Stiffness of frog muscle fibres during rise of tension and relaxation in fixed-end or length-clamped tetani

Sarcomere level mechanics of the fast skeletal muscle of the medaka fish larva

The medaka fish (Oryzias latipes) is a vertebrate model used in developmental biology and genetics. Here we explore its suitability as a model for investigating the molecular mechanisms of human myopathies caused by mutations in sarcomeric proteins. To this end, the relevant mechanical parameters of the intact skeletal muscle of wild-type medaka are determined using the transparent tail at larval stage 40. Tails were mounted at sarcomere length of 2.1 μm in a thermoregulated trough containing physiological solution. Tetanic contractions were elicited at physiological temperature (10°C-30°C) by electrical stimulation, and sarcomere length changes were recorded with nanometer-microsecond resolution during both isometric and isotonic contractions with a striation follower. The force output has been normalized for the actual fraction of the cross section of the tail occupied by the myofilament lattice, as established with transmission electron microscopy (TEM), and then for the actual density of myofilaments, as established with X-ray diffraction. Under these conditions, the mechanical performance of the contracting muscle of the wild-type larva can be defined at the level of the half-thick filament, where ∼300 myosin motors work in parallel as a collective motor, allowing a detailed comparison with the established performance of the skeletal muscle of different vertebrates. The results of this study point out that the medaka fish larva is a suitable model for the investigation of the genotype/phenotype correlations and therapeutic possibilities in skeletal muscle diseases caused by mutations in sarcomeric proteins.NEW & NOTEWORTHY The suitability of the medaka fish as a model for investigating the molecular mechanisms of human myopathies caused by mutations of sarcomeric proteins is tested by combining structural analysis and sarcomere-level mechanics of the skeletal muscle of the tail of medaka larva. The mechanical performance of the medaka muscle, scaled at the level of the myosin-containing thick filament, together with its reduced genome duplication makes this model unique for investigations of the genotype/phenotype correlations in human myopathies.

Contracting striated muscle has a dynamic I-band spring with an undamped stiffness 100 times larger than the passive stiffness

KEY POINTS

Fast sarcomere-level mechanics in contracting intact fibres from frog skeletal muscle reveal an I-band spring with an undamped stiffness 100 times larger than the known static stiffness. This undamped stiffness remains constant in the range of sarcomere length 2.7-3.1 µm, showing the ability of the I-band spring to adapt its length to the width of the I-band. The stiffness and tunability of the I-band spring implicate titin as a force contributor that, during contraction, allows weaker half-sarcomeres to equilibrate with in-series stronger half-sarcomeres, preventing the development of sarcomere length inhomogeneity. This work opens new possibilities for the detailed in situ description of the structural-functional basis of muscle dysfunctions related to mutations or site-directed mutagenesis in titin that alter the I-band stiffness.

ABSTRACT

Force and shortening in the muscle sarcomere are due to myosin motors from thick filaments pulling nearby actin filaments toward the sarcomere centre. Thousands of serially linked sarcomeres in muscle make the shortening (and the shortening speed) macroscopic, while the intrinsic instability of in-series force generators is likely prevented by the cytoskeletal protein titin that connects the thick filament with the sarcomere end, working as an I-band spring that accounts for the rise of passive force with sarcomere length (SL). However, current estimates of titin stiffness, deduced from the passive force-SL relation and single molecule mechanics, are much smaller than what is required to avoid the development of large inhomogeneities among sarcomeres. In this work, using 4 kHz stiffness measurements on a population of sarcomeres selected along an intact fibre isolated from frog skeletal muscle contracting at different SLs (temperature 4°C), we measure the undamped stiffness of an I-band spring that at SL > 2.7 µm attains a maximum constant value of ∼6 pN nm-1 per half-thick filament, two orders of magnitude larger than expected from titin-related passive force. We conclude that a titin-like dynamic spring in the I-band, made by an undamped elastic element in-series with damped elastic elements, adapts its length to the SL with kinetics that provide force balancing among serially linked sarcomeres during contraction. In this way, the I-band spring plays a fundamental role in preventing the development of SL inhomogeneity.

X-ray Diffraction Evidence for Low Force Actin-Attached and Rigor-Like Cross-Bridges in the Contractile Cycle

