Roles of Ca²⁺ and Crossbridge Kinetics in Determining the Maximum Rates of Ca²⁺ Activation and Relaxation in Rat and Guinea Pig Skinned Trabeculae

From the Department of Pharmacology, United Medical and Dental Schools, St. Thomas's Hospital, London, UK.

Correspondence to Dr J.C. Kentish, Department of Pharmacology, United Medical and Dental Schools, St. Thomas's Hospital, London SE1 7EH, UK. E-mail j.kentish{at}umds.ac.uk

	Abstract

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Abstract—We examined the influences of Ca²⁺ and crossbridge kinetics on the maximum rate of force development during Ca²⁺ activation of cardiac myofibrils and on the maximum rate of relaxation. Flash photolysis of diazo-2 or nitrophenyl-EGTA was used to produce a sudden decrease or increase, respectively, in [Ca²⁺] within Triton-skinned trabeculae from rat and guinea pig hearts (22°C). Trabeculae from both species had similar Ca²⁺ sensitivities, suggesting that the rate of dissociation of Ca²⁺ from troponin C (k_off) is similar in the 2 species. However, the rate of relaxation after diazo-2 photolysis was 5 times faster in the rat (16.1±0.9 s^-1, mean±SEM, n=11) than in the guinea pig (2.99±0.26 s^-1, n=7). This indicates that the maximum relaxation rate is limited by crossbridge kinetics rather than by k_off. The maximum rates of rapid activation by Ca²⁺ after nitrophenyl-EGTA photolysis (k_act) and of force redevelopment after forcible crossbridge dissociation (k_tr) were similar and were 5-fold faster in rat (k_act=14.4±0.9 s^-1, k_tr=13.0±0.6 s^-1) than in guinea pig (k_act=2.57±0.14 s^-1, k_tr=2.69±0.30 s^-1) trabeculae. This too may be mainly due to species differences in crossbridge kinetics. Both k_act and k_tr increased as [Ca²⁺] increased. This Ca²⁺ dependence of the rates of force development is consistent with current models for the Ca²⁺ activation of the crossbridge cycle, but these models do not explain the similarity in the maximal rates of activation and relaxation within a given species.

Key Words: crossbridge • photolysis • Ca²⁺ activation • cardiac myofibril • relaxation

	Introduction

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Cardiac muscle contraction is initiated by Ca²⁺ binding to troponin C (TnC), which triggers structural changes in the thin filament and allows actomyosin crossbridges to generate force. However, relatively little is known about the precise mechanism by which Ca²⁺ regulates crossbridge force generation. In the original "steric blocking" model,¹ Ca²⁺ was considered to act as a switch controlling the number, but not the kinetics, of cycling crossbridges. However, Brenner² showed that Ca²⁺ accelerates crossbridge kinetics, as measured by the rate of force redevelopment (k_tr) after forcible detachment of the crossbridges during Ca²⁺ activation. He therefore proposed a kinetic model² in which Ca²⁺ activates both force and k_tr by increasing the rate of transition of crossbridges from the non–force-generating (detached or weakly bound) state to the force-generating state (f_app). On the other hand, it has been suggested more recently^{3 4 5} that a Ca²⁺ dependence of k_tr is also consistent with the steric blocking model if the rate of crossbridge attachment is influenced by the activation of the thin filament by strongly binding crossbridges. Thus, the fact that k_tr is found to be Ca²⁺ dependent in skeletal fibers^{2 4 6} does not distinguish between these models. In cardiac muscle, however, Hancock and colleagues^{7 8} found that k_tr was independent of [Ca²⁺], which is consistent only with the steric blocking model in the Ca²⁺ regulation of cardiac muscle. At present, this is the source of some controversy, since other groups have found k_tr to be activated by Ca²⁺ in cardiac muscle.^{9 10 11} In the present study, we addressed this controversy by examining the Ca²⁺ dependence of k_tr in skinned cardiac muscles using an optimized length change protocol.

