the potential to determine near-atomic resolution structures from helical specimens. In the meantime, real-space image processing of helices in a stack of single particles was developed and enabled the structure determination of specimens that resisted classical Fourier helical reconstruction and also facilitated high-resolution structure determination. Despite the progress in real-space analysis, the combination of Fourier and real-space processing is still commonly used to better estimate the symmetry parameters as the imposition of the correct helical symmetry is essential for high-resolution structure determination. Recent hardware advancement by the introduction of direct electron detectors has significantly enhanced the image quality and together with improved image processing procedures has made segmented helical reconstruction a very productive cryo-EM structure determination method.

Tropomyosin-binding properties modulate competition between tropomodulin isoforms.

The formation and fine-tuning of cytoskeleton in cells are governed by proteins that influence actin filament dynamics. Tropomodulin (Tmod) regulates the length of actin filaments by capping the pointed ends in a tropomyosin (TM)-dependent manner. Tmod1, Tmod2 and Tmod3 are associated with the cytoskeleton of non-muscle cells and their expression has distinct consequences on cell morphology. To understand the molecular basis of differences in the function and localization of Tmod isoforms in a cell, we compared the actin filament-binding abilities of Tmod1, Tmod2 and Tmod3 in the presence of Tpm3.1, a non-muscle TM isoform. Tmod3 displayed preferential binding to actin filaments when competing with other isoforms. Mutating the second or both TM-binding sites of Tmod3 destroyed its preferential binding. Our findings clarify how Tmod1, Tmod2 and Tmod3 compete for binding actin filaments. Different binding mechanisms and strengths of Tmod isoforms for Tpm3.1 contribute to their divergent functional capabilities.

Cryo-EM structures of the actin:tropomyosin filament reveal the mechanism for the transition from C- to M-state.

Tropomyosin (Tm) is a key factor in the molecular mechanisms that regulate the binding of myosin motors to actin filaments (F-Actins) in most eukaryotic cells. This regulation is achieved by the azimuthal repositioning of Tm along the actin (Ac):Tm:troponin (Tn) thin filament to block or expose myosin binding sites on Ac. In striated muscle, including involuntary cardiac muscle, Tm regulates muscle contraction by coupling Ca(2+) binding to Tn with myosin binding to the thin filament. In smooth muscle, the switch is the posttranslational modification of the myosin. Depending on the activation state of Tn and the binding state of myosin, Tm can occupy the blocked, closed, or open position on Ac. Using native cryogenic 3DEM (three-dimensional electron microscopy), we have directly resolved and visualized cardiac and gizzard muscle Tm on filamentous Ac in the position that corresponds to the closed state. From the 8-Å-resolution structure of the reconstituted Ac:Tm filament formed with gizzard-derived Tm, we discuss two possible mechanisms for the transition from closed to open state and describe the role Tm plays in blocking myosin tight binding in the closed-state position.

Familial hypertrophic cardiomyopathy related E180G mutation increases flexibility of human cardiac α-tropomyosin.

α-Tropomyosin (αTm) is central to Ca(2+)-regulation of cardiac muscle contraction. The familial hypertrophic cardiomyopathy mutation αTm E180G enhances Ca(2+)-sensitivity in functional assays. To investigate the molecular basis, we imaged single molecules of human cardiac αTm E180G by direct probe atomic force microscopy. Analyses of tangent angles along molecular contours yielded persistence length corresponding to ~35% increase in flexibility compared to wild-type. Increased flexibility of the mutant was confirmed by fitting end-to-end length distributions to the worm-like chain model. This marked increase in flexibility can significantly impact systolic and possibly diastolic phases of cardiac contraction, ultimately leading to hypertrophy.

Electron microscopy and 3D reconstruction of F-actin decorated with cardiac myosin-binding protein C (cMyBP-C).

