Mechanical properties of tropomyosin and implications for muscle regulation

Tropomyosin is a protein that controls the interactions of actin and myosin as a part of the regulation of muscle contraction. The 420 Å long α-helical coiled-coil molecules form long filaments, both in muscle and in crystals. The x-ray diffraction data from tropomyosin crystals have indicated large scale motions of the filaments that can be related to the inherent mechanical properties of the molecule, and by extension, to the role of tropomyosin in the cooperative activation of the thin filaments of muscle. Diffuse scattering analysis has provided information about the amplitudes of the motions that has been used to calculate the intrinsic flexibility of the molecule. It can then be shown that each tropomyosin molecule by itself can only mediate interactions of the nearest-neighboring tropomyosin molecules along the filament. The repeating nature of the thin filament, however, allows the entire filament to activate cooperatively. © 1996 John Wiley & Sons, Inc.     

The active cross-bridge motions of isolated thick filaments from myosin-regulated muscles detected by quasi-elastic light scattering.

Intensity fluctuation spectroscopy has been used successfully as a probe that can detect an increase in high-frequency internal motions of isolated thick filaments of Limulus muscle upon the addition of calcium ions. We have attributed such motions to cross-bridge motion instead of to an increase in the flexibility of the filament backbone. Here we show that after cleavage of the S-1 and then the S-2 moieties with papain, cross-linking the myosin heads to the filament backbone, or heat denaturation (42 degrees C, 10 min), the increase in the high frequency internal motions in the thick filaments no longer occurs. Congo Red, which has been shown to induce shortening of isolated myofibrils, also increases the high-frequency motions of the isolated filaments. Furthermore, the increase is suppressed by treating the filaments with a myosin ATPase inhibitor such as vanadate ions (10 mM) or by replacing ATP with either an equimolar CrADP or the nonhydrolyzable ATP analogue beta, gamma-imido-adenine-5'-triphosphate (AMP-PNP). Calcium ions have a similar effect on isolated thick filaments from scallop muscle, where the myosin is known to be regulatory. Calcium ions have no such effect on thick filaments isolated from frog muscle, which is believed not to be regulated by calcium binding to myosin. These results confirm our earlier supposition that the additional high frequency internal motions of the thick filaments isolated from striated muscle of Limulus are related to the energy dependent, active cross-bridge motions.     

Unsteady wall shear stress in a distensible tube

An asymptotic expression of the wall shear stress (WSS) in an elastic tube is deduced for small values of the Womersley parameter. In the case of a rigid tube this asymptotic expression is shown to compare better with the exact solution than Poiseuille's or Lambossy's approximations. Its integration in a one-dimensional model of the internal carotid artery blood flow predicts more marked systolic and less marked diastolic WSS than those predicted by the commonly used Poiseuille's approximation.     

Stabilizing the Central Part of Tropomyosin Increases the Bending Stiffness of the Thin Filament

A two-beam optical trap was used to measure the bending stiffness of F-actin and reconstructed thin filaments. A dumbbell was formed by a filament segment attached to two beads that were held in the two optical traps. One trap was static and held a bead used as a force transducer, whereas an acoustooptical deflector moved the beam holding the second bead, causing stretch of the dumbbell. The distance between the beads was measured using image analysis of micrographs. An exact solution to the problem of bending of an elastic filament attached to two beads and subjected to a stretch was used for data analysis. Substitution of noncanonical residues in the central part of tropomyosin with canonical ones, G126R and D137L, and especially their combination, caused an increase in the bending stiffness of the thin filaments. The data confirm that the effect of these mutations on the regulation of actin-myosin interactions may be caused by an increase in tropomyosin stiffness.     

