Changes in force and stiffness during stretch of skeletal muscle fibers, effects of hypertonicity.

Slow stretch ramps (velocity: 0.17 fiber lengths s-1) were imposed during fused tetanic contractions of intact muscle fibers of the frog (1.4-3.0 degrees C; sarcomere length: 2.12-2.21 microns). Instantaneous force-extension relations were derived both under isometric conditions and during slow stretch by applying fast (0.2 ms) length steps to the fiber. An increase in tonicity (98 mM sucrose added to control Ringer solution) led to significant reduction of the maximum isometric tension but at the same time to marked increase in the force enhancement during slow stretch. The maximum force level reached during the stretch was affected very little. Experiments on relaxed fibers showed that recruitment of passive parallel elastic components were of no relevance for these effects. Hypertonicity slightly increased the instantaneous stiffness of the active fiber both in the presence and in the absence of stretch. The total extension of the undamped fiber elasticity was considerably reduced by increased tonicity under isometric conditions but was only slightly affected during slow stretch. The change in length of the undamped cross-bride elasticity upon stretch was thus greater in the hypertonic than in the normotonic solution suggesting a greater increase in force per cross-bridge in the hypertonic medium. The contractile effects are consistent with the assumptions that hypertonicity reduces the capability of the individual cross-bridge to produce active force and, furthermore, that hypertonicity has only minor effects on the number of attached cross-bridges and the maximum load-bearing capacity of the individual bridge.     

Stiffness and tension during and after sudden length changes of glycerinated single insect fibrillar muscle fibres

Rapid length changes were applied (within 0.2 ms or 0.4 ms) to single isometrically contracted glycerol extracted muscle fibres of the dorsal longitudinal muscle ofLethocerus maximus suspended in an Ca²⁺ and ATP containing solution at 20–23‡ C. Force transients and the fibre stiffness were measured during and after rapid length changes. At length changesbelow 0.5% of the initial fibre length (∼ 2.4 Μm sarcomere length) the mechanical transients were characterized as follows: (1) After stretch and after release the force regains at least partly the value of tension before the length change within a quick phase of tension recovery. The quick phase induced by stretch was nearly completed within 1–2 ms. (2) A pulse in length of 1.5 ms duration, i.e., a stretch followed by a release to the initial length or a release followed by a stretch to the initial length, was applied to the fibre. The force transient induced by this procedure regains after the second length change the value of the isometric tension before the procedure. (3) The stiffness was constant during each length change of the “pulse” and was equal during the first and the second length changes. These findings are predicted by the muscle contraction model of Huxley and Simmons (1971): The identical force before and after a length pulse may indicate that the rotation of cross bridges after the first length change is followed by a rotation into the original position after the second length change. The constancy of the stiffness during the length changes may indicate a Hookean elastic element of the cross bridge. The similarity of the stiffness during the first and the second length changes, i.e., before and after the quick phase, gives evidence that the quick phases after stretch and after release are not accompanied by a change in the net number of attached cross bridges. If stretches ofmore than 0.5% of the initial length were applied, the mechanical transient of the muscle fibre changed as follows: (1) An ultra fast tension decay phase (duration < 0.4 ms) was observed in addition to the slower decay phase induced by the smaller stretches. (2) If the initial stretch was followed by a release to the initial length, no fast recovery phase was observed, which returns the force to the value before the stretch. The reduced tension value persists for a longer period in time than 10 ms. (3) If the muscle was stretched and released repetitively an ultra fast quick phase was induced only by the first stretch. (4) The stiffness increased during stretch, but was found to be the same in the isometrically contracting muscle and after the quick tension decay phase following a large stretch. These findings indicate that the contraction model of Huxley and Simmons has to be extended by a further process additional to cross bridge rotation in case of large stretches (> 0.5%L ini). The findings are taken to indicate a rapid detachment and reattachment of overstrained cross bridges, i.e., a cross bridge slippage induced by large stretches.     