Little is also known about the factors that govern the kinetics of Ca²⁺ activation and of relaxation of cardiac myofibrils, although these are likely to be important in determining the normal duration of the heartbeat. Theoretically, the maximum rates of activation and relaxation could be governed by (1) the rate at which Ca²⁺ binds to or dissociates from TnC or (2) the rate of crossbridge cycling. A major aim of the present study was therefore to examine the relative roles of Ca²⁺ and crossbridges in determining the intrinsic rates of myofibrillar activation and relaxation rates, by comparing these rates in rat myofibrils with those in guinea pig myofibrils, which have much slower crossbridge kinetics^{12 13} but similar myofibrillar Ca²⁺ sensitivities¹³ (and probably, therefore, similar kinetics of Ca²⁺ interaction with TnC). The measurement of the intrinsic rates of myofibrillar activation or relaxation has recently been made possible by development of "caged" Ca²⁺ compounds, which can be photolysed to either release or chelate Ca²⁺ after they have diffused into the myofibrils. Photolysis of these compounds causes solution [Ca²⁺] to change in 1 millisecond, so the subsequent force change takes place at a rate that is limited by the intrinsic properties of the myofibrils rather than by the rate of change of [Ca²⁺]. To study the relaxation rate, we used the "caged" chelator of Ca²⁺, diazo-2,^{14 15} whereas for the activation rate, we used the "caged" Ca²⁺ compound, nitrophenyl-EGTA (NP-EGTA).^{16 17}

A comparison of the maximum rate of Ca²⁺ activation of the thin filament (k_act) with the maximum k_tr can provide information on whether Ca²⁺-activated force development is limited by crossbridge kinetics rather than by k_act. This was previously achieved using the caged Ca²⁺, nitr-7,¹¹ but this compound did not lead to full activation of the myofibrils. We therefore repeated these experiments using NP-EGTA, which releases sufficient Ca²⁺ so that the maximal activation is achieved and k_act can be compared with k_tr. Our experiments also allowed the first comparison of maximum k_act and relaxation rates in the same muscles. The above crossbridge models predict that the relaxation rate should be slower than the activation rate, and our experiments allowed us to test this.

	Materials and Methods

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Preparations and Equipment
Animals were supplied by Bantin & Kingman Universal Ltd (Hull, UK). The general procedure and apparatus were as described in detail previously.^{15 18} In summary, male Wistar rats (250 g) were stunned by a blow to the head and then killed by cervical dislocation. Male Dunkin Hartley guinea pigs (250 g) were killed directly by cervical dislocation. These procedures were in accordance with UK Home Office guidelines (schedule 1). The hearts were removed, and trabeculae (diameter, 50 to 200 µm; length, 1.5 to 8 mm) were dissected from the right ventricles in Tyrode's solution containing 25 mmol/L 2,3-butanedione monoxime to minimize cell contracture. Trabeculae were skinned for 30 minutes in the standard skinned muscle solution (see below) to which was added 1% Triton X-100, 10 mmol/L K₂EGTA, and 0.1 mmol/L phenylmethylsulfonyl fluoride. A trabecula was then mounted in monofilament snares attached to an isometric force transducer (AE801, SensoNor) and to a servomotor (300S, Cambridge Technology Inc). The muscle bath system included a bath of reduced volume (10 µL) specially designed for photolysis experiments.¹⁵ Bath temperature was 22°C or 12°C (±0.1°C). Sarcomere length (SL) was measured by laser diffraction and was set to 2.1 µm in the relaxed muscle at 22°C.

Diazo-2 and NP-EGTA were photolysed by light from a xenon flashlamp (Hi-Tech Ltd), filtered with a UG5 bandpass filter (300 to 400 nm). The light was focused, and its area of incidence on the muscle was optimized as described previously.¹⁵ PClamp software (Axon Instruments) was used to trigger the flashlamp or to impose rapid length changes on the trabeculae for k_tr measurements (see below). Force, muscle length, and SL were recorded on a 4-channel chart recorder and on a computer using a 12-bit analog/digital board sampling at 2 kHz.