Complexes of RecA with LexA and RecX differentiate between active and inactive RecA nucleoprotein filaments

The bacterial RecA protein has been the dominant model system for understanding homologous genetic recombination. Although a crystal structure of RecA was solved ten years ago, we still do not have a detailed understanding of how the helical filament formed by RecA on DNA catalyzes the recognition of homology and the exchange of strands between two DNA molecules. Recent structural and spectroscopic studies have suggested that subunits in the helical filament formed in the RecA crystal are rotated when compared to the active RecA-ATP-DNA filament. We examine RecA-DNA-ATP filaments complexed with LexA and RecX to shed more light on the active RecA filament. The LexA repressor and RecX, an inhibitor of RecA, both bind within the deep helical groove of the RecA filament. Residues on RecA that interact with LexA cannot be explained by the crystal filament, but can be properly positioned in an existing model for the active filament. We show that the strand exchange activity of RecA, which can be inhibited when RecX is present at very low stoichiometry, is due to RecX forming a block across the deep helical groove of the RecA filament, where strand exchange occurs. It has previously been shown that changes in the nucleotide bound to RecA are associated with large motions of RecA's C-terminal domain. Since RecX binds from the C-terminal domain of one subunit to the nucleotide-binding core of another subunit, a stabilization of RecA's C-terminal domain by RecX can likely explain the inhibition of RecA's ATPase activity by RecX.     

Orientation changes of the myosin light chain domain during filament sliding in active and rigor muscle

Structural changes in myosin power many types of cell motility including muscle contraction. Tilting of the myosin light chain domain (LCD) seems to be the final step in transducing the energy of ATP hydrolysis, amplifying small structural changes near the ATP binding site into nanometer-scale motions of the filaments. Here we used polarized fluorescence measurements from bifunctional rhodamine probes attached at known orientations in the LCD to describe the distribution of orientations of the LCD in active contraction and rigor. We applied rapid length steps to perturb the orientations of the population of myosin heads that are attached to actin, and thereby characterized the motions of these force-bearing myosin heads. During active contraction, this population is a small fraction of the total. When the filaments slide in the shortening direction in active contraction, the long axis of LCD tilts towards its nucleotide-free orientation with no significant twisting around this axis. In contrast, filament sliding in rigor produces coordinated tilting and twisting motions.     

Molecular dynamics simulations of evolved collective motions of atoms in the myosin motor domain upon perturbation of the ATPase pocket

A crucial point for mechanical force generation in actomyosin systems is how the energy released by ATP hydrolysis in the myosin motor domain gives rise to the movement of the myosin head along the actin filament. We assumed the signal of the ATP hydrolysis to be transmitted as modulated atomic vibrations from the nucleotide-binding site throughout the myosin head, and carried out 1-ns all-atom molecular dynamics simulations for that signal transmission. We distributed the released energy to atoms located around the ATPase pocket as kinetic energies and examined how the effect of disturbance extended throughout the motor domain. The result showed that the disturbance signal extended over the motor domain in 150 ps and induced slowly varying collective motions of atoms at the actin-binding site and the junction with the neck, both of which are relevant to the movement of the myosin head along the actin filament. We also performed a principal component analysis of thermal atomic motions for the motor domain, and the first principal component was consistent with the response to the disturbance given to the ATPase pocket.     

Origin of Twist-Bend Coupling in Actin Filaments

Actin filaments are semiflexible polymers that display large-scale conformational twisting and bending motions. Modulation of filament bending and twisting dynamics has been linked to regulatory actin-binding protein function, filament assembly and fragmentation, and overall cell motility. The relationship between actin filament bending and twisting dynamics has not been evaluated. The numerical and analytical experiments presented here reveal that actin filaments have a strong intrinsic twist-bend coupling that obligates the reciprocal interconversion of bending energy and twisting stress. We developed a mesoscopic model of actin filaments that captures key documented features, including the subunit dimensions, interaction energies, helicity, and geometrical constraints coming from the double-stranded structure. The filament bending and torsional rigidities predicted by the model are comparable to experimental values, demonstrating the capacity of the model to assess the mechanical properties of actin filaments, including the coupling between twisting and bending motions. The predicted actin filament twist-bend coupling is strong, with a persistence length of 0.15-0.4 μm depending on the actin-bound nucleotide. Twist-bend coupling is an emergent property that introduces local asymmetry to actin filaments and contributes to their overall elasticity. Up to 60% of the filament subunit elastic free energy originates from twist-bend coupling, with the largest contributions resulting under relatively small deformations. A comparison of filaments with different architectures indicates that twist-bend coupling in actin filaments originates from their double protofilament and helical structure.     