Activation dependence of stretch activation in mouse skinned myocardium: implications for ventricular function

Recent evidence suggests that ventricular ejection is partly powered by a delayed development of force, i.e., stretch activation, in regions of the ventricular wall due to stretch resulting from torsional twist of the ventricle around the apex-to-base axis. Given the potential importance of stretch activation in cardiac function, we characterized the stretch activation response and its Ca2+ dependence in murine skinned myocardium at 22 degrees C in solutions of varying Ca2+ concentrations. Stretch activation was induced by suddenly imposing a stretch of 0.5-2.5% of initial length to the isometrically contracting muscle and then holding the muscle at the new length. The force response to stretch was multiphasic: force initially increased in proportion to the amount of stretch, reached a peak, and then declined to a minimum before redeveloping to a new steady level. This last phase of the response is the delayed force characteristic of myocardial stretch activation and is presumably due to increased attachment of cross-bridges as a consequence of stretch. The amplitude and rate of stretch activation varied with Ca2+ concentration and more specifically with the level of isometric force prior to the stretch. Since myocardial force is regulated both by Ca2+ binding to troponin-C and cross-bridge binding to thin filaments, we explored the role of cross-bridge binding in the stretch activation response using NEM-S1, a strong-binding, non-force-generating derivative of myosin subfragment 1. NEM-S1 treatment at submaximal Ca2+-activated isometric forces significantly accelerated the rate of the stretch activation response and reduced its amplitude. These data show that the rate and amplitude of myocardial stretch activation vary with the level of activation and that stretch activation involves cooperative binding of cross-bridges to the thin filament. Such a mechanism would contribute to increased systolic ejection in response to increased delivery of activator Ca2+ during excitation-contraction coupling.     

Force enhancement above the initial isometric force on the descending limb of the force-length relationship

Edman et al. (J. General Physiol. 80 (1982) 769) observed in single fibres of frog that the steady-state forces following active fibre stretch were greater than the purely isometric force obtained at the length from which the stretch was initiated. Operating on the descending limb of the force-length relationship, such a result can only be explained within the framework of the sarcomere length non-uniformity theory, if some fibre segments shortened during the fibre stretch. However, such a result was not found, leaving Edman's observation unexplained. Force enhancement above the initial isometric force has not been investigated systematically in whole muscle, and therefore it is not known whether this property is also part of whole muscle mechanics. The purpose of this study was to test if the steady-state forces following active stretch of cat semitendinosus were greater than the corresponding purely isometric forces at the muscle length from which the stretch was started. Cat semitendinosus was stretched by various amounts on the descending limb of the force-length relationship, and the steady-state forces following these stretches were compared to the corresponding isometric forces at the initial and final muscle lengths. In 109 of 131 tests, the steady-state forces following stretching were greater than the isometric forces at the initial muscle lengths. Force enhancement increased with increasing amounts of stretching, and force enhancement above the initial isometric force was more likely to occur following stretches of great compared to small amplitude. Passive forces following active muscle stretching were often significantly greater than the passive forces at the same muscle length following an isometric contraction or a passive stretching of the muscle. This observation was made consistently at the longest muscle lengths tested. It appears, therefore, that there is a passive force that accounts for part of the force enhancement above the isometric force at the initial muscle length, and that provides increased passive force when a muscle is actively, rather than passively, stretched at long muscle lengths. We conclude that cat semitendinosus demonstrates steady-state force enhancement above the corresponding purely isometric force at the initial muscle length on the descending limb of the force-length relationship for many contractile conditions, and that a unique, and so far undetected, passive, parallel element contributes to this force enhancement, particularly at long muscle lengths where muscle is assumed to be most vulnerable to injuries associated with sarcomere length instability.     

Residual force enhancement after stretch of contracting frog single muscle fibers

Single fibers from the tibialis anterior muscle of Rana temporaria at 0.8-3.8 degrees C were subjected to long tetani lasting up to 8 s. Stretch of the fiber early in the tetanus caused an enhancement of force above the isometric control level which decayed only slowly and stayed higher throughout the contraction. This residual enhancement was uninfluenced by velocity of stretch and occurred only on the descending limb of the length-tension curve. The absolute magnitude of the effect increased with sarcomere length to a maximum at approximately 2.9 micrometers and then declined. The phenomenon was further characterized by its dependence on the amplitude of stretch. The final force level reached after stretch was usually higher than the isometric force level corresponding to the starting length of the stretch. The possibility that the phenomenon was caused by nonuniformity of sarcomere length along the fiber was examined by (a) laser diffraction studies that showed sarcomere stretch at all locations and (b) studies of 9-10 segments of approximately 0.6-0.7 mm along the entire fiber, which all elongated during stretch. Length-clamped segments showed residual force enhancement after stretch when compared with the tetanus produced by the same segment held at the short length as well as at the long length. It is concluded that residual force enhancement after stretch is a property shown by all individual segments along the fiber.     