Myosin-binding protein C (MyBP-C) is an ∼130-kDa rod-shaped protein of the thick (myosin containing) filaments of vertebrate striated muscle. It is composed of 10 or 11 globular 10-kDa domains from the immunoglobulin and fibronectin type III families and an additional MyBP-C-specific motif. The cardiac isoform cMyBP-C plays a key role in the phosphorylation-dependent enhancement of cardiac function that occurs upon ß-adrenergic stimulation, and mutations in MyBP-C cause skeletal muscle and heart diseases. In addition to binding to myosin, MyBP-C can also bind to actin via its N-terminal end, potentially modulating contraction in a novel way via this thick-thin filament bridge. To understand the structural basis of actin binding, we have used negative stain electron microscopy and three-dimensional reconstruction to study the structure of F-actin decorated with bacterially expressed N-terminal cMyBP-C fragments. Clear decoration was obtained under a variety of salt conditions varying from 25 to 180 mM KCl concentration. Three-dimensional helical reconstructions, carried out at the 180-mM KCl level to minimize nonspecific binding, showed MyBP-C density over a broad portion of the periphery of subdomain 1 of actin and extending tangentially from its surface in the direction of actin's pointed end. Molecular fitting with an atomic structure of a MyBP-C Ig domain suggested that most of the N-terminal domains may be well ordered on actin. The location of binding was such that it could modulate tropomyosin position and would interfere with myosin head binding to actin.

Tropomyosin position on F-actin revealed by EM reconstruction and computational chemistry.

Electron microscopy and fiber diffraction studies of reconstituted F-actin-tropomyosin filaments reveal the azimuthal position of end-to-end linked tropomyosin molecules on the surface of actin. However, the longitudinal z-position of tropomyosin along F-actin is still uncertain. Without this information, atomic models of F-actin-tropomyosin filaments, free of constraints imposed by troponin or other actin-binding proteins, cannot be formulated, and thus optimal interfacial contacts between actin and tropomyosin remain unknown. Here, a computational search assessing electrostatic interactions for multiple azimuthal locations, z-positions, and pseudo-rotations of tropomyosin on F-actin was performed. The information gleaned was used to localize tropomyosin on F-actin, yielding an atomic model characterized by protein-protein contacts that primarily involve clusters of basic amino acids on actin subdomains 1 and 3 juxtaposed against acidic residues on the successive quasi-repeating units of tropomyosin. A virtually identical model generated by docking F-actin and tropomyosin atomic structures into electron microscopy reconstructions of F-actin-tropomyosin validated the above solution. Here, the z-position of tropomyosin alongside F-actin was defined by matching the seven broad and narrow motifs that typify tropomyosin's twisting superhelical coiled-coil to the wide and tapering tropomyosin densities seen in surface views of F-actin-tropomyosin reconstructions. The functional implications of the F-actin-tropomyosin models determined in this work are discussed.

X-ray diffraction evidence for myosin-troponin connections and tropomyosin movement during stretch activation of insect flight muscle.

Stretch activation is important in the mechanical properties of vertebrate cardiac muscle and essential to the flight muscles of most insects. Despite decades of investigation, the underlying molecular mechanism of stretch activation is unknown. We investigated the role of recently observed connections between myosin and troponin, called "troponin bridges," by analyzing real-time X-ray diffraction "movies" from sinusoidally stretch-activated Lethocerus muscles. Observed changes in X-ray reflections arising from myosin heads, actin filaments, troponin, and tropomyosin were consistent with the hypothesis that troponin bridges are the key agent of mechanical signal transduction. The time-resolved sequence of molecular changes suggests a mechanism for stretch activation, in which troponin bridges mechanically tug tropomyosin aside to relieve tropomyosin's steric blocking of myosin-actin binding. This enables subsequent force production, with cross-bridge targeting further enhanced by stretch-induced lattice compression and thick-filament twisting. Similar linkages may operate in other muscle systems, such as mammalian cardiac muscle, where stretch activation is thought to aid in cardiac ejection.

Electron microscopy and persistence length analysis of semi-rigid smooth muscle tropomyosin strands.

