Two-dimensional reconstruction of birefringence map of the skeletal muscle sarcomere in relaxed and rigor states studied by interference microscopy]

A new method of automatized quantitative interferometry of skeletal muscle fibers was developed for the investigation of birefringence. A device based on the Linnic microscope was constructed to obtain phase images, which are two-dimensional pictures of birefringence. For the first time, two-and-three-dimensional maps of both total birefringence and birefringence for individual sarcomeres in the central part of muscle fiber were visualized using large databases. It was shown that total birefringence of fibers at rest length in the rigor state was lower as compared with the relaxed. Birefringence values from individual sarcomere interferograms revealed also that normalized A-disk birefringence was lower in the rigor state. The results obtained could be explained by a decrease of thick filaments anisotropy, due to the moving away of myosin heads from the rod during transition into the rigor state.     

Form birefringence of muscle.

We investigate the sensitivity of measurements of muscle birefringence to cross-bridge dynamics in the resting, active, and rigor states. The theory of form birefringence is reviewed, and an optical model is constructed for the form birefringence of muscle. Values for the parameters in the model are selected or deduced from the literature. As an illustration of the use of the model, plausible distributions for the orientations of cross-bridges in the resting, active, and rigor states are constructed using a model for cross-bridge dynamics suggested by Huxley and Kress (1985). The general magnitude of the predictions of our model is comparable with that of published measurements of muscle birefringence. However, the precise values of the predicted birefringence for the resting, active, and rigor states are sensitive to the assumed orientations of cross-bridges. We also investigate the dependence of muscle birefringence on sarcomere length and on disorder in the orientation of the myofilament array. We conclude that measurements of muscle birefringence can play a useful role in distinguishing between proposed models of cross-bridge dynamics.     

Optical depolarization changes on the diffraction pattern in the transition of skinned muscle fibers from relaxed to rigor state

Light diffraction spectra from single or small bundles of skinned striated muscle fibers show large changes in polarization properties when muscles are placed into rigor. The technique of combining optical diffraction and ellipsometry measurements has previously been shown by Yeh and Pinsky to be a sensitive probe of periodic anisotropic regions of the fiber. In the present work, using this method, the observed spectrum shows marked decrease in the measured phase angle, delta, as the fiber approaches the rigor state. The degree of phase angle change is a function of sarcomere length: Maximum overlap of approximately 2.3 microns gives the most change in delta a delta delta R-R approximately 35 degrees decrease for a bundle of three fibers. At a sarcomere length of 2.9 microns this delta delta R-R value is only 10 degrees. At a nonoverlapping length of approximately 3.8 microns, delta does not vary at all upon the removal of ATP. The rigor state was confirmed by stiffness measurements made after small-amplitude (0.75%), quick length changes. Upon re-relaxation, the stiffness of the skinned fiber decreased to the value of the resting state (4 mM ATP) and the phase angle delta returned to its original value. A model based on either anisotropic subunit-2 (S-2) movements or other cross-bridge-related structural anisotropy (form birefringence) changes during the relaxed-rigor transition is suggested.     

位相分辨偏振灵敏光学相干层析术:组织双折射特性的成像与定量分析

我们研制了一种基于光纤的位相分辨偏振灵敏光学相干层析成像系统。该系统中的偏振状态控制设量在参考臂而非光源臂上,因而使得光抵达样品的传输效率大大提高。鉴于光源的部分偏振性,入射于样品上的光含有任意偏振状态的分量,通过对参考光偏振状态的调制,就可相干地提取对应于入射光四种正交偏振状态并经样品后向散射的光信号。基于斯托克斯矢量夹角在无损光纤系统传输的变换不变性,我们能利用测量臂中光信号的斯托克斯参数来确定双折射样品深度分辨的位相延迟信息。利用所研制的偏振灵敏光学相干层析成像系统,不仅确认了韧带和软骨的双折射性质,而且定量分析了不同条件下韧带的双折射变化．研究结果表明：韧带松弛可使其双折射特性明显减弱,而韧带经拉伸后,其双折射特性的变化却不明显。     