Force produced by isolated sarcomeres and half-sarcomeres after an imposed stretch

When a stretch is imposed to activated muscles, there is a residual force enhancement that persists after the stretch; the force is higher than that produced during an isometric contraction in the corresponding length. The mechanisms behind the force enhancement remain elusive, and there is disagreement if it represents a sarcomeric property, or if it is associated with length nonuniformities among sarcomeres and half-sarcomeres. The purpose of this study was to investigate the effects of stretch on single sarcomeres and myofibrils with predetermined numbers of sarcomeres (n = 2, 3. . . , 8) isolated from the rabbit psoas muscle. Sarcomeres were attached between two precalibrated microneedles for force measurements, and images of the preparations were projected onto a linear photodiode array for measurements of half-sarcomere length (SL). Fully activated sarcomeres were subjected to a stretch (5-10% of initial SL, at a speed of 0.3 μm·s(-1)·SL(-1)) after which they were maintained isometric for at least 5 s before deactivation. Single sarcomeres showed two patterns: 31 sarcomeres showed a small level of force enhancement after stretch (10.46 ± 0.78%), and 28 sarcomeres did not show force enhancement (-0.54 ± 0.17%). In these preparations, there was not a strong correlation between the force enhancement and half-sarcomere length nonuniformities. When three or more sarcomeres arranged in series were stretched, force enhancement was always observed, and it increased linearly with the degree of half-sarcomere length nonuniformities. The results show that the residual force enhancement has two mechanisms: 1) stretch-induced changes in sarcomeric structure(s); we suggest that titin is responsible for this component, and 2) stretch-induced nonuniformities of half-sarcomere lengths, which significantly increases the level of force enhancement.     

Does residual force enhancement increase with increasing stretch magnitudes?

It is generally accepted that force enhancement in skeletal muscles increases with increasing stretch magnitudes. However, this property has not been tested across supra-physiological stretch magnitudes and different muscle lengths, thus it is not known whether this is a generic property of skeletal muscle, or merely a property that holds for small stretch magnitudes within the physiological range. Six cat soleus muscles were actively stretched with magnitudes varying from 3 to 24 mm at three different parts of the force–length relationship to test the hypothesis that force enhancement increases with increasing stretch magnitude, independent of muscle length. Residual force enhancement increased consistently with stretch amplitudes on the descending limb of the force–length relationship up to a threshold value, after which it reached a plateau. Force enhancement did not increase with stretch amplitude on the ascending limb of the force–length relationship. Passive force enhancement was observed for all test conditions, and paralleled the behavior of the residual force enhancement. Force enhancement increased with stretch magnitude when stretching occurred at lengths where there was natural passive force within the muscle. These results suggest that force enhancement does not increase unconditionally with increasing stretch magnitude, as is generally accepted, and that increasing force enhancement with stretch appears to be tightly linked to that part of the force–length relationship where there is naturally occurring passive force.     

Sarcomere length dependence of the force-velocity relation in single frog muscle fibers.

The force-velocity relation of single frog fibers was measured at sarcomere lengths of 2.15, 2.65, and 3.15 microns. Sarcomere length was obtained on-line with a system that measures the distance between two markers attached to the surface of the fiber, approximately 800 microns apart. Maximal shortening velocity, determined by extrapolating the Hill equation, was similar at the three sarcomere lengths: 6.5, 6.0, and 5.7 microns/s at sarcomere lengths of 2.15, 2.65, and 3.15 microns, respectively. For loads not close to zero the shortening velocity decreased with increasing sarcomere length. This was the case when force was expressed as a percentage of the maximal force at optimal fiber length or as a percentage of the sarcomere-isometric force at the respective sarcomere lengths. The force-velocity relation was discontinuous around zero velocity: load clamps above the level that kept sarcomeres isometric resulted in stretch that was much slower than when the load was decreased below isometric by a similar amount. We fitted the force-velocity relation for slow shortening (less than 600 nm/s) and for slow stretch (less than 200 nm/s) with linear regression lines. At a sarcomere length of 2.15 microns the slopes of these lines was 8.6 times higher for shortening than for stretch. At 2.65 and 3.15 microns the values were 21.8 and 14.1, respectively. At a sarcomere length of 2.15 microm, the velocity of stretch abruptly increased at loads that were 160-170% of the sarcomere isometric load, i.e., the muscle yielded. However, at a sarcomere length of 2.65 and 3.15 microm yield was absent at such loads. Even the highest loads tested (260%) resulted in only slow stretch.(ABSTRACT TRUNCATED AT 250 WORDS)     

