Length-dependent filament formation assessed from birefringence increases during activation of porcine tracheal muscle
1 Krannert Institute of Cardiology, Department of Medicine, Indiana University School of Medicine, 1800 N. Capitol Avenue, Indianapolis, IN 46202, USA
2 The James Hogg iCAPTURE Centre for Cardiovascular and Pulmonary Research, St Paul's Hospital, University of British Columbia, Vancouver, BC, Canada V6T 1Z3
Abstract
Birefringence and force produced by pig tracheal smooth muscles were recorded every 100 ms during electrically stimulated tetani at muscle lengths that varied 1.5-fold and at the peak of acetylcholine contractures at the same lengths. Isometric force was nearly the same at all lengths. Resting birefringence at the longest length was 30% greater than that at the shortest length. During tetani, birefringence increased with approximately the same time course as force, rising by 20% at the shortest length and 9% at the longest length, and continued to increase by an additional 0.5–1.5% of the resting value for 2–8 s after stimulation ended and force began to fall. This late increase was greatest and more sustained at longer lengths. During contractures, birefringence increased by 25 and 18% at the shortest and longest lengths, respectively. Comparison of these results with our published thick-filament densities suggests that thick-filament density increased by about 80, 72 and 50% during contractures at the short, intermediate and long lengths, and that 35% of birefringence in the resting muscle at the longest length was not due to thick filaments. These findings support the hypotheses that tracheal smooth muscle adapts to longer lengths by increasing thick-filament mass and that myosin thick filaments are evanescent, dissociating partially during relaxation and reforming upon activation. The results further suggest that thick-filament formation is sufficiently rapid to account for the velocity slowing and some of the force increase observed during the rise of activation of tracheal smooth muscle.
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Introduction
The large functional range of some types of smooth muscle suggests that they adapt to longer lengths by placing more contractile filaments in series (Ford et al. 1994; Pratusevich et al. 1995). Such plasticity would be facilitated if thick filaments were labile, dissociating partially during relaxation and reforming upon activation (Kelly & Rice, 1968; Shoenberg, 1969). Filament lengthening could account for the well-known velocity slowing and some of the force increase during the rise of activation (Seow et al. 2000). Support for these proposals came first from analysis of contractile parameters at different lengths and levels of activation (Pratusevich et al. 1995; Seow et al. 2000) and, more recently, from electron microscope measurements of thick-filament densities in relaxed and contracted muscles (Herrera et al. 2002, 2004; Kuo et al. 2003). To assess whether the structural changes are sufficiently rapid to account for the observed mechanical events, we have measured birefringence continuously in tracheal smooth muscle during contraction–relaxation cycles at different lengths. The birefringence signal was calibrated by comparing these optical responses during acetylcholine-induced contractures with our previously measured thick-filament densities (Kuo et al. 2003). Godfraind-De Becker & Gillis (1988a,b) and Gillis et al. (1988) have demonstrated that steady-state birefringence values and thick-filament densities increased when resting rat anococcygeus muscle passed from rest to noradrenaline contractures at a single length. Here we extend their findings to include dynamic changes during the rise of activation and assessments at different lengths. A brief account of this work has been presented to the Biophysical Society (Smolensky et al. 2004).
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Methods
Principle of the method
Birefringent material has two refractive indices, i.e. the speed of light is fastest when the plane of polarization of the light is parallel to one axis of the material and slowest when the plane of polarization is at right angles to this axis. It can either be an intrinsic property of molecular structures (intrinsic birefringence) or due to parallel structures, e.g. filaments, with dielectric constants different from the medium in which they reside (form birefringence). Form birefringence is a well-known property of striated muscle; A-bands are distinguished on the basis of being ‘anisotropic’, i.e. birefringent, and their birefringence results from the presence of thick filaments. Thus, increased density of smooth-muscle thick filaments should increase muscle birefringence. Furthermore, when the filaments occupy only a few per cent of muscle volume, birefringence varies nearly linearly with their density (see Appendix).
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The strength of birefringence, B, is defined as
where s and f, are the indices of refraction for the slow and fast axes, respectively. In muscle, the slow axis is parallel to the filaments and to the longitudinal muscle axis. It was measured here by passing plane-polarized light through a muscle with its plane of polarization at 45 deg to the slow and fast muscle axes. This single beam can be regarded as two beams with planes of polarization at right angles to each other, one parallel to the slow axis and the other parallel to the fast axis. Light traversing the slow axis is retarded relative to that traversing the fast axis by an amount, D, called the path difference, equal to the path length through the muscle, L, multiplied by the strength of birefringence:
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Path difference can be expressed either in dimensions of length or as a multiple of the wavelength of the light expressed as an angle, called the ‘phase angle.’ It was measured here using an extension of the method of de Senarmont-Friedel (Bennett, 1950; pp. 655–660). The retardation of light traversing the slow axis caused the trajectory of the tip of the electric vector of the light beam to widen from its initial, linear form to an ellipse. The elliptically polarized beam emerging from the muscle was collected by an objective and passed through a 1/4-waveplate specific to the wavelength of the He–Ne laser, 632.8 nm. This ‘de Senarmont compensator’ converted the elliptically polarized beam to a plane-polarized beam with its plane of polarization rotated from its initial orientation by half the phase angle.
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The beam exiting the compensator passed through a beam-splitting cube that separated it into two polarized beams with planes of polarization at right angles to each other. One beam, designated R, was reflected by an interface in the cube and passed horizontally out the side (Fig. 1). The other, designated T, passed upward through the interface. The two beams exiting the cubes were focused onto separate photodiodes.
See text for details.
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The beam-splitting cube was mounted in a rotatable tube fitted with a scale for measuring the angle of rotation of the cube. As the tube was rotated, the photodiode signals varied in proportion to the squares of sine and cosine of the angle of rotation. Angular deviation, a, from a reference point where the two signals were equal could thus be calculated as:
where IT and IR are the intensities of the two beams exiting the cube. The square root term arises because the photodiodes signal light intensity, which is proportional to the square of the amplitude of light oscillation in the beam.
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In the absence of a muscle, the photodiode signals were equal when the faces of the cube were at 45 deg to the plane of polarization of the light beam, and this position was taken as the zero rotational reference. The steady-state phase angle of a muscle could be determined as the degree of rotation needed to make the signals equal. The photodiode signals are most sensitive to tube rotation when they are equal. Thus, when making continuous measurements, tube rotation, C, was set so that a would pass through the value zero during recording. Birefringence at each time point was calculated from tube rotation C, and muscle thickness, L, as:
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where 632.8 is the wavelength of the laser light and a is in degrees.
Two potential sources of ambiguity can be recognized in eqn (3): (1) the sign of the square root is not revealed by the measurements themselves, and (2) an unrecognized passage of the phase angle through one or more half circles will produce substantially larger changes of phase angle for a given change in birefringence. Both ambiguities were avoided by using thin muscle segments. The mean values of phase angles for all conditions studied fell within the range of 86 to 138 deg, so that the rotation of the beam by the 1/4-waveplate ranged from 43 to 69 deg and were well within the first quadrant of rotation.
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Preparation and solutions
Pig tracheae were acquired from an abattoir licensed and supervised by the State of Indiana and studied using a protocol approved by the Animal Care and Use Committee of the Indiana University School of Medicine. The tracheae were stored at 4°C in physiological saline buffered with Hepes for up to 48 h before muscles were dissected for study. Strips measuring 0.8 mm wide x 0.3 mm thick x 3.5–4.0 mm at the longest length studied were dissected and mounted in aluminium foil clips (Ford et al. 1977), used to attach them to the apparatus. Muscle thickness was the extreme distance between the upper and lower surfaces measured with a reticle in the eyepiece of a dissecting microscope after rotating the muscle by 90 deg around its long axis and sighting along the two surfaces.
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To maintain a constant optical path length and to reduce tissue movement during contraction, a small area near the centre of the muscle was positioned in the optical path and compressed vertically by glass blocks. The lower block was a horizontal bar with edges ground away at 45 deg to leave a smooth, flat area 0.8 mm wide. When the muscle was stretched over this bar, its initial 0.3 mm thickness was reduced to 0.2 mm, mainly from a levelling of the irregular upper and lower surfaces. The upper block was glued to the underside of the cover glass for the trough. Its lower edges were ground at 45 deg to leave a flat square 0.8 mm on a side. This upper block was pressed into the upper surface of the muscle to reduce its thickness to 110 μm. This compression was relieved during muscle length changes.
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Muscles were studied at 37°C in physiological saline containing (mM): NaCl 112.5, NaHCO3 27.5, KCl 4.0, NaH2PO4 1.2, MgSO4 2.0, CaCl2 2, glucose 5 and perfused with 95% O2–5% CO2 to achieve pH 7.4.
