Size and speed of the working stroke of cardiac myosin in situ

Marco Caremani; Francesca Pinzauti; Massimo Reconditi; Gabriella Piazzesi; Ger J. M. Stienen; Vincenzo Lombardi; Marco Linari

doi:10.1073/pnas.1525057113

New Research In

Edited by James A. Spudich, Stanford University School of Medicine, Stanford, CA, and approved February 19, 2016 (received for review December 18, 2015)

Significance

To our knowledge, this paper represents a major advancement in the physiology and pathophysiology of the heart as it gives the first quantitative description of the working stroke of the motor protein cardiac myosin II. The experiments demonstrate that our sarcomere-level mechanical methods on trabeculae have the full potential for the in situ investigation of cardiomyopathy-causing mutations in cardiac myosin and tests on specific therapeutic interventions.

Abstract

The power in the myocardium sarcomere is generated by two bipolar arrays of the motor protein cardiac myosin II extending from the thick filament and pulling the thin, actin-containing filaments from the opposite sides of the sarcomere. Despite the interest in the definition of myosin-based cardiomyopathies, no study has yet been able to determine the mechanokinetic properties of this motor protein in situ. Sarcomere-level mechanics recorded by a striation follower is used in electrically stimulated intact ventricular trabeculae from the rat heart to determine the isotonic velocity transient following a stepwise reduction in force from the isometric peak force T_P to a value T (0.8–0.2 T_P). The size and the speed of the early rapid shortening (the isotonic working stroke) increase by reducing T from ∼3 nm per half-sarcomere (hs) and 1,000 s⁻¹ at high load to ∼8 nm⋅hs⁻¹ and 6,000 s⁻¹ at low load. Increases in sarcomere length (1.9–2.2 μm) and external [Ca2+]o (1–2.5 mM), which produce an increase of T_P, do not affect the dependence on T, normalized for T_P, of the size and speed of the working stroke. Thus, length- and Ca²⁺-dependent increase of T_P and power in the heart can solely be explained by modulation of the number of myosin motors, an emergent property of their array arrangement. The motor working stroke is similar to that of skeletal muscle myosin, whereas its speed is about three times slower. A new powerful tool for investigations and therapies of myosin-based cardiomyopathies is now within our reach.

The performance of heart depends on the power developed by the myocardium, which in turn is strongly dependent on the end-diastolic volume modulating the systolic pressure development (Frank–Starling law of the heart). At the level of the sarcomere, the structural unit of striated muscle, the Frank–Starling law originates from the increase in the force of contraction with an increase in sarcomere length (length-dependent activation). Mutations of sarcomere proteins affect power output and are considered responsible for various forms of cardiomyopathy (1, 2). Over 250 mutations in cardiac myosin II have been reported as the cause of cardiomyopathies (1, 3, 4). Defining the mechanokinetic properties of the cardiac myosin in situ is therefore fundamental to understand the pathomechanisms of these cardiomyopathies and to provide previously unidentified therapeutic opportunities.

In the sarcomere, the myosin motors are organized in two bipolar arrays extending from the thick filament and pulling the thin actin-containing filaments from the opposite sides of the sarcomere toward its center. In each array, the myosin motors are connected in parallel via their attachments to the thick filament and the resulting collective motor provides steady force and shortening by cyclic asynchronous ATP-driven actin–myosin interactions. Thus, the performance of the heart relies on the integration of the mechanokinetic properties of the myosin motor and the properties emerging from its array arrangement in the half-sarcomere (hs). Using sarcomere-level mechanics in intact cells from the skeletal muscle, it has been shown that the isotonic velocity transient following stepwise changes in force imposed on the otherwise isometric contraction contains information on both the working stroke of the myosin motor and the steady-state force–velocity (T–V) relation resulting from the cyclic actin–myosin interactions and accounting for the power output (5 ⇓⇓⇓–9).

Here, this approach is applied for the first time (to our knowledge) to a multicellular cardiac preparation like the intact trabecula dissected from the right ventricle of the rat heart. A striation follower (10) proved to be a reliable tool for measurement of sarcomere length changes with nanometer–microsecond resolution owing to optical averaging of the image of the sarcomeres that reduces the background noise originating from intracellular and intercellular components of the trabecula. Following the original idea by ter Keurs et al. (11), the sarcomere shortening recorded during the force development in a fixed-end twitch is used as a feedforward signal to maintain sarcomere length constant during the next twitch. By switching from length control to force control, a stepwise drop in force was imposed at the peak of force (T_P) to record the isotonic velocity transient. In this way, the amplitude and speed of the rapid phase of the transient (phase 2), which is the mechanical manifestation of the myosin working stroke, could be determined. Increases in sarcomere length (SL) from 1.9 to 2.2 μm and in the external Ca²⁺ concentration ([Ca2+]o) from 1 to 2.5 mM, which produce an increase in T_P, do not affect the myosin working stroke. This indicates that length-dependent potentiation of cardiac contractility is fully accounted for by an increase in the number of attached myosin motors. These experiments demonstrate that our sarcomere-level mechanical methods have the full potential for the in situ investigation of cardiomyopathy-causing mutations in cardiac myosin.

Results and Discussion

Force–SL Relation.

