Dynamic and elastic properties of F-actin: a normal-modes analysis.

We examine the dynamic, elastic, and mechanical consequences of the proposed atomic models of F-actin, using a normal mode analysis. This initial analysis is done in vacuo and assumes that all monomers are rigid and equivalent. Our computation proceeds from the atomic level and, relying on a single fitting parameter, reproduces various experimental results, including persistence lengths, elastic moduli, and contact energies. The computations reveal modes of motion characteristic to all polymers, such as longitudinal pressure waves, torsional waves, and bending, as well as motions unique to F-actin. Motions typical to actin include a "groove-swinging" motion of the two long-pitch helices, as well as an axial slipping motion of the two strands. We prepare snapshots of thermally activated filaments and quantify the accumulation of azimuthal angular "disorder," variations in cross-over lengths, and various other fluctuations. We find that the orientation of a small number of select residues has a surprisingly large effect on the filament flexibility and elasticity characteristics.     

On the elastic properties of arteries

A new coefficient of elasticity is proposed that relates to the elastic state of the blood vessels. This measure is proposed as a result of the realization, from personal experience as well as from the international literature, of the difficulty in measuring the thickness of the blood vessels in vivo with acceptable precision. The measurement of E being dependent on the measurement of the thickness of the vessels becomes a highly unreliable proposition. Its relation to E (Young modulus) and to the pulse wave velocity (PWV) is established. We give three examples showing how the proposed coefficient can be measured.     

On the interaction between myosin A and F-actin

The interaction of myosin and actin was studied by means of two techniques: (1) the inhibition of myosin ATPase (ATP-phosphohydrolase, E.C. 3.6.1.3) by actin addition, and (2) centrifugation experiments, carried out so that only free myosin appears in the supernatant. Association constants are calculated and a binding curve for myosin is obtained. The maximum binding agrees with a weight percentage of 3.7 myosin to 1 actin. The effects of urea, p-chloromercuribenzoate, CaCl₂, temperature and pyrophosphate were studied. It is concluded that ATP and actin bind to the same myosin site and that pyrophosphate binds also to this same site. The association constant for pyrophosphate was calculated from its inhibitory effect on the actin-myosin interaction, while this constant for the actin-myosin interaction was also calculated from experiments by Gergelyet al. on the inhibition of pyrophosphate binding to myosin by actin.The temperature dependence of the binding was found to be quite small and the conclusion was made that the free-energy effect is nearly all due to entropy change.     

Passive elastic properties of the rat ankle

Passive properties of muscles and tendons, including their elasticity, have been suggested to influence motor control. We examine here the potential role of passive elastic muscle properties at the rat ankle joint, focusing on their potential to specify an equilibrium position of the ankle. We measured the position-dependent passive torques at the rat ankle before and after sequential cuts of flexor (a.k.a. dorsiflexor) and extensor (a.k.a. plantarflexor) ankle muscles. We found that there was a passive equilibrium position of the ankle that shifted systematically with the cuts, demonstrating that the passive torques produced by ankle flexor and extensor muscles work in opposition in order to maintain a stable equilibrium. The mean equilibrium position of the intact rat ankle ranged from 9.3° to 15.7° in extension relative to the orthogonal position, depending on the torque metric. The mean shift in equilibrium position due to severing extensors ranged from 4.4° to 7.7°, and the mean shift due to severing flexors was smaller, ranging from 0.9° to 2.5°. The restoring torques generated by passive elasticity are large enough (approximately 1.5-5 mNm for displacements of 18° from equilibrium) to affect ankle movement during the swing phase of locomotion, and the asymmetry of larger extension vs. flexion torques is consistent with weight support, demonstrating the importance of accounting for passive muscle properties when considering the neural control of movement.     

Passive elastic properties of the rat aorta

The passive anisotropic elastic properties of rat's aorta were studied in vitro by subjecting cylindrical segments of thoracic and abdominal aorta to a wide range of deformations. Using data on pressure, axial stretch, outer diameter, axial force and wall thickness, incremental moduli of elasticity in the circumferential, axial and radial directions were computed. Results indicate that while the elastic behavior of the aortic wall is globally anisotropic, there exists a state of deformation at which the vessel displays incremental isotropy. This state of deformation corresponds approximately to the loading conditions to which the aorta is exposed in situ. Values of the moduli, analyzed as a function of transmural pressure, show that the stiffness of the aortic wall is fairly constant at low pressures but raises steeply for pressures higher than physiological. For axial stretches as occurring in situ, the magnitudes of the circumferential and radial moduli do not differ significantly for the thoracic aorta; hence this vessel can be regarded as transversely isotropic over a wide range of pressures. The same observation is valid also for the abdominal aorta when pressures equal or smaller than physiological are considered. For both the thoracic and abdominal segments of the aorta, the circumferential and radial moduli are smaller than the axial modulus at low pressures, while the reverse is true for large pressures.     

