Quantized nature of sarcomere shortening steps

STEP SIZE IN ACTIVATED RABBIT SARCOMERES IS INDEPENDENT OF FILAMENT OVERLAP

Investigations carried out on single cardiac and bumblebee myofibrils have shown stepwise sarcomere-length change of ~2.7 nm.1 We have carried out parallel measurements on single myofibrils from rabbit psoas muscle. Activated specimens were released or stretched using a motor-imposed ramp. With a high-resolution algorithm, we found that step sizes were always integer multiples of 2.7 nm, whether the length change was positive or negative, and independent of ramp velocity. Also, the influence of initial sarcomere length was studied, and found to be negligible. The value 2.7 nm, seen consistently, is equal to the linear repeat of actin monomers along the thin filament, a result that ties dynamical events to molecular structure, and places narrow constraints on any proposed molecular mechanism.

The role of aqueous interfaces in the cell

The cell is rich with biopolymeric surfaces. Yet, the role of these surfaces and attendant surface-water interfaces has received little attention among biologists, most of whom consider water as a neutral carrier. This review aims to begin bridging the gap between biology and interface science-to show that a surface-oriented approach has power to bring fresh insights into an otherwise impenetrably complex maze. In this approach the cell is treated as a polymer gel. If the cell is a gel, then a logical approach to the understanding of cell function is through an understanding of gel function. Great strides have been made recently in understanding the principles of polymer-gel dynamics, and particularly the role of the polymer-water interface. It has become clear that a central mechanism in biology is the phase-transition-a major structural change prompted by a subtle change of environment. Phase-transitions are capable of doing work and such work could be responsible for much of the work of the cell. Here, we pursue this approach. We set up a polymer-gel-based foundation for cell behavior, and explore the extent to which this foundation explains how the cell achieves its everyday tasks.

Is the cell a gel--and why does it matter?

That the cell is a gel is broadly acknowledged. Textbooks begin with this assertion-and then proceed with great abandon to derive mechanisms based on free diffusion, as though the gel concept were groundless and cell was an aqueous solution. This disconnect emerges in part because the behavior of gels is not well understood, particularly among most biologists. Recently, great strides have been made in the understanding of gel behavior. It has become clear, for example, that a central mechanism in gel function is the phase-transition-a qualitative structural change prompted by a subtle change of environment, not unlike the transition from ice to water. Phase-transitions are capable of doing work. If the cell is a gel, then a logical approach to understanding cell function is to understand gel function-especially whether some role may be played by the phase-transition. Here we pursue this approach. We first consider the dichotomy of the cell as a gel and the cell as an aqueous solution. We then set up a gel-based foundation for cell behavior, in which the gels' physical chemical features are used to explore how the cell achieves its everyday tasks. If there is a common underlying mechanism of cell function, it appears that the polymer gel phase-transition could well be a candidate.

Cardiac twitch properties simulated by three-states model

We examined whether the three states model can explain the systolic and relaxation properties of cardiac muscle to clarify what factors affect these properties. Changing the values of the parameters describing the calcium transient and calcium sensitivity, we estimated the effects of these parameters on the systolic and relaxation properties of twitch contraction. The simulations showed the following four features: 1) An increase in the maximum calcium concentration and calcium sensitivity, and a prolongation of the calcium transient led to an increase in peak tension associated with an increase in the time to peak tension. 2) An increase in myosin ATPase activity led to an increase in peak tension associated with a decrease in the time to peak tension. 3) An increase of peak tension was accompanied by a prolongation of the late systolic period. 4) The constant of the late tension relaxation from 25% to 10% of the peak tension was altered when the crossbridge cycling rate, the resting calcium concentration or the late decline of the calcium transient was changed. The simulation were not contradictory to the experimental results and showed that three state muscle model can provide qualitative descriptions on the systolic and relaxation characteristics of cardiac muscle.

Quantal length changes in single contracting sarcomeres

The time course of shortening was investigated in the single sarcomere, the smallest contractile unit that retains natural structure. We projected the striation patterns of single bumblebee flight-muscle myofibrils onto a linear photodiode array, which was scanned periodically to produce repetitive traces of intensity vs. position along the array. Sarcomere length was taken as the span between adjacent A-band or Z-line centroids. When myofibrils were ramp-released by a motor, individual sarcomeres shortened in steps punctuated by pauses. The single sarcomere-shortening trace was consistently stepwise both in activated and relaxed specimens. Although step size was variable, the size distribution showed a signature-like feature: the histogram comprised distinct peaks that were spaced quasi-regularly. In the activated myofibrils the interpeak separation corresponded to 2.71 nm per half-sarcomere. This value is equal to the linear advance of actin subunits along the thin filament. Thus, actin filaments translate over thick filaments by steps that may be integer multiples of the actin-subunit spacing.