The twitch in response to an electrical stimulus at the steady state of 0.5-Hz electrical pacing with 1 mM [Ca2+]o in fixed-end conditions is shown in Fig. 1A (black trace). During force development (Upper), sarcomeres shorten against the compliant end regions by 80 nm per hs (Lower), corresponding to 7.3% L₀. This internal shortening was prevented in the next twitch (gray trace) by feeding the summing point of the motor servo-system with an equivalent inverted signal (Middle). The peak force (T_P) attained in these sarcomere-isometric conditions was considerably larger (30%) than that attained under fixed-end conditions, while the sarcomere shortening was completely prevented (Lower). The relation between T_P and SL (range, 1.9–2.4 μm) obtained in 1 mM [Ca2+]o is shown in Fig. 1B (circles). The plotted data indicate T_P after subtraction of the passive force (squares) that starts to rise at SL >2.15 µm (see also Fig. S1). It can be seen that data from fixed-end conditions (filled circles) lie on the same relation as those in sarcomere-isometric conditions (open circles). Thus, there is a unique relation between peak force and SL, independently of the shortening undergone during force rise. At SL of 2.3 μm, T_P reaches a value of 87 ± 6 kPa (mean ± SEM), almost twice the value at SL of 2.0 μm. These results agree with the original study by ter Keurs et al. (11), who used laser diffraction to record and clamp SL.

Fig. 1.

Force developed in a twitch and its relation with SL. (A) Force development upon electrical stimulation at 0.5 Hz and 1.0 mM [Ca2+]o, during fixed-end (black trace) and isometric-sarcomere conditions (gray trace) at an initial SL of 2.2 μm.Upper trace, force; middle trace, motor position; lower trace, hs length change. The isometric-sarcomere force development is obtained by the feedforward lengthening imposed on the trabecula as detailed in the text and prevents sarcomere shortening during force development. The bar on the force trace marks the stimulus start. Length of the trabecula, 3.35 mm; segment length under the striation follower, 1.28 mm; average SL, 2.18 μm; cross-sectional area, 26,700 μm²; temperature, 27.2 °C. (B) Relations between peak force (T_P) and SL at 1 mM [Ca2+]o (active force, circles; passive force, squares) and 2.5 mM (active force, triangles). The lines are polynomial fits to data. The relation between active force and SL obtained in fixed-end conditions (filled circles) does not differ from that under sarcomere-isometric conditions (open circles) in which the initial SL shortening was prevented by the feedforward method. Mean values ± SEM from eight trabeculae for 1 mM [Ca2+]o and four trabeculae for 2.5 mM [Ca2+]o. Each point is the average of three to eight data points from different trabeculae.

Fig. S1.

Relation between SL and trabecula length (relative to L₀) in a quiescent trabecula. Points are the mean ± SD (two trabeculae with L₀ of 1.1 and 2.5 mm). A progressive deviation of SL from the value expected from the linear relation (dashed line) appears with the rise of passive force, as part of the imposed lengthening is taken by the compliant ends of the trabecula. The continuous line is a parabolic fit to data.

The rise in [Ca2+]o to 2.5 mM increases T_P at any SL, so that the relation is shifted upward (triangles). Actually, the two curves do not run parallel, because with [Ca2+]o of 2.5 mM the relation is more concave, apparently reaching a force maximum at SL of 2.3 μm (see also ref. 11).

Isotonic Velocity Transients.

The isotonic velocity transient was elicited by superimposing, on the peak force of an otherwise isometric contraction at 1 mM [Ca2+]o, a stepwise drop in force from T_P to a value in the range of 0.2–0.8 T_P. Fig. 2 A and B show the isotonic velocity transient in response to a drop in force to 0.5 T_P from a typical experiment at SL of 2.2 µm. Several phases could be distinguished, named after those first described in single fibers from frog skeletal muscle (8, 12): phase 1, a shortening simultaneous with the drop in force, due to the hs elasticity; phase 2, the early rapid shortening, which is attributed to the synchronous execution of the working stroke in the attached myosin motors; phase 4, the late steady shortening at constant velocity due to cyclic detachment-reattachment of motors. Apparently, in contrast to skeletal muscle, there is not a pause (phase 3) in shortening between the end of phase 2 and beginning of phase 4.

Fig. 2.

Isotonic velocity transients following a stepwise drop in force. (A) Shortening of the hs (lower trace) in response to a step to 0.5 T_P superimposed on the force at a time just before the attainment of the peak force developed under sarcomere-isometric conditions (upper trace); middle trace, motor position. (B) Same shortening response as in A on a faster timescale. Numbers close to the shortening record identify the phases of the transient named after those first described in skeletal muscle (8). (C and D) Early components of the isotonic velocity transient to show the methods for estimating L₁ and L₂ (C in response to a step to 0.75 T_P, and D for the same record as in A). L₁ is measured by extrapolating the tangent to the initial part of phase 2 (magenta line) back to the half-time of the force step (t_1/2, indicated by the vertical dashed line). L₂ is measured by extrapolating the ordinate intercept of the straight line fitted to phase 4 shortening (green line in C and D, the slope of which measures the steady shortening velocity) back to t_1/2. (E) Time course of phase 2 shortening calculated by subtracting the green line fitted to phase 4 shortening from the overall shortening transient. L_T, the size of the isotonic working stroke, is obtained by subtracting the elastic response L₁ from L₂. The green dashed line is the exponential fit to the trace starting from the end of the force step (Fig. S2). (F) Superimposed SL signal (black) and motor lever signal (red dashed) after subtraction of phases 1 and 4. Length of the trabecula, 2.5 mm; segment length under the striation follower, 1.4 mm; average SL, 2.19 μm; cross-sectional area, 14,100 μm²; temperature, 27.1 °C.