Solutions
All solutions contained (mmol/L) BES 100, Na₂H₂ATP 6.3, Na₂ phosphocreatine 10, MgCl₂ 5.4 to 6.2 (to maintain [Mg²⁺] at 1 mmol/L), potassium phosphate 1, glutathione 5, leupeptin 0.001, and potassium propionate 50 to 80 (to give an ionic strength of 200 mmol/L) (pH 7.1). Details of solution manufacture and calculation of free ion concentrations have been given elsewhere.^{15 18} For determination of the force-pCa relationship and of k_tr, solutions also contained 10 mmol/L EGTA and 0 to 10 mmol/L Ca²⁺, giving a pCa (-log₁₀[Ca²⁺]) of 9 to 4.5. For the photolysis experiments, solutions were as above but contained 0.25 mmol/L diazo-2 and 0 to 0.25 mmol/L CaCl₂ (final pCa 7.5 to 4.9), or 2 mmol/L NP-EGTA and 0.6 to 0.8 mmol/L Ca²⁺ (pCa 7.0 to 6.0). In the absence of caged compounds, relaxation or maximal Ca²⁺ activation in the photolysis experiments was produced by solutions containing 1 mmol/L EGTA (pCa 8.5) or 1 mmol/L CaEGTA+0.1 mmol/L CaCl₂ (pCa 4.5), respectively. Diazo-2 and NP-EGTA (tetrapotassium salts from Molecular Probes) were stored frozen in aqueous stock solutions (25 and 10 mmol/L, respectively); other chemicals were from Sigma or B.D.H.

Protocols
As previously described,¹⁵ each skinned trabecula was first maximally activated several times at 22°C until a reproducible level of force was obtained. For the photolysis parts of the experiment, the muscle was placed in either a diazo-2 solution or an NP-EGTA solution, with total [Ca] adjusted so that the muscle developed 40% to 80% of maximum force in the diazo-2 solution but only a small force (<10% maximum) in the NP-EGTA solution. Once force had stabilized, the flashlamp was triggered, giving a flash of near-UV light (160 mJ in 1 millisecond) to the muscle. After the force response, each muscle was returned to the relaxing solution. Any gradual decline in maximum force due to deterioration of the muscles was corrected for by assuming a linear decrease between activations. Muscles were discarded when maximum force had fallen by 25%.

k_tr after a rapid release and restretch of the muscle was measured at both 22°C and 12°C. During maximal activation, the muscle length was decreased by 20% in 1 millisecond, held for a 25- or 100-millisecond "holding period" (for rat and guinea pig trabeculae, respectively), and then stretched back to the original length in 1 millisecond. The force redevelopment was recorded. The muscle was subsequently relaxed. The procedure was repeated at various submaximal [Ca²⁺] levels, ending with a repeat of the maximal activation. The force-pCa relationship of the trabecula was thereby determined simultaneously with k_tr.

In most trabeculae we could record at least 2 of the 3 sets of measurements (k_tr, rapid activation, and rapid relaxation) before maximum force declined by 25%.

Data Analysis
The relationship between steady-state force and pCa in each muscle was fitted by the Hill equation: relative force=maximum forcex[Ca²⁺]^n_H/(K^n_H+[Ca²⁺]^n_H), where n_H is the Hill coefficient and K is a dissociation constant. The changes of force after diazo-2 or NP-EGTA photolysis and the release/restretch protocol were fitted with single-exponential curves (except relaxation in the rat, which was fitted with a double exponential) using Clampfit software (Axon Instruments). Values are given as mean±SEM from n trabeculae (each from a different heart). Unless stated otherwise, unpaired t tests were applied, and a significant difference was taken as P<0.05.

	Results

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Ca²⁺ Sensitivity of Rat and Guinea Pig Myofibrils
In maximal activating solution (pCa 4.5) at 22°C, rat skinned trabeculae (mean diameter, 121±7 µm; n=45) generated a stress of 78.9±7.8 mN · mm^-2, which was not significantly different from that (50.6±8.2 mN · mm^-2) produced by guinea pig skinned trabeculae (mean diameter, 131±12 µm; n=9). Resting SL was 2.14±0.01 µm (n=36) in rat trabeculae and 2.13±0.01 (n=7) in guinea pig trabeculae. The force-pCa relationships for both species were sigmoidal and were well fitted by the Hill equation (Figure 1). The pCa required for 50% activation (pCa₅₀) was 5.60±0.02 (n=39) in rat trabeculae and 5.58±0.04 (n=8) in guinea pig trabeculae. Myofibrillar Ca²⁺ sensitivity was therefore the same in the 2 species, confirming the results of Ventura-Clapier et al.¹³ In addition, the slopes of the force-pCa relationships were not significantly different, with Hill coefficients (n_H) of 3.05±0.17 (n=39) and 2.49±0.28 (n=8) for rat and guinea pig, respectively.