Apparatus
A monocular microscope was modified to measure birefringence in functioning muscle. The stage of the microscope was equipped with a muscle chamber and force transducer (Fig. 1). Muscle strips were suspended in a 3 mm x 3 mm trough perfused with physiological saline at a rate of 1 ml min–1. Blacked platinum electrodes 8 mm x 3 mm were glued to sides of the trough. The trough was milled through the bottom in its central region, and an easily cleaned, 1-mm-thick glass plate was fitted into the bottom of the chamber. Solution was warmed as it entered the trough by passage through a hypodermic needle wrapped with wire. Constant electrical current through the wire maintained temperature at 37°C when the muscle was not being stimulated. Temperature rose by 0.5°C at the onset of stimulation and remained constant until stimulation ended.
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The trough was covered with a 1-mm glass plate from its upstream end to a point several millimetres downstream from the muscle. Solution was drawn away by suction from the uncovered end of the trough, producing a vertical meniscus where the cover-plate ended. The vertical lever arm of a laser-diode force transducer (Barb et al. 2000) projected into the uncovered trough, and horizontal tubing passed from the end of this lever through the vertical meniscus to reach the downstream end of the muscle. The position of the downstream clip was adjusted by a rack-and-pinion manipulator holding the force transducer to the microscope stage plate. At the upstream, covered end of the trough, a length of stainless-steel tubing passed through a seal to reach the muscle. The upstream clip was positioned by adjusting the hypodermic tubing in its seal. Separate positioning of the two ends of the muscle allowed the central region of muscle to be kept in the microscope's optical axis when muscle length was changed.
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Optics
For electronic measurements, illumination was provided by a He–Ne laser beam polarized at 45 deg to the muscle axes and focused to a circle 300 μm in diameter at the muscle (Fig. 1). Light passing through the muscle was collected by a 10 x (0.25 NA) objective and passed first through a 1/4-waveplate specific to the wavelength of the laser (632.8 nm) (part no. K43-698, Edmund Industrial Optics, Barrington, NJ, USA) and then through a beam-splitting cube (part no. K45-199, Edmund Industrial Optics). Polarizing filters were placed over the exit faces of the cube to improve its selectivity. The two beams exiting the cube were focused onto separate photodiodes.
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In addition to the arrangements described above for quantifying birefringence, colour changes resulting from the birefringence were observed using white light. A beam of incandescent light below the muscle was directed upward by a mirror mounted on a slide so that it could be moved in and out of the optical axis of the microscope. A photodiode and focusing lens could be replaced by a microscope eyepiece so that the muscle could be observed visually. When this was done, the beam-splitting cube served as an analyser, i.e. it passed plane-polarized light to an observer at one of the eyepieces, and the angle of polarization could be altered by rotating the cube.
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Recording and experiment control
Experiment control and digital data collection were achieved with a personal computer equipped with a Tecmar (Solon, OH, USA) Labmaster interface board driven by the SALT software package (Fenster & Ford, 1985). Muscles were stimulated to produce 12.5 s tetani at 5 min intervals throughout the experiments. The stimulator produced 1 ms square pulses of alternate polarity at 60 Hz. To reduce 60 Hz artifact and higher frequency noise, values of force and photodiode signals for each 100 ms interval consisted of averages of 67 points collected at 1 ms intervals, i.e. the signals were averaged over four cycles of the 60 Hz mains frequency. After averaging, the signals were stored and plotted before the next 100 ms cycle began.
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Protocols
After dissecting and mounting, muscles were adapted to the experimental environment by stimulating them to produce 12.5 s tetani for at least 1 h. During this adaptation, the length at which rest force was 10% of developed force, L10%, was determined, and this was the starting length in all experiments. For the experiments described here, force and birefringence responses were measured during multiple 12.5 s tetani at 5 min intervals, followed by the responses to a final acetycholine contracture. This contracture was initiated by electrical stimulation on the same 5 min schedule as the tetani and then sustained for 5 min by perfusing the muscle with physiological saline containing 10–4 M acetylcholine.
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The data presented here were obtained from 21 muscles studied in three groups of 7 muscles each. For the first group, data were collected only at L10%, although each muscle was first tested to be certain that developed force was relatively insensitive to length changes. The 14 muscles in the next two groups were studied first at L10%, at two-thirds this length, and at an intermediate length where rest force was 2% of developed force, which averaged 87% L10%. The second group was studied at the shortest length and then at the intermediate length so that the final contracture occurred at the intermediate length. In the final group, the order of length change was reversed, and the final contracture was made at shortest length. Thus, 7 muscles were studied with contractures at each length, 21 muscles were studied with tetani at L10% and 14 studied with tetani at each of the other two lengths.
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Muscles were adapted to each new length with at least six tetani before force and birefringence signals were recorded in five consecutive tetani. These five records were signal-averaged to obtain a single record for each length. At the end of the study, the averaged records for each muscle at each length were signal-averaged together to make the records displayed below. Mean values and standard errors of the means (S.E.M.) of force and birefringence were also calculated by averaging the values in the signal-averaged records for each muscle.
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Control observations
Specimen homogeneity. The Appendix considers the issue of whether local concentration of filaments, as within cells, affects measured birefringence and concludes that the effect depends upon the ability of the optical system to resolve the separate volumes. Such resolution causes dispersion of the angles of polarization of light passing through the 1/4-waveplate compensator, and thereby decreases extinction of light by the analyser cube. To assess such dispersion, extinction was measured in the presence and absence of seven resting muscles. In the absence of a muscle, the intensity of light reflected out the side of the analyser cube averaged 0.76% of the maximum value obtained when the cube was rotated by 90 deg. A muscle in the optical path increased transmission at maximum extinction insignificantly by a further 0.37 ± 0.38% (P > 0.3) of the maximum value obtained in the absence of the muscle. The corresponding values for the light passing upward through the interface in the cube were 1.32% without a muscle and a further 0.06 ± 0.47% (P > 0.8) in the presence of a muscle (level of significance was assessed using Student's paired t tests.)
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Absence of tissue movement in the optical path. An increase in the volume of tissue in the optical path would increase the optical retardation and apparent birefringence. As discussed below, Godfraind-De Becker & Gillis (1988b) found that smooth muscle thickness and cell cross-sectional area decline during prolonged contractures. This finding raises the question whether changes in cell volume might have influenced the present results. As discussed below, a decrease in cell volume, without a change in tissue volume, would have no effect, but an increase in the number of cells being sampled by the optical beam would increase the apparent birefringence. Compression of tissue between glass blocks limits tissue movement to reductions of the width of the tissue, with new tissue moving into the optical path from the edges of the muscle. Such movement into the optical path was not seen when muscles were observed directly. In addition, movement of any sort distorted the optical records in a recognizable way. In the absence of movement, the records from the two diodes were nearly mirror images when the records were scaled in proportion to their maximum amplitude. By contrast, movement of the tissue in the beam, particularly when associated with a change in tissue volume, caused the two signals to deviate in the same direction. When such signals were recorded, the muscle was discarded.
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Results
Muscles were studied over a 1.5-fold length range, with the longest length being that where rest force was 10% of developed force (L10%). Signal-averaged records of birefringence during tetani at three lengths are shown on an absolute scale in Fig. 2. Resting birefringence was substantially greater at the longer lengths, while the increase in birefringence during tetanic stimulation was greatest at the shortest length. To illustrate the time course of birefringence relative to force, the two signals were normalized to the increase they underwent during electrical stimulation and are superimposed in Fig. 3, with separate plots for each of the three lengths studied. Birefringence and force rose in close association, with force leading slightly at the longest length and lagging slightly at the shortest length but when stimulation ended, the records diverged. Force began to fall almost immediately, while birefringence continued to rise for 2–8 s before falling. At the longest length, where the late rise was greatest, there appeared to be a slight acceleration in the rate of rise. At this length, there was also a very small decrease in birefringence shortly after the onset of stimulation, shown in the inset of Fig. 2.
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Muscles were adapted at the three lengths indicated at the ends of the records, and recording began 0.1 s before a 12.5 s electrical stimulation. The inset below the upper record shows the first 0.8 s of recording at this length, with the birefringence scale amplified 50-fold and the time scale amplified 15-fold.
Increase in force and birefringence with 12.5 s electrical stimulation, normalized to their increases during the stimulation.
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To compare the time course of the birefringence changes at the three lengths, the records have been scaled to the increase that occurred during stimulation and superimposed in Fig. 4, which shows that they were almost exactly coincident during the rise of activation and diverged when stimulation ended. Thus, the slight changes in the time course of force relative to birefringence shown in Fig. 3 were due entirely to small lags in force development at the shorter lengths and not to increases in the relative speed of the optical signal at the longer length.
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Birefringence records at three lengths superimposed to show the similarity of time course during the rise of activation and the divergence when stimulation ended.