The merging between the end of the elastic shortening (phase 1) and the early rapid shortening (phase 2) might result in an overestimation of the elastic response at the expenses of the working stroke response (8). Therefore—as illustrated in Fig. 2C (for a force drop to 0.75 T_P) and Fig. 2D (same record as Fig. 2A)—to estimate the size of phase 1 (L₁), the contribution of phase 2 to phase 1 is subtracted by back-extrapolating, to the force step half-time (t_1/2, vertical dashed line), the tangent to the initial part of phase 2 (magenta line). Phase 2 following the elastic response has a nearly exponential time course and its size can be estimated by subtracting, from the length trace, the linear back extrapolation of the phase 4 shortening trace to t_1/2 (green line in Fig. 2 C and D). The distance between the horizontal trace obtained with the subtraction procedure and the length before the step (Fig. 2E, from the same record as in Fig. 2A) estimates the total amount of shortening at the end of phase 2 (L₂). The difference (L₂ − L₁) estimates L_T, the amount of shortening accounted for by the working stroke of the myosin motors at the force T. Assuming an exponential time course of phase 2 shortening, the time elapsed between t_1/2 and the abscissa intercept of the tangent to the initial part of the trace (magenta line) is an estimate of the time constant of phase 2 shortening and its reciprocal is an estimate of the rate constant of the process (r₂). r₂ can be estimated also by fitting the shortening trace with an exponential starting from the end of the imposed force step (green dashed line in Fig. 2E, and Fig. S2). As shown in the table in Fig. S2, the two methods gave similar results and the value of r₂ obtained with the exponential fit has been used throughout the paper.

Fig. S2.

Estimate of the rate of phase 2 velocity transient. Shortening transient elicited by a force step to ∼0.5 T_P (Upper) and to ∼0.75 T_P (Lower) after subtraction of phase 4 shortening. r₂ is estimated either as the reciprocal of the time between t_1/2 (vertical dashed line as in Fig. 2C) and the abscissa intercept of the tangent to the initial part of phase 2 shortening (magenta line as in Fig. 2C), r_2,tg, or from the exponential fit (green dashed line) of the trace starting from the end of the force step (dotted vertical line), r_2,exp. As shown in the table, the two methods gave similar results (mean ± SEM from four trabeculae).

After the elastic phase 1 response occurring during force drop, the rest of shortening transient occurs at constant force and thus is independent of the amount of series compliance. In fact, as shown in Fig. 2F (from the same record as Fig. 2A), the phase 2 shortening obtained as described above from the position of the motor hook (motor lever position, red dashed trace) perfectly superimposes on that obtained from the SL signal (L, black trace).

L₁ (triangles) and L₂ (circles) dependence on T is shown in Fig. 3A. L_T calculated from these data (open circles in Fig. 3B) and L_T estimated from the motor lever position signal show the same dependence on T.

Fig. 3.

Force dependence of the parameters of phase 2 velocity transient and effect of changes in SL and Ca²⁺ concentration. (A) L₁ relation (triangles) and L₂ relation (circles) at SL of 2.2 µm and 1 mM [Ca2+]o (pooled data from three trabeculae). Lines are the linear regression fit to data. (B) L_T–T relation for the same experiments as in A, open circles from the striation follower signal, filled circles from the motor position signal. The line is the linear regression fit. (C) L_T–T relations at different SL and Ca²⁺ concentration. Circles refer to the SL experiments with [Ca2+]o of 1 mM (open circles, 2.2 µm; filled circles, 1.9 µm), and squares refer to the Ca²⁺ experiments at SL of 2.2 µm (open squares, 1 mM [Ca2+]o; filled squares, 2.5 mM [Ca2+]o). Lines are the linear regression fits to data: continuous, SL of 2.2 µm and 1 mM; dashed, 1.9 µm and 1 mM; dot-dashed, 2.2 µm and 2.5 mM. (D) Rate of the isotonic working stroke (r₂) in relation to T. Lines are the parabolic fit to data. Symbol and line codes are as in C. In all plots, T is relative T_P in each condition. Data are mean values ± SEM from eight trabeculae.

The results pooled from the eight trabeculae analyzed at SL of 2.2 µm and 1 mM Ca²⁺ are shown by the open symbols in Fig. 3C. L_T increases with the reduction of T from 3 nm⋅hs⁻¹ at 0.8 T_P to 8 nm⋅hs⁻¹ at 0.2 T_P. The intercept on the ordinate of the linear fit (continuous line) to the L_T data (the size of the working stroke at zero load) is 9.7 ± 0.3 nm. r₂ increases with the reduction of the load (open symbols in Fig. 3D) from ∼1,000 s⁻¹ at 0.8 T_P to ∼6,000 s⁻¹ at 0.2 T_P.

Phase 2 evolves directly into the final steady shortening characteristic of the force–velocity relation (phase 4, open symbols in Fig. 4 A and B). The curvature (a/T_P= 0.33 ± 0.03) and the ordinate intercept (the unloaded shortening velocity, V₀ = 8.40 ± 0.25 μm/s per hs) of the relation are estimated by fitting the hyperbolic Hill equation to data.

Fig. 4.