View larger version (13K): [in this window] [in a new window]   Figure 1. Ca2+ sensitivities of skinned trabeculae from rat (A) and guinea pig (B). Forces are expressed relative to maximum force developed (at pCa 4.5). Sigmoidal curves were generated from the Hill equation using the mean values of pCa50 and nH. Points represent mean±SEM of 39 experiments for rat and 8 experiments for guinea pig.

Rapid Relaxation of Myofibrils
We used flash photolysis of diazo-2, a caged chelator of Ca²⁺, to produce a sudden drop in solution [Ca²⁺] and thereby measure the intrinsic rate of myofibrillar relaxation.^{14 15} Trabeculae were activated in solutions containing Ca²⁺ and diazo-2, and once force was steady the diazo-2 was photolysed (Figure 2). Relaxation of rat trabeculae followed a double-exponential curve, the initial fast phase of which represents the maximum intrinsic rate of myofibrillar relaxation. However, the guinea pig relaxation was fitted best by a single-exponential curve. As found with rat muscles,¹⁵ the relaxation rate of guinea pig trabeculae was independent of both preflash [Ca²⁺] and force (results not shown).

View larger version (21K): [in this window] [in a new window]   Figure 2. Typical traces showing relaxation of rat and guinea pig skinned trabeculae after photolysis of diazo-2. Muscles were activated in Ca2+ and 0.25 mmol/L diazo-2 before the flash (160 mJ) was triggered. Force was normalized between the mean preflash value and the mean force between 990 and 1000 milliseconds. In this example, preflash and postflash forces in the rat were 0.40 and 0.10 (relative to maximum force) and in the guinea pig were 0.61 and 0.33, respectively. Relaxations were fitted with single-exponential (for guinea pig) or double-exponential (for rat) curves (solid lines).

As shown in Figure 2, guinea pig trabeculae relaxed much more slowly than did rat trabeculae. The rate constants for the 2 phases of relaxation in rat muscles were 16.1±0.9 s^-1 and 0.97±0.13 s^-1 (n=11) at 22°C and that for guinea pig muscles was 2.99±0.26 s^-1 (n=7). The maximum rate of myofibrillar relaxation in rat myofibrils was therefore 5 times faster (P<0.01) than that of the guinea pig. This difference was not due to the different fitting protocols, because fitting the rat data with a single-exponential fit (over the first 200 milliseconds) gave a rate constant of 18.9±0.9 s^-1 (n=11, results not shown).

It could be argued that both muscles had a slow phase of relaxation but that only the rat muscle also had a fast phase; however, this is untenable because the rate constant for the slow phase in the rat was significantly less (P<0.01) than the guinea pig single rate constant. The origin of the slow phase of the biexponential relaxation remains unclear.

Rapid Activation of Myofibrils
The rate constant for Ca²⁺ activation of force, k_act, in the trabeculae was measured using flash photolysis of the "caged" Ca²⁺ compound, NP-EGTA, to produce a sudden elevation of solution [Ca²⁺].^{16 17} As shown in Figure 3A, photolysis of NP-EGTA produced rapid activation of force in trabeculae from both species, and full Ca²⁺ activation from the resting state was achieved with a 160-mJ flash. In some cases, peak force (expressed relative to the maximum steady-state force) exceeded 1.0 in the few seconds after photolysis. This overshoot of force occurred in all the guinea pig muscles and in a subset of the rat muscles (Figure 3B and 3C). The reasons for the secondary decrease of force are unclear but could include time-dependent SL rearrangement or accumulation of P_i inside the muscles. The postflash rise in force was well fitted by a single-exponential curve, with a k_act at maximum flash energy (160 mJ) of 14.4±0.9 s^-1 (n=20) in the rat compared with 2.57±0.14 s^-1 (n=8, P<0.01) in the guinea pig (Figure 3A). Thus rat trabeculae activated 5-fold faster than did trabeculae from guinea pigs. These rates were not significantly different from the corresponding maximum rates of relaxation.