Average electrostatic potential between the filaments in striated muscle and its relation to a simple Donnan potential.

An approximate analytical solution to the Poisson-Boltzmann equation for a cylindrical particle was used to calculate the relationship between the charge on the filaments and the average electrostatic potential. Both thick and then filaments were considered in the muscle lattice with a filament charge ratio of 4 to 1. Comparing this with a similar relationship obtained using simple Donnan theory showed a discrepancy at high charge where the Poisson-Boltzmann equation leads to saturation of the average potential. However, using two separate experiments from the literature, we have shown that at pH 7.0 muscle must not be close to saturation and thus is in a region of the curve where the two approaches agree.     

Differential dynamic behavior of actin filaments containing tightly-bound Ca2+ or Mg2+ in the presence of myosin heads actively hydrolyzing ATP.

We have investigated how Ca2+ or Mg2+ bound at the high-affinity cation binding site in F-actin modulates the dynamic response of these filaments to ATP hydrolysis by attached myosin head fragments (S1). Rotational motions of the filaments were monitored using steady-state phosphorescence emission anisotropy of the triplet probe erythrosin-5-iodoacetamide covalently attached to cysteine 374 of actin. The anisotropy of filaments containing only Ca2+ increased from 0.080 to 0.137 upon binding S1 in a rigor complex and decreased to 0.065 in the presence of ATP, indicating that S1 induced additional rotational motions in the filament during ATP hydrolysis. The comparable anisotropy values for Mg(2+)-containing filaments were 0.067, 0.137, and 0.065, indicating that S1 hydrolysis did not induce measurable rotational motions in these filaments. Phalloidin, a fungal toxin which stabilizes F-actin and increases its rigidity, increased the anisotropy of F-actin containing either Ca2+ or Mg2+ but not the anisotropy of the 1:1 S1-actin complexes of these filaments. Mg(2+)-containing filaments with phalloidin bound also displayed increased rotational motions during S1 ATP hydrolysis. A strong positive correlation between the phosphorescence anisotropy of F-actin under specific conditions and the extent of the rotational motions induced by S1 during ATP hydrolysis suggested that the long axis torsional rigidity of F-actin plays a crucial role in modulating the dynamic response of the filaments to ATP hydrolysis by S1. Cooperative responses of F-actin to dynamic perturbations induced by S1 during ATP hydrolysis may thus be physically mediated by the torsional rigidity of the filament.     

Compliant realignment of binding sites in muscle: transient behavior and mechanical tuning.

The presence of compliance in the lattice of filaments in muscle raises a number of concerns about how one accounts for force generation in the context of the cross-bridge cycle--binding site motions and coupling between cross-bridges confound more traditional analyses. To explore these issues, we developed a spatially explicit, mechanochemical model of skeletal muscle contraction. With a simple three-state model of the cross-bridge cycle, we used a Monte Carlo simulation to compute the instantaneous balance of forces throughout the filament lattice, accounting for both thin and thick filament distortions in response to cross-bridge forces. This approach is compared to more traditional mass action kinetic models (in the form of coupled partial differential equations) that assume filament inextensibility. We also monitored instantaneous force generation, ATP utilization, and the dynamics of the cross-bridge cycle in simulations of step changes in length and variations in shortening velocity. Three critical results emerge from our analyses: 1) there is a significant realignment of actin-binding sites in response to cross-bridge forces, 2) this realignment recruits additional cross-bridge binding, and 3) we predict mechanical behaviors that are consistent with experimental results for velocity and length transients. Binding site realignment depends on the relative compliance of the filament lattice and cross-bridges, and within the measured range of these parameters, gives rise to a sharply tuned peak for force generation. Such mechanical tuning at the molecular level is the result of mechanical coupling between individual cross-bridges, mediated by thick filament deformations, and the resultant realignment of binding sites on the thin filament.     