Sequence-dependent elastic properties of DNA

Harmonic elastic constants of 3-11 bp duplex DNA fragments were evaluated using four 5 ns unrestrained molecular dynamics simulation trajectories of 17 bp duplexes with explicit inclusion of solvent and counterions. All simulations were carried out with the Cornell et al. force-field and particle mesh Ewald method for long-range electrostatic interactions. The elastic constants including anisotropic bending and all coupling terms were derived by analyzing the correlations of fluctuations of structural properties along the trajectories. The following sequences have been considered: homopolymer d(ApA)(n) and d(GpG)(n), and alternating d(GPC)(n) and d(APT)(n). The calculated values of elastic constants are in very good overall agreement with experimental values for random sequences. The atomic-resolution molecular dynamics approach, however, reveals a pronounced sequence-dependence of the stretching and torsional rigidity of DNA, while sequence-dependence of the bending rigidity is smaller for the sequences considered. The earlier predicted twist-bend coupling emerged as the most important cross-term for fragments shorter than one helical turn. The calculated hydrodynamic relaxation times suggest that damping of bending motions may play a role in molecular dynamics simulations of long DNA fragments. A comparison of elasticity calculations using global and local helicoidal analyses is reported. The calculations reveal the importance of the fragment length definition. The present work shows that large-scale molecular dynamics simulations represent a unique source of data to study various aspects of DNA elasticity including its sequence-dependence.     

The elastic properties of elastin

The thermoelastic properties of elastin immersed in water or in aqueous solutions of alcohols closely resemble those of typical polymers in the rubber elastic state. The evolution of heat much in excess of the work performed on elastin when it is stretched while immersed in water at ca. 25°C is attributable to the exothermic heat of dilution by water absorbed into the polymer during elongation. The negative sign of the temperature coefficient of swelling is confirmatory of this explanation. A network of random chains within the elastin fibers, like that in a typical rubber, is clearly indicated. The elastic properties of elastin are not explicable in terms of a two-phase model consisting of discrete globules of compact elastin molecules fused one to another by cross-linkages, with diluent (water) filling the interstices.     

Smooth muscle caldesmon. Rapid purification and F-actin cross-linking properties

A method for the rapid purification of caldesmon, an F-actin binding protein of smooth muscle, has been developed. Caldesmon remains native after heating at 90 degrees C, a property that provides the basis for the purification in high yield of both caldesmon and tropomyosin, another heat-stable protein of smooth muscle. Caldesmon purified by this procedure is a highly asymmetric protein with a sedimentation coefficient of approximately 2.7 S and a Stokes radius of about 91 A. The protein exists as two polypeptide chains of Mr = 135,000 and 140,000, with each Mr polypeptide being resolvable into several isoelectric species. Estimates based on densitometry of stained gels suggest that caldesmon is more abundant in smooth muscle than filamin or alpha-actinin. Purified caldesmon bound to F-actin in the pH range 6-8. Binding was unaffected by Ca2+ or Mg2+ at up to millimolar levels. Binding was saturable, with a polypeptide molar ratio of about one caldesmon to six actins at saturation. F-actin binding was not inhibited by saturating levels of tropomyosin. Caldesmon dramatically increased the viscosity of F-actin. Light microscopy and electron microscopy of negatively stained material revealed that caldesmon induced the formation of massive F-actin bundles which contained up to hundreds of filaments. Electron microscopy of sectioned caldesmon-saturated F-actin mixtures revealed large bundles which appeared to include linear arrays of regularly spaced actin filaments cut transversely, exhibiting a center to center spacing of 15 nm. Possible structural implications based on the existence of these structures is presented.     

Annexin A8 displays unique phospholipid and F-actin binding properties

Annexin A8 is a poorly characterized member of the annexin family of Ca2+-regulated membrane binding proteins. Initially only identified at the cDNA level it had been tentatively linked to acute promyelocytic leukaemia (APL) due to its high and regulated expression in APL-derived cells. Here we identify unique properties of the annexin A8 protein. We show that it binds Ca2+-dependently and with high specificity to phosphatidylinositol (4,5)-bisphosphate (PtdIns(4,5)P2) and is also capable of interacting with F-actin. In line with these characteristics annexin A8 is recruited to F-actin-associated PtdIns(4,5)P2-rich membrane domains formed in HeLa cells upon infection with non-invading enteropathogenic Escherichia coli. These properties suggest a role of annexin A8 in the organization of certain actin-associated membrane domains.     