Force dependence of the parameters of phase 4 of the velocity transient and effect of changes in SL and Ca²⁺ concentration. Symbol and line codes are as in Fig. 3C. (A) Relation between steady shortening in phase 4 (V) and force. (B) Same relations as in A after normalization of the abscissa for the peak force (T_P) in each condition. (C) Comparison between shortening velocity in phase 2 (V₂ = L_T·r₂, blue symbols) and in phase 4 (V, black symbols) in relation to T relative to T_P in each condition. (D) Power–force relations calculated from the data in C. The lower abscissa is the force in units relative to T_P at SL of 2.2 µm and 1 mM [Ca2+]o (T_P, _2.2, _1mM). Lines in A–C are the fits to the data using the hyperbolic Hill equation (Methods). Lines in D are calculated from the lines in A. Data are mean values ± SEM from eight trabeculae (the same as in Fig. 3 C and D).

The sliding velocity in phase 2 (V₂), estimated as the product of L_T times r₂, has also a hyperbolic dependence on T (Fig. 4C, blue open symbols). V₂ increases from ∼3,000 nm/s per hs at 0.8 T_P to 50,000 nm/s per hs at 0.2 T_P. Thus, as in frog muscle fibers (6, 8), the sliding velocity accounted for by the execution of the working stroke is one order of magnitude higher than that accounted for by cyclic ATP-driven actin–myosin interactions during steady shortening (Fig. 4C, black open symbols).

The Size and Speed of the Working Stroke Do Not Depend on SL and External Ca²⁺ Concentration.

The reduction in SL from 2.2 to 1.9 μm, which reduces T_P from 70 to 30 kPa (circles in Fig. 1B), does not affect the size and the rate of the working stroke nor its dependence on T relative to T_P at the corresponding SL. L_T– and r₂–T relations at SL of 1.9 μm (filled circles in Fig. 3 C and D, respectively) superimpose on those at SL of 2.2 μm (open circles). The relation between steady shortening velocity and force at SL of 1.9 μm (filled circles in Fig. 4A) is shifted below with respect to that determined at 2.2 μm (open symbols), as expected from the effect of SL on T_P. In fact, the parameters of the Hill equation a/T_P (0.39 ± 0.13) and V₀ (8.02 ± 0.76 μm/s per hs) are not significantly different (P > 0.6) from those estimated from the data obtained at SL of 2.2 μm and the two relations superimpose when force is plotted relative to T_P at the corresponding SL (Fig. 4B). The finding that V₀ is similar at 1.9- and 2.2-μm SL is in agreement with previous work on intact rat trabeculae (13).

The effect of [Ca2+]o on the isotonic velocity transient was determined in another series of experiments at SL of 2.2 μm. As shown in Fig. 3 C and D, the increase in [Ca2+]o from 1 mM (open squares) to 2.5 mM (filled squares), which increases T_P from 66 ± 6 to 99 ± 10 kPa, does not affect the dependence on T of either the size (Fig. 3C) or the speed (Fig. 3D) of the working stroke. The force–velocity relation is shifted above by the increase in [Ca2+]o (filled squares in Fig. 4A), as expected from the effect of [Ca2+]o on T_P. In fact, when the force is normalized for the corresponding value of T_P, the relations at the two [Ca2+]o superimpose (Fig. 4B). The parameters of the Hill equation a/T_P (0.39 ± 0.06) and V₀ (8.74 ± 0.31 μm/s per hs) are not significantly different (P > 0.3) from those estimated with [Ca2+]o of 1 mM at either 2.2- or 1.9-μm SL. Thus, in agreement with the original work of ter Keurs and collaborators (11, 13, 14), the potentiating effects of the increases of [Ca2+]o and SL on force appear to act through the same mechanism.

The power at each T can be calculated as the product V⋅T. The power–T relation with [Ca2+]o of 1 mM and SL of 2.2 µm (Fig. 4D, open symbols, used as the control for the normalization of all T values for a unique value of T_P, defined as T_P, _2.2, _1mM) shows a maximum at 0.3 peak force. Decrease of SL to 1.9 µm, which reduces the peak force to 0.3 T_{P, 2.2, 1mM}, reduces the maximum power (filled circles), which is still attained at force 0.3 its peak value, to ∼0.3 the maximum power in control, an effect that is fully accounted for by the effect on T_P. Increase of [Ca2+]o at SL of 2.2 µm from 1 to 2.5 mM, which increases the force peak to 1.5 T_P, _2.2, _1mM, increases the maximum power (filled squares), attained again at force 0.3 its peak value, to 1.5 the maximum power in control.

In conclusion, all of the data reported in Figs. 3 and 4, either transient or steady state, converge to the conclusion that increase of [Ca2+]o and increase of SL in the range considered increase the isometric force through a common underlying mechanism, which is not related to modulation of the motor mechanokinetic properties but rather to change in the number of active force-generating motors, which is an emergent property of the array arrangement of the motors in the hs.

The Working Stroke of Cardiac Myosin in Situ in Relation to Previous Work.