High-definition mapping of neural activity using voltage-sensitive dyes

The distribution of patterns of activity in different brain structures has been related to the encoding and processing of sensory information. Consequently, it is important to be able to image the distribution of these patterns to understand basic brain functions. The spatial resolution of voltage-sensitive dye (VSD) methods has recently been enhanced considerably by the use of video imaging techniques. The main factor that now hampers the resolution of VSD patterns is the inherent limitation of the optical systems. Unfortunately, the intrinsic characteristics of VSD images impose important limitations that restrict the use of general deconvolution techniques. To overcomes this problem, in this study an image restoration procedure has been implemented that takes into consideration the limiting characteristics of VSD signals. This technique is based on applying a set of imaging processing steps. First, the signal-to-noise (S/N) ratio of the images was improved to avoid an increase in the noise levels during the deconvolution procedures. For this purpose, a new filter technique was implemented that yielded better results than other methods currently used in optical imaging. Second, focal plane images were deconvolved using a modification of the well-known nearest-neighbor deconvolution algorithm. But to reduce the light exposure of the preparation and simplify image acquisition procedures, adjacent image planes were modeled according to the in-focus image planes and the empirical point spread function (PSF) profiles. Third, resulting focal plane responses were processed to reduce the contribution of optical responses that originate in distant image planes. This method was found to be satisfactory under simulated and real experimental conditions. By comparing the restored and unprocessed images, it was clearly demonstrated that this method can effectively remove the out-of-focus artifacts and produce focal plane images of better quality. Evaluations of the tissue optical properties allowed assessment of the maximum practical optical section thickness using this deconvolution technique in the optical system tested. Determination of the three-dimensional PSF permitted the correct application of deconvolution algorithms and the removal of the contaminating light arising from adjacent as well as distant optical planes. The implementation of this deconvolution approach in salamander olfactory bulb allowed the detailed study of the laminar distribution of voltage-sensitive changes across the bulb layer. It is concluded that (1) this deconvolution procedure is well suited to deconvolved low-contrast images and offers important advantages over other alternatives; (2) this method can be properly used only when the tissue optical properties are first determined; (3) high levels of light scattering in the tissue reduce the optical section capabilities of this technique as well as other deconvolution procedures; and (4) use of the highest numerical aperture in the objectives is advisable because this improves not only the light-collecting efficiency to detect poor-contrast images, but also the spatial frequency differences between adjacent image planes. Under this condition it is possible to overcome some of the limitations imposed by the light scattering/birefringence of the tissue.     

Studies of the birefringence and birefringence dispersion of polypeptides and proteins

An apparatus has been constructed which permits the polarimetric observation of streaming solutions of macromolecules. The apparatus is a streaming birefringence device allowing the usual measurements of birefringence parallel to the cylinder axis but which in addition transmits light in the radial direction. Installation of the apparatus between the polarizer and analyzer of a Rudolph polarimeter makes possible the measurement of changes in optical rotation, dichroism and birefringence. The present work is concerned with the latter effect. The systems studied were α-helical polyglutamic acid, paramyosin, and collagen (ichthyocol). The combined measurements of radial and axial birefringence completely determines the refractive index ellipsoid of the streaming fluid. This result in turn permits the testing of the Peterlin-Stuart distribution function for streaming in a Couette device, apart from a proportionality constant. The comparison between theory and experiment is very satisfactory provided the system is reasonably homogeneous with regard to molecular length and is sufficiently dilute. On the other hand, it is concluded that the Peterlin-Stuart optical factor seriously overestimates the “form” birefringence in agreement with recent results and conclusions of Taylor and co-workers. The apparatus permits the study of the dispersion of the birefringence in the radial direction. The dispersion of collagen follows a one-term Sellmeier formula and is dominated by absorption bands in the neighborhood of 2000 A. On the other hand, the dispersion of the α-helical systems is complex and requires a multiterm Sellmeier formula. This contrast between the two kinds of polypeptidc helices is similar to results obtained with other optical techniques and is attributed to the splitting of absorption bands in the α-helix.     