The structural mechanics of tropomyosin are essential determinants of its affinity and positioning on F-actin. Thus, tissue-specific differences among tropomyosin isoforms may influence both access of actin-binding proteins along the actin filaments and the cooperativity of actin-myosin interactions. Here, 40 nm long smooth and striated muscle tropomyosin molecules were rotary-shadowed and compared by means of electron microscopy. Electron microscopy shows that striated muscle tropomyosin primarily consists of single molecules or paired molecules linked end-to-end. In contrast, smooth muscle tropomyosin is more a mixture of varying-length chains of end-to-end polymers. Both isoforms are characterized by gradually bending molecular contours that lack obvious signs of kinking. The flexural stiffness of the tropomyosins was quantified and evaluated. The persistence lengths along the shaft of rotary-shadowed smooth and striated muscle tropomyosin molecules are equivalent to each other (approximately 100 nm) and to values obtained from molecular-dynamics simulations of the tropomyosins; however, the persistence length surrounding the end-to-end linkage is almost twofold higher for smooth compared to cardiac muscle tropomyosin. The tendency of smooth muscle tropomyosin to form semi-rigid polymers with continuous and undampened rigidity may compensate for the lack of troponin-based structural support in smooth muscles and ensure positional fidelity on smooth muscle thin filaments.

The shape and flexibility of tropomyosin coiled coils: implications for actin filament assembly and regulation.

Wrapped superhelically around actin filaments, the coiled-coil alpha-helices of tropomyosin regulate muscle contraction by cooperatively blocking or exposing myosin-binding sites on actin. In non-muscle cells, tropomyosin additionally controls access of actin-binding proteins involved in cytoskeletal actin filament maintenance and remodeling. Tropomyosin's global shape and flexibility play a key role in the assembly, maintenance, and regulatory switching of thin filaments yet remain insufficiently characterized. Here, electron microscopy and molecular dynamics simulations yielded conformations of tropomyosin closely resembling each other. The electron microscopy and simulations show that isolated tropomyosin has an average curved conformation with a design well matched to its superhelical shape on F-actin. In addition, they show that tropomyosin bends smoothly yet anisotropically about its distinctive helically curved conformation, without any signs of unfolding, chain separation, localized kinks, or joints. Previous measurements, assuming tropomyosin to be straight on average, mistakenly suggested considerable flexibility (with persistence lengths only approximately 3 times the protein's length). However, taking the curved average structure determined here as reference for the flexibility measurements yields a persistence length of approximately 12 lengths, revealing that tropomyosin actually is semirigid. Corresponding simulation of a triple mutant (A74L-A78V-A81L) with weak actin affinity shows that it lacks shape complementarity to F-actin. Thus, tropomyosin's pre-shaped semirigid architecture is essential for the assembly of actin filaments. Further, we propose that once bound to thin filaments, tropomyosin will be stiff enough to act as a cooperative unit and move on actin in a concerted way between known regulatory states.

Electron microscopy and three-dimensional reconstruction of native thin filaments reveal species-specific differences in regulatory strand densities.

Throughout the animal kingdom striated muscle contraction is regulated by the thin filament troponin-tropomyosin complex. Homologous regulatory components are shared among vertebrate and arthropod muscles; however, unique protein extensions and/or components characterize the latter. The Troponin T (TnT) isoforms of Drosophila indirect flight and tarantula femur muscle for example contain distinct C-terminal extensions and are approximately 20% larger overall than their vertebrate counterpart. Using electron microscopy and three-dimensional helical reconstruction of native Drosophila, tarantula and frog muscle thin filaments we have identified species-specific differences in tropomyosin regulatory strand densities. The strands on the arthropod thin filaments were significantly larger in diameter than those from vertebrates, although not significantly different from each other. These findings reflect differences in the regulatory troponin-tropomyosin complex, which are likely due to the larger TnT molecules aligning and extending along much of the tropomyosin strands' length. Such an arrangement potentially alters the physical properties of the regulatory strands and may help establish contractile characteristics unique to certain arthropod muscles.

Ultrastructural features of the columellar muscle and contractile protein analyses in different muscle groups of Megalobulimus abbreviatus (Gastropoda, Pulmonata).