Mathematical analysis of a model for the renal concentrating mechanism

A system of ordinary differential equations, designed to model the counterflow system in the renal medulla, is studied. An existence theorem for solutions of the model equations is obtained. An exact solution of the system is obtained in the limiting case of infinite water permeability. If there is diffusion in the core, evaluation of the exact solution leads to multiple stable solutions of the model equations. One solution has a large concentration ratio, which tends to a finite asymptotic limit as the pump strength tends to infinity.     

Elastic behavior of RecA-DNA helical filaments

Escherichia coli RecA protein forms a right-handed helical filament with DNA molecules and has an ATP-dependent activity that exchanges homologous strands between single-stranded DNA (ssDNA) and duplex DNA. We show that the RecA-ssDNA filamentous complex is an elastic helical molecule whose length is controlled by the binding and release of nucleotide cofactors. RecA-ssDNA filaments were fluorescently labelled and attached to a glass surface inside a flow chamber. When the chamber solution was replaced by a buffer solution without nucleotide cofactors, the RecA-ssDNA filament rapidly contracted approximately 0.68-fold with partial filament dissociation. The contracted filament elongated up to 1.25-fold when a buffer solution containing ATPgammaS was injected, and elongated up to 1.17-fold when a buffer solution containing ATP or dATP was injected. This contraction-elongation behavior was able to be repeated by the successive injection of dATP and non-nucleotide buffers. We propose that this elastic motion couples to the elastic motion and/or the twisting rotation of DNA strands within the filament by adjusting their helical phases.     

Fluorescence depolarization studies of filamentous actin analyzed with a genetic algorithm

A new method, in which a genetic algorithm was combined with Brownian dynamics and Monte Carlo simulations, was developed to analyze fluorescence depolarization data collected by the time-correlated single photon-counting technique. It was applied to studies of BODIPY-labeled filamentous actin (F-actin). The technique registered the local order and reorienting motions of the fluorophores, which were covalently coupled to cysteine 374 (C374) in actin and interacted by electronic energy migration within the actin polymers. Analyses of F-actin samples composed of different fractions of labeled actin molecules revealed the known helical organization of F-actin, demonstrating the usefulness of this technique for structure determination of complex protein polymers. The distance from the filament axis to the fluorophore was found to be considerably less than expected from the proposed position of C374 at a high filament radius. In addition, polymerization experiments with BODIPY-actin suggest a 25-fold more efficient signal for filament formation than pyrene-actin.     

Genetic variability due to geographical inhomogeneity

The frequency of one of two alleles is studied as a function of position and time in a one, two, or three dimensional region. A nonlinear diffusion equation is employed. Each allele is assumed to have a selective advantage in some part of the region. An asymptotic solution is constructed for the case when the selection coefficient is large compared to the diffusion coefficient, i.e. when selection acts more rapidly than diffusion. Then as time increases, the solution tends to a cline, i.e. an equilibrium distribution in which both alleles are present everywhere, each predominating where it has the advantage. In a narrow region around the boundary where the selective advantage switches from one allele to the other, both alleles are present with comparable frequencies. Along a line normal to this boundary, the frequency varies as in a one dimensional habitat with a simple variation in selective advantage. The asymptotic solution is compared with the numerical solution for a special two dimensional case, and the agreement is found to be good.Research supported by the National Science Foundation.     