Defining the structural changes involved in the myosin cross-bridge cycle on actin in active muscle by X-ray diffraction will involve recording of the whole two dimensional (2D) X-ray diffraction pattern from active muscle in a time-resolved manner. Bony fish muscle is the most highly ordered vertebrate striated muscle to study. With partial sarcomere length (SL) control we show that changes in the fish muscle equatorial A-band (10) and (11) reflections, along with (10)/(11) intensity ratio and the tension, are much more rapid than without such control. Times to 50% change with SL control were 19.5 (±2.0) ms, 17.0 (±1.1) ms, 13.9 (±0.4) ms and 22.5 (±0.8) ms, respectively, compared to 25.0 (±3.4) ms, 20.5 (±2.6) ms, 15.4 (±0.6) ms and 33.8 (±0.6) ms without control. The (11) intensity and the (10)/(11) intensity ratio both still change ahead of tension, supporting the likelihood of the presence of a head population close to or on actin, but producing little or no force, in the early stages of the contractile cycle. Higher order equatorials (e.g., (30), (31), and (32)), more sensitive to crossbridge conformation and distribution, also change very rapidly and overshoot their tension plateau values by a factor of around two, well before the tension plateau has been reached, once again indicating an early low-force cross-bridge state in the contractile cycle. Modelling of these intensity changes suggests the presence of probably two different actin-attached myosin head structural states (mainly low-force attached and rigor-like). No more than two main attached structural states are necessary and sufficient to explain the observations. We find that 48% of the heads are off actin giving a resting diffraction pattern, 20% of heads are in the weak binding conformation and 32% of the heads are in the strong (rigor-like) state. The strong states account for 96% of the tension at the tetanus plateau.

The non-linear elasticity of the muscle sarcomere and the compliance of myosin motors

Force in striated muscle is due to attachment of the heads of the myosin, the molecular motors extending from the myosin filament, to the actin filament in each half-sarcomere, the functional unit where myosin motors act in parallel. Mechanical and X-ray structural evidence indicates that at the plateau of isometric contraction (force T0), less than half of the elastic strain of the half-sarcomere is due to the strain in the array of myosin motors (s), with the remainder being accounted for by the compliance of filaments acting as linear elastic elements in series with the motor array. Early during the development of isometric force, however, the half-sarcomere compliance has been found to be less than that expected from the linear elastic model assumed above, and this non-linearity may affect the estimate of s. This question is investigated here by applying nanometre-microsecond-resolution mechanics to single intact fibres from frog skeletal muscle at 4 °C, to record the mechanical properties of the half-sarcomere throughout the development of force in isometric contraction. The results are interpreted with mechanical models to estimate the compliance of the myosin motors. Our conclusions are as follows: (i) early during the development of an isometric tetanus, an elastic element is present in parallel with the myosin motors, with a compliance of ∼200 nm MPa(-1) (∼20 times larger than the compliance of the motor array at T0); and (ii) during isometric contraction, s is 1.66 ± 0.05 nm, which is not significantly different from the value estimated with the linear elastic model.

Mechanics of myosin function in white muscle fibres of the dogfish, Scyliorhinus canicula

The contractile properties of muscle fibres have been extensively investigated by fast perturbation in sarcomere length to define the mechanical characteristics of myofilaments and myosin heads that underpin refined models of the acto-myosin cycle. Comparison of published data from intact fast-twitch fibres of frog muscle and demembranated fibres from fast muscle of rabbit shows that stiffness of the rabbit myosin head is only ∼62% of that in frog. To clarify if and how much the mechanical characteristics of the filaments and myosin heads vary in muscles of different animals we apply the same high resolution mechanical methods, in combination with X-ray diffraction, to fast-twitch fibres from the dogfish (Scyliorhinus canicula). The values of equivalent filament compliance (C_f) measured by X-ray diffraction and in mechanical experiments are not significantly different; the best estimate from combining these values is 17.1 ± 1.0 nm MPa⁻¹. This value is larger than C_f in frog, 13.0 ± 0.4 nm MPa⁻¹. The longer thin filaments in dogfish account for only part of this difference. The average isometric force exerted by each attached myosin head at 5°C, 4.5 pN, and the maximum sliding distance accounted for by the myosin working stroke, 11 nm, are similar to those in frog, while the average myosin head stiffness of dogfish (1.98 ± 0.31 pN nm⁻¹) is smaller than that of frog (2.78 ± 0.30 pN nm⁻¹). Taken together these results indicate that the working stroke responsible for the generation of isometric force is a larger fraction of the total myosin head working stroke in the dogfish than in the frog.

Force decline during fatigue is due to both a decrease in the force per individual cross-bridge and the number of cross-bridges

Fatigue occurring during exercise can be defined as the inability to maintain the initial force or power output. As fatigue becomes pronounced, force and maximum velocity of shortening are greatly reduced and force relaxation is prolonged. In principle, force loss during fatigue can result from a decrease in the number of cross-bridges generating force or a decrease of the individual cross-bridge force or to both mechanisms. The present experiments were made to investigate this point in single fibres or small fibre bundles isolated from flexor digitorum brevis (FDB) of C57BL/6 mice at 22-24◦C. During a series of 105 tetanic contractions, we measured force and fibre stiffness by applying small sinusoidal length oscillations at 2.5 or 4 kHz frequency to the activated preparation and measuring the resulting force changes. Stiffness data were corrected for the influence of compliance in series with the cross-bridge ensemble. The results show that the force decline during the first 20 tetani is due to the reduction of force developed by the individual cross-bridges and thereafter as fatigue becomes more severe, the number of cross-bridges decreases. In spite of the force reduction in the early phase of fatigue, there was an increased rate of tetanic force development and relaxation. In the latter stages of fatigue, the rate of force development and relaxation became slower. Thus, the start of fatigue is characterised by decreased cross-bridge force development and as fatigue becomes more marked, the number of cross-bridges decreases. These findings are discussed in the context of the current hypotheses about fatigue mechanisms.