Quantitative studies on the polarization optical properties of living cells. I. Microphotometric birefringence detection system

A method of polarization optical analysis is described in which phase retardation attributable to birefringence of a minute area in a microscopic object is determined. The optical system consists of a polarizing microscope with "rectified" strain-free lenses, a photoelectric detector to determine the intensity of the light passing through a minute window located at the image plane of the specimen, and a stage that moves the specimen at appropriate velocities for scanning. The error resulting from any flare of light emerging from outside of the area to be measured is minimized by limiting the illuminated area. The specimen can be observed during the measurement of light intensity by illuminating the whole microscope field at a wavelength different from that of the light used for the measurement. The retardation of the specimen is determined by comparing the specimen and background intensities as functions of the azimuth of a Brace-Koherl compensator. Alternatively, retardation is obtained directly from the light intensity at a fixed compensator angle, using the theory of polarization optics. The basal noise level for the present apparatus is approximately 0.03 nm when measuring birefringence of a 4-micron2 area in 0.1 s, using a X 40, NA 0.65 objective. The noise decreases in inverse proportion to the square root of the area times the duration of measurement.     

Theory of optical ellipsometric measurements from muscle diffraction studies.

A theory of optical ellipsometry describing the complete phase shift and ellipticity of light diffracted from a single muscle fiber is developed. We show that both the phase shift information, described commonly by the birefringence of the fiber, and the ellipticity information, described by the differential polarizability ratio, are necessary to provide a complete picture of the complex contributions to the total optical anisotropy spectra from a diffraction pattern derived from the striated muscle cell. Both form and intrinsic contributions play significant roles in either the birefringence measurement or the differential field ratio measurement. However, we show that their relative weights in these two measured quantities are different, and measuring both of these parameters is necessary to obtain a more complete assessment of the cross-bridge structure and dynamics. The theoretical results have been tested for three different situations: solvent index matching, passive stretch of a resting fiber, and cross-bridge changes under isometric conditions. Comparisons between experimental data and simple model calculations provide much information regarding cross-bridge orientation and structure.     

Optical birefringence of phosphatidylcholine liposomes in gel phases

A simple and rapid method for studying optical anisotropic properties of liposomes was proposed. Intensities of transmitted light through one spherical liposome of dipalmitoylphosphatidylcholine placed between two polarizers were measured at various wavelengths by a microscopic spectrophotometer. Large increases in the intensities were observed at the prephase-transition temperature, which were caused by an increase in the birefringence of the multilayer of the liposome. The birefringence values obtained from the intensity data were about 0.020 below the pretransition temperature and 0.028 above that temperature. These values are in good agreement with the results reported for the plane samples in which lipid bilayers are stacked. The obtained values of the birefringence were far lower than the values estimated from polarizabilities. This lower birefringence is attributed to disordering of the tilt direction in the multilayer. The degree of order of the liposome multilayers calculated from the birefringence increased by 38% at the pretransition. This simple method is applicable to the study of the multilayer structure of liposomes in water.     

Measuring collagen fiber orientation: a two-dimensional quantitative macroscopic technique.

This paper describes the design, evaluation, and application of a new system for quantifying two-dimensional collagen fiber orientation in soft tissue. Series of transmitted polarized light images were collected using a custom-designed macroscope. Combined analysis of pixel brightness, and hue from images collected with a compensator plate, permitted the assignment of each pixel into the appropriate orientation band. Experiments were performed to quantify the linearity and noise of the system. Validation was performed on a specimen composed of strain-birefringent plastic strips at various orientations. Preliminary collagen fiber orientation data is presented from a tendon specimen. This study demonstrates the utility of this approach for studying collagen fiber orientation across large areas.     