Literature concerning the in situ measurement of the mechanical manifestation of the working stroke of cardiac myosin is scarce (e.g., refs. 15 and 16). In myocytes extracted from the atrium of frog heart, Colomo et al. found that the maximum size of the working stroke, measured by the abscissa intercept of the relation between the force attained during the quick phase of force recovery and the amplitude of the length step (5), is ∼15 nm, a value similar to that estimated here from the ordinate intercept of the L₂ curve in Fig. 3A. They determined also the dependence on the size of the length step of the rate of the quick force recovery, which at 10 °C varied with the increase in size of the step release (range, 2–8 nm⋅hs⁻¹) from ∼500 to ∼2,000 s⁻¹. In this respect, it must be considered that the rate of the working stroke estimated from the early phase of the force recovery following a step is underestimated by any compliance in series with the myosin motors (17, 18). Instead, in the complementary approach of the isotonic velocity transient used in this work, the effect of the series compliance is eliminated and the speed of the early shortening is the direct expression of the rate of the structural change in the myosin motor (7, 8, 18).

We find that, at 27 °C, the size (L_T) and the speed (r₂) of the isotonic working stroke vary from ∼3 nm and 1,000 s⁻¹ at high load to ∼8 nm and 6,000 s⁻¹ at low load. Comparison of the kinetic values with those obtained for skeletal muscle myosin is not straightforward, due to the much lower temperature used in experiments on skeletal muscle fibers, either intact [frog tibialis anterior, 2–17 °C (8, 9)] or demembranated [rabbit psoas, 12 °C (19)]. Moreover, possible differences in temperature sensitivity between poikilotherms (frog) and homeotherms (mammals) must be taken into account. Therefore, the comparison here is limited to mammalian data. r₂ in the rabbit psoas at 12 °C varies from 1,000 to 8,000 s⁻¹ at high and low load, respectively (19). Assuming a Q₁₀ of 2.5, r₂ in trabeculae at 12 °C should be at least three times lower than at 27 °C, that is 300 and 2,000 s⁻¹ at high and low load, respectively. Thus, the rate of the working stroke estimated from r₂ appears three to four times higher in the fast skeletal myosin from the rabbit than in the cardiac myosin from the rat. This indicates that the cardiac myosin of the rat, even if it is predominantly composed of the fast α-isoform of the myosin heavy chain (MHC) isoform, is slower than the myosin isoform of fast skeletal muscle of the rabbit (MHC 2X). The difference is even more marked considering that the increase in size across species (rabbit versus rat) is in general expected to be accompanied by slower kinetics (20, 21). This may also provide an explanation for the absence of the phase 3 pause in the isotonic velocity transient of rat trabecula: if the execution of the working stroke at a given load is slower, the subsequent steps consisting of motor detachment, accelerated by the execution of the working stroke, and reattachment further along the actin filament (7) will no longer appear rate limiting for the transition to steady shortening.

As regards the size of the working stroke and its load dependence, comparison of the relations in Fig. 3 A–C with the corresponding relations determined in the rabbit psoas (figure 2 E–G in ref. 19) makes it evident that the working stroke size is a conserved characteristic across the different myosin isoforms, in agreement with the conclusion of previous in vitro experiments (22, 23).

Perspectives.

The application of fast sarcomere-level mechanics to intact trabeculae from rat heart enabled the mechanical and kinetic description of the working stroke of the cardiac myosin in situ, showing that, although the size of the working stroke and its load dependence are quite similar to those of fast skeletal muscle myosin, the working stroke kinetics is slower. Mutations of cardiac myosin have been proposed to be responsible for dilated or hypertrophic cardiomyopathy (1, 2). Studies using in vitro kinetics and mechanics (23, 24) can only define the size of the working stroke and the time the motor remains attached (that is, the reciprocal of the detachment rate) under almost unloaded conditions. The results of our in situ study demonstrate that this approach is the only one able to quantitatively describe the mechanokinetic properties of the motor, providing a powerful new tool for defining the mechanism of the cardiomyopathy-causing mutations in cardiac myosin and for testing specific therapeutic interventions.

Methods

Sample Preparation and Mechanical Setup.

Thin, unbranched uniform cardiac trabeculae were dissected from the right ventricle from male Wistar rats (weighing 230–280 g) in agreement with the Italian regulation on animal experimentation (Authorization 956/2015-PR in compliance with Decreto legislativo 26/2014) and transferred into a thermoregulated trough perfused with a modified Krebs–Henseleit solution equilibrated with carbogen (95% O₂, 5% CO₂) for attachment via titanium double hooks to the lever arms of a capacitance gauge force transducer and a motor servosystem. The temperature of the solution was maintained at 27 °C. The SL was set at 2.2 μm at rest, and the length of the trabecula (L₀) was measured. A striation follower was used to record SL changes in a 0.7- to 1.5-mm segment across the central region of the preparation (10). Force, motor lever position, SL, and stimulus signals were recorded with a multifunction I/O board (National Instruments; PCI-6110E).

Experimental Protocol and Data Analysis.

Trabeculae were electrically stimulated at 0.5 Hz to produce twitches. An iterative feedforward method was used to keep SL constant during systole until the final part of force relaxation (Fig. 1A). When the force had attained 95% of the peak (T_P), the control was switched from fixed-end mode to force-clamp mode and 1 ms later a step in force (rise time ∼200 μs) to a fraction of T_P (range 0.2–0.9 T_P) was imposed to elicit the isotonic velocity transient, until a preset shortening level was reached (Fig. 2 A and B). The protocol was repeated at two SLs (1.9 and 2.2 μm) and at two [Ca2+]o (1.0 and 2.5 mM). Force is expressed as force per cross-sectional area of the preparation (in kilopascals). A dedicated program written in LabVIEW (National Instruments) and Origin 2015 (OriginLab Corporation) was used for analysis.

