Dark energy from modified F(R)-scalar-Gauss-Bonnet gravity

The modified F(R)-scalar-Gauss-Bonnet gravity is proposed as dark energy model. The reconstruction program for such theory is developed. It is explicitly demonstrated that the known classical universe expansion history (deceleration epoch, transition to acceleration and effective quintessence, phantom or cosmological constant era) may naturally occur in such unified theory for some (reconstructed) classes of scalar potentials. Gauss-Bonnet assisted dark energy is also proposed. The possibility of cosmic acceleration is studied there.Comment: LaTeX, 8 pages, no figure, refs. added, version to appear in Physics Letters

Elementary steps of the cross-bridge cycle in bovine myocardium with and without regulatory proteins.

The role of regulatory proteins in the elementary steps of the cross-bridge cycle in bovine myocardium was investigated. The thin filament was selectively removed by gelsolin and the actin filament was reconstituted without tropomyosin or troponin. Further reconstitution was achieved by adding tropomyosin and troponin. The effects of MgATP and phosphate (Pi) on the rate constants of exponential processes were studied in control, actin filament-reconstituted, and thin filament-reconstituted myocardium at pCa < or = 4.66, pH 7.00, 25 degrees C. In control myocardium, the MgATP association constant was 9.1 +/- 1.3 mM(-1), and the Pi association constant 0.14 +/- 0.04 mM(-1). The equilibrium constant of the cross-bridge detachment step was 2.6 +/- 0.4, and the equilibrium constant of the force generation step was 0.59 +/- 0.04. In actin filament-reconstituted myocardium without regulatory proteins, the MgATP association constant was approximately the same, and the Pi association constant increased to 2.8x. The equilibrium constant of cross-bridge detachment decreased to 0.2x, but the equilibrium constant of the force generation step increased to 4x. These kinetic constants regained control values after reconstitution of the thin filament. These results indicate that tension/cross-bridge in the presence of regulatory proteins is approximately 1.5-1.7x of that in the absence of regulatory proteins. These results further indicate that regulatory proteins promote detachment of cross-bridges

Correlation between corrected sliding force per unit length and angle of the force vector.

<p>(A) Distribution of sliding force (<i>F</i>) per unit length of filament. Reconstituted thin filament (red circles); +Ca²⁺, 4.0 ± 1.7 pN/μm (<i>n</i> = 71);–Ca²⁺, 0.17 ± 0.08 pN/μm (<i>n</i> = 22). Actin filament (white circles); 2.6 ± 1.0 pN/μm (<i>n</i> = 66). (B) Distribution of <i>F</i> per unit length of filament with a compensation of the angle of force vector (cos<i>θ</i>). Horizontal bars indicate average values. Reconstituted thin filament, 4.3 ± 1.8 pN/μm. Actin filament, 2.8 ± 1.0 pN/μm. (C) Correlation between (<i>F</i>/cos<i>θ</i>) per unit length of filament and the angle between the thin filament and the glass surface (<i>θ</i>). Regression lines (red for reconstituted thin filament, y = – 0.092x + 6.4, R = 0.28; black for actin filament, y = – 0.078x + 4.4, R = 0.45) are for visual guide. (D) Distribution of <i>F</i> per unit length of filament with a compensation of the angle of force vector (cos<i>θ</i>) at 0°< <i>θ</i> ≤ 25° or <i>θ</i> > 25°. Reconstituted thin filament; 4.6 ± 2.0 pN/μm at 0°< <i>θ</i> ≤ 25°(<i>n</i> = 48), 3.7 ± 1.1 pN/μm at <i>θ</i> > 25° (<i>n</i> = 23). Actin filament; 3.0 ± 1.0 pN/μm at 0° < <i>θ</i> ≤ 25°(<i>n</i> = 50), 2.2 ± 0.91 pN/μm at <i>θ</i> > 25° (<i>n</i> = 16). Red and gray symbols indicate data obtained from reconstituted thin filaments in the presence (<i>n</i> = 71) and in the absence (<i>n</i> = 22) of Ca²⁺, respectively. White symbols indicate data obtained from actin filaments (<i>n</i> = 66). Data were statistically compared by using two-sided student's t-test (*0.01≤ p < 0.05, **0.001≤ p < 0.01, ***p < 0.001).</p

Schematic illustration of the <i>in vitro</i> motility assay system showing the parameters considered.