Spectral analysis of muscle fiber images as a means of assessing sarcomere heterogeneity.

A new image-analysis-based method is described for assessing sarcomere heterogeneity in skinned rabbit psoas muscle fiber segments. This method consists of off-line, two-dimensional Fourier spectral analysis of video-taped muscle images. Local sarcomere length is assessed by partitioning the muscle images into half and quarter images spanning the original image and analyzing the associated spectra. The spectra are analyzed in two different ways, yielding two measures of sarcomere length. The first measure is obtained by calculating and inverting the centroid frequency of the first-order peak associated with each two-dimensional Fourier spectrum. The second measure is obtained in a similar manner, the only difference being that the two-dimensional spectra are first collapsed into one-dimensional line spectra by summing the pixels perpendicular to the fiber axis. Comparison of the two measures provides a measure of striation skewness that cannot be obtained by other image analysis based methods that determine sarcomere length by analyzing selected line luminance profiles.     

Formation of liquid crystalline phase of actin filament solutions and its dependence on filament length as studied by optical birefringence.

We studied the formation and structure of liquid crystalline phase of F-actin solutions by polarized light photometry, assuming that a small domain of the liquid crystalline phase works as a linear retardation plate. Transmittance of polarized light due to the birefringence of liquid crystalline phase appeared above a threshold concentration of F-actin. The threshold increased with a decrease in filament length, which was regulated by calcium-activated gelsolin. The intensity increased linearly with increasing concentrations until it reached a stationary value. The deviation of optical axis direction of the putative retardation plate was estimated 7-15 degrees. These results indicate that:(a) the liquid crystalline phase is formed above a threshold concentration of F-actin; (b) the threshold is proportional to the inverse of filament length; (c) the ordered phase coexists with the isotropic one, increasing the volume fraction with increasing concentrations until all filaments take the liquid crystalline structure; (d) the filaments in liquid crystalline phase take a highly ordered array. These results can be attributed to the excluded volume effect of rod-like molecules on the formation of liquid crystalline structure.     

A birefringence study of changes in myosin orientation during relaxation of skinned muscle fibers induced by photolytic ATP release.

The birefringence of isolated skinned fibers from rabbit psoas muscle was measured continuously during relaxation from rigor produced by photolysis of caged ATP at sarcomere length 2.8-2.9 microns, ionic strength 0.1 M, 15 degrees C. Birefringence, the difference in refractive index between light components polarized parallel and perpendicular to the fiber axis, depends on the average degree of alignment of the myosin head domain with the fiber axis. After ATP release birefringence increased by 5.8 +/- 0.7% (mean +/- SE, n = 6) with two temporal components. A small fast component had an amplitude of 0.9 +/- 0.2% and rate constant of 63 s-1. By the completion of this component, the instantaneous stiffness had decreased to about half the rigor value, and the force response to a step stretch showed a rapid (approximately 1000 s-1) recovery phase. Subsequently a large slow birefringence component with rate constant 5.1 s-1 accompanied isometric force relaxation. Inorganic phosphate (10 mM) did not affect the fast birefringence component but accelerated the slow component and force relaxation. The fast birefringence component was probably caused by formation of myosin.ATP or myosin.ADP.Pi states that are weakly bound to actin. The average myosin head orientation at the end of this component is slightly more parallel to the fiber axis than in rigor.     

Polarization states of diffracted light. Changes accompanying fiber activation.