The values of birefringence and force at the different lengths are plotted in Fig. 5. The force plots (Fig. 5 lower panel) include rest force, total tetanic force (rest force plus force developed during tetani), and total force achieved during acetylcholine contractures. These force plots show that developed force was relatively constant over the range of length studied, especially during contractures. For tetanic stimulation, two birefringence values are plotted in Fig. 5 upper panel: the level achieved at the end of stimulation and the peak value achieved after stimulation ended. The birefringence plots show that, for electrical stimulation, the birefringence increase was greatest at the shortest length (20.5% of the resting value at end stimulation, 21.1% at peak) and smallest at the longest length (8.7% at end stimulation, 10.2% at peak). For contractures, the relative increases of birefringence were more similar, 25, 25 and 18%, at the short, intermediate and long lengths, respectively.
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Each panel plots separately the resting values (), values at the end of electrical stimulation (), and peak values achieved during acetylcholine contractures (). For the electrically stimulated muscles, two birefringence values are plotted: the value at the end of stimulation () and the peak value achieved after stimulation ended (). Active force plotted is total force, i.e. rest force plus developed force. Error bars indicate S.E.M. for the absolute values.
These optical findings are compared with our published values of thick filament density below.
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Discussion
The principal findings in these experiments are that birefringence of tracheal smooth muscle was greater at longer muscle lengths, increased immediately with activation, and decreased following relaxation. Together with earlier measurements of thick filament density in electron micrographs, the results suggest that thick filaments dissociate partially during relaxation and reform with activation. The observation that the optical changes occurred on the same time scale as force further suggests that filament elongation was likely to alter contractile properties of the muscle as activation rose. Longer filaments will develop more force per filament and therefore contribute to the overall force development during activation (Gillis et al. 1988; Seow et al. 2000). Filament lengthening is also likely to contribute to a parallel decline in velocity, since fewer long filaments are needed to span the length of the muscle (Seow et al. 2000). It is well known that velocity declines during the rise of activation (Johansson, 1973; Dillon et al. 1981; Dillon & Murphy, 1982; Kamm & Stull, 1985). The optical records here indicate that filament formation was sufficiently rapid to account for the observed decline.
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The results also indicate that there was a greater fractional volume of thick filaments at longer adapted muscle lengths. The volume of muscle sampled at the different lengths was the same in all cases because the cross-sectional area of the sampling light beam was the same, and compression of the muscle between glass blocks ensured that sample thickness and optical path remained constant at different lengths. To the extent that overall muscle volume was also constant at the different lengths (Kuo et al. 2003), the volume sampled was a constant fraction of the overall muscle volume at all lengths. The finding that birefringence of the fixed sample volume was increased at the longer lengths is strong evidence that the fractional volume of thick filaments in the muscle increased at longer lengths, further supporting the hypothesis that length adaptation is achieved by plastic alterations that place more thick filaments in series at longer lengths (Ford et al. 1994; Pratusevich et al. 1995).
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Dynamics of filament formation
It has been observed that thick filaments form in solution even when the light chains are not phosphorylated, and that phosphorylation increases the tendency of filament formation (Kendrick-Jones et al. 1987). This observation suggests that filament formation proceeds by mass action and that phospholylation is not a requirement for filament formation but simply a facilitator. The apparent dynamic equilibrium between filamentous and monomeric myosin would also explain the speed of filament formation, once phosphorylation begins. It would also explain why filaments do not dissociate completely during relaxation and why interventions, such as length oscillations (Kuo et al. 2001) or lowered calcium (Herrera et al. 2002), which lower thick filament density, do not cause filaments to dissociate completely. The presence of a substantial number of filaments in the resting state explains how force development and filament formation occur simultaneously without a delay in force production.
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Factors other than filament formation which may alter birefringence
Crossbridge head movement. Opposite changes in birefringence occur in skeletal muscle, which have more permanent thick filaments; birefringence falls by 9–11% upon activation (Eberstein & Rosenfalck, 1963; Irving, 1984, 1993). This decline is associated with a change in X-ray diffraction patterns suggesting swinging of crossbridge heads away from the thick-filament backbone and possibly changes in crossbridge orientation with respect to the filament axis (Peckham & Irving, 1989). The birefringence increase after stimulation ended in the present experiments suggests that similar movements of crossbridge heads diminished birefringence during activation. Thus, there appear to be two competing effects that contributed to the change in optical signal during the rise of activation: an increase caused by the formation of new filaments and a smaller decrease caused by crossbridge head movement on formed thick filaments. In comparing the birefringence signal from contracted and relaxed muscle, it is important to take account of the decreased signal expected in contracted muscle, as is done below.
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Further suggestion of crossbridge movement is provided by the small birefringence decrease at the outset of activation at the longest length and by the observation that the greatest rise at the end of stimulation also occurred at the longest length. The more obvious changes at this length are due to at least two factors: (1) more formed thick filaments in the resting muscle at the outset of activation, as indicated by the higher resting birefringence, and therefore more crossbridges moving at the onset of activation; and (2) less birefringence increase to obscure the small fall due to crossbridge movement. These factors only partially explain the differences, however, because the rise in birefingence is prolonged as well as increased at longer lengths. It seems likely that thick filaments are more stable at longer lengths, and this increased stability may be reflected in the delay in the decline of birefringence after stimulation ended.
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Cell volume changes. An important issue that must be considered is the effect of cell volume changes on measured birefringence. Godfraind-De Becker & Gillis (1988b) found a substantially larger birefringence increase, 48%, during contractures of anococcygeous muscle, but a large part of this increase was calculated on the basis of muscle thinning and therefore reduction of the optical path through the muscle. The increase in optical retardation, 30%, was much closer to the 18–25% increase observed here. Some of their observed increase in optical retardation may also have been due to decreases in muscle width bringing more cells into the field of view. The decrease in muscle thickness in these experiments was matched by a proportional decrease in the cross-sectional areas of the cells measured by electron microscopy (Gillis et al. 1988).
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Tissue volume changes as seen by Godfraind-De Becker & Gillis (1988b) are unlikely in the present experiments because the muscle was compressed between glass blocks that impeded lateral tissue movement while maintaining a constant optical path. Tissue volume shrinkage during activation must result from volume contraction of the individual cells caused by water movement from the intracellular to the extracellular spaces. By itself, this change in the distribution of water will not alter the population of cells being monitored or the number of filaments being sampled optically. As explained in the Appendix, the concentration of the filaments in smaller cells will not alter the optical retardation signal. An increase in optical retardation requires that the number of cells and filaments be increased. In the present experiments, an increase in the number of cells would require that tissue move into the area being compressed by the glass blocks. As explained at the end of Methods, such movement was not observed. In addition, it seems unlikely, because it would require the simultaneous exchange of extracellular water for cells within the relatively small gap between the blocks.
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Filament alignment. Birefringence would have increased if filaments became straighter and more parallel during the rise of force. While a small contribution from such straightening cannot be excluded, there are two distinctly different arguments against a large contribution. The first is that very little deviation from parallel alignment is seen in the relaxed muscle (Gillis et al. 1988; Kuo & Seow, 2004). Gillis et al. calculated that half the filaments would have to have deviated by +25 deg and half by –25 deg to account for all the birefringence increases they measured, while the observed deviations from a parallel orientation are very much smaller.
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The second argument against filament realignment is that the filaments would support relatively little force until their alignment became parallel to the direction of stress. If such realignment were substantial, it would produce a large increase in birefringence before much force was developed. The absence of a substantial initial lead in birefringence as compared with force thus argues against filament straightening as a major cause of the rise in birefringence.
, http://www.100md.com Correlation with prior measurements of filament density
We have previously measured thick-filament densities in electron micrographs of the preparation studied here in similar contractures over the same length range (Kuo et al. 2003). These densities, expressed as the number of filaments per square micrometre of organelle-free cytoplasm, are compared graphically in Fig. 6 with the birefringence values in Fig. 5. The filament densities in the present experiments were estimated by interpolating the values determined from the earlier electron microscope studies and are plotted (as filled symbols) against the birefringence values obtained during contractures. The relationship is linear, as expected when the volume fraction of the thick filaments is less than a few per cent (see Gillis et al. 1988 for discussion).
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For relaxed muscles (open symbols), birefringence values have been reduced by 10% to account for crossbridge movement during activation and plotted on the line fitted to the data for muscles in contracture. The values for filament density in the relaxed muscle were read from the abscissa scale.
A linear regression fitted to these three points extrapolates to a birefringence intercept of 6.2 x 104 with a slope of 14 x 104 per 100 filaments μm–2. The intercept corresponds to 35% of the value in the resting muscle at the longest length and 45% of the resting value at the shortest length. Godfraind-De Becker & Gillis (1988a) found a similar 30–35% residual birefringence when myosin was extracted from their resting muscles at a single length. They also found that extraction of actin reduced this residual to 18–20% of the total resting birefringence.
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Estimation of filament density increase during activation
To estimate filament densities in relaxed muscles, the birefringence values at each length were reduced by 10% to account for crossbridge movement and plotted (open symbols) on the line fitted to the values for contractures. Filament densities in the relaxed muscle at the three lengths were then read from the abscissa scale of Fig. 6. Comparison of the filament densities in relaxed and contracted muscle in Fig. 6 indicates that the estimated value of filament density increased by 80, 72 and 50%, respectively, for short, medium and long lengths.