Contributions of stretch activation to length-dependent contraction in murine myocardium

The steep relationship between systolic force production and end diastolic volume (Frank-Starling relationship) in myocardium is a potentially important mechanism by which the work capacity of the heart varies on a beat-to-beat basis, but the molecular basis for the effects of myocardial fiber length on cardiac work are still not well understood. Recent studies have suggested that an intrinsic property of myocardium, stretch activation, contributes to force generation during systolic ejection in myocardium. To examine the role of stretch activation in length dependence of activation we recorded the force responses of murine skinned myocardium to sudden stretches of 1% of muscle length at both short (1.90 microm) and long (2.25 microm) sarcomere lengths (SL). Maximal Ca(2+)-activated force and Ca(2+) sensitivity of force were greater at longer SL, such that more force was produced at a given Ca(2+) concentration. Sudden stretch of myocardium during an otherwise isometric contraction resulted in a concomitant increase in force that quickly decayed to a minimum and was followed by a delayed development of force, i.e., stretch activation, to levels greater than prestretch force. At both maximal and submaximal activations, increased SL significantly reduced the initial rate of force decay following stretch; at submaximal activations (but not at maximal) the rate of delayed force development was accelerated. This combination of mechanical effects of increased SL would be expected to increase force generation during systolic ejection in vivo and prolong the period of ejection. These results suggest that sarcomere length dependence of stretch activation contributes to the steepness of the Frank-Starling relationship in living myocardium.     

Elastic properties of isolated thick filaments measured by nanofabricated cantilevers.

Using newly developed nanofabricated cantilever force transducers, we have measured the mechanical properties of isolated thick filaments from the anterior byssus retractor muscle of the blue mussel Mytilus edulis and the telson levator muscle of the horseshoe crab Limulus polyphemus. The single thick filament specimen was suspended between the tip of a flexible cantilever and the tip of a stiff reference beam. Axial stress was placed on the filament, which bent the flexible cantilever. Cantilever tips were microscopically imaged onto a photodiode array to extract tip positions, which could be converted into force by using the cantilever stiffness value. Length changes up to 23% initial length (Mytilus) and 66% initial length (Limulus) were fully reversible and took place within the physiological force range. When stretch exceeded two to three times initial length (Mytilus) or five to six times initial length (Limulus), at forces approximately 18 nN and approximately 7 nN, respectively, the filaments broke. Appreciable and reversible strain within the physiological force range implies that thick-filament length changes could play a significant physiological role, at least in invertebrate muscles.     

物种演化对人类活动作用下不同性质栖息地毁坏的响应

栖息地毁坏是物种多样性减少的首要因素之一, 因此研究物种演化对栖息地毁坏的响应是非常必要的。而栖息地的毁坏又有瞬间毁坏和持续毁坏两种, 以往对栖息地毁坏的研究集中在瞬间毁坏上, 而该文则是通过N_物种 竞争共存模型分析对比了物种演化对栖息地瞬间毁坏和持续毁坏的响应特征。研究发现 :不同性质的栖息地毁坏都会导致物种强弱关系的变化, 并非如通常所认为的强物种将免于遭受物种灭绝的威胁, 也不是强物种首先灭绝, 而是因集合种群结构的不同而异。在热带雨林群落, 瞬间毁坏下物种演化一般经历了强迫适应和恢复上升阶段, 而持续毁坏下物种得不到恢复, 只能持续衰退, 在较长一段时间内持续毁坏比瞬间毁坏更有利于物种的续存 ;而在温带森林群落, 瞬间毁坏下物种演化一般经历强迫适应, 恢复上升和准周期振荡, 最后平衡, 而持续毁坏下物种只能持续衰退, 出现了在栖息地持续毁坏率小于瞬间毁坏率时, 物种的栖息地占有率却小于瞬间毁坏时的占有率。     