Measurement of the state of optical polarization of light diffracted from single, skinned and intact fibers of anterior tibialis muscle from Rana pipiens revealed a dependence upon rigor, activation, and sarcomere length (SL) change. Changes in total birefringence, delta nT, and differential field ratio value, rT, were determined. In a relaxed, skinned fiber the total birefringence value, delta nT, decreases as sarcomere length is increased from 2.1 microns to approximately 2.8-3.0 microns. From there it increases significantly to a value of approximately 1.8 x 10(-3) at a sarcomere length of 3.6 microns. The differential field ratio, rT, also shows a biphasic response to increasing sarcomere length, first exhibiting a rapid decrease over shorter SL and leveling out after the SL is beyond 3.0 microns. In comparison, relaxed intact fibers change substantially less upon sarcomere length change, showing little change in birefringence and a small bi-phasic change in rT. Skinned fibers were activated using a solution that has the same ionic strength as the relaxing solution and allows repeatable, and sustained activation. A decrease in both delta nT and rT was observed upon fiber activation. The decrease in delta nT and rT was slightly larger at shorter sarcomere lengths than at longer lengths. Relaxed fibers placed in rigor showed changes in delta nT and rT similar to those observed in activated fibers. These results are consistent with the hypothesis that, after activation, a significant portion of the thick filament cross-bridges rotate towards the actin filament resulting in redistribution of the interfilament mass content. They are also consistent with an average orientation of crossbridges in the overlap region different from that in the nonoverlap region.     

A Flexible Calibration Method Using the Planar Target with a Square Pattern for Line Structured Light Vision System

A flexible calibration approach for line structured light vision system is proposed in this paper. Firstly a camera model is established by transforming the points from the 2D image plane to the world coordinate frame, and the intrinsic parameters of camera can be obtained accurately. Then a novel calibration method for structured light projector is presented by moving a planar target with a square pattern randomly, and the method mainly involves three steps: first, a simple linear model is proposed, by which the plane equation of the target at any orientations can be determined based on the square’s geometry information; second, the pixel coordinates of the light stripe center on the target images are extracted as the control points; finally, the points are projected into the camera coordinate frame with the help of the intrinsic parameters and the plane equations of the target, and the structured light plane can be determined by fitting these three-dimensional points. The experimental data show that the method has good repeatability and accuracy.     

Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle

Difficulties of quantitation of hemoglobin/myoglobin absorption changes in muscle have led to the development of a new approach using short pulses of light. This method uses input light pulses sufficiently short so that the time course of travel of light through the brain can be precisely measured. The time of arrival of light at the detector gives the optical path length, given the velocity of light in tissues. The intensity profile of photon migration in tissues permits determination of the path length that the exiting photons have traveled and the concentration change of the pigments. A cavity-dumped liquid dye laser illuminates the tissue with 130-ps pulses detected as 600-ps duration at a half height at 3.0-cm distance from the input point. The decay of intensity from the 50% point onward to 0.1% follows a logarithmic function of slope mu which is attributed to the total absorption coefficient of the tissue. Increments of mu due to deoxyhemoglobin absorption at 760 and 630 nm are used to calculate the concentration change. This permits the calculation of the path length for continuous light measurements of 2 cm for a particular geometry. Variation of the wavelength of the laser affords determination of a spectrum of changes in the tissue.     

A NEW METHOD OF POLARIZATION MICROSCOPIC ANALYSIS : I. Scanning with a Birefringence Detection System

A new method of polarized light analysis is described in which a highly sensitive electronic detector specific for birefringence is used to identify the crystalline axes of an object and then measure its phase retardation due to birefringence. The microscopic system employed in the method consists of an electronic birefringence detection system (BDS), a microscope with strain-free lenses, and a driven stage for passing the specimen at appropriate velocities across the image of an aperture placed at the field stop and imaged in the specimen plane by the condenser. The detector registers retardations directly as voltage at a constant deflection sensitivity of ca. 1.1 v per angstrom unit over a range of 120 angstrom units. The basal rms noise level is 0.002 A for a spot 36 µ in diameter formed by a 95 x, N. A. 1.25 objective pair, and increases in proportion to the reciprocal of the diameter of the scanning spot. The increase in noise with high resolution scanning can be offset by increasing the instrumental time constant, which is adjustable in decades between 0.004 and 0.4 seconds. A number of difficult problems in high extinction polarization microscopy are avoided by the use of modulated light and a rapid electronic detector. For example: (a) The measured distribution of birefringence is unaffected by the usual diffraction anomaly; therefore polarization rectifiers are not required. (b) The detector is selective for birefringence, so that there is no problem in separating contrast due to different optical properties (e.g. dichroism, light scattering). (c) The speed and sensitivity are both increased by between one and two orders of magnitude over that attainable by visual or photographic methods, thereby rendering a vast number of weakly birefringent, light-scattering, and motile objects readily analyzable for the first time with polarized light.     