Z-line structural diversity in frog single muscle fiber in the passive state

The structural changes of the Z-line between small square net (ss) and basket weave (bw) cross-sectional patterns were examined using intact single fibers and mechanically skinned fibers in the passive state to determine if the pattern is related to the sarcomere length (SL) and if the pattern undergoes a reversible transition in low- and high-osmotic medium. Frog single fibers were isolated from the anterior tibial muscle in Ringer's solution. Entirely or partially skinned single fibers were prepared in relaxing solution (also called low-osmotic medium). The high osmotic medium contained 10% polyvinylpyrrolidone (PVP) in relaxing solution. The sarcomere length (SL) of each fiber was measured directly by use of a laser beam or indirectly from electron micrographs with use of a correction factor. The ss and bw forms in cross sections were quantified by analysis of electron micrographs. The results show that the structural change of Z-line occurs around bw << 2.3-2.4 microns << ss (n = 25) and bw << 3.1-3.2 microns << ss (n = 13) in intact single fibers and skinned fibers, respectively. With the quick freeze-freeze substitution method, an intact single fiber with a SL of 2.35 microns showed almost 100% of ss form. The structural transition in cross section was also confirmed in four partially skinned fibers, where patterns went from mostly ss form (intact portion) to mostly bw form (skinned portion) at the SL between 2.40 to 3.20 microns. The reversibility of the change between ss and bw was proved by using low- and high-osmotic medium. The transition and reversion of cross-sectional patterns both occur in the passive state.

Implications of quantal motor action in biological systems

We demonstrate in this paper that quantal behavior is a central feature of biological motile and contractile systems. Step-like behavior has been demonstrated in the interaction between single molecules and filaments both in the kinesin-microtubule system and in the myosin-actin filament system. We show here that the step-like molecular features appear also in the single intact sarcomere. We studied single sarcomeres of single bumble-bee myofibrils, both in the unactivated and activated states. Myofibril-length changes induced by a motor-imposed ramp were accompanied by corresponding sarcomere-length changes. However, the sarcomere-length changes were stepwise. Computer analysis of the stepwise shortening patterns revealed a step-size distribution containing multiple peaks. In the activated state, the peaks were separated by 2.7 nm per half-sarcomere which is the linear actin-subunit spacing. Thus, translation steps are an integer multiple of the actin-subunit spacing. This result parallels the one observed in the kinesin-tubulin spacing, where step size is a multiple of the tubulin-subunit spacing. In the muscle system, however, the steps are preserved on a macroscopic scale, implying high synchrony. The quantal steps are easily explained by a model in which the actin filament propels itself over stationary cross-bridges: if actin binds to the cross-bridges between steps, then the observed quantal result is inevitable. As probes of contractile phenomena approach the molecular level, the discrete unitary events underlying contraction begin to emerge. Thus, step-like behavior is observed as the single kinesin molecule translates along the microtubule, as the single myosin molecule translates over the actin filament, and as the single isolated titin molecule is stretched.

Stepwise dynamics of connecting filaments measured in single myofibrillar sarcomeres

Single relaxed myofibrils of bumblebee flight muscle were subjected to motor-imposed ramp-length changes. The image of the striations was projected onto a linear photodiode array, and sarcomere length was computed as the spacing between centroids of contiguous A-bands. Centroid position was determined by integrating the respective A-band intensity peak and computing the location at which the area on one side was equal to the other. The resulting trace of centroid to centroid span versus time was stepwise, with periods of rapid shortening alternating with periods of pause. An alternative nondiscrete sensor gave similar steps. If thick filament length remains constant, stepwise sarcomere length changes imply that length changes in the connecting filament must be stepwise. Thus, shortening of the connecting filament occurs as a sequence of discrete events rather than as a continuous event.