View larger version (16K): [in this window] [in a new window]   Figure 3. Panel A shows typical traces of maximal activations of rat and guinea pig trabeculae produced by NP-EGTA photolysis (160 mJ). Force was normalized between the mean preflash value and the mean force between 1490 and 1500 milliseconds. Relative to maximum steady-state force, preflash and peak postflash forces in the rat were 0.07 and 1.0 and in guinea pig were 0.02 and 1.0, respectively. Solid lines are single exponential fits ending at 98% of peak force. In panels B (rat) and C (guinea pig), the rate constant of the exponential rise in force (kact) is plotted against the peak force achieved after photolysis. Peak force was varied by altering flash energy and is expressed relative to maximum steady-state force. Each symbol type refers to a different muscle.

To determine whether k_act varied with postflash [Ca²⁺], the energy of the flash was altered between 50 and 160 mJ to vary the degree of NP-EGTA photolysis. The peak force achieved after photolysis gave an indirect measure of postflash [Ca²⁺]. (Calculation of the postflash [Ca²⁺] was precluded because the precise degree of photolysis of NP-EGTA was unknown.) Plotting this peak force against k_act (Figure 3B and 3C) clearly demonstrated that the rate of activation increased with postphotolysis force (and hence [Ca²⁺]) in trabeculae from both rat and guinea pig. In both cases, the relationship between k_act and force was curved upward.

Rate of Redevelopment of Force
We investigated whether the difference in k_act between species (Figure 3) was paralleled by a difference in crossbridge kinetics, as measured at constant [Ca²⁺] by k_tr after forcible detachment of the crossbridges.² Crossbridges were detached by releasing the muscles by 20% (to allow unloaded shortening to occur) and then restretching them rapidly. SL was not controlled in these experiments, partly to make the results comparable to those from the flash photolysis experiments and partly because the sarcomere diffraction pattern was usually lost during maximal activation at 22°C. We found that the value of k_tr depended on the duration of the holding period, becoming faster in both species as the duration of the holding period was shortened (Figure 4). This may reflect incomplete detachment of crossbridges at short holding durations. On the other hand, when the holding period was increased beyond 25 milliseconds for rat and 100 milliseconds for guinea pig, force started to redevelop during the holding period once the slack in the muscle had been taken up. Thus, we used different optimal holding periods (25 and 100 milliseconds for rat and guinea pig, respectively) to ensure that minimal numbers of crossbridges were attached before redevelopment of force after the restretch.

View larger version (21K): [in this window] [in a new window]   Figure 4. Influence on ktr of the duration of the holding period between muscle release and restretch. Panel A shows the force responses to a step shortening of variable duration in a typical rat trabecula. Single-exponential curves (superimposed solid lines) were fitted to the force data to determine the rate of force redevelopment after restretch (ktr). Panels B and C show the mean ktr results for rat (B) and guinea pig (C) at pCa 4.5. Data points represent 1 or 2 determinations or the mean±SEM of 3 or 4 muscles, and data were fitted arbitrarily with double-exponential curves (dashed lines). Vertical dashed lines indicate the mean time at which force redevelopment occurred while the muscle was at the shorter length.

A comparison of k_tr in rat and guinea pig is shown in Figure 5. Generally, the residual force (the point from which force redevelops after the length increase) was larger in the guinea pig than in the rat. Force redevelopment was well fitted by a single exponential curve in both species. The mean k_tr during maximal activation (pCa 4.5) was 13.0±0.6 s^-1 for the rat (n=17) and 2.69±0.30 s^-1 for the guinea pig (n=9) (P<0.01). The large (4.5-fold) difference in k_tr between species was not due to the different holding periods used, since k_tr recorded from guinea pig trabeculae using a holding period of 25 milliseconds (as for rat) was 2.80±0.20 s^-1 (n=3), which was still much slower than k_tr recorded from rat trabeculae (Figure 5). The k_tr values above were not significantly different from the maximum values of k_act measured in the same species. Thus, the different rates of Ca²⁺ activation in the 2 species apparently reflect the relative rates of the force-generating processes.