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A recent electron microscope study of thick-filament density (Herrera et al. 2004) found similar increases of 63 and 82% during acetylcholine contractures at in situ length and 1.5 times that length. It should be emphasized, however, that there is some variability in thick-filament density increases in different studies. An earlier study by Herrera et al. (2002) found a 144% increase in thick filament density associated with contracture. Similarly, an early study by Gillis et al. (1988) found a 95% increase in filament density, while a later study by Gillis and coworkers (Xu et al. 1997) found only a 23% increase in density in the same muscle under similar conditions. The mean of these two values, 59%, is similar to the increases found here. The main point to be made from these comparisons is that in some smooth muscles, including tracheal muscle and anococcygeus muscle, thick-filament density definitely increases with activation. Equally importantly, it should be emphasized that one study showing a definite increase in filament density during activation of anococcygeus muscle (Xu et al. 1997) showed no increase in the taenia coli muscle. Thus, it is possible that filament dissociation during relaxation occurs in only some smooth muscles.
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Thin filament density changes. This analysis has focused on thick-filament density changes, partly because there are more electron microscope data about thick-filament densities and partly because thin filaments create less brirefringence, particularly in striated muscle. On the other hand, the ratio of thin to thick filaments is much higher in smooth muscle, creating 18–20% of resting birefringence (Godfraind-De Becker & Gillis, 1988b). A recent study found that mean actin filament density increased by 24% when muscles were placed in contracture (Herrera et al. 2004). If actin filament density increased by 24%, it would increase birefringence by 5%, equivalent to 20–25% of the total birefringence increase seen during contractures here. Such an increase would not change the conclusions here if thick and thin filaments change density in parallel.
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Comparison with earlier work
As described above, Godfraind-De Becker & Gillis (1988a,b) and Gillis et al. (1988) have measured similar increases in birefringence in rat anococcygeus muscle during contractures. In these earlier experiments, only one length was studied, and birefringence was measured manually in a two-step process, focusing separately on the muscle surfaces to measure their thickness and then adjusting the analyser to measure light extinction. Measurements could not be made when the optical changes were occurring rapidly, as at the onset of activation. Their earliest measurements were made about 5 min after the onset of a contracture, and time resolution after that was about 1 min. Thus, the present experiments extend their pioneering work to different muscle lengths and more rapid time resolution at the onset of activation.
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Although a different preparation was used and much higher time resolution achieved, the steady-state results described here are in close agreement with the earlier studies. The resting birefringence at the shortest length measured here, 13.6 x 10–4, was close to the 8.8 x 10–4 for anococcycgeus and 13.4 x 10–4 for taenia coli in the earlier experiments. The increase in birefringence during contractures was substantially greater in the earlier experiments, 48 versus 25% for the shortest length studied here, but, as discussed above, 38% of the increases was due to decreases in muscle thickness. The increase in optical retardation, 30%, was not much greater than the 25% found during contractures here.
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Finally, we would be remiss if we did not acknowledge that the inspiration for this work derived from the early work of Shoenberg (1969) and Rice et al. (1970), who suggested that the thick filaments in the smooth muscles they studied were evanescent, forming on activation and dissociating during relaxation. Although their suggestion was not widely accepted, it did offer a plausible explanation for the ability of some smooth muscles to adapt to wide ranges of length, namely through filament lattice plasticity. The present work suggests that the earlier interpretations were correct.
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Appendix
The issue considered is whether birefringence measured in whole muscle is influenced by a non-uniform distribution of filaments, and, more specifically, whether cell volume changes during activation alter the measured birefringence independently of changes in average filament density. Such local volume changes could be produced, for example, by water movement into or out of cells during activation, without a change in the overall tissue volume or population of cells sampled by the light beam. The effects of such local concentration differences depend upon the system of illumination and/or the resolving power of the optical system. Before considering this issue, it is important to recognize that there should be a linear relationship between average filament density and overall birefringence when the optics permit.
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As discussed by Gillis et al. (1988), Wiener's equation for form birefringence, B, in terms of the volume fractions and refractive indices of filaments and medium suggest that birefringence is a nearly linear function of filament density when the filaments occupy only a few per cent of overall tissue volume. To the extent that the relationship is linear, each domain in the muscle will contribute to the overall birefringence in proportion to the number of filaments it contains. Overall muscle birefringence will then reflect the average filament density when the optical arrangements do not cause domains with different filament concentrations to contribute disproportionately to the measured birefringence.
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To show the effect of the different optical systems, two extreme forms of illumination are considered. For both cases, the specimen is divided into two areas. One is non-birefringent and occupies the fractional volume 1 – f. The other area occupies the fractional volume f and has birefringence equal to B/f, where B is the average birefringence of the muscle. This causes the phase angle produced by the birefringent area to equal /f, where is the mean phase angle for the muscle. For the specific case illustrated in Fig. 7, is 80 deg, slightly less than the lowest minimum mean value recorded here, 86 deg, and f is 67%, slightly greater than the 65% value for the intracellular area measured by Gillis et al. (1988).
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See text for details.
Case I. Coherent laser illumination arranged so that phase and intensity are the same at all points in the field
(A similar result would probably occur if the volumes of material containing different concentrations of filaments are smaller than the resolving power of the microscope.)
Figure 7 shows the patterns traced by the tips of the electric vectors of monochromatic light beams before and after passing through a muscle lying in the plane of the paper and then through a 1/4-waveplate compensator. The long (slow) muscle axis is parallel to the x-axis (labelled S), the transverse axis (fast) is parallel to the y-axis (labelled F), and the light passes along the z-axis, through the paper. The incident beam is plane-polarized at 45 deg to the muscle axes, and the tip of its electric vector traces a straight line (continuous line in Fig. 7A). This beam can be regarded as consisting of two perpendicular beams polarized parallel to the two muscle axes. Light passing along the slow axis is retarded relative to that passing along the fast axis by the path difference. Because of the coherence of the laser beam, light coming from the two domains within the muscle cannot be distinguished, and all light parallel to the slow muscle axis is retarded equally. This retardation causes the tip of the electric vector of the beam emerging from the muscle to trace a single ellipse with axes parallel and perpendicular to the original beam.
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The 1/4-waveplate compensator converts the elliptical beam to a plane-polarized beam rotated by half the phase angle, /2, from the original 45 deg orientation of the incident beam (dashed line in Fig. 7A). In the absence of any other factors, this beam will be extinguished completely by the analyser.
Case II. Standard microscope illumination of uniform brightness with optics capable of resolving the two domains
In this case, the phase of the light varies randomly from one point in the field to another, and there is no interference of light from different points in the field. The plane-polarized beam incident on the muscle is regarded as two separate, superimposed beams passing through the birefringent and non-birefringent domains, respectively, and having intensities 0.67 and 0.33 of the original beam (narrow and wide continuous lines in Fig. 7B). (The amplitudes of oscillations illustrated for these beams are 0.82 = 0.67 and 0.58 = 0.33 times the amplitude of the initial beam because their intensities, proportional to the square of their amplitudes, are additive.) The beam passing through the non-birefringent domain emerges from the muscle unchanged. In addition, since its axis is parallel to that of the 1/4-waveplate compensator, it is also not altered by this compensator. By contrast, the other beam, after passing through the birefringent domain, emerges from the muscle as an ellipse. This elliptical beam is converted by the 1/4-waveplate to a plane-polarized beam with its plane of polarization rotated by 0.5 x /0.67 = 60 deg relative to incident beam (dotted line in Fig. 7B). The beams from the two domains will not recombine and, since they are at different angles, will not be extinguished by an analyser set at any angle. Thus, a test for a lack of effect due to heterogeneity of filament density is whether the analyser can completely extinguish the light passing through the muscle and compensator.
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The relatively wide angle between the thick line and the dotted line in Fig. 7B suggests that even a small contribution from non-birefringent portions of the specimen would increase the intensity of light coming through the analyser when it was crossed with respect to the beam derived from the birefringent portions of the muscle. To make a quantitative appraisal, consider the example of a resting muscle at the shortest length, which produced a mean phase angle of 86 deg with an optical system capable of resolving a 1% area that had no birefringence. Birefringence of the muscle tissue would cause the plane of polarized light emerging from the 1/4-waveplate to be rotated by 43.43 deg (= 0.5 x 86 deg/0.99). With the analyser set to 43.43 deg to extinguish light coming through the birefringent tissue, the 1% of light coming through the non-birefringent area would increase the detected intensity by 0.01 x sin243.43 deg = 0.47% of the total. This is 8 times greater than the 0.06% increase in the light reflected by the interface of the beam-splitting cube when a muscle was placed in the optical path, and 25% greater than the 0.37% increase in the light reflected by the interface (described under ‘Control observations’ in Methods). Thus the finding that the presence of a muscle did not significantly decrease light extinction strongly suggests: (1) that the optical system was incapable of resolving areas with different refractive indices; (2) that the relative absence of birefringence in the extracellular space had no effect on the measured value of mean birefringence; and (3) that changes of filament density due to cell shrinkage would not alter the measurements of overall birefringence.