The force–velocity data are fitted with the hyperbolic Hill equation (25):(T+a)(V+b)=(V0+b)a,

where a and b are the distances between the asymptotes and the ordinate and abscissa axes, and V₀ (the ordinate intercept) estimates the unloaded shortening velocity. The power output (W) at any force is calculated by the product between force and velocity. Data are expressed as mean ± SEM unless differently specified. An expanded version of Methods is given in SI Methods. Source mechanical data can be found in Dataset S1.

SI Methods

Sample Preparation.

Male rats (Wistar, 230–280 g) were anesthetized with isoflurane [5% (vol/vol)]. The heart was rapidly excised, placed in a dissection dish, and retrogradely perfused with a modified Krebs–Henseleit solution (composition, in mM: NaCl, 115; KCl, 4.7; MgSO₄, 1.2; KH₂PO₄, 1.2; NaHCO₃, 25; CaCl₂, 0.5; glucose, 10), containing 20 mM 2,3-butanedione monoxime [which has been shown to protect the myocardium during dissection (26)], and oxygenated with 95% O₂ and 5% CO₂ (pH 7.4). A thin, unbranched, and uniform trabecula was dissected from the right ventricle using a stereomicroscope. The axial orientation of the trabecula was determined by means of the attachment of the two extremities using a double titanium hook. The width (w) and the height (h) of the trabecula were measured by an eyepiece with a graduate scale (10 μm per division) with the trabecula stretched to be just taught. The trabecula was mounted horizontally in a temperature-controlled trough (1.2-mL volume) attaching the triangular vertex of the double hook to the lever arms of a capacitance gauge force transducer (valve side) and a loudspeaker motor servosystem (wall side). In this way, the trabecula was aligned with the transducer levers, and, during contraction, the transversal movements were minimized. The characteristics of the force and length transducers have been already reported (ref. 27 and reference therein). The through was perfused at 1.2 mL/min, and the temperature of the solution was maintained at 27 °C. The sarcomere length (SL) was set at 2.2 μm at rest by using a 40× objective, and L₀, the trabecula length at SL of 2.2 µm, was estimated as the distance between the double-hook attachment at the wall side and the attachment of the trabecula to the valve, at the valve side. The cross-sectional area was calculated by assuming an elliptical cross-section. The dimensions of the preparations were as follows (mean ± SD, n = 10): w, 83–350 μm (211 ± 97 μm); h, 63–200 µm (97 ± 37 µm); cross-sectional area, 4,800–47,100 μm² (17,660 ± 13,300 μm²); L₀, 1.0–4.2 mm (2.7 ± 0.7 mm).

Experimental Protocol.

Trabeculae were electrically stimulated by means of two platinum plate electrodes, 4 mm apart, with bipolar pulses of 0.5-ms duration and amplitude 1.5× the threshold voltage. Measurements with specific mechanical protocols were made at the steady state of the contraction–relaxation cycle during electrical pacing at 0.5 Hz. A striation follower was used to record SL changes in a segment of 0.7–1.5 mm selected along the central region of the preparation (10). The relation between the force peak (T_P) and the SL was determined by changing the length of the trabecula with the micromanipulator carrying the loudspeaker motor and measuring the SL with the outputs of either spot delimiting the segment selected for the striation follower signal (10). The relation between SL and trabecula length was linear up to SL of 2.2 µm and then deviated downward (Fig. S1).

To determine the isotonic velocity transient, the control was switched from length to force feedback at 95% of the peak of the isometric contraction, and 1 ms later a stepwise reduction in force, rise time of ∼200 μs, was imposed by using as a command signal the output of an integrated circuit that generated steps to preset fractions of T_P (8, 19). When the isotonic shortening attained ∼60 nm⋅hs⁻¹, the control was shifted back to length feedback to terminate the twitch in fixed-end mode at the new length. In force-clamp mode, the direct signal of force was used in the feedback, and the velocity signal was taken from the motor position signal. At any clamped force, several trials were necessary to adjust the gains of direct, velocity and integrative amplifiers and minimize the duration to optimize the shape of the step. The isotonic velocity transient (range, 0.2–0.8 T_P) was elicited at different SLs (1.9 and 2.2 μm) and at different extracellular Ca²⁺ concentrations (1 and 2.5 mM).

Acknowledgments

We thank Mario Dolfi for skilled technical assistance. This work was supported by MIUR-PRIN Project 2010R8JK2X (Italy), Ente Cassa di Risparmio di Firenze Project 2012.0611 (Italy), and Telethon Project GGP12282 (Italy).

Footnotes

↵¹Present address: Department of Experimental and Clinical Medicine, Università di Firenze, 50134 Florence, Italy.
↵²To whom correspondence should be addressed. Email: vincenzo.lombardi{at}unifi.it.

Author contributions: M.C., F.P., M.R., G.P., G.J.M.S., V.L., and M.L. designed research; M.C., F.P., M.R., G.P., G.J.M.S., and M.L. performed research; M.C., F.P., and M.R. analyzed data; and G.P., G.J.M.S., V.L., and M.L. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1525057113/-/DCSupplemental.