View larger version (21K): [in this window] [in a new window]   Figure 5. Comparison of ktr in rat (A to C) and guinea pig (D to F) trabeculae. Muscles were given a step shortening of 25 or 100 milliseconds (A and D). Force was normalized to that before the length change, in this case maximum Ca2+-activated force (B and E). Exponential curves were fitted to the first 1 second of the force redevelopment traces (superimposed solid lines). Panel E also illustrates that ktr increased only slightly when the holding period was decreased from 100 to 25 milliseconds in the guinea pig. In panels C and F, ktr is plotted against the force before the length change. The step was held for 25 milliseconds for rat and 100 milliseconds for guinea pig. Each symbol type refers to a different muscle.

The relationship between k_tr and steady-state force was also determined for each species (Figure 5C and 5F) in order to compare the dependencies of k_tr and of k_act on force. Force was varied by altering the [Ca²⁺] of the activating solutions. Because there was scatter in the data between muscles, particularly for the guinea pig (Figure 5F), to compare k_tr values at different force levels we pooled data for each muscle. Values of k_tr in the relative force range of 0.5 to 0.7 were not significantly different (P>0.05, paired t test) from those in the force range of 0.1 to 0.3 in either rat or guinea pig but were significantly lower (P<0.005) than maximal k_tr values (relative force, 1.0) in both species. Thus, k_tr was independent of force below 60% of maximum but increased at higher force levels. The data in Figure 5C and 5F were averaged and replotted as k_tr against pCa (Figure 6). As [Ca²⁺] rose from pCa 6.0 to 4.5, k_tr increased 2-fold in the guinea pig and 10-fold in the rat. In both species, the pCa required to give 50% of the maximal k_tr value (5.4, Figure 6) was less than the pCa₅₀ for force (5.6, Figure 1). Thus, force was more sensitive than k_tr to Ca²⁺, which may account for the downward curvature in the force-k_tr relationships (Figure 5).

View larger version (15K): [in this window] [in a new window]   Figure 6. Ca2+ dependence of ktr in rat and guinea pig trabeculae. Points represent mean±SEM from 9 rat muscles and 6 guinea pig muscles.

Role of Compliance in Determining k_tr
Brenner and Eisenberg¹⁹ showed that force redevelopment is slowed considerably if there is internal shortening in muscles due to end compliance. Thus, the slower force kinetics recorded in guinea pig compared with rat trabeculae could have been due to greater internal shortening in the guinea pig muscles. Although at 22°C the sarcomere pattern was usually lost during activation, at 12°C it was more stable, and we were able to measure SL during k_tr determinations at 12°C in 1 guinea pig trabecula and 8 rat trabeculae. The resting SL was increased for these experiments (to 2.23±0.01 µm for rat [n=8 trabeculae] and 2.25 µm for the one guinea pig trabecula) to increase the SL during maximal activation, which helped to maintain the sarcomere pattern in the active muscle. As shown in Figure 7, force redevelopment at 12°C was much slower than at 22°C, but k_tr was still markedly faster in the rat (6.41±0.51 s^-1, n=8) than in the guinea pig (0.97 s^-1, n=1). During force redevelopment, SL varied by <3% in both rat and guinea pig trabeculae. Thus, the 6-fold faster k_tr value for the rat is unlikely to be explained by greater internal shortening in the guinea pig.

View larger version (22K): [in this window] [in a new window]   Figure 7. Simultaneous measurements of ktr and sarcomere length at 12°C in typical trabeculae from rat (A to C) or guinea pig (D to F). Exponential curves were fitted to the first 1 second of the force redevelopment traces (superimposed solid lines [B and E]). Sarcomere length remained approximately constant during force redevelopment in both rat (C) and guinea pig (F).