Structural changes in the myosin filament and cross-bridges during active force development in single intact frog muscle fibres: stiffness and X-ray diffraction measurements

Structural and mechanical changes occurring in the myosin filament and myosin head domains during the development of the isometric tetanus have been investigated in intact frog muscle fibres at 4 degrees C and 2.15 microm sarcomere length, using sarcomere level mechanics and X-ray diffraction at beamline ID2 of the European Synchrotron Radiation Facility (Grenoble, France). The time courses of changes in both the M3 and M6 myosin-based reflections were recorded with 5 ms frames using the gas-filled RAPID detector (MicroGap Technology). Following the end of the latent period (11 ms after the start of stimulation), force increases to the tetanus plateau value (T(0)) with a half-time of 40 ms, and the spacings of the M3 and M6 reflections (S(M3) and S(M6)) increase by 1.5% from their resting values, with time courses that lead that of force by approximately 10 and approximately 20 ms, respectively. These temporal relations are maintained when the increase of force is delayed by approximately 10 ms by imposing, from 5 ms after the first stimulus, 50 nm (half-sarcomere)(-1) shortening at the velocity (V(0)) that maintains zero force. Shortening at V(0) transiently reduces S(M3) following the latent period and delays the subsequent increase in S(M3), but only delays the S(M6) increase without a transient decrease. Shortening at V(0) imposed at the tetanus plateau causes an abrupt reduction of the intensity of the M3 reflection (I(M3)), whereas the intensity of the M6 reflection (I(M6)) is only slightly reduced. The changes in half-sarcomere stiffness indicate that the isometric force at each time point is proportional to the number of myosin heads bound to actin. The different sensitivities of the intensity and spacing of the M3 and M6 reflections to the mechanical responses support the view that the M3 reflection in active muscle originates mainly from the myosin heads attached to the actin filament and the M6 reflection originates mainly from a fixed structure in the myosin filament signalling myosin filament length changes during the tetanus rise.

A combined mechanical and X-ray diffraction study of stretch potentiation in single frog muscle fibres

The nature of the force (T) response during and after steady lengthening has been investigated in tetanized single muscle fibres from Rana temporaria (4 C; 2.15 micrometer sarcomere length) by determining both the intensity of the third order myosin meridional X-ray reflection (IM3) and the stiffness (e) of a selected population of sarcomeres within the fibre. With respect to the value at the isometric tetanus plateau (To), IM3 was depressed to 0.67 +/- 0.04 during steady lengthening at approximately 160 nm s(-1) (T approximately 1.7) and recovered to 0.86 +/- 0.05 during the 250 ms period of after-stretch potentiation following the rapid decay of force at the end of lengthening (T approximately 1.3); under the same conditions stiffness increased to 1.25 +/- 0.02 and to 1.12 +/- 0.03, respectively. After subtraction of the contribution of myofilaments to the half-sarcomere compliance, stiffness measurements indicated that (1) during lengthening the cross-bridge number rises to 1.8 times the original isometric value and the average degree of cross-bridge strain is similar to that induced by the force-generating process in isometric conditions (2.3 nm), and (2) after-stretch potentiation is explained by a residual larger cross-bridge number. Structural data are compatible with mechanical data if the axial dispersion of attached heads is doubled during steady lengthening and recovers half-way towards the original isometric value during after-stretch potentiation.

Cross-bridge movement and stiffness during the rise of tension in skeletal muscle--a theoretical analysis

Predictions for the time courses of cross-bridge attachment. N(t), stiffness, S(t), and force, T(t), during the tetanus rise were analysed for a special class of cross-bridge models where cross-bridges initially attach in a non-stereospecific weak-binding state, AW. This state is in rapid equilibrium (equilibrium constant K) with detached states and the force generating transition (rate constant F+) is delayed. One model (model IA) which assumed step-function rise of activation at onset of tetanus, gave a poor fit to the experimental data (judged by root mean square error, RMSe approximately 0.038) but the experimentally observed lead of N(t) over T(t) was reproduced qualitatively. An activation mechanism where K increased towards its maximum value according to an exponential function (Model IB) improved the fit considerably (RMSe approximately 0.013). However, the activation time constant (r = 30 ms) derived in the fit was too high to reflect Ca2+ binding to troponin. In a further developed model (model II) both Ca2+ -binding to troponin and cross-bridge attachment were assumed to be required for full activation. This more complex model gave a good fit to the experimental data (RMSe approximately 0.013) with a realistic time constant for Ca2+ binding to troponin (9 ms). In both model IB and model II the best fit was obtained with F+ approximately 40 s(-1). An extended version of model IB, with distributed cross-bridge attachment and a series elastic element, gave a fit of similar quality (RMSe approximately 0.009) as obtained with model IB and model II and with a similar value of F+. The results support the view that weakly bound cross-bridges (state AW) may account for the lead of cross-bridge movement over force during tension rise. It is also shown that, if the stiffness of the myofilaments is non-linear (stiffness increasing with tension) the experimentally observed lead of S(t) over T(t) may, to a significant degree, be attributed to cross-bridges in the state AW.