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OpenUrl
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1. Linari M,
2. Piazzesi G,
3. Lombardi V
(2009) The effect of myofilament compliance on kinetics of force generation by myosin motors in muscle. Biophys J 96(2):583–592
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1. Piazzesi G, et al.
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1. Caremani M,
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OpenUrl CrossRef PubMed
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1. Pellegrino MA, et al.
(2003) Orthologous myosin isoforms and scaling of shortening velocity with body size in mouse, rat, rabbit and human muscles. J Physiol 546(Pt 3):677–689
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↵
1. Andruchov O,
2. Wang Y,
3. Andruchova O,
4. Galler S
(2004) Functional properties of skinned rabbit skeletal and cardiac muscle preparations containing alpha-cardiac myosin heavy chain. Pflugers Arch 448(1):44–53
.
OpenUrl CrossRef PubMed
↵
1. Palmiter KA,
2. Tyska MJ,
3. Dupuis DE,
4. Alpert NR,
5. Warshaw DM
(1999) Kinetic differences at the single molecule level account for the functional diversity of rabbit cardiac myosin isoforms. J Physiol 519(Pt 3):669–678
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OpenUrl CrossRef PubMed
↵
1. Tyska MJ,
2. Warshaw DM
(2002) The myosin power stroke. Cell Motil Cytoskeleton 51(1):1–15
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OpenUrl CrossRef PubMed
↵
1. Alpert NR, et al.
(2002) Molecular mechanics of mouse cardiac myosin isoforms. Am J Physiol Heart Circ Physiol 283(4):H1446–H1454
.
OpenUrl Abstract/FREE Full Text
↵
1. Hill AV
(1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci 126:136–195
.
OpenUrl FREE Full Text
↵
1. Mulieri LA,
2. Hasenfuss G,
3. Ittleman F,
4. Blanchard EM,
5. Alpert NR
(1989) Protection of human left ventricular myocardium from cutting injury with 2,3-butanedione monoxime. Circ Res 65(5):1441–1449
.
OpenUrl Abstract/FREE Full Text
↵
1. Lombardi V,
2. Piazzesi G
(1990) The contractile response during steady lengthening of stimulated frog muscle fibres. J Physiol 431:141–171
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OpenUrl CrossRef PubMed

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Article Classifications

Biological Sciences
Physiology

[1] ↵
Spudich JA
(2014) Hypertrophic and dilated cardiomyopathy: Four decades of basic research on muscle lead to potential therapeutic approaches to these devastating genetic diseases. Biophys J 106(6):1236–1249
.
OpenUrl CrossRef PubMed

[2] Spudich JA

[3] ↵
Moore JR,
Leinwand L,
Warshaw DM
(2012) Understanding cardiomyopathy phenotypes based on the functional impact of mutations in the myosin motor. Circ Res 111(3):375–385
.
OpenUrl Abstract/FREE Full Text

[4] Moore JR,

[5] Leinwand L,

[6] Warshaw DM

[7] ↵
Marston SB
(2011) How do mutations in contractile proteins cause the primary familial cardiomyopathies? J Cardiovasc Transl Res 4(3):245–255
.
OpenUrl CrossRef PubMed

[8] Marston SB

[9] ↵
Aksel T,
Choe Yu E,
Sutton S,
Ruppel KM,
Spudich JA
(2015) Ensemble force changes that result from human cardiac myosin mutations and a small-molecule effector. Cell Rep 11(6):910–920
.
OpenUrl CrossRef PubMed

[10] Aksel T,

[11] Choe Yu E,

[12] Sutton S,

[13] Ruppel KM,

[14] Spudich JA

[15] ↵
Huxley AF,
Simmons RM
(1971) Proposed mechanism of force generation in striated muscle. Nature 233(5321):533–538
.
OpenUrl CrossRef PubMed

[16] Huxley AF,

[17] Simmons RM

[18] ↵
Piazzesi G, et al.
(2007) Skeletal muscle performance determined by modulation of number of myosin motors rather than motor force or stroke size. Cell 131(4):784–795
.
OpenUrl CrossRef PubMed

[19] Piazzesi G, et al.

[20] ↵
Reconditi M, et al.
(2004) The myosin motor in muscle generates a smaller and slower working stroke at higher load. Nature 428(6982):578–581
.
OpenUrl CrossRef PubMed

[21] Reconditi M, et al.

[22] ↵
Piazzesi G,
Lucii L,
Lombardi V
(2002) The size and the speed of the working stroke of muscle myosin and its dependence on the force. J Physiol 545(Pt 1):145–151
.
OpenUrl CrossRef PubMed

[23] Piazzesi G,

[24] Lucii L,

[25] Lombardi V

[26] ↵
Decostre V,
Bianco P,
Lombardi V,
Piazzesi G
(2005) Effect of temperature on the working stroke of muscle myosin. Proc Natl Acad Sci USA 102(39):13927–13932
.
OpenUrl Abstract/FREE Full Text

[27] Decostre V,

[28] Bianco P,

[29] Lombardi V,

[30] Piazzesi G

[31] ↵
Huxley AF,
Lombardi V,
Peachey D
(1981) A system for fast recording of longitudinal displacement of a striated muscle fibre. J Physiol 317:12–13
.
OpenUrl

[32] Huxley AF,

[33] Lombardi V,

[34] Peachey D

[35] ↵
ter Keurs HE,
Rijnsburger WH,
van Heuningen R,
Nagelsmit MJ
(1980) Tension development and sarcomere length in rat cardiac trabeculae. Evidence of length-dependent activation. Circ Res 46(5):703–714
.
OpenUrl FREE Full Text