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2 The James Hogg iCAPTURE Centre for Cardiovascular and Pulmonary Research, St Paul's Hospital, University of British Columbia, Vancouver, BC, Canada V6T 1Z3
Abstract
Birefringence and force produced by pig tracheal smooth muscles were recorded every 100 ms during electrically stimulated tetani at muscle lengths that varied 1.5-fold and at the peak of acetylcholine contractures at the same lengths. Isometric force was nearly the same at all lengths. Resting birefringence at the longest length was 30% greater than that at the shortest length. During tetani, birefringence increased with approximately the same time course as force, rising by 20% at the shortest length and 9% at the longest length, and continued to increase by an additional 0.5–1.5% of the resting value for 2–8 s after stimulation ended and force began to fall. This late increase was greatest and more sustained at longer lengths. During contractures, birefringence increased by 25 and 18% at the shortest and longest lengths, respectively. Comparison of these results with our published thick-filament densities suggests that thick-filament density increased by about 80, 72 and 50% during contractures at the short, intermediate and long lengths, and that 35% of birefringence in the resting muscle at the longest length was not due to thick filaments. These findings support the hypotheses that tracheal smooth muscle adapts to longer lengths by increasing thick-filament mass and that myosin thick filaments are evanescent, dissociating partially during relaxation and reforming upon activation. The results further suggest that thick-filament formation is sufficiently rapid to account for the velocity slowing and some of the force increase observed during the rise of activation of tracheal smooth muscle.
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Introduction
The large functional range of some types of smooth muscle suggests that they adapt to longer lengths by placing more contractile filaments in series (Ford et al. 1994; Pratusevich et al. 1995). Such plasticity would be facilitated if thick filaments were labile, dissociating partially during relaxation and reforming upon activation (Kelly & Rice, 1968; Shoenberg, 1969). Filament lengthening could account for the well-known velocity slowing and some of the force increase during the rise of activation (Seow et al. 2000). Support for these proposals came first from analysis of contractile parameters at different lengths and levels of activation (Pratusevich et al. 1995; Seow et al. 2000) and, more recently, from electron microscope measurements of thick-filament densities in relaxed and contracted muscles (Herrera et al. 2002, 2004; Kuo et al. 2003). To assess whether the structural changes are sufficiently rapid to account for the observed mechanical events, we have measured birefringence continuously in tracheal smooth muscle during contraction–relaxation cycles at different lengths. The birefringence signal was calibrated by comparing these optical responses during acetylcholine-induced contractures with our previously measured thick-filament densities (Kuo et al. 2003). Godfraind-De Becker & Gillis (1988a,b) and Gillis et al. (1988) have demonstrated that steady-state birefringence values and thick-filament densities increased when resting rat anococcygeus muscle passed from rest to noradrenaline contractures at a single length. Here we extend their findings to include dynamic changes during the rise of activation and assessments at different lengths. A brief account of this work has been presented to the Biophysical Society (Smolensky et al. 2004).
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Methods
Principle of the method
Birefringent material has two refractive indices, i.e. the speed of light is fastest when the plane of polarization of the light is parallel to one axis of the material and slowest when the plane of polarization is at right angles to this axis. It can either be an intrinsic property of molecular structures (intrinsic birefringence) or due to parallel structures, e.g. filaments, with dielectric constants different from the medium in which they reside (form birefringence). Form birefringence is a well-known property of striated muscle; A-bands are distinguished on the basis of being ‘anisotropic’, i.e. birefringent, and their birefringence results from the presence of thick filaments. Thus, increased density of smooth-muscle thick filaments should increase muscle birefringence. Furthermore, when the filaments occupy only a few per cent of muscle volume, birefringence varies nearly linearly with their density (see Appendix).
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The strength of birefringence, B, is defined as
where s and f, are the indices of refraction for the slow and fast axes, respectively. In muscle, the slow axis is parallel to the filaments and to the longitudinal muscle axis. It was measured here by passing plane-polarized light through a muscle with its plane of polarization at 45 deg to the slow and fast muscle axes. This single beam can be regarded as two beams with planes of polarization at right angles to each other, one parallel to the slow axis and the other parallel to the fast axis. Light traversing the slow axis is retarded relative to that traversing the fast axis by an amount, D, called the path difference, equal to the path length through the muscle, L, multiplied by the strength of birefringence:
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Path difference can be expressed either in dimensions of length or as a multiple of the wavelength of the light expressed as an angle, called the ‘phase angle.’ It was measured here using an extension of the method of de Senarmont-Friedel (Bennett, 1950; pp. 655–660). The retardation of light traversing the slow axis caused the trajectory of the tip of the electric vector of the light beam to widen from its initial, linear form to an ellipse. The elliptically polarized beam emerging from the muscle was collected by an objective and passed through a 1/4-waveplate specific to the wavelength of the He–Ne laser, 632.8 nm. This ‘de Senarmont compensator’ converted the elliptically polarized beam to a plane-polarized beam with its plane of polarization rotated from its initial orientation by half the phase angle.
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The beam exiting the compensator passed through a beam-splitting cube that separated it into two polarized beams with planes of polarization at right angles to each other. One beam, designated R, was reflected by an interface in the cube and passed horizontally out the side (Fig. 1). The other, designated T, passed upward through the interface. The two beams exiting the cubes were focused onto separate photodiodes.
See text for details.
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The beam-splitting cube was mounted in a rotatable tube fitted with a scale for measuring the angle of rotation of the cube. As the tube was rotated, the photodiode signals varied in proportion to the squares of sine and cosine of the angle of rotation. Angular deviation, a, from a reference point where the two signals were equal could thus be calculated as:
where IT and IR are the intensities of the two beams exiting the cube. The square root term arises because the photodiodes signal light intensity, which is proportional to the square of the amplitude of light oscillation in the beam.
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In the absence of a muscle, the photodiode signals were equal when the faces of the cube were at 45 deg to the plane of polarization of the light beam, and this position was taken as the zero rotational reference. The steady-state phase angle of a muscle could be determined as the degree of rotation needed to make the signals equal. The photodiode signals are most sensitive to tube rotation when they are equal. Thus, when making continuous measurements, tube rotation, C, was set so that a would pass through the value zero during recording. Birefringence at each time point was calculated from tube rotation C, and muscle thickness, L, as:
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where 632.8 is the wavelength of the laser light and a is in degrees.
Two potential sources of ambiguity can be recognized in eqn (3): (1) the sign of the square root is not revealed by the measurements themselves, and (2) an unrecognized passage of the phase angle through one or more half circles will produce substantially larger changes of phase angle for a given change in birefringence. Both ambiguities were avoided by using thin muscle segments. The mean values of phase angles for all conditions studied fell within the range of 86 to 138 deg, so that the rotation of the beam by the 1/4-waveplate ranged from 43 to 69 deg and were well within the first quadrant of rotation.
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Preparation and solutions
Pig tracheae were acquired from an abattoir licensed and supervised by the State of Indiana and studied using a protocol approved by the Animal Care and Use Committee of the Indiana University School of Medicine. The tracheae were stored at 4°C in physiological saline buffered with Hepes for up to 48 h before muscles were dissected for study. Strips measuring 0.8 mm wide x 0.3 mm thick x 3.5–4.0 mm at the longest length studied were dissected and mounted in aluminium foil clips (Ford et al. 1977), used to attach them to the apparatus. Muscle thickness was the extreme distance between the upper and lower surfaces measured with a reticle in the eyepiece of a dissecting microscope after rotating the muscle by 90 deg around its long axis and sighting along the two surfaces.
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To maintain a constant optical path length and to reduce tissue movement during contraction, a small area near the centre of the muscle was positioned in the optical path and compressed vertically by glass blocks. The lower block was a horizontal bar with edges ground away at 45 deg to leave a smooth, flat area 0.8 mm wide. When the muscle was stretched over this bar, its initial 0.3 mm thickness was reduced to 0.2 mm, mainly from a levelling of the irregular upper and lower surfaces. The upper block was glued to the underside of the cover glass for the trough. Its lower edges were ground at 45 deg to leave a flat square 0.8 mm on a side. This upper block was pressed into the upper surface of the muscle to reduce its thickness to 110 μm. This compression was relieved during muscle length changes.
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Muscles were studied at 37°C in physiological saline containing (mM): NaCl 112.5, NaHCO3 27.5, KCl 4.0, NaH2PO4 1.2, MgSO4 2.0, CaCl2 2, glucose 5 and perfused with 95% O2–5% CO2 to achieve pH 7.4.