	Discussion

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Relaxation Rate Is Limited by Properties of Crossbridges
Theoretically, myofibrillar relaxation rate may be limited either by the rate at which Ca²⁺ dissociates from TnC (k_off) and causes thin filament deactivation (which may also be affected by the presence of strongly bound crossbridges; see below) or by the net rate at which myosin crossbridges detach from actin once Ca²⁺ is lost from TnC. The identical force-pCa relationships of the 2 species (Figure 1 and Reference 13¹³ ) imply that k_off should be similar in the 2 species. (Ca²⁺ sensitivity is largely determined by the Ca²⁺ affinity constant of TnC, which is equal to the ratio of the on and off rate constants for Ca²⁺ binding: affinity=k_on/k_off. Since k_on has been reported to be diffusion-limited²⁰ and therefore is constant, affinity may be determined chiefly by k_off.) Crossbridge kinetics, however, are known to be faster in the rat than in the guinea pig.^{12 13} Using photolysis of diazo-2 to measure the intrinsic relaxation rate of cardiac myofibrils, we found relaxation rates of 16.1 s^-1 and 2.99 s^-1, respectively, in rat and guinea pig trabeculae under identical conditions. This 5-fold difference in relaxation rate between the 2 species therefore suggests that the relaxation rate is limited not by k_off but rather by the detachment rate of the crossbridges themselves.

Activation Rate Is Determined by Properties of Crossbridges
Although measurements were made without SL control, and internal shortening could have slowed force development,¹⁹ our k_tr value of 13.0 s^-1 at 22°C in maximally activated rat trabeculae was similar to, or faster than, that found in other studies with SL control^{8 9 10} when differences in temperature were taken into account. k_tr, which reflects the rate of crossbridge reattachment and transition to force-generating states,² was measured under constant activation by Ca²⁺, thus bypassing any direct influence of [Ca²⁺] or species on the rate at which Ca²⁺ triggers conformational changes in the regulatory proteins of the thin filament. Our finding that in a given species, and under identical conditions, k_act is similar to k_tr suggests that the maximum rate of Ca²⁺-activated force development is limited by the rate at which detached or weakly bound crossbridges enter the force-generating state rather than by the rate at which the thin filament is switched on by Ca²⁺ binding to TnC.

Overall, we found that the maximum values for k_act, k_tr, and the rate of relaxation were 5 times faster in rats compared with guinea pigs, even when internal shortening was minimal (Figure 7). It seems likely that the different activation and relaxation rates of the 2 species relate to differences in their crossbridges. Rat ventricle contains mostly V₁ myosin (composed of -myosin heavy chains), whereas in guinea pig V₂ and V₃ myosins (ß- and ßß-myosin heavy chains) predominate.¹² Unpublished experiments (1997), performed by Dr P. Reiser (Ohio State University), showed that our rat muscles contained 80% to 90% -myosin heavy chains (ie, mostly V₁ myosin), whereas guinea pig contained only 40% to 50% -myosin heavy chains. In general, crossbridges composed of V₁ myosin have a 2- to 6-fold higher cycling rate than crossbridges with V₃ myosin, as judged by various biochemical and mechanical assays.^{12 13 21 22} The faster crossbridge kinetics of V₁ compared with V₃ myosin probably explain a large part of the faster activation and relaxation rates in rats compared with guinea pigs, although there may be other species differences that lead to differing crossbridge kinetics between the corresponding myosin isoforms.

Another factor that could potentially explain, or at least contribute to, the species-specific difference in maximal activation and relaxation rates is the cooperative activation of the thin filament by the attachment of strongly binding crossbridges.^{3 4 5} This phenomenon tends to slow k_tr, particularly at low [Ca²⁺].⁵ Thus, if cooperative activation due to attachment of strong-binding crossbridges were greater in guinea pig myofilaments than in rat myofilaments, this could explain why k_tr, k_act, and possibly the rate of relaxation were slower in the guinea pig. However, we think this explanation is unlikely, because (1) this effect of strongly binding crossbridges is small at maximal Ca²⁺ activation^{4 5} and thus would have little effect on the maximum values of k_tr and k_act, and (2) enhanced cooperativity of strongly bound crossbridges in guinea pig myofilaments would tend to make the force-pCa relationship steeper for guinea pig than for rat, yet there was no evidence for this (Figure 1).