Comparison of energy output during ramp and staircase shortening in frog muscle fibres

1. We compared the rates of work and heat production during ramp shortening with those during staircase shortening (sequence of step releases of the same amplitude, separated by regular time intervals). Ramp or staircase shortening was applied to isolated muscle fibres (sarcomere length, 2.2 microns; temperature, approximately 1 degree C) at the plateau of an isometric tetanus. The total amount of shortening was no greater than 6% of the fibre length. 2. During ramp shortening the power output showed a maximum at about 0.8 fibre lengths per second (Lo s-1), which corresponds to 1/3 the maximum shortening velocity (Vo). For the same average shortening velocity during staircase shortening (step size, approximately 0.5% Lo) the power output was 40-60% lower. The rate of heat production for the same average shortening velocity was approximately 45% higher during staircase shortening than during ramp shortening. 3. The relation between rate of total energy output and shortening velocity was well described by a second order regression line in the range of velocities used (0.1-2.3 Lo s-1). For any shortening velocity the rate of total energy output (power plus heat rate) was not statistically different for staircase (step size, approximately 0.5% Lo) and ramp shortening. 4. The mechanical efficiency (the ratio of the power over the total energy rate) during ramp shortening had a maximum value of 0.36 at 1/5 Vo; during staircase shortening, for any given shortening velocity, the mechanical efficiency was reduced compared with ramp shortening: with a staircase step of about 0.5% Lo at 1/5 Vo the efficiency was approximately 0.2. 5. The results indicate that a cross-bridge is able to convert different quantities of energy into work depending on the different shortening protocol used. The fraction of energy dissipated as heat is larger during staircase shortening than during ramp shortening.

A force transducer and a length-ramp generator for mechanical investigations of frog-heart myocytes

An apparatus for studying the mechanics of isolated frog heart myocytes is described. The cells are held horizontal in a through of Ringer solution by means of two suction micropipettes. Myocyte force is measured with an opto-electronic system recording the deflection of the tip of one micropipette, which acts as a cantilever force probe. The force probes are selected for compliance according to the force a myocyte is expected to develop in a given condition, so as to limit myocyte shortening during force development to no more than 1% of the slack cellular length (l0). The other micropipette, which is stiff relative to the forces measured, is mounted on an electromagnetic-loudspeaker motor by which controlled-velocity length changes, of preset size and in either direction, are imposed on myocytes. The force transducer has a sensitivity of 5-10 mV/nN, with a frequency response of 700-900 Hz in Ringer solution and a resolution of 0.5-1 nN. The motor with a suction micropipette can complete controlled-velocity length ramps within 1.5-2.0 ms, across a range of +/- 100 microns at a resolution of 8.0 nm. These values correspond, for frog-heart myocytes 200 microns and 400 microns long, to 25%-50% l0 and 0.002%-0.004% l0 respectively.

Kinetics of regeneration of cross-bridge power stroke in shortening muscle

The force developed by a muscle during steady shortening is due to cyclic interactions between the cross-bridges extending from the thick myosin filament to the thin actin filament. Each interaction consists of a power stroke of the myosin molecule that accounts for a limited amount of sliding between the two sets of filaments (about 12 nm according to quick release experiments), and is widely believed to be coupled to the hydrolysis of one ATP molecule. On the other hand both energetics studies in muscle and in vitro motility assays, indicating that shortening per ATP split is much larger than 12 nm, postulate that during shortening cross-bridges interact at a rate much faster than the ATP splitting rate. In the experiments reported here, made on intact fibres from frog skeletal muscle, the rate of regeneration of the power stroke was determined. Tension transients were elicited by imposing test step releases at different times (2-20 ms) after a conditioning release of about 5 nm. When the test step was imposed at 2 ms after the conditioning step, the tension attained at the end of the quick phase of recovery (T2, due to the force generating stroke of the attached cross-bridges) was depressed and the T2 curve (the plot of T2 tension versus size of the test step) intercepted the length axis to the right, with respect to the intercept of the control T2 curve, by an amount similar to the size of the conditioning step. By increasing the interval between conditioning and test step the T2 tension increased progressively and the T2 curve intercept approached the intercept of the control curve with a time constant of 6-7 ms. These results indicate that the force generating stroke elicited by a shortening step is followed by a relatively rapid process of detachment and reattachment by most of the cross-bridges, allowing for the generation of another power stroke. The rate of this process, 150/s, is one order of magnitude higher than that expected from the ATPase rate, suggesting that several actomyosin interactions occur in shortening muscle by the time one ATP is split. The results are stimulated with a mechanical kinetic model of contraction, in which, for a critical amount of shortening, cross-bridges can detach, rapidly reattach and generate force before the completion of the "normal" isometric cycle.