<p>A reconstituted thin filament (actin is illustrated by open circles, Tpm thin curved lines, and Tn black spheres) attached to a polystyrene bead (1.0 µm in diameter) via gelsolin (red sphere) was manipulated by optical tweezers. In the presence of ATP, the thin filament was interacted with HMM molecules that were attached to the surface of a collodion-coated glass coverslip. The region indicated by <i>a</i>, the part of the thin filament which interacted with HMM molecules that was visualized with the total internal reflection fluorescence (TIRF) microscopy system. The region indicated by <i>b</i>, the distance between the center of the bead and the end of the thin filament interacting with HMM (<i>P</i>), was determined from the epifluorescence microscopy. <i>θ</i>, the angle between the thin filament and the glass surface at <i>P</i>, determined geometrically from the distance of the bead from the glass surface (<i>h</i>) and <i>b</i> as <i>θ</i> = <i>arctan</i> (<i>h</i>/<i>b</i>). The actual size of HMM is small enough to be ignored compared to <i>h</i> (see text). Sliding force in horizontal direction (<i>F</i>) was obtained from the trap stiffness (range: 0.042 pN/nm to 0.15 pN/nm) and the displacement of the bead in the <i>X</i>-<i>Y</i> plane. The corrected force vector was calculated as <i>F</i>/cos<i>θ</i>.</p

Analysis of sliding force and filament length.

<p>(A) A representative time course of the bead displacement during measurement. At first, a bead-tailed reconstituted thin filament (<i>a</i> = 3.3 μm) was trapped in the activating solution, where the displacement of the bead is defined as 0 (the bead is at the trap center) because there is no interaction between the thin filament and HMM (during the period shown by a horizontal line). Then, the coverslip was elevated to the focal plane of the fluorescence microscopy, which is below the focal plane of the bright-field microscopy and the focus of the optical tweezers. When the thin filament started to interact with HMM on the coverslip, the bead was displaced away from the trap center (arrow). To calculate the sliding force in the <i>X-Y</i> plane, the displacement was multiplied by the trap stiffness. (B) Representative fluorescence images of the same bead-tailed actin filament trapped (upper photo) and released (lower photo), and the result of their intensity analysis. While the bead is trapped above the glass surface, only a part of the actin filament interacting with HMM on the coverslip was visible under the TIRF microscopy. Therefore, the actin filament appears shorter when the bead is trapped (upper photo) than when it is released (lower photo). Fluorescence images shown are the region of interest (ROI) within which the fluorescence intensities were averaged along the columns in <i>Y</i>-axis to produce the 1D intensity profile along the <i>X</i>-axis (red and blue curves correspond to the upper and lower fluorescence micrographs, respectively). Background signal was determined from the other ROI (set next to the actin filament) which was subtracted from the signal of the actin filament. Frequently, the background was none. The parameter '<i>a</i>' as defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0192558#pone.0192558.g001" target="_blank">Fig 1</a> was determined as the distance between the points where the fluorescence intensity was half of the maximum (bottom).</p

Schematic diagram of the optical setup.

<p>The optical setup for optical tweezers, bright-field microscopy and fluorescence microscopy were built on an inverted microscope. The position of the objective lens was fixed, whereas <i>X</i>, <i>Y</i> and <i>Z</i> positions of the sample stage were adjustable (indicated by arrows). The focal plane of 1064 nm laser for optical tweezers can be adjusted by shifting the position of a lens ('Lens' with a double-headed arrow placed in the light path of 1064 nm laser) along the light path. A xenon lamp was used as the light source at 710–900 nm to obtain bright-field images of beads. The bright-field images split by a beam sampler (BS) were projected onto two individual CCD cameras. One CCD camera worked at 200 fps, and its images were captured by a PC and analyzed in real time to track the position of the bead. The other CCD camera (30 fps) was connected to a multi viewer. The focal planes of these two CCD cameras were adjusted individually by the position of the camera along the light path (indicated by double-headed arrows). For fluorescence imaging, 532 nm laser and mercury lamp were used as light sources for total internal reflection microscopy and epifluorescence microscopy, respectively. These two fluorescence imaging methods could be alternated by shifting the mirror position (M1, shown with a double-headed arrow). Fluorescence images were captured by an EB-CCD camera (30 fps) serially connected with an image intensifier (I.I.) and transmitted to the multi viewer. Bright-field and fluorescence images combined by the multi viewer were shown side-by-side and captured by a PC for recording and analysis purposes. All images were shown in a PC display during the experiment. F, filter. M, mirror. DM, dichroic mirror. BS, beam sampler. ND, neutral density filter. T, transmitted wavelength. R, reflected wavelength.</p

The procedure to determine the height of the trap center from the focal plane of the fluorescence microscopy.