k_act and k_tr Are Ca²⁺ Dependent
The values of k_act and k_tr increased as Ca²⁺-activated force rose above 60% of maximum in both rat and guinea pig trabeculae (Figures 3, 5, and 6). There is currently controversy over a possible Ca²⁺ dependence of k_tr in cardiac muscle. Hancock and colleagues^{7 8} reported no change in k_tr when Ca²⁺ was varied in intact⁷ and skinned⁸ cardiac muscles, whereas a Ca²⁺ dependence of k_tr was observed by other groups using rat skinned trabeculae⁹ and myocytes.^{10 11} In the present study, we confirm that k_tr is increased as [Ca²⁺] rises. Possible reasons why Hancock and colleagues^{7 8} reached the opposite conclusion have been discussed elsewhere^{5 8 9 10} ; one difference is that some of their experiments used a length change with a minimal holding period, which leads to a higher value (Figure 4), and possibly a Ca²⁺ independence, of k_tr. Our results (Figure 4) show the importance of defining the optimal holding period for k_tr measurements. Although we found that k_tr was activated by Ca²⁺ in both species, this was less for the guinea pig (2-fold, Figure 6) than for the rat (10-fold), which is similar to the observation that activation of k_tr is greater in fast skeletal than in slow skeletal fibers.⁶ The significance of the Ca²⁺ dependence of k_tr (and k_act) remains to be clarified: as with previous studies, our finding that k_tr and k_act are Ca²⁺ dependent could support Brenner's kinetic model,² in which Ca²⁺ regulates force by increasing f_app, or could be the result of cooperative binding of strong crossbridges in the steric blocking model.^{3 4 5}

The present report, which represents the first comparison of activation and relaxation rates in the same muscles, shows that the maximum relaxation rate can be as fast as maximum k_tr or k_act. This similarity is difficult to reconcile with any of the models for the Ca²⁺ dependence of k_tr. From the kinetic model,² the rate constant of force change after a sudden alteration of [Ca²⁺] should equal f'_app+g_app, where f'_app is the new f_app at the final [Ca²⁺] level, and g_app is the Ca²⁺-independent rate of crossbridge detachment; thus, f'_app when [Ca²⁺] is low after photolysis of diazo-2 will be much smaller than when [Ca²⁺] is high after photolysis of NP-EGTA or during maximal k_tr measurements, and the maximum relaxation rate should correspondingly be substantially smaller than the maximum k_act or k_tr. We observed no such difference in rates. Our calculations using Campbell's cooperative model⁵ indicate that relaxation in this model should also be slower than k_act or k_tr (results not shown). Thus, the rapidity of relaxation remains to be explained. It is unlikely to be due to SL changes during relaxation, since the sarcomeres would relengthen during relaxation and (from the force-velocity relationship) this would tend to maintain force, thereby slowing relaxation. Another possibility is that relaxation involves a reversal of the crossbridge working stroke. It is well established that the force-generating step (which is closely associated with the P_i release step) is reversible.²³ Neither of the above models includes this concept. We suggest that during relaxation a substantial fraction of crossbridges may lose force by a reversal of the force-generating transition rather than by the slower forward detachment step. The net rate of the backward strong-weak transition is relatively fast (8 s^-1 for rat at 1.7 mmol/L P_i and 15°C; estimated from Reference 17¹⁷ ), and a contributory loss of crossbridge force via this route could potentially account for the fast rate of relaxation.

In conclusion, (1) the relaxation rate is not limited by the rate of dissociation of Ca²⁺ from TnC but reflects the kinetics of the crossbridges, (2) faster myofibrillar activation and relaxation rates in rat trabeculae compared with guinea pig trabeculae most likely relate to myosin type, and (3) the similarity of the rates of relaxation and activation (or force redevelopment) in a given species is difficult to reconcile with previous crossbridge models for the Ca²⁺ regulation of k_tr but may be explained if a reversal of the crossbridge working stroke contributes to relaxation.

	Acknowledgments

 
This study was supported by the British Heart Foundation and The Royal Society. We are grateful to Dr P. Reiser for performing the gel analysis and to Dr J. Layland and D. McCloskey for commenting on the manuscript.

Received November 5, 1997; accepted April 30, 1998.

	References

Top Abstract Introduction Materials and Methods Results Discussion References

 

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