[36] ter Keurs HE,

[37] Rijnsburger WH,

[38] van Heuningen R,

[39] Nagelsmit MJ

[40] ↵
Huxley AF
(1974) Muscular contraction. J Physiol 243(1):1–43
.
OpenUrl CrossRef PubMed

[41] Huxley AF

[42] ↵
Daniels M,
Noble MI,
ter Keurs HE,
Wohlfart B
(1984) Velocity of sarcomere shortening in rat cardiac muscle: Relationship to force, sarcomere length, calcium and time. J Physiol 355:367–381
.
OpenUrl CrossRef PubMed

[43] Daniels M,

[44] Noble MI,

[45] ter Keurs HE,

[46] Wohlfart B

[47] ↵
de Tombe PP,
ter Keurs HE
(1992) An internal viscous element limits unloaded velocity of sarcomere shortening in rat myocardium. J Physiol 454:619–642
.
OpenUrl CrossRef PubMed

[48] de Tombe PP,

[49] ter Keurs HE

[50] ↵
Colomo F,
Poggesi C,
Tesi C
(1994) Force responses to rapid length changes in single intact cells from frog heart. J Physiol 475(2):347–350
.
OpenUrl CrossRef PubMed

[51] Colomo F,

[52] Poggesi C,

[53] Tesi C

[54] ↵
De Winkel ME,
Blangé T,
Treijtel BW
(1995) Viscoelastic properties of cross bridges in cardiac muscle. Am J Physiol 268(3 Pt 2):H987–H998
.
OpenUrl

[55] De Winkel ME,

[56] Blangé T,

[57] Treijtel BW

[58] ↵
Linari M,
Piazzesi G,
Lombardi V
(2009) The effect of myofilament compliance on kinetics of force generation by myosin motors in muscle. Biophys J 96(2):583–592
.
OpenUrl CrossRef PubMed

[59] Linari M,

[60] Piazzesi G,

[61] Lombardi V

[62] ↵
Piazzesi G, et al.
(2014) The myofilament elasticity and its effect on kinetics of force generation by the myosin motor. Arch Biochem Biophys 552-553:108–116
.
OpenUrl CrossRef

[63] Piazzesi G, et al.

[64] ↵
Caremani M,
Melli L,
Dolfi M,
Lombardi V,
Linari M
(2013) The working stroke of the myosin II motor in muscle is not tightly coupled to release of orthophosphate from its active site. J Physiol 591(20):5187–5205
.
OpenUrl CrossRef PubMed

[65] Caremani M,

[66] Melli L,

[67] Dolfi M,

[68] Lombardi V,

[69] Linari M

[70] ↵
Pellegrino MA, et al.
(2003) Orthologous myosin isoforms and scaling of shortening velocity with body size in mouse, rat, rabbit and human muscles. J Physiol 546(Pt 3):677–689
.
OpenUrl CrossRef PubMed

[71] Pellegrino MA, et al.

[72] ↵
Andruchov O,
Wang Y,
Andruchova O,
Galler S
(2004) Functional properties of skinned rabbit skeletal and cardiac muscle preparations containing alpha-cardiac myosin heavy chain. Pflugers Arch 448(1):44–53
.
OpenUrl CrossRef PubMed

[73] Andruchov O,

[74] Wang Y,

[75] Andruchova O,

[76] Galler S

[77] ↵
Palmiter KA,
Tyska MJ,
Dupuis DE,
Alpert NR,
Warshaw DM
(1999) Kinetic differences at the single molecule level account for the functional diversity of rabbit cardiac myosin isoforms. J Physiol 519(Pt 3):669–678
.
OpenUrl CrossRef PubMed

[78] Palmiter KA,

[79] Tyska MJ,

[80] Dupuis DE,

[81] Alpert NR,

[82] Warshaw DM

[83] ↵
Tyska MJ,
Warshaw DM
(2002) The myosin power stroke. Cell Motil Cytoskeleton 51(1):1–15
.
OpenUrl CrossRef PubMed

[84] Tyska MJ,

[85] Warshaw DM

[86] ↵
Alpert NR, et al.
(2002) Molecular mechanics of mouse cardiac myosin isoforms. Am J Physiol Heart Circ Physiol 283(4):H1446–H1454
.
OpenUrl Abstract/FREE Full Text

[87] Alpert NR, et al.

[88] ↵
Hill AV
(1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci 126:136–195
.
OpenUrl FREE Full Text

[89] Hill AV

[90] ↵
Mulieri LA,
Hasenfuss G,
Ittleman F,
Blanchard EM,
Alpert NR
(1989) Protection of human left ventricular myocardium from cutting injury with 2,3-butanedione monoxime. Circ Res 65(5):1441–1449
.
OpenUrl Abstract/FREE Full Text

[91] Mulieri LA,

[92] Hasenfuss G,

[93] Ittleman F,

[94] Blanchard EM,

[95] Alpert NR

[96] ↵
Lombardi V,
Piazzesi G
(1990) The contractile response during steady lengthening of stimulated frog muscle fibres. J Physiol 431:141–171
.
OpenUrl CrossRef PubMed

[97] Lombardi V,

[98] Piazzesi G

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Size and speed of the working stroke of cardiac myosin in situ

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