Effects of inorganic phosphate analogues on stiffness and unloaded shortening of skinned muscle fibres from rabbit

1. We examined the effects of aluminofluoride (AlFx) and orthovanadate (Vi), tightly binding analogues of orthophosphate (Pi), on the mechanical properties of glycerinated fibres from rabbit psoas muscle. Maximum Ca(2+)-activated force, stiffness, and unloaded shortening velocity (Vus) were measured under conditions of steady-state inhibition (up to 1 mM of inhibitor) and during the recovery from inhibition. 2. Stiffness was measured using either step or sinusoidal (1 kHz) changes in fibre length. Sarcomere length was monitored continuously by helium-neon laser diffraction during maximum Ca2+ activation. Stiffness was determined from the changes in sarcomere length and the corresponding changes in force. Vus was measured using the slack test method. 3. AlF chi and Vi each reversibly inhibited force, stiffness and Vus. Actively cycling cross-bridges were required for reversal of these inhibitory effects. Recovery from inhibition by AlF chi was 3- to 4-fold slower than that following removal of V1. 4. At various degrees of inhibition, AlF chi and Vi both inhibited steady-state isometric force more than either Vus or stiffness. For both AlF chi and Vi, the relatively greater inhibition of force over stiffness persisted during recovery from steady-state inhibition. We interpret these results to indicate that the cross-bridges with AlF chi or Vi bound are analogous to those which occur early in the cross-bridge cycle.

Mechanics and structure of cross-bridges during contractions initiated by photolysis of caged Ca2+

Cross-bridge structure and mechanics were studied during development of skinned frog muscle fiber contractions initiated by photolysis of DM-nitrophen (a caged Ca2+). Stiffness rises earlier than tension following photo-release of Ca2+. A similar lead of stiffness in electrically stimulated fibers and the early rise of the I11/I10 ratio of equatorial X-ray reflections are thought to signal attachment of cross-bridges into states with lower force than in steady-state contraction. We investigated the structure of the early attachments by electron microscopy of fibers activated by photolysis of DM-nitrophen and then ultra-rapidly frozen and freeze substituted with tannic acid and OsO4. Sections from relaxed fibers show helical tracks of myosin heads on the thick filaments surface. Optical diffraction patterns show strong meridional intensities and layer lines up to the 6th order of 1/43 nm, indicating preservation and resolution of periodic structures smaller than 10 nm. Following photo-release of Ca2+, the 1/43 nm myosin layer line becomes less intense, and higher orders disappear. A approximately 1/36 nm layer line appears early (12-15 ms) and becomes stronger at later times. The 1/14.3 nm meridional spot weakens initially and recovers at a later time, while it broadens laterally. The 1/43 nm meridional spot is present during contraction, but the 2nd order meridional spot (1/21.5 nm) is weak or absent. These results are consistent with time resolved X-ray diffraction data on the periodic structures within the fiber. In sections along the 1,1 plane of activated fibers, the individual cross-bridges have a wide range of shapes and angles, perpendicular to the fiber axis or pointing toward or away from the Z-line. Fibers frozen at 13 ms, 33 ms, and 220 ms after photolysis all show surprisingly similar cross-bridges. Thus, a highly variable distribution of cross-bridge shapes and angles is established early in contraction.

Force and stiffness in glycerinated rabbit psoas fibers. Effects of calcium and elevated phosphate

Force (F) and stiffness (K) were measured in glycerinated psoas fibers at various calcium levels with 0, 10, 20, and 30 mM orthophosphate (Pi) added to the bathing solutions. The concentrations of bathing solution constituents were as follows: 110 mM potassium, 40 mM sodium, 4 mM MgATP, 10 mM total EGTA, and variable amounts of MOPS (pH buffer). The pH was 7.0, the ionic strength was 200 mM, and the temperature was 10 degrees C. Calcium levels were established by adding various amounts of CaCl2. All solutions contained 4% Dextran T-500. Fiber K was measured by imposing sinusoidal length changes (0.03-0.1%) at 1 kHz and by applying rapid steps in length and measuring the resulting F changes. At all [Pi] tested, K was more sensitive to calcium than F. Elevating bathing solution [Pi] caused a decrease in the calcium sensitivity of both F and K, while the slopes of F-calcium and K-calcium relations increased. In maximally activating calcium, raising [Pi] caused a continuous decrease in F over the range tested, while from very low to 10 mM Pi K remained constant. Above 10 mM Pi K declined, but to a lesser extent than did F. The results suggest that under our experimental conditions strongly attached crossbridges can exist in both force-producing and non-force-producing states, and that the relative population of these states may be calcium dependent.