In Megalobulimus abbreviatus, the ultrastructural features and the contractile proteins of columellar, pharyngeal and foot retractor muscles were studied. These muscles are formed from muscular fascicles distributed in different planes that are separated by connective tissue rich in collagen fibrils. These cells contain thick and thin filaments, the latter being attached to dense bodies, lysosomes, sarcoplasmic reticulum, caveolae, mitochondria and glycogen granules. Three types of muscle cells were distinguished: T1 cells displayed the largest amount of glycogen and an intermediate number of mitochondria, suggesting the highest anaerobic metabolism; T2 cells had the largest number of mitochondria and less glycogen, which suggests an aerobic metabolism; T3 cells showed intermediate glycogen volumes, suggesting an intermediate anaerobic metabolism. The myofilaments in the pedal muscle contained paramyosin measuring between 40 and 80nm in diameter. Western Blot muscle analysis showed a 46-kDa band that corresponds to actin and a 220-kDa band that corresponds to myosin filaments. The thick filament used in the electrophoresis showed a protein band of 100kDa in the muscles, which may correspond to paramyosin.

The C terminus of cardiac troponin I stabilizes the Ca2+-activated state of tropomyosin on actin filaments.

RATIONALE: Ca(2+) control of troponin-tropomyosin position on actin regulates cardiac muscle contraction. The inhibitory subunit of troponin, cardiac troponin (cTn)I is primarily responsible for maintaining a tropomyosin conformation that prevents crossbridge cycling. Despite extensive characterization of cTnI, the precise role of its C-terminal domain (residues 193 to 210) is unclear. Mutations within this region are associated with restrictive cardiomyopathy, and C-terminal deletion of cTnI, in some species, has been associated with myocardial stunning. OBJECTIVE: We sought to investigate the effect of a cTnI deletion-removal of 17 amino acids from the C terminus- on the structure of troponin-regulated tropomyosin bound to actin. METHODS AND RESULTS: A truncated form of human cTnI (cTnI(1-192)) was expressed and reconstituted with troponin C and troponin T to form a mutant troponin. Using electron microscopy and 3D image reconstruction, we show that the mutant troponin perturbs the positional equilibrium dynamics of tropomyosin in the presence of Ca(2+). Specifically, it biases tropomyosin position toward an "enhanced C-state" that exposes more of the myosin-binding site on actin than found with wild-type troponin. CONCLUSIONS: In addition to its well-established role of promoting the so-called "blocked-state" or "B-state," cTnI participates in proper stabilization of tropomyosin in the "Ca(2+)-activated state" or "C-state." The last 17 amino acids perform this stabilizing role. The data are consistent with a "fly-casting" model in which the mobile C terminus of cTnI ensures proper conformational switching of troponin-tropomyosin. Loss of actin-sensing function within this domain, by pathological proteolysis or cardiomyopathic mutation, may be sufficient to perturb tropomyosin conformation.

Structural basis for the activation of muscle contraction by troponin and tropomyosin.

The molecular regulation of striated muscle contraction couples the binding and dissociation of Ca(2+) on troponin (Tn) to the movement of tropomyosin on actin filaments. In turn, this process exposes or blocks myosin binding sites on actin, thereby controlling myosin crossbridge dynamics and consequently muscle contraction. Using 3D electron microscopy, we recently provided structural evidence that a C-terminal extension of TnI is anchored on actin at low Ca(2+) and competes with tropomyosin for a common site to drive tropomyosin to the B-state location, a constrained, relaxing position on actin that inhibits myosin-crossbridge association. Here, we show that release of this constraint at high Ca(2+) allows a second segment of troponin, probably representing parts of TnT or the troponin core domain, to promote tropomyosin movement on actin to the Ca(2+)-induced C-state location. With tropomyosin stabilized in this position, myosin binding interactions can begin. Tropomyosin appears to oscillate to a higher degree between respective B- and C-state positions on troponin-free filaments than on fully regulated filaments, suggesting that tropomyosin positioning in both states is troponin-dependent. By biasing tropomyosin to either of these two positions, troponin appears to have two distinct structural functions; in relaxed muscles at low Ca(2+), troponin operates as an inhibitor, while in activated muscles at high Ca(2+), it acts as a promoter to initiate contraction.

Ca2+ -induced tropomyosin movement in scallop striated muscle thin filaments.