Apparatus
A monocular microscope was modified to measure birefringence in functioning muscle. The stage of the microscope was equipped with a muscle chamber and force transducer (Fig. 1). Muscle strips were suspended in a 3 mm x 3 mm trough perfused with physiological saline at a rate of 1 ml min–1. Blacked platinum electrodes 8 mm x 3 mm were glued to sides of the trough. The trough was milled through the bottom in its central region, and an easily cleaned, 1-mm-thick glass plate was fitted into the bottom of the chamber. Solution was warmed as it entered the trough by passage through a hypodermic needle wrapped with wire. Constant electrical current through the wire maintained temperature at 37°C when the muscle was not being stimulated. Temperature rose by 0.5°C at the onset of stimulation and remained constant until stimulation ended.
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The trough was covered with a 1-mm glass plate from its upstream end to a point several millimetres downstream from the muscle. Solution was drawn away by suction from the uncovered end of the trough, producing a vertical meniscus where the cover-plate ended. The vertical lever arm of a laser-diode force transducer (Barb et al. 2000) projected into the uncovered trough, and horizontal tubing passed from the end of this lever through the vertical meniscus to reach the downstream end of the muscle. The position of the downstream clip was adjusted by a rack-and-pinion manipulator holding the force transducer to the microscope stage plate. At the upstream, covered end of the trough, a length of stainless-steel tubing passed through a seal to reach the muscle. The upstream clip was positioned by adjusting the hypodermic tubing in its seal. Separate positioning of the two ends of the muscle allowed the central region of muscle to be kept in the microscope's optical axis when muscle length was changed.
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Optics
For electronic measurements, illumination was provided by a He–Ne laser beam polarized at 45 deg to the muscle axes and focused to a circle 300 μm in diameter at the muscle (Fig. 1). Light passing through the muscle was collected by a 10 x (0.25 NA) objective and passed first through a 1/4-waveplate specific to the wavelength of the laser (632.8 nm) (part no. K43-698, Edmund Industrial Optics, Barrington, NJ, USA) and then through a beam-splitting cube (part no. K45-199, Edmund Industrial Optics). Polarizing filters were placed over the exit faces of the cube to improve its selectivity. The two beams exiting the cube were focused onto separate photodiodes.
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In addition to the arrangements described above for quantifying birefringence, colour changes resulting from the birefringence were observed using white light. A beam of incandescent light below the muscle was directed upward by a mirror mounted on a slide so that it could be moved in and out of the optical axis of the microscope. A photodiode and focusing lens could be replaced by a microscope eyepiece so that the muscle could be observed visually. When this was done, the beam-splitting cube served as an analyser, i.e. it passed plane-polarized light to an observer at one of the eyepieces, and the angle of polarization could be altered by rotating the cube.
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Recording and experiment control
Experiment control and digital data collection were achieved with a personal computer equipped with a Tecmar (Solon, OH, USA) Labmaster interface board driven by the SALT software package (Fenster & Ford, 1985). Muscles were stimulated to produce 12.5 s tetani at 5 min intervals throughout the experiments. The stimulator produced 1 ms square pulses of alternate polarity at 60 Hz. To reduce 60 Hz artifact and higher frequency noise, values of force and photodiode signals for each 100 ms interval consisted of averages of 67 points collected at 1 ms intervals, i.e. the signals were averaged over four cycles of the 60 Hz mains frequency. After averaging, the signals were stored and plotted before the next 100 ms cycle began.
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Protocols
After dissecting and mounting, muscles were adapted to the experimental environment by stimulating them to produce 12.5 s tetani for at least 1 h. During this adaptation, the length at which rest force was 10% of developed force, L10%, was determined, and this was the starting length in all experiments. For the experiments described here, force and birefringence responses were measured during multiple 12.5 s tetani at 5 min intervals, followed by the responses to a final acetycholine contracture. This contracture was initiated by electrical stimulation on the same 5 min schedule as the tetani and then sustained for 5 min by perfusing the muscle with physiological saline containing 10–4 M acetylcholine.
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The data presented here were obtained from 21 muscles studied in three groups of 7 muscles each. For the first group, data were collected only at L10%, although each muscle was first tested to be certain that developed force was relatively insensitive to length changes. The 14 muscles in the next two groups were studied first at L10%, at two-thirds this length, and at an intermediate length where rest force was 2% of developed force, which averaged 87% L10%. The second group was studied at the shortest length and then at the intermediate length so that the final contracture occurred at the intermediate length. In the final group, the order of length change was reversed, and the final contracture was made at shortest length. Thus, 7 muscles were studied with contractures at each length, 21 muscles were studied with tetani at L10% and 14 studied with tetani at each of the other two lengths.
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Muscles were adapted to each new length with at least six tetani before force and birefringence signals were recorded in five consecutive tetani. These five records were signal-averaged to obtain a single record for each length. At the end of the study, the averaged records for each muscle at each length were signal-averaged together to make the records displayed below. Mean values and standard errors of the means (S.E.M.) of force and birefringence were also calculated by averaging the values in the signal-averaged records for each muscle.
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Control observations
Specimen homogeneity. The Appendix considers the issue of whether local concentration of filaments, as within cells, affects measured birefringence and concludes that the effect depends upon the ability of the optical system to resolve the separate volumes. Such resolution causes dispersion of the angles of polarization of light passing through the 1/4-waveplate compensator, and thereby decreases extinction of light by the analyser cube. To assess such dispersion, extinction was measured in the presence and absence of seven resting muscles. In the absence of a muscle, the intensity of light reflected out the side of the analyser cube averaged 0.76% of the maximum value obtained when the cube was rotated by 90 deg. A muscle in the optical path increased transmission at maximum extinction insignificantly by a further 0.37 ± 0.38% (P > 0.3) of the maximum value obtained in the absence of the muscle. The corresponding values for the light passing upward through the interface in the cube were 1.32% without a muscle and a further 0.06 ± 0.47% (P > 0.8) in the presence of a muscle (level of significance was assessed using Student's paired t tests.)
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Absence of tissue movement in the optical path. An increase in the volume of tissue in the optical path would increase the optical retardation and apparent birefringence. As discussed below, Godfraind-De Becker & Gillis (1988b) found that smooth muscle thickness and cell cross-sectional area decline during prolonged contractures. This finding raises the question whether changes in cell volume might have influenced the present results. As discussed below, a decrease in cell volume, without a change in tissue volume, would have no effect, but an increase in the number of cells being sampled by the optical beam would increase the apparent birefringence. Compression of tissue between glass blocks limits tissue movement to reductions of the width of the tissue, with new tissue moving into the optical path from the edges of the muscle. Such movement into the optical path was not seen when muscles were observed directly. In addition, movement of any sort distorted the optical records in a recognizable way. In the absence of movement, the records from the two diodes were nearly mirror images when the records were scaled in proportion to their maximum amplitude. By contrast, movement of the tissue in the beam, particularly when associated with a change in tissue volume, caused the two signals to deviate in the same direction. When such signals were recorded, the muscle was discarded.
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Results
Muscles were studied over a 1.5-fold length range, with the longest length being that where rest force was 10% of developed force (L10%). Signal-averaged records of birefringence during tetani at three lengths are shown on an absolute scale in Fig. 2. Resting birefringence was substantially greater at the longer lengths, while the increase in birefringence during tetanic stimulation was greatest at the shortest length. To illustrate the time course of birefringence relative to force, the two signals were normalized to the increase they underwent during electrical stimulation and are superimposed in Fig. 3, with separate plots for each of the three lengths studied. Birefringence and force rose in close association, with force leading slightly at the longest length and lagging slightly at the shortest length but when stimulation ended, the records diverged. Force began to fall almost immediately, while birefringence continued to rise for 2–8 s before falling. At the longest length, where the late rise was greatest, there appeared to be a slight acceleration in the rate of rise. At this length, there was also a very small decrease in birefringence shortly after the onset of stimulation, shown in the inset of Fig. 2.
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Muscles were adapted at the three lengths indicated at the ends of the records, and recording began 0.1 s before a 12.5 s electrical stimulation. The inset below the upper record shows the first 0.8 s of recording at this length, with the birefringence scale amplified 50-fold and the time scale amplified 15-fold.
Increase in force and birefringence with 12.5 s electrical stimulation, normalized to their increases during the stimulation.
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To compare the time course of the birefringence changes at the three lengths, the records have been scaled to the increase that occurred during stimulation and superimposed in Fig. 4, which shows that they were almost exactly coincident during the rise of activation and diverged when stimulation ended. Thus, the slight changes in the time course of force relative to birefringence shown in Fig. 3 were due entirely to small lags in force development at the shorter lengths and not to increases in the relative speed of the optical signal at the longer length.
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Birefringence records at three lengths superimposed to show the similarity of time course during the rise of activation and the divergence when stimulation ended.
The values of birefringence and force at the different lengths are plotted in Fig. 5. The force plots (Fig. 5 lower panel) include rest force, total tetanic force (rest force plus force developed during tetani), and total force achieved during acetylcholine contractures. These force plots show that developed force was relatively constant over the range of length studied, especially during contractures. For tetanic stimulation, two birefringence values are plotted in Fig. 5 upper panel: the level achieved at the end of stimulation and the peak value achieved after stimulation ended. The birefringence plots show that, for electrical stimulation, the birefringence increase was greatest at the shortest length (20.5% of the resting value at end stimulation, 21.1% at peak) and smallest at the longest length (8.7% at end stimulation, 10.2% at peak). For contractures, the relative increases of birefringence were more similar, 25, 25 and 18%, at the short, intermediate and long lengths, respectively.