Rapid regeneration of the actin-myosin power stroke in contracting muscle

At the molecular level, muscle contraction is the result of cyclic interaction between myosin crossbridges, which extend from the thick filament, and the thin filament, which consists mainly of actin. The energy for work done by a single crossbridge during a cycle of attachment, generation of force, shortening and detachment is believed to be coupled to the hydrolysis of one molecule of ATP. The distance the actin filament slides relative to the myosin filament in one crossbridge cycle has been estimated as 12 nm by step-length perturbation studies on single fibres from frog muscle. The 'mechanical' power stroke of the attached crossbridge can therefore be defined as 12-nm shortening with a force profile like that shown by the quick recovery of force following a length perturbation. According to this definition, power strokes cannot be repeated faster than the overall ATPase rate. Here, however, we show that the power stroke can be regenerated much faster than expected from the ATPase rate. This contradiction can be resolved if, in the shortening muscle, the free energy of ATP hydrolysis is used in several actin-myosin interactions consisting of elementary power strokes each of 5-10 nm.

Tension transients during steady lengthening of tetanized muscle fibres of the frog

1. Steady lengthenings at different velocities (0.02-1.6 microns/s per half-sarcomere, temperature 2.5-5.5 degrees C) were imposed on isolated frog muscle fibres at the plateau of the isometric tetanus (tension T0). When tension during lengthening had attained a steady value (Ti), which varied from about 1.5 to about 2 times T0 depending on lengthening velocity, tension transients were elicited by applying step length changes of different amplitudes. The change in length of a selected segment, close to the end of the fibre connected to the force transducer, was controlled by means of a striation follower. 2. The instantaneous plots of tension versus the length change during the step itself showed that at the high forces developed during steady lengthening, as at the plateau of isometric tetanus, the elasticity of the fibre was almost undamped in the whole range of lengthening velocities used. 3. The tension transient elicited by step length changes imposed in isometric conditions exhibited the characteristic four phases described previously: following the tension change simultaneous with the step (phase 1), there was a quick partial recovery (phase 2, the speed of which increased going from the largest step stretch to the largest step release), a subsequent pause or inversion in recovery (phase 3) and finally a slower approach to the tension before the step (phase 4). 4. In the region of small steps the plot of the extreme tension attained during the step (T1) versus step amplitude appeared more linear during steady lengthening than in isometric conditions and deviated progressively from linearity with increase in the size of step releases. The amount of instantaneous shortening necessary to drop tension to zero (Y0), measured by the abscissa intercept of the straight line drawn through T1 points for small steps, was about 4.1 nm per half-sarcomere in isometric conditions and 5.4 nm per half-sarcomere during lengthening at low speed (0.09 microns/s per half-sarcomere, Ti about 1.6 T0). Taken altogether this indicates, in agreement with previous work, that force enhancement during steady lengthening is due to increase in both number and extension of attached cross-bridges. During lengthening at high speed (0.8 microns/s per half-sarcomere), further enhancement in steady force (Ti about 1.9 T0) was accompanied by increase of Y0 to 6.3 nm per half-sarcomere, indicating that increase in lengthening velocity exclusively produces increase in cross-bridge extension.(ABSTRACT TRUNCATED AT 400 WORDS)

Null-balance transducer for isometric force measurements and length control of single heart cells

Recently, an ultrasensitive, optical-fiber-based force transducer was developed to measure the microscopic force of contraction of single heart cells. Since force in cardiac muscle is length and velocity dependent, it is desirable to maintain a constant (isometric) cell length. The original design permits approximately 1% shortening of cell length to occur during twitch contractions. The shortening can be reduced significantly by adding a piezoelectric bimorph actuator and closed-loop control, as described in this paper. As a result, the effective stiffness of the transducer can be increased by a factor of about 100, and cell shortening reduced to approximately 0.01%. For the force probes typically used, this is equivalent to a movement of less than 20 nm for a typical value of 100 nN peak cell force in single frog ventricular cells. The gain in stiffness is obtained without sacrificing sensitivity, although at the expense of frequency response. The new design also permits control of cell length and is applicable to studies of the mechanical stiffness of cardiac cells.

Time-resolved changes in equatorial x-ray diffraction and stiffness during rise of tetanic tension in intact length-clamped single muscle fibers

We report the first time-resolved x-ray diffraction studies on tetanized intact single muscle fibers of the frog. The 10, 11, 20, 21, 30, and Z equatorial reflections were clearly resolved in the relaxed fiber. The preparation readily withstood 100 1-s duration (0.4-s beam exposure) tetani at 4 degrees C (less than 4% decline of force and no deterioration in the 10, 11 equatorial intensity ratio at rest or during activation). Equatorial intensity changes (10 and 11) and fiber stiffness led tension (t1/2 lead 20 ms at 4 degrees C) during the tetanus rise and lagged during the isometric phase of relaxation. These findings support the existence of a low force cross-bridge state during the rise of tetanic tension and isometric relaxation that is not evident at the tetanus plateau. In "fixed end" tetani lattice expansion occurred with a time course similar to stiffness during the tetanus rise. During relaxation, lattice spacing increased slightly, while the sarcomere length remained isometric, but underwent large changes after the "shoulder" of tension. Under length clamp control, lattice expansion during the tetanus rise was reduced or abolished, and compression (2%) of the lattice was observed. A lattice compression is predicted by certain cross-bridge models of force generation (Schoenberg, M. 1980. Biophys. J. 30:51-68; Schoenberg, M. 1980. Biophys. J. 30:69-78).