Theoretical treatment of striated muscle: Dynamic extension of four-state model

We constructed a muscle model, based on the model first proposed by Gray and Gonda [6,7), that simulates the twitch contraction of striated muscle. Their original model postulated four basic states in the contraction cycle and predicted the properties of steady state contraction in striated muscle. Using the relationship between steady state tension and calcium concentration, we described several rate constants as functions of calcium concentration and calculated the number of attached crossbridges at various calcium concentration values. The results for both skeletal and cardiac muscle were approximately consistent with those of X-ray studies. Assuming that rate constants change immediately with the phasic alteration of intracellular calcium concentration, we estimated the time course of crossbridge distribution during twitch contraction; these findings were also consistent with those of X-ray studies. We also simulated the effects of calcium concentration and sarcomere length on the magnitude of twitch tension. These simulations suggest that the major determinants of crossbridge distribution during twitch contraction are the time courses of calcium transients and the rate constants of crossbridge kinetics. Our findings suggest that the model used in this study provides a theoretical basis for interpreting the characteristics of cardiac muscle encountered in the clinical setting.

Identification of source of oscillations in apparent sarcomere length measured by laser diffraction

The most widely used technique for dynamic estimates of sarcomere length in muscle is laser light diffraction. We have identified conditions under which artifactual oscillations can arise in apparent sarcomere length measured by this technique and report methods to reduce the effect. Altringham et al. (1984) first reported that the diffraction angle can exhibit one cycle of oscillation for each sarcomere length displacement of the illuminated portion of the fiber. We find that the amplitude of similar oscillations is strongly dependent on the intensity of light scattered from objects near the fiber and on the spacing between fiber and scatterer. The oscillations can be eliminated by minimizing scattered light and positioning the fiber a few millimeters from sources of scattering. A theoretical description shows that oscillations of this kind are expected from interference of scattered and diffracted light. Interference fringes were observed along the meridian of the pattern, and these moved during translation of either a fiber or a grating. The movement of fringes across the diffraction order shifts the centroid back and forth and, when associated with steady shortening, can give rise to "steps" and "pauses" in apparent striation spacing.

Measurements of sarcomere dynamics simultaneously with auxotonic force in isolated cardiac cells

We developed an easy to use and non-invasive method to study sarcomere motion of enzymatically isolated myocytes which can be simultaneously combined with auxotonic force detection, thus being very useful when studying the contractile performance of cardiac cells. This method basically consists in analyzing the periodicity of the cell striation pattern using the Cooley-Tukey fast Fourier transform (FFT) algorithm on a video image of the cell during the course of the experiment. A longitudinal fraction of the cell image is recorded with a CCD TV camera, digitized, then transiently stored on a computer and used to calculate the spectrum corresponding to the distribution of the sarcomere lengths (SL). The method gives a real-time measurement of the most probable value of sarcomere length in one isolated cell with a temporal resolution of 20 ms. When used on a cell attached between two carbon fibers, the auxotonic force developed by the cell upon electrical stimulation can be simultaneously measured together with the SL in various conditions of stretch. Preliminary results have been presented in abstract form (Gannier et al., vol 24, pp. S47, 1992).

Sarcomere dynamics during isotonic velocity transients in single frog muscle fibers

If the load on a tetanized fiber is abruptly changed to a new steady value, the ensuing fiber length change shows the well-known "isotonic velocity transient," in which the velocity oscillates before settling at some steady value. We studied sarcomere dynamics during these transients using two methods: optical diffraction and a segment-length method. Our principal aim was to determine whether these transients might be a reflection of the fact that sarcomere shortening is often found to be stepwise. We found that pauses in sarcomere shortening occurred during the low-velocity phases of the transient and that steps of sarcomere shortening occurred during the high-velocity phases. Thus the isotonic transient appears to arise from the steps. In addition to the isotonic transient, we studied the well-known isometric transient, in which fiber length is abruptly changed, and ensuing tension response is measured. Again, we found that the transient may be a reflection of the stepwise shortening pattern.