Quantitative analysis of extension-torsion coupling of actin filaments

Actin filaments have a double-helix structure consisting of globular actin molecules. In many mechanical cellular activities, such as cell movement, division, and shape control, modulation of the extensional and torsional dynamics of the filament has been linked to regulatory actin-binding protein functions. Therefore, it is important to quantitatively evaluate extension-torsion coupling of filament to better understand the actin filament dynamics. In the present study, the extension-torsion coupling was investigated using molecular dynamics simulations. We constructed a model for the actin filament consisting of 14 actin subunits in an ionic solvent as a minimal functional unit, and analyzed longitudinal and twisting Brownian motions of the filament. We then derived the expected value of energy associated with extension and torsion at equilibrium, and evaluated the extension-torsion stiffness of the filament from the thermal fluctuations obtained from the MD simulations. The results demonstrated that as the analyzed sampling-window duration was increased, the extension-torsion coupling stiffness evaluated on a nanosecond scale tended to converge to a value of 7.6×10(-11) N. The results obtained from this study will contribute to the understanding of biomechanical events, under mechanical tension and torque, involving extension-torsion coupling of filaments.     

Adsorption of protein GlnB of Herbaspirillum seropedicae on Si(111) investigated by AFM and XPS

The protein GlnB-Hs (GlnB of Herbaspirillum seropedicae) in diazotroph micro-organisms signalizes levels of nitrogen, carbon, and energy for a series of proteins involved in the regulation of expression and control of the activity of nitrogenase complex that converts atmospheric nitrogen in ammonia, resulting in biological nitrogen fixation. Its structure has already been determined by X-ray diffraction, revealing a trimer of (36 kDa) with lateral cavities having hydrophilic boundaries. The interactions of GlnB-Hs with the well-known Si(111) surface were investigated for different incubation times, protein concentrations in initial solution, deposition conditions, and substrate initial state. The protein solution was deposited on Si(111) and dried under controlled conditions. An atomic force microscope operating in dynamic mode shows images of circular, linear, and more complex donut-shaped protein arrangement, and also filament types of organization, which vary from a few nanometers to micrometers. Apparently, the filament formation was favored because of protein surface polarity when in contact with the silicon surface, following some specific orientation. The spin-coating technique was successfully used to obtain more uniform surface covering.     

Evolution of the internal dynamics of two globular proteins from dry powder to solution.

Myoglobin and lysozyme picosecond internal dynamics in solution is compared to that in hydrated powders by quasielastic incoherent neutron scattering. This technique is sensitive to the motions of the nonexchangeable hydrogen atoms in a sample. Because these are homogeneously distributed throughout the protein structure, the average dynamics of the protein is described. We first propose an original data treatment to deal with the protein global motions in the case of solution samples. The validity of this treatment is checked by comparison with classical measurements of the diffusion constants. The evolution with the scattering vector of the width and relative contribution of the quasielastic component was then used to derive information on the amount of local diffusive motions and their characteristic average relaxation time. From dry powder to coverage by one water layer, the surface side chains progressively acquire the possibility to diffuse locally. On subsequent hydration, the main effect of water is to improve the rate of these diffusive motions. Motions with higher average amplitude occur in solution, about three times more than for a hydrated powder at complete coverage, with a shorter average relaxation time, approximately 4.5 ps compared to 9.4 ps for one water monolayer.     

In-cell protein dynamics

The native intracellular environment of proteins is crowded with metabolites and macromolecules. However, most biophysical information concerning proteins is acquired in dilute solution. To determine whether there are differences in dynamics, nuclear magnetic resonance spectroscopy can be used to measure 15N relaxation in uniformly 15N-enriched apocytochrome b5 inside living Escherichia coli and in dilute solution. Such data can then be used to compare the fast backbone dynamics of the partially folded protein in cells to its dynamics in dilute solution by using Lipari-Szabo analysis. It appears that the intracellular environment does not alter the protein's structure, or significantly change its fast dynamics. Specifically, the cytosol does not change the amplitude of fast backbone motions, but does increase the average timescale of these motions, most likely due to the increase in viscosity of the cytosol.