The contractile response during steady lengthening of stimulated frog muscle fibres

1. Steady lengthenings at different velocities (0.025-1.2 microns/s per half-sarcomere; temperature 2-5.5 degrees C) were imposed on isolated frog muscle fibres at the isometric tetanus plateau by means of a loudspeaker motor. The lengthening at the sarcomere level was measured by means of a striation follower either in fixed-end or in length-clamp mode. The force response was measured by a capacitance gauge transducer (resonance frequency 50 kHz). Preparations showing gross non-homogeneity during lengthening were excluded. 2. A steady tension was in all cases reached after about 20 nm per half-sarcomere of lengthening. Tension during this steady phase rose with speed of elongation up to 0.25-0.4 micron/s per half-sarcomere, when tension was 1.9-2 times isometric tetanic force (T0). Further increase in speed produced only very little increase in the steady tension. 3. During the transitory phase, before steady tension was reached, the tension rose monotonically if speed of lengthening was less than 0.25-0.3 micron/s per half-sarcomere; at higher speed the tension rose above the steady level, reaching a peak when extension was 10-14 nm per half-sarcomere, and then fell to the steady level. Tension at the peak continued to rise with speed of lengthening above 0.3 micron/s per half-sarcomere. 4. During the tension rise within the transitory phase of force response the segment elongated at a speed 15-20% lower than that imposed on the whole fibre, as a consequence of tendon compliance. 5. During the steady phase, non-homogeneity of lengthening speed began above a speed of lengthening which varied from fibre to fibre. At speeds below this value, segments elongated at the same speed as that imposed on the fibre. 6. Tension responses to large step stretches (up to 12 nm per half-sarcomere), applied at the plateau of isometric tetanus, showed that the instantaneous elasticity of contractile machinery is not responsible for the limit in force attained with high-speed lengthening. 7. Instantaneous stiffness was determined during the steady state of force response by superposing small steps (less than 1.5 nm per half-sarcomere) on steady lengthening at different velocities. Stiffness was 10-20% larger during lengthening than at the plateau of isometric tetanus and remained practically constant, independent of lengthening velocity, in the range of velocities used. 8. The results indicate that steady lengthening of a tetanized fibre induces a cross-bridge cycle characterized by fast detachment of the cross-bridge extended beyond a critical level.(ABSTRACT TRUNCATED AT 400 WORDS)

Myofilament spacing and force generation in intact frog muscle fibres

1. The relation between sarcomere length and steady tetanic tension was determined at 10-12 degrees C for 70-80 microns long length-clamped segments of single fibres isolated from the tibialis anterior muscle of the frog, in normal and hypertonic or hypotonic Ringer solutions. 2. The tension depression and potentiation observed in hypertonic and hypotonic Ringers solutions varied with sarcomere length, so that, as opposed to myofilament overlap predictions, the optimum length for tension development was shorter in hypertonic Ringer solution and longer in hypotonic Ringer solution than in normal Ringer solution. As the fibres were stretched from 1.96 to 2.24 microns sarcomere length, both tension depression in hypertonic Ringer solution and tension potentiation in hypotonic Ringer solution increased by 9 and 5%, respectively. 3. Within this range of sarcomere lengths the length-stiffness relation in hypotonic and in hypertonic Ringer solutions exhibit little or no change relative to that in normal Ringer solution. 4. The results indicate that separation between the thick and the thin myofilaments influences the mechanism of force generation. There is an optimum interfilament distance (10-12 nm surface to surface between the thick and the thin filaments) for tension production. In isotonic Ringer solution, this corresponds to the interfilament distance at sarcomere lengths around 2.10 microns. The force per attached cross-bridge, rather than their number, appears to decrease as the interfilament distance is brought above or below the optimum length. Even if this effect is moderate in isotonic Ringer solution, it should be taken into account in models of the force-generation mechanism.