A laser diffraction system with improved sensitivity for long-time measurements of sarcomere dynamics in isolated cardiac myocytes

To measure the mechanical activity of enzymatically isolated mammalian myocytes the principle of laser light diffraction was used. Since the viability of isolated cardiac myocytes showed a marked dependence on the laser power used, an opto-electronic system with improved light sensitivity and low susceptibility to optical noise was developed. The high sensitivity was achieved by a novel approach in the detection of diffraction patterns, that provides a significant reduction of the amount of laser power required. This improvement rendered possible the application of laser diffraction during extended experiments including pharmacological interventions. The static performance of the system, as assessed by means of calibration gratings, showed a resolution in the order of 5 nm for small changes in sarcomere length in the range from 1.2 microns to 2.0 microns. Examples of measurements on resting and contracting cells are presented, and the limitations of the application of the system to biological specimens are discussed.

Theoretical Fraunhofer light diffraction patterns calculated from three-dimensional sarcomere arrays imaged from isolated cardiac cells at rest

Sarcomere striation positions have been obtained throughout the volumes of calcium-tolerant resting heart cells by direct computer interfaced high-resolution optical imaging. Each sarcomere position is stored in a three-dimensional (3-D) matrix array from which Fraunhofer light diffraction patterns have been calculated using numerical methods based on Fourier transforms. Diffraction patterns have been calculated from heart cell data arrays oriented normal to a theoretical laser beam. Twelve characteristic features have been identified and described from these diffraction patterns that correlate to diffraction phenomena observed from both cardiac and skeletal muscle. This numerical approach provides the means to directly assess diffraction pattern formulation, the precision of layer line angular separation, layer-line intensity and angular asymmetries, line widths and fine structures in terms of the known diffracting source structures. These results confirm that theoretical calculations can predict real muscle diffraction patterns and their asymmetries.

Stepwise shortening of muscle fibre segments

Shortening dynamics were measured in single fibres of frog skeletal muscle using a system that could track the spacing between hairs mounted on the fibre surface. Segment length changes were predominantly stepwise. The objective of the study was to identify potential artifacts and check their relevance. Several possible causes of artifactual steps were evaluated quantitatively and ruled out. In addition, the surface marker method and an independent length-detection method based on light diffraction were used simultaneously. The concurrence of results confirmed that it is highly unlikely that stepwise shortening could arise out of instrument artifact. Possible mechanisms underlying the phenomenon are considered.

Nonsteady motion in unloaded contractions of single frog cardiac cells

We studied the mode of shortening of enzymatically isolated single frog cardiac cells with a high-speed videosystem to see whether or not shortening is smooth. The segmental shortening of the cell in response to electrical stimulation exhibited a clear pause following the initial shortening over a distance of approximately 11 nm/half-sarcomere. Several preparations showed a second pause following the initial one. Nonsteady motion with a pause lasted usually a few tens of milliseconds. The duration of nonsteady motion was shorter in cells with large velocities of steady shortening following the pause than those with smaller velocities.

Stepwise shortening in unstimulated frog skeletal muscle fibres

We investigated the dynamics of sarcomere length change during imposed stretches and releases of unstimulated single fibres of frog skeletal muscle. Three independent methods were used: an on-line method in which sarcomere length is computed from the striation pattern; laser diffraction; and a segment length tracking device. During steady ramp releases and stretches, both sarcomere and segment length changes occurred in stepwise fashion; i.e. periods of pause were interspersed between periods of rapid shortening. The above result indicates that activation of the fibre is not required to elicit stepwise length changes. Increasing the ramp velocity caused the steps to increase in size and the pauses to decrease in duration. Ramp releases and stretches were imposed at each of several initial sarcomere lengths up to 4.0 microns. Stepwise length changes were observed at all lengths, and their size was independent of initial sarcomere length. The observation of stepwise length changes beyond overlap indicates that the underlying mechanism probably does not lie in synchronous action of cross-bridges; an alternative hypothesis is advanced.

Is stepwise sarcomere shortening an artefact? A response

Like any other signals, optical signals from muscle fibres inevitably contain noise. The noise here is of predictable character. Because the structure of muscle is periodic, or almost so, translational movement of an illuminated fibre will inevitably give rise to a periodic noise fluctuation as striations pass across the optical field. The frequency of this fluctuation should be linearly related to the speed at which the fibre translates. By mistaking this noise component for the signal, Altringham and colleagues have amply succeeded in confirming this expected relationship, but they have left unanswered the question of the source and nature of stepwise shortening. I show here that: (1) by having obtained records in conditions in which the noise dominated, Altringham et al. have inadvertently confused the steps with the translation-induced fluctuation; and (2) when records are obtained using a method designed specifically to circumvent the effects of translation, the steps still remain in evidence.