On the elastic properties of mineralized turkey leg tendon tissue: multiscale model and experiment

The key parameters influencing the elastic properties of the mineralized turkey leg tendon (MTLT) were investigated. Two structurally different tissue types appearing in the MTLT were considered: circumferential and interstitial tissue. These differ in their amount of micropores and their average diameter of the mineralized collagen fibril bundles. A multiscale model representing the apparent elastic stiffness tensor of MTLT tissue was developed using the Mori–Tanaka and the self-consistent homogenization schemes. The volume fraction of mineral (hydroxyapatite) in the fibril bundle, \(\hbox {vf}_{{\text {ha}}}^{{\text {MCFB}}}\) , and the tissue microporosity are the variables of the model. The MTLT model was analyzed performing a global sensitivity analysis (Elementary Effects method) and a parametric study. The stiffnesses parallel (axial) and perpendicular (transverse) to the MTLT long axis were the only significantly sensitive components of the apparent stiffness tensor of MTLT tissue. The most important parameters influencing these apparent stiffnesses are \(\hbox {vf}_{{\text {ha}}}^{{\text {MCFB}}}\) , tissue microporosity, as well as shape and distribution of the minerals in the fibril bundle (intra- vs. interfibrillar). The predicted apparent stiffness was converted to acoustic impedance for model validation. From measurements on embedded MTLT samples, including 50- and 200-MHz scanning acoustic microscopy as well as synchrotron radiation micro-computed tomography, we obtained site-matched acoustic impedance and \(\hbox {vf}_{{\text {ha}}}^{{\text {MCFB}}}\) data of circumferential and interstitial tissue. The experimental and the model data compare very well for both tissue types (relative error 6–8 %).     

The interplay between viscoelastic and thermodynamic properties determines the birefringence of F-actin gels

F-actin gels of increasing concentrations (25-300 microM) display in vitro a progressive onset of birefringence due to orientational ordering of actin filaments. At F-actin concentrations <100 microM, this birefringence can be erased and restored at will by sonication and gentle flow, respectively. Hence, the orientational ordering does not result from a thermodynamic transition to a nematic phase but instead is due to mechanical stresses stored in the gels. In contrast, at F-actin concentrations > or =100 microM, gels display spontaneous birefringence recovery, at rest, which is the sign of true nematic ordering, in good agreement with statistical physics models of the isotropic/nematic transition. Well-aligned samples of F-actin gels could be produced and their small-angle x-ray scattering patterns are quite anisotropic. These patterns show no sign of filament positional short-range order and could be modeled by averaging the form factor with the Maier-Saupe nematic distribution function. The derived nematic order parameter S of the gels ranged from S = 0.7 at 300 microM to S = 0.4 at 25 microM. Both birefringence and small-angle x-ray scattering data indicate that, even in absence of cross-linking proteins, spontaneous cooperative alignment of actin filaments may arise in motile regions of living cells where F-actin concentrations can reach values of a few 100 microM.     

Viscoelasticity of F-actin and F-actin/gelsolin complexes

Actin is the major protein of eukaryote peripheral cytoplasm where its mechanical effects could determine cell shape and motility. The mechanical properties of purified F-actin, whether it is a viscoelastic fluid or an elastic solid, have been a subject of controversy. Mainstream polymer theory predicts that filaments as long as those found in purified F-actin are so interpenetrated as to appear immobile in measurements over a reasonable time with available instrumentation and that the fluidity of F-actin could only be manifest if the filaments were shortened. We show that the static and dynamic elastic moduli below a critical degree of shear strain are much higher than previously reported, consistent with extreme interpenetration, but that higher strain or treatment with very low concentrations of the F-actin severing protein gelsolin greatly diminish the moduli and cause F-actin to exhibit rheologic behavior expected for independent semidilute rods, and defined by the dimensions of the filaments, including shear rate independent viscosity below a critical shear rate. The findings show that shortening of actin filaments sufficiently to permit reasonable measurements brings out their viscoelastic fluid properties. Since gelsolin shortens F-actin, it is likely that the effect of high strain is also to fragment a population of long actin filaments. We confirmed recent findings that the viscosity of F-actin is inversely proportional to the shear rate, consistent with an indeterminate fluid, but found that gelsolin abolishes this unusual shear rate dependence, indicating that it results from filament disruption during the viscosity measurements.(ABSTRACT TRUNCATED AT 250 WORDS)