Birefringence of glycerinated crab muscle fiber under various conditions.

By using glycerinated single fibers of crab muscle (Sesarma haematocheir) which has long sarcomeres, the birefringence of the I band, H band and the overlapping region between thin and thick filaments was measured separately, under various environmental conditions. At the resting length, the birefringence of the fiber was decreased by the addition of Ca2+ in the absence of ATP, by about 0.35%. This birefringence decrease was found to take place in the overlapping region. The decrease corresponded to about 2% of the birefringence of thin filaments in this region. The birefringence of the fiber was increased by the addition of ATP in the absence of Ca2+, by about 6%. This birefringence increase also took place mostly in the overlapping region. The increase of birefringence by pyrophosphate was about half of that by ATP. The birefringence of the fiber was decreased by the increase of the ionic strength from 0.12 to 0.20. The origin of the observed changes of birefringence is discussed.     

Birefringence of Protein Solutions and Biological Systems. I

The quantitative interpretation of birefringence of biological structures such as muscle requires a knowledge of intrinsic birefringence of the components. The intrinsic birefringence of fibrous structures as determined by variation of solvent index is positive while the intrinsic birefringence of proteins in solution is negative as calculated by the Peterlin-Stuart theory. As a first step in clarifying this discrepancy the basis of the Peterlin-Stuart theory has been re-examined. The theory has been recalculated from the standpoint of light scattering and extended to particles whose length is not small compared to the wavelength. The birefringence of a system of particles possessing a shell with index different from the bulk solvent has been obtained in order to interpret measurements in mixed solvents.     

Cooperativity of the phase transition in single- and multibilayer lipid vesicles.

The effect of membrane morphology on the cooperativity of the ordered-fluid, lipid phase transition has been investigated by comparing the transition widths in extended, multibilayer dispersons of dimyristoyl phosphatidyl-choline, and also of dipalmitoyl phosphatidylcholine, with those in the small, single-bilayer vesicles obtained by sonication. The electron spin resonance spectra of three different spin-labelled probes, 2,2,6,6-tetramethylpiperdine-N-oxyl, phosphatidylcholine and stearic acid, and also 90 degrees light scattering and optical turbidity measurements were used as indicators of the phase transition. In all cases the transition was broader in the single-bilayer vesicles than in the multibilayer dispersions, corresponding to a decreased cooperativity on going to the small vesicles. Comparison of the light scattering properties of centrifuged and uncentrifuged, sonicated vesicles suggests that these are particularly sensitive to the presence of intermediate-size particles, and thus the spin label measurements are likely to give a more reliable measure of the degree of cooperativity of the small, single-bilayer vesicles. Application of the Zimm and Bragg theory ((1959) J. Chem. Phys. 31, 526-535) of cooperative transitions to the two-dimensional bilayer system shows that the size of the cooperative unit, 1/square root sigma, is a measure of the mean number of molecules per perimeter molecule, in a given region of ordered or fluid lipid at the centre of the transition. From this result it is found that it is the vesicle size which limits the cooperativity of the transition in the small, single-bilayer vesicles. The implications for the effect of membrane structure and morphology on the cooperativity of phase transitions in biological membranes, and for the possibility of achieving lateral communication in the plane of the membrane, are discussed.