Mechanical strain memory in airway smooth muscle

We investigated the effect of a singlerapid stretch on poststretch force and myosin phosphorylation in bovinetracheal smooth muscle. When unstimulated muscle strips were stretchedfrom suboptimal length to optimal length (L_o),poststretch steady-state force was not significantly different fromthat of unstretched control at L_o. However, whencarbachol-activated muscle strips were stretched from suboptimal lengthto L_o, poststretch force and myosin phosphorylation were lower than control and significantly correlated with initial length. When poststretch muscle strips were allowed to relax for 1 hand then activated by K⁺ depolarization, the developedforce remained significantly correlated with initial length. When thesame strain was applied in 23 increments to minimize peak stress,poststretch force and myosin phosphorylation increased significantly,approaching the levels expected at L_o. Furthermore,poststretch force development increased after each cycle of contractionand relaxation, approaching the control level after four cycles. Theseresults suggest that activated airway smooth muscle cells can retainrelatively precise memory of past strain when they are stretchedrapidly with high stress.

     

Phase transition in force during ramp stretches of skeletal muscle.

Active glycerinated rabbit psoas fibers were stretched at constant velocity (0.1-3.0 lengths/s) under sarcomere length control. As observed by previous investigators, force rose in two phases: an initial rapid increase over a small stretch (phase I), and a slower, more modest rise over the remainder of the stretch (phase II). The transition between the two phases occurred at a critical stretch (LC) of 7.7 +/- 0.1 nm/half-sarcomere that is independent of velocity. The force at critical stretch (PC) increased with velocity up to 1 length/s, then was constant at 3.26 +/- 0.06 times isometric force. The decay of the force response to a small step stretch was much faster during stretch than in isometric fibers. The addition of 3 mM vanadate reduced isometric tension to 0.08 +/- 0.01 times control isometric tension (P0), but only reduced PC to 0.82 +/- 0.06 times P0, demonstrating that prepowerstroke states contribute to force rise during stretch. The data can be explained by a model in which actin-attached cross-bridges in a prepowerstroke state are stretched into regions of high force and detach very rapidly when stretched beyond this region. The prepowerstroke state acts as a mechanical rectifier, producing large forces during stretch but small forces during shortening.     

Stretch of active muscle during the declining phase of the calcium transient produces biphasic changes in calcium binding to the activating sites

In voltage-clamped barnacle single muscle fibers, muscle shortening during the declining phase of the calcium transient increases myoplasmic calcium. This extra calcium is probably released from the activating sites by a change in affinity when cross-bridges break (Gordon, A. M., and E. B. Ridgway, 1987. J. Gen. Physiol. 90:321-340). Stretching the muscle at similar times causes a more complex response, a rapid increase in intracellular calcium followed by a transient decrease. The amplitudes of both phases increase with the rate and amplitude of stretch. The rapid increase, however, appears only when the muscle is stretched more than approximately 0.4%. This is above the length change that produces the breakpoint in the force record during a ramp stretch. This positive phase in response to large stretches is similar to that seen on equivalent shortening at the same point in the contraction. For stretches at different times during the calcium transient, the peak amplitude of the positive phase has a time course that is delayed relative to the calcium transient, while the peak decrease during the negative phase has an earlier time course that is more similar to the calcium transient. The amplitudes of both phases increase with increasing strength of stimulation and consequent force. When the initial muscle the active force. A large decrease in length (which drops the active force to zero) decreases the extra calcium seen on a subsequent restretch. After such a shortening step, the extra calcium on stretch recovers (50 ms half time) toward the control level with the same time course as the redeveloped force. Conversely, stretching an active fiber decreases the extra calcium on a subsequent shortening step that is imposed shortly afterward. Enhanced calcium binding due to increased length alone cannot explain our data. We hypothesize that the calcium affinity of the activating sites increases with cross-bridge attachment and further with cross-bridge strain. This accounts for the biphasic response to stretch as follows: cross-bridges detached by stretch first decrease calcium affinity, then upon reattachment increase calcium affinity due to the strained configuration brought on by the stretch. The experiments suggest that cross-bridge attachment and strain can modify calcium binding to the activating sites in intact muscle.     