Striated muscle contraction in most animals is regulated at least in part by the troponin-tropomyosin (Tn-Tm) switch on the thin (actin-containing) filaments. The only group that has been suggested to lack actin-linked regulation is the mollusks, where contraction is regulated through the myosin heads on the thick filaments. However, molluscan gene sequence data suggest the presence of troponin (Tn) components, consistent with actin-linked regulation, and some biochemical and immunological data also support this idea. The presence of actin-linked (in addition to myosin-linked) regulation in mollusks would simplify our general picture of muscle regulation by extending actin-linked regulation to this phylum as well. We have investigated this question structurally by determining the effect of Ca(2+) on the position of Tm in native thin filaments from scallop striated adductor muscle. Three-dimensional reconstructions of negatively stained filaments were determined by electron microscopy and single-particle image analysis. At low Ca(2+), Tm appeared to occupy the "blocking" position, on the outer domain of actin, identified in earlier studies of regulated thin filaments in the low-Ca(2+) state. In this position, Tm would sterically block myosin binding, switching off filament activity. At high Ca(2+), Tm appeared to move toward a position on the inner domain, similar to that induced by Ca(2+) in regulated thin filaments. This Ca(2+)-induced movement of Tm is consistent with the hypothesis that scallop thin filaments are Ca(2+) regulated.

Structural basis for the regulation of muscle contraction by troponin and tropomyosin.

The molecular switching mechanism governing skeletal and cardiac muscle contraction couples the binding of Ca2+ on troponin to the movement of tropomyosin on actin filaments. Despite years of investigation, this mechanism remains unclear because it has not yet been possible to directly assess the structural influence of troponin on tropomyosin that causes actin filaments, and hence myosin-crossbridge cycling and contraction, to switch on and off. A C-terminal domain of troponin I is thought to be intimately involved in inducing tropomyosin movement to an inhibitory position that blocks myosin-crossbridge interaction. Release of this regulatory, latching domain from actin after Ca2+ binding to TnC (the Ca2+ sensor of troponin that relieves inhibition) presumably allows tropomyosin movement away from the inhibitory position on actin, thus initiating contraction. However, the structural interactions of the regulatory domain of TnI (the "inhibitory" subunit of troponin) with tropomyosin and actin that cause tropomyosin movement are unknown, and thus, the regulatory process is not well defined. Here, thin filaments were labeled with an engineered construct representing C-terminal TnI, and then, 3D electron microscopy was used to resolve where troponin is anchored on actin-tropomyosin. Electron microscopy reconstruction showed how TnI binding to both actin and tropomyosin at low Ca2+ competes with tropomyosin for a common site on actin and drives tropomyosin movement to a constrained, relaxing position to inhibit myosin-crossbridge association. Thus, the observations reported reveal the structural mechanism responsible for troponin-tropomyosin-mediated steric interference of actin-myosin interaction that regulates muscle contraction.

Two-crystal structures of tropomyosin C-terminal fragment 176-273: exposure of the hydrophobic core to the solvent destabilizes the tropomyosin molecule.

Tropomyosin (Tm) is a two-stranded alpha-helical coiled-coil protein, and when associated with troponin, it is responsible for the actin filament-based regulation of muscle contraction in vertebrate skeletal and cardiac muscles. It is widely believed that Tm adopts a flexible rod-like structure in which the flexibility must play a crucial role in its functions. To obtain more information about the flexibility of Tm, we solved and compared two crystal structures of the identical C-terminal segments, spanning approximately 40% of the entire length. We also compared these structures with our previously reported crystal structure of an almost identical Tm segment in a distinct crystal form. The parameters specifying the local coiled-coil geometry, such as the separation between two helices and the local helical pitch, undulate along the length of Tm in the same way as among the three crystal structures, indicating that these parameters are defined by the amino acid sequence. In the region of increased separation, around Glu-218 and Gln-263, the hydrophobic core is disrupted by three holes. Moreover, for the first time to our knowledge, for Tm, water molecules have been identified in these holes. In some structures, the B-factors are higher around the holes than in the rest of the molecule. The Tm coiled-coil must be destabilized and therefore may be flexible, not only in the alanine clusters but also in the regions of the broken core. A closer look at the local staggering between the two chains and the local bending revealed that the strain accumulates at the alanine cluster and may be relaxed in the broken core region. Moreover, the strain is distributed over a long range, even when a deformation like bending may occur at a limited number of spots. Thus, Tm should not be regarded as a train of short rigid rods connected by flexible linkers, but rather as a seamless rubber rod patched with relatively more flexible regions.