Tension and stiffness of frog muscle fibres at full filament overlap

Stiffness measurements in activated skeletal muscle fibres are often used as one means of estimating the number of attached crossbridges on the assumption that myofilament compliances do not contribute significantly to the fibre compliance. This assumption was tested by studying the effects of sarcomere length on fibre stiffness in the plateau region of the length-tension diagram (from 1.96 to 2.16 microns sarcomere length in the tibialis anterior muscle of the frog). Lengthening of the sarcomere across this region in fact, produces only an increase in the proportion of actin filament free from cross-bridges without altering the amount of effective overlap; no change in fibre stiffness is therefore expected if actin filaments are perfectly rigid. The results show that while tetanic tension remained constant within 1.5%, as the sarcomere length was increased from 1.96 to 2.16 microns fibre stiffness decreased by about 4%, indicating that a significant proportion of sarcomere compliance is localized in the actin filaments. A simple model based on the sliding filament theory was used in order to calculate the relative contribution of actin filaments to fibre compliance. In the model it was assumed that fibre compliance resulted from the combination of crossbridge compliance (distributed over the overlap zone) in series with thin filament and tendon compliances. The calculations show that the experimental data could be adequately predicted only assuming that about 19% of sarcomere compliance is due to actin filament compliance.

Crossbridge activity monitored from the state of polarization of light diffracted by activated frog muscle fibres

The polarization properties of the first diffraction order have been measured when single frog fibres are illuminated by laser light. The relative difference in the amplitudes of the orthogonal electric field polarization components (differential field ratio) as well as their phase shift normalized by the pathlength (birefringence) have been obtained from fibres at rest and during fixed-end twitches and tetani. The differential field ratio decreased during contraction and the change during a single twitch averaged 69% of that during a companion tetanus. The birefringence of the first order averaged 2.80 +/- 0.59 x 10(-3) (mean +/- SD) at rest and the average decrease during a tetanus was 8.4% +/- 6.4%. The decrease in the differential field ratio upon activation was a decreasing function of sarcomere length, maximum at rest length and falling to zero at about 3.7 microns. Differences between the two first diffraction orders were observed for both the differentiated field ratio and the birefringence. At the time when force had risen to half the value reached at the end of the fast rise of tension, the change in the differential field ratio lead the tension by about 10-15 ms. The differential field ratio returned to its resting value after the fall of tension. The above results suggest that the differential field ratio is a sensitive indicator of intact fibre structure. The temporal lead in the differential field ratio with respect to tension rise supports models in which crossbridges initially attach in a non-force-producing state.

Mechanisms relating force and high-frequency stiffness in skeletal muscle

Muscle stiffness increases faster than muscle force during the rising phase of a tetanic contraction, and decreases more slowly during the falling phase. Different models of the stiffness arising from series, parallels, and crossbridge elasticity were compared to determine whether they could account quantitatively for the observed time course of force and stiffness. Data for slow and fast twitch mouse muscles at temperatures from 6 to 37 degrees C (Stein and Gordon, Can. J. Physiol. Pharmacol. 64, 1236-1244, 1986) and for single frog muscle fibers (Cecchi et al., Contractile Mechanisms in Muscle, pp. 641-655. Plenum, New York, 1984) were compared. The results showed that a good fit to the data for mouse muscles could be obtained with a model in which: (1) a nonlinear series elasticity contributed significantly to stiffness; (2) the attached crossbridges went from a stiff, force-generating state to a stiff, non-force-generating state; and (3) the rate of transition between these two states increased abruptly at the onset of relaxation. The increased transition rate probably arises from the internal rearrangement in which some sarcomeres shorten at the expense of other sarcomeres, once the muscle begins to relax. A significant series elasticity was not required for the frog data, but a pre-tension state was then needed to obtain a good fit.

A model of force production that explains the lag between crossbridge attachment and force after electrical stimulation of striated muscle fibers

Whereas the mechanical behavior of fully activated fibers can be explained by assuming that attached force-producing crossbridges exist in at least two configurations, one exerting more force than the other (Huxley A. F., and R. M. Simmons. 1971. Nature [Lond.]. 233:533-538), and the behavior of relaxed fibers can be explained by assuming a single population of weakly binding rapid-equilibrium crossbridges (Schoenberg, M. 1988. Biophys. J. 54:135-148), it has not been possible to explain the transition between rest and activation in these terms. The difficulty in explaining why, after electrical stimulation of resting intact frog skeletal muscle fibers at 1-5 degrees C, force development lags stiffness development by more than 15 ms has led a number of investigators to postulate additional crossbridge states. However, postulation of an additional crossbridge state will not explain the following three observations: (a) Although the lag between force and stiffness is very different after stimulation, during the redevelopment of force after an extended period of high velocity shortening, and during relaxation of a tetanus, nonetheless, the plots of force versus stiffness in each of these cases are approximately the same. (b) When the lag between stiffness and force during the rising phase of a twitch is changed nearly fourfold by changing temperature, again the plot of force versus stiffness remains essentially unchanged. (c) When a muscle fiber is subjected to a small quick length change, the rate constant for the isometric force recovery is faster when the length change is applied during the rising phase of a tenanus than when it is applied on the plateau. We have been able to explain all the above findings using a model for force production that is similar to the 1971 model of Huxley and Simmons, but which makes the additional assumption that the force-producing transition envisioned by them is a cooperative one, with the back rate constant of the force-producing transition decreasing as more crossbridges attach.