Stretch-induced,steady-state force enhancement in single skeletal muscle fibers exceeds the isometric force at optimum fiber length

Stretch-induced force enhancement has been observed in a variety of muscle preparations and on structural levels ranging from single fibers to in vivo human muscles. It is a well-accepted property of skeletal muscle. However, the mechanism causing force enhancement has not been elucidated, although the sarcomere-length non-uniformity theory has received wide support. The purpose of this paper was to re-investigate stretch-induced force enhancement in frog single fibers by testing specific hypotheses arising from the sarcomere-length non-uniformity theory. Single fibers dissected from frog tibialis anterior (TA) and lumbricals (n=12 and 22, respectively) were mounted in an experimental chamber with physiological Ringer's solution (pH=7.5) between a force transducer and a servomotor length controller. The tetantic force-length relationship was determined. Isometric reference forces were determined at optimum length (corresponding to the maximal, active, isometric force), and at the initial and final lengths of the stretch experiments. Stretch experiments were performed on the descending limb of the force-length relationship after maximal tetanic force was reached. Stretches of 2.5-10% (TA) and 5-15% lumbricals of fiber length were performed at 0.1-1.5 fiber lengths/s. The stretch-induced, steady-state, active isometric force was always equal or greater than the purely isometric force at the muscle length from which the stretch was initiated. Moreover, for stretches of 5% fiber length or greater, and initiated near the optimum length of the fiber, the stretch-enhanced active force always exceeded the maximal active isometric force at optimum length. Finally, we observed a stretch-induced enhancement of passive force. We conclude from these results that the sarcomere length non-uniformity theory alone cannot explain the observed force enhancement, and that part of the force enhancement is associated with a passive force that is substantially greater after active compared to passive muscle stretch.     

Critical sarcomere extension required to recruit a decaying component of extra force during stretch in tetanic contractions of frog skeletal muscle fibers

29 single frog skeletal muscle fibers were stretched during fused tetanic contractions. The force increase during stretch exhibited a breakpoint at a critical length change (average: 16.6 nm per one-half sarcomere) that was independent of velocity of stretch and of sarcomere length between 1.8 and 2.8 microns. After stretch there was an early decaying force component with a force-extension curve similar to that during stretch, which disappeared over approximately 2 s. This component was removed by a small, quick release, leaving a longer- lasting component. The critical amplitude of release required to produce this result was found by clamping the fiber to a load at which there was zero velocity of shortening. This amplitude increased with time up to the angle in the force record during stretch, was constant for the remainder of the stretch, and decreased with time after the end of stretch; it was consistently less than the critical amplitude of stretch required to reach the breakpoint of force enhancement during stretch but was also independent of sarcomere length. The force drop accompanying the critical release showed a small increase up to an optimum magnitude at 2.4--2.7 microns sarcomere length, with a decrease at longer lengths.     

Force enhancement and relaxation rates after stretch of activated muscle fibres

The residual force enhancement following muscle stretch might be associated with an increase in the proportion of attached cross-bridges, as supported by stiffness measurements. In this case, it could be caused by an increase in the attachment or a decrease in the detachment rate of cross-bridges, or a combination of the two. The purpose of this study was to investigate if the stretch-induced force enhancement is related to cross-bridge attachment/detachment kinetics. Single muscle fibres dissected from the lumbrical muscle of frog were place at a length approximately 20% longer than the plateau of the force-length relationship; they were maximally activated, and after full isometric force was reached, ramp stretches were imposed with amplitudes of 5 and 10% fibre length, at a speed of 40% fibre length s(-1). Experiments were performed in Ringer's solution, and with the addition of 2, 5 and 10 nM of 2,3-butanedione monoxime (BDM), a drug that places cross-bridges in a pre-power-stroke, state, inhibiting force production. The total force following stretch was higher than the corresponding force measured after isometric contraction at the corresponding length. This residual force enhancement was accompanied by an increase relaxation time. BDM, which decreases force production during isometric contractions, considerably increased the relative levels of force enhancement. BDM also increased relaxation times after stretch, beyond the levels observed during reference contractions in Ringer's solution, and beyond isometric control tests at the corresponding BDM concentrations. Together, these results support the idea that force enhancement is caused, at least in part, by a decrease in cross-bridge detachment rates, as manifested by the increased relaxation times following fibre stretch.     