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Each panel plots separately the resting values (), values at the end of electrical stimulation (), and peak values achieved during acetylcholine contractures (). For the electrically stimulated muscles, two birefringence values are plotted: the value at the end of stimulation () and the peak value achieved after stimulation ended (). Active force plotted is total force, i.e. rest force plus developed force. Error bars indicate S.E.M. for the absolute values.
These optical findings are compared with our published values of thick filament density below.
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Discussion
The principal findings in these experiments are that birefringence of tracheal smooth muscle was greater at longer muscle lengths, increased immediately with activation, and decreased following relaxation. Together with earlier measurements of thick filament density in electron micrographs, the results suggest that thick filaments dissociate partially during relaxation and reform with activation. The observation that the optical changes occurred on the same time scale as force further suggests that filament elongation was likely to alter contractile properties of the muscle as activation rose. Longer filaments will develop more force per filament and therefore contribute to the overall force development during activation (Gillis et al. 1988; Seow et al. 2000). Filament lengthening is also likely to contribute to a parallel decline in velocity, since fewer long filaments are needed to span the length of the muscle (Seow et al. 2000). It is well known that velocity declines during the rise of activation (Johansson, 1973; Dillon et al. 1981; Dillon & Murphy, 1982; Kamm & Stull, 1985). The optical records here indicate that filament formation was sufficiently rapid to account for the observed decline.
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The results also indicate that there was a greater fractional volume of thick filaments at longer adapted muscle lengths. The volume of muscle sampled at the different lengths was the same in all cases because the cross-sectional area of the sampling light beam was the same, and compression of the muscle between glass blocks ensured that sample thickness and optical path remained constant at different lengths. To the extent that overall muscle volume was also constant at the different lengths (Kuo et al. 2003), the volume sampled was a constant fraction of the overall muscle volume at all lengths. The finding that birefringence of the fixed sample volume was increased at the longer lengths is strong evidence that the fractional volume of thick filaments in the muscle increased at longer lengths, further supporting the hypothesis that length adaptation is achieved by plastic alterations that place more thick filaments in series at longer lengths (Ford et al. 1994; Pratusevich et al. 1995).
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Dynamics of filament formation
It has been observed that thick filaments form in solution even when the light chains are not phosphorylated, and that phosphorylation increases the tendency of filament formation (Kendrick-Jones et al. 1987). This observation suggests that filament formation proceeds by mass action and that phospholylation is not a requirement for filament formation but simply a facilitator. The apparent dynamic equilibrium between filamentous and monomeric myosin would also explain the speed of filament formation, once phosphorylation begins. It would also explain why filaments do not dissociate completely during relaxation and why interventions, such as length oscillations (Kuo et al. 2001) or lowered calcium (Herrera et al. 2002), which lower thick filament density, do not cause filaments to dissociate completely. The presence of a substantial number of filaments in the resting state explains how force development and filament formation occur simultaneously without a delay in force production.
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Factors other than filament formation which may alter birefringence
Crossbridge head movement. Opposite changes in birefringence occur in skeletal muscle, which have more permanent thick filaments; birefringence falls by 9–11% upon activation (Eberstein & Rosenfalck, 1963; Irving, 1984, 1993). This decline is associated with a change in X-ray diffraction patterns suggesting swinging of crossbridge heads away from the thick-filament backbone and possibly changes in crossbridge orientation with respect to the filament axis (Peckham & Irving, 1989). The birefringence increase after stimulation ended in the present experiments suggests that similar movements of crossbridge heads diminished birefringence during activation. Thus, there appear to be two competing effects that contributed to the change in optical signal during the rise of activation: an increase caused by the formation of new filaments and a smaller decrease caused by crossbridge head movement on formed thick filaments. In comparing the birefringence signal from contracted and relaxed muscle, it is important to take account of the decreased signal expected in contracted muscle, as is done below.
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Further suggestion of crossbridge movement is provided by the small birefringence decrease at the outset of activation at the longest length and by the observation that the greatest rise at the end of stimulation also occurred at the longest length. The more obvious changes at this length are due to at least two factors: (1) more formed thick filaments in the resting muscle at the outset of activation, as indicated by the higher resting birefringence, and therefore more crossbridges moving at the onset of activation; and (2) less birefringence increase to obscure the small fall due to crossbridge movement. These factors only partially explain the differences, however, because the rise in birefingence is prolonged as well as increased at longer lengths. It seems likely that thick filaments are more stable at longer lengths, and this increased stability may be reflected in the delay in the decline of birefringence after stimulation ended.
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Cell volume changes. An important issue that must be considered is the effect of cell volume changes on measured birefringence. Godfraind-De Becker & Gillis (1988b) found a substantially larger birefringence increase, 48%, during contractures of anococcygeous muscle, but a large part of this increase was calculated on the basis of muscle thinning and therefore reduction of the optical path through the muscle. The increase in optical retardation, 30%, was much closer to the 18–25% increase observed here. Some of their observed increase in optical retardation may also have been due to decreases in muscle width bringing more cells into the field of view. The decrease in muscle thickness in these experiments was matched by a proportional decrease in the cross-sectional areas of the cells measured by electron microscopy (Gillis et al. 1988).
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Tissue volume changes as seen by Godfraind-De Becker & Gillis (1988b) are unlikely in the present experiments because the muscle was compressed between glass blocks that impeded lateral tissue movement while maintaining a constant optical path. Tissue volume shrinkage during activation must result from volume contraction of the individual cells caused by water movement from the intracellular to the extracellular spaces. By itself, this change in the distribution of water will not alter the population of cells being monitored or the number of filaments being sampled optically. As explained in the Appendix, the concentration of the filaments in smaller cells will not alter the optical retardation signal. An increase in optical retardation requires that the number of cells and filaments be increased. In the present experiments, an increase in the number of cells would require that tissue move into the area being compressed by the glass blocks. As explained at the end of Methods, such movement was not observed. In addition, it seems unlikely, because it would require the simultaneous exchange of extracellular water for cells within the relatively small gap between the blocks.
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Filament alignment. Birefringence would have increased if filaments became straighter and more parallel during the rise of force. While a small contribution from such straightening cannot be excluded, there are two distinctly different arguments against a large contribution. The first is that very little deviation from parallel alignment is seen in the relaxed muscle (Gillis et al. 1988; Kuo & Seow, 2004). Gillis et al. calculated that half the filaments would have to have deviated by +25 deg and half by –25 deg to account for all the birefringence increases they measured, while the observed deviations from a parallel orientation are very much smaller.
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The second argument against filament realignment is that the filaments would support relatively little force until their alignment became parallel to the direction of stress. If such realignment were substantial, it would produce a large increase in birefringence before much force was developed. The absence of a substantial initial lead in birefringence as compared with force thus argues against filament straightening as a major cause of the rise in birefringence.
, http://www.100md.com Correlation with prior measurements of filament density
We have previously measured thick-filament densities in electron micrographs of the preparation studied here in similar contractures over the same length range (Kuo et al. 2003). These densities, expressed as the number of filaments per square micrometre of organelle-free cytoplasm, are compared graphically in Fig. 6 with the birefringence values in Fig. 5. The filament densities in the present experiments were estimated by interpolating the values determined from the earlier electron microscope studies and are plotted (as filled symbols) against the birefringence values obtained during contractures. The relationship is linear, as expected when the volume fraction of the thick filaments is less than a few per cent (see Gillis et al. 1988 for discussion).
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For relaxed muscles (open symbols), birefringence values have been reduced by 10% to account for crossbridge movement during activation and plotted on the line fitted to the data for muscles in contracture. The values for filament density in the relaxed muscle were read from the abscissa scale.
A linear regression fitted to these three points extrapolates to a birefringence intercept of 6.2 x 104 with a slope of 14 x 104 per 100 filaments μm–2. The intercept corresponds to 35% of the value in the resting muscle at the longest length and 45% of the resting value at the shortest length. Godfraind-De Becker & Gillis (1988a) found a similar 30–35% residual birefringence when myosin was extracted from their resting muscles at a single length. They also found that extraction of actin reduced this residual to 18–20% of the total resting birefringence.
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Estimation of filament density increase during activation
To estimate filament densities in relaxed muscles, the birefringence values at each length were reduced by 10% to account for crossbridge movement and plotted (open symbols) on the line fitted to the values for contractures. Filament densities in the relaxed muscle at the three lengths were then read from the abscissa scale of Fig. 6. Comparison of the filament densities in relaxed and contracted muscle in Fig. 6 indicates that the estimated value of filament density increased by 80, 72 and 50%, respectively, for short, medium and long lengths.