<p>(A) Schematics showing the procedure to measure the trap height. Objective lens is fixed in space. (i) The focal plane of the bright-field microscopy (dotted line, adjustable by the position of the camera) is preset at about 1 μm above that of the fluorescence microscopy (dashed line). A floating bead is trapped. (ii) While the other bead is attached to the coverslip, the sample stage is elevated in steps (200 nm each). (iii) When the coverslip touches the trapped bead, the bead is adsorbed to the coverslip. (iv) Both beads are elevated together with the sample stage. (B and C) Data showing the changes in fluorescence intensity during the trap height measurement obtained with beads with the diameter of 1.0 μm (B) or 2.0 μm (C). Dots represent the change in the fluorescence intensity of the beads adsorbed to the coverslip when the sample stage was lifted upwards. The symbols (+, x, ◊) indicate the fluorescence intensity of the trapped beads. Three individual trials are represented by three different colors. The fluorescence intensities were determined in square regions. The size for the beads with the diameter of 1.0 μm was 2.2 μm X 2.2 μm for the data indicated in black or 1.8 μm X 1.8 μm for the data indicated in blue and red. For the beads with the diameter of 2.0 μm, the size was 3.3 μm X 3.4 μm. The change of the fluorescence intensities along the <i>Z</i> axis can be fit to the Gaussian distribution (shown in thin curves with the same color as corresponding dots). The peak position of the Gaussian distribution is the focal plane of the fluorescence microscopy (<i>Z</i> = 0, vertical dotted line). After the intensity peaks at about <i>Z</i> = 1 μm (arrows with the same color as corresponding symbols), it begins to decrease in the same way as those of the bead adsorbed to the coverslip. This is because the trapped bead is adsorbed to the coverslip and it moves together with the pre-adsorbed bead. From the peak positions (1.1 ± 0.15 μm and 1.3 ± 0.18 μm for beads with the diameter of 1.0 μm and 2.0 μm, respectively; mean ± SD, vertical dashed line), we estimated the distance of the trapped 1.0 μm beads from the focal plane as <i>Z</i> = 0.88 μm after the correction for aberration (see main text for details).</p

Estimation of actomyosin active force maintained by tropomyosin and troponin complex under vertical forces in the <i>in vitro</i> motility assay system

<div><p>The interaction between actin filaments and myosin molecular motors is a power source of a variety of cellular functions including cell division, cell motility, and muscular contraction. <i>In vitro</i> motility assay examines actin filaments interacting with myosin molecules that are adhered to a substrate (e.g., glass surface). This assay has been the standard method of studying the molecular mechanisms of contraction under an optical microscope. While the force generation has been measured through an optically trapped bead to which an actin filament is attached, a force vector vertical to the glass surface has been largely ignored with the <i>in vitro</i> motility assay. The vertical vector is created by the gap (distance) between the trapped bead and the glass surface. In this report, we propose a method to estimate the angle between the actin filament and the glass surface by optically determining the gap size. This determination requires a motorized stage in a standard epi-fluorescence microscope equipped with optical tweezers. This facile method is applied to force measurements using both pure actin filaments, and thin filaments reconstituted from actin, tropomyosin and troponin. We find that the angle-corrected force per unit filament length in the active condition (pCa = 5.0) decreases as the angle between the filament and the glass surface increases; i.e. as the force in the vertical direction increases. At the same time, we demonstrate that the force on reconstituted thin filaments is approximately 1.5 times larger than that on pure actin filaments. The range of angles we tested was between 11° and 36° with the estimated measurement error less than 6°. These results suggest the ability of cytoplasmic tropomyosin isoforms maintaining actomyosin active force to stabilize cytoskeletal architecture.</p></div