Estimation of Instantaneous Complex Dynamics through Lyapunov Exponents: A Study on Heartbeat Dynamics

Measures of nonlinearity and complexity, and in particular the study of Lyapunov exponents, have been increasingly used to characterize dynamical properties of a wide range of biological nonlinear systems, including cardiovascular control. In this work, we present a novel methodology able to effectively estimate the Lyapunov spectrum of a series of stochastic events in an instantaneous fashion. The paradigm relies on a novel point-process high-order nonlinear model of the event series dynamics. The long-term information is taken into account by expanding the linear, quadratic, and cubic Wiener-Volterra kernels with the orthonormal Laguerre basis functions. Applications to synthetic data such as the Hénon map and Rössler attractor, as well as two experimental heartbeat interval datasets (i.e., healthy subjects undergoing postural changes and patients with severe cardiac heart failure), focus on estimation and tracking of the Instantaneous Dominant Lyapunov Exponent (IDLE). The novel cardiovascular assessment demonstrates that our method is able to effectively and instantaneously track the nonlinear autonomic control dynamics, allowing for complexity variability estimations.     

A mathematical model of muscle containing heterogeneous half-sarcomeres exhibits residual force enhancement

A skeletal muscle fiber that is stimulated to contract and then stretched from L₁ to L₂ produces more force after the initial transient decays than if it is stimulated at L₂. This behavior has been well studied experimentally, and is known as residual force enhancement. The underlying mechanism remains controversial. We hypothesized that residual force enhancement could reflect mechanical interactions between heterogeneous half-sarcomeres. To test this hypothesis, we subjected a computational model of interacting heterogeneous half-sarcomeres to the same activation and stretch protocols that produce residual force enhancement in real preparations. Following a transient period of elevated force associated with active stretching, the model predicted a slowly decaying force enhancement lasting >30 seconds after stretch. Enhancement was on the order of 13% above isometric tension at the post-stretch muscle length, which agrees well with experimental measurements. Force enhancement in the model was proportional to stretch magnitude but did not depend strongly on the velocity of stretch, also in agreement with experiments. Even small variability in the strength of half-sarcomeres (2.1% standard deviation, normally distributed) was sufficient to produce a 5% force enhancement over isometric tension. Analysis of the model suggests that heterogeneity in half-sarcomeres leads to residual force enhancement by storing strain energy introduced during active stretch in distributions of bound cross-bridges. Complex interactions between the heterogeneous half-sarcomeres then dissipate this stored energy at a rate much slower than isolated cross-bridges would cycle. Given the variations in half-sarcomere length that have been observed in real muscle preparations and the stochastic variability inherent in all biological systems, half-sarcomere heterogeneity cannot be excluded as a contributing source of residual force enhancement.     

Extra calcium on shortening in barnacle muscle. Is the decrease in calcium binding related to decreased cross-bridge attachment,force, or length?

Barnacle single muscle fibers were microinjected with the calcium-specific photoprotein aequorin. We have previously shown (Ridgway, E. B., and A. M. Gordon, 1984, Journal of General Physiology, 83:75-104) that when barnacle fibers are stimulated under voltage clamp and length control and allowed to shorten during the declining phase of the calcium transient, extra myoplasmic calcium is observed. The time course of the extra calcium for shortening steps at different times during the calcium transient is intermediate between those of free calcium and muscle force. Furthermore, the amplitude increases with an increased stimulus, calcium transient, and force. Therefore, the extra calcium probably comes from the activating sites on the myofilaments, possibly as a result of changes in calcium binding by the activating sites. The change in calcium binding may be due, in turn, to the change in muscle length and/or muscle force and/or cross-bridge attachment per se. In the present article, we show that the amount of the extra calcium depends on the initial muscle length, declining at shorter lengths. This suggests length-dependent calcium binding. The relation between initial length and extra calcium, however, parallels that between initial length and peak active force. The ratio of extra calcium to active force is therefore virtually independent of initial length. These data do not distinguish between a direct effect of length on calcium binding and an indirect effect owing to changes in cross-bridge attachment and force through some geometrical factor. The amount of extra calcium increases with the size of the shortening step, tending toward saturation for steps of greater than or equal to 10%. This experiment suggests that calcium binding depends on muscle force or cross-bridge attachment, not just length (if at all). There is much less extra calcium seen with shortening steps at high force when the high force results from stretch of the active muscle than when it results from increased stimulation of muscle.(ABSTRACT TRUNCATED AT 400 WORDS)