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A recent electron microscope study of thick-filament density (Herrera et al. 2004) found similar increases of 63 and 82% during acetylcholine contractures at in situ length and 1.5 times that length. It should be emphasized, however, that there is some variability in thick-filament density increases in different studies. An earlier study by Herrera et al. (2002) found a 144% increase in thick filament density associated with contracture. Similarly, an early study by Gillis et al. (1988) found a 95% increase in filament density, while a later study by Gillis and coworkers (Xu et al. 1997) found only a 23% increase in density in the same muscle under similar conditions. The mean of these two values, 59%, is similar to the increases found here. The main point to be made from these comparisons is that in some smooth muscles, including tracheal muscle and anococcygeus muscle, thick-filament density definitely increases with activation. Equally importantly, it should be emphasized that one study showing a definite increase in filament density during activation of anococcygeus muscle (Xu et al. 1997) showed no increase in the taenia coli muscle. Thus, it is possible that filament dissociation during relaxation occurs in only some smooth muscles.
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Thin filament density changes. This analysis has focused on thick-filament density changes, partly because there are more electron microscope data about thick-filament densities and partly because thin filaments create less brirefringence, particularly in striated muscle. On the other hand, the ratio of thin to thick filaments is much higher in smooth muscle, creating 18–20% of resting birefringence (Godfraind-De Becker & Gillis, 1988b). A recent study found that mean actin filament density increased by 24% when muscles were placed in contracture (Herrera et al. 2004). If actin filament density increased by 24%, it would increase birefringence by 5%, equivalent to 20–25% of the total birefringence increase seen during contractures here. Such an increase would not change the conclusions here if thick and thin filaments change density in parallel.
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Comparison with earlier work
As described above, Godfraind-De Becker & Gillis (1988a,b) and Gillis et al. (1988) have measured similar increases in birefringence in rat anococcygeus muscle during contractures. In these earlier experiments, only one length was studied, and birefringence was measured manually in a two-step process, focusing separately on the muscle surfaces to measure their thickness and then adjusting the analyser to measure light extinction. Measurements could not be made when the optical changes were occurring rapidly, as at the onset of activation. Their earliest measurements were made about 5 min after the onset of a contracture, and time resolution after that was about 1 min. Thus, the present experiments extend their pioneering work to different muscle lengths and more rapid time resolution at the onset of activation.
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Although a different preparation was used and much higher time resolution achieved, the steady-state results described here are in close agreement with the earlier studies. The resting birefringence at the shortest length measured here, 13.6 x 10–4, was close to the 8.8 x 10–4 for anococcycgeus and 13.4 x 10–4 for taenia coli in the earlier experiments. The increase in birefringence during contractures was substantially greater in the earlier experiments, 48 versus 25% for the shortest length studied here, but, as discussed above, 38% of the increases was due to decreases in muscle thickness. The increase in optical retardation, 30%, was not much greater than the 25% found during contractures here.
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Finally, we would be remiss if we did not acknowledge that the inspiration for this work derived from the early work of Shoenberg (1969) and Rice et al. (1970), who suggested that the thick filaments in the smooth muscles they studied were evanescent, forming on activation and dissociating during relaxation. Although their suggestion was not widely accepted, it did offer a plausible explanation for the ability of some smooth muscles to adapt to wide ranges of length, namely through filament lattice plasticity. The present work suggests that the earlier interpretations were correct.
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Appendix
The issue considered is whether birefringence measured in whole muscle is influenced by a non-uniform distribution of filaments, and, more specifically, whether cell volume changes during activation alter the measured birefringence independently of changes in average filament density. Such local volume changes could be produced, for example, by water movement into or out of cells during activation, without a change in the overall tissue volume or population of cells sampled by the light beam. The effects of such local concentration differences depend upon the system of illumination and/or the resolving power of the optical system. Before considering this issue, it is important to recognize that there should be a linear relationship between average filament density and overall birefringence when the optics permit.
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As discussed by Gillis et al. (1988), Wiener's equation for form birefringence, B, in terms of the volume fractions and refractive indices of filaments and medium suggest that birefringence is a nearly linear function of filament density when the filaments occupy only a few per cent of overall tissue volume. To the extent that the relationship is linear, each domain in the muscle will contribute to the overall birefringence in proportion to the number of filaments it contains. Overall muscle birefringence will then reflect the average filament density when the optical arrangements do not cause domains with different filament concentrations to contribute disproportionately to the measured birefringence.
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To show the effect of the different optical systems, two extreme forms of illumination are considered. For both cases, the specimen is divided into two areas. One is non-birefringent and occupies the fractional volume 1 – f. The other area occupies the fractional volume f and has birefringence equal to B/f, where B is the average birefringence of the muscle. This causes the phase angle produced by the birefringent area to equal /f, where is the mean phase angle for the muscle. For the specific case illustrated in Fig. 7, is 80 deg, slightly less than the lowest minimum mean value recorded here, 86 deg, and f is 67%, slightly greater than the 65% value for the intracellular area measured by Gillis et al. (1988).
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See text for details.
Case I. Coherent laser illumination arranged so that phase and intensity are the same at all points in the field
(A similar result would probably occur if the volumes of material containing different concentrations of filaments are smaller than the resolving power of the microscope.)
Figure 7 shows the patterns traced by the tips of the electric vectors of monochromatic light beams before and after passing through a muscle lying in the plane of the paper and then through a 1/4-waveplate compensator. The long (slow) muscle axis is parallel to the x-axis (labelled S), the transverse axis (fast) is parallel to the y-axis (labelled F), and the light passes along the z-axis, through the paper. The incident beam is plane-polarized at 45 deg to the muscle axes, and the tip of its electric vector traces a straight line (continuous line in Fig. 7A). This beam can be regarded as consisting of two perpendicular beams polarized parallel to the two muscle axes. Light passing along the slow axis is retarded relative to that passing along the fast axis by the path difference. Because of the coherence of the laser beam, light coming from the two domains within the muscle cannot be distinguished, and all light parallel to the slow muscle axis is retarded equally. This retardation causes the tip of the electric vector of the beam emerging from the muscle to trace a single ellipse with axes parallel and perpendicular to the original beam.
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The 1/4-waveplate compensator converts the elliptical beam to a plane-polarized beam rotated by half the phase angle, /2, from the original 45 deg orientation of the incident beam (dashed line in Fig. 7A). In the absence of any other factors, this beam will be extinguished completely by the analyser.
Case II. Standard microscope illumination of uniform brightness with optics capable of resolving the two domains
In this case, the phase of the light varies randomly from one point in the field to another, and there is no interference of light from different points in the field. The plane-polarized beam incident on the muscle is regarded as two separate, superimposed beams passing through the birefringent and non-birefringent domains, respectively, and having intensities 0.67 and 0.33 of the original beam (narrow and wide continuous lines in Fig. 7B). (The amplitudes of oscillations illustrated for these beams are 0.82 = 0.67 and 0.58 = 0.33 times the amplitude of the initial beam because their intensities, proportional to the square of their amplitudes, are additive.) The beam passing through the non-birefringent domain emerges from the muscle unchanged. In addition, since its axis is parallel to that of the 1/4-waveplate compensator, it is also not altered by this compensator. By contrast, the other beam, after passing through the birefringent domain, emerges from the muscle as an ellipse. This elliptical beam is converted by the 1/4-waveplate to a plane-polarized beam with its plane of polarization rotated by 0.5 x /0.67 = 60 deg relative to incident beam (dotted line in Fig. 7B). The beams from the two domains will not recombine and, since they are at different angles, will not be extinguished by an analyser set at any angle. Thus, a test for a lack of effect due to heterogeneity of filament density is whether the analyser can completely extinguish the light passing through the muscle and compensator.
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The relatively wide angle between the thick line and the dotted line in Fig. 7B suggests that even a small contribution from non-birefringent portions of the specimen would increase the intensity of light coming through the analyser when it was crossed with respect to the beam derived from the birefringent portions of the muscle. To make a quantitative appraisal, consider the example of a resting muscle at the shortest length, which produced a mean phase angle of 86 deg with an optical system capable of resolving a 1% area that had no birefringence. Birefringence of the muscle tissue would cause the plane of polarized light emerging from the 1/4-waveplate to be rotated by 43.43 deg (= 0.5 x 86 deg/0.99). With the analyser set to 43.43 deg to extinguish light coming through the birefringent tissue, the 1% of light coming through the non-birefringent area would increase the detected intensity by 0.01 x sin243.43 deg = 0.47% of the total. This is 8 times greater than the 0.06% increase in the light reflected by the interface of the beam-splitting cube when a muscle was placed in the optical path, and 25% greater than the 0.37% increase in the light reflected by the interface (described under ‘Control observations’ in Methods). Thus the finding that the presence of a muscle did not significantly decrease light extinction strongly suggests: (1) that the optical system was incapable of resolving areas with different refractive indices; (2) that the relative absence of birefringence in the extracellular space had no effect on the measured value of mean birefringence; and (3) that changes of filament density due to cell shrinkage would not alter the measurements of overall birefringence.
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