Roles of Ca2+ and Crossbridge Kinetics in Determining the Maximum Rates of Ca2+ Activation and Relaxation in Rat and Guinea Pig Skinned Trabeculae
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 (koff) 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 koff. The maximum rates of rapid activation by Ca2+ after nitrophenyl-EGTA photolysis (kact) and of force redevelopment after forcible crossbridge dissociation (ktr) were similar and were ≈5-fold faster in rat (kact=14.4±0.9 s−1, ktr=13.0±0.6 s−1) than in guinea pig (kact=2.57±0.14 s−1, ktr=2.69±0.30 s−1) trabeculae. This too may be mainly due to species differences in crossbridge kinetics. Both kact and ktr 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.
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 (ktr) after forcible detachment of the crossbridges during Ca2+ activation. He therefore proposed a kinetic model2 in which Ca2+ activates both force and ktr by increasing the rate of transition of crossbridges from the non–force-generating (detached or weakly bound) state to the force-generating state (fapp). On the other hand, it has been suggested more recently3 4 5 that a Ca2+ dependence of ktr 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 ktr is found to be Ca2+ dependent in skeletal fibers2 4 6 does not distinguish between these models. In cardiac muscle, however, Hancock and colleagues7 8 found that ktr 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 ktr 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 ktr 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 kinetics12 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 (kact) with the maximum ktr can provide information on whether Ca2+-activated force development is limited by crossbridge kinetics rather than by kact. 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 kact can be compared with ktr. Our experiments also allowed the first comparison of maximum kact 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
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 ktr 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.
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 ktr, 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.
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%.
ktr 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 ktr.
In most trabeculae we could record at least 2 of the 3 sets of measurements (ktr, rapid activation, and rapid relaxation) before maximum force declined by 25%.
The relationship between steady-state force and pCa in each muscle was fitted by the Hill equation: relative force=maximum force×[Ca2+]nh/(Knh+[Ca2+]nh), where nH 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.
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 (nH) of 3.05±0.17 (n=39) and 2.49±0.28 (n=8) for rat and guinea pig, respectively.
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).
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, kact, 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 Pi inside the muscles. The postflash rise in force was well fitted by a single-exponential curve, with a kact 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.
To determine whether kact 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 kact (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 kact and force was curved upward.
Rate of Redevelopment of Force
We investigated whether the difference in kact between species (Figure 3⇑) was paralleled by a difference in crossbridge kinetics, as measured at constant [Ca2+] by ktr 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 ktr 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.
A comparison of ktr 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 ktr 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 ktr between species was not due to the different holding periods used, since ktr 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 ktr recorded from rat trabeculae (Figure 5⇓). The ktr values above were not significantly different from the maximum values of kact 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.
The relationship between ktr and steady-state force was also determined for each species (Figure 5C⇑ and 5F⇑) in order to compare the dependencies of ktr and of kact 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 ktr values at different force levels we pooled data for each muscle. Values of ktr 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 ktr values (relative force, 1.0) in both species. Thus, ktr 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 ktr against pCa (Figure 6⇓). As [Ca2+] rose from pCa 6.0 to 4.5, ktr 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 ktr value (≈5.4, Figure 6⇓) was less than the pCa50 for force (5.6, Figure 1⇑). Thus, force was more sensitive than ktr to Ca2+, which may account for the downward curvature in the force-ktr relationships (Figure 5⇑).
Role of Compliance in Determining ktr
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 ktr 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 ktr 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 ktr value for the rat is unlikely to be explained by greater internal shortening in the guinea pig.
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 (koff) 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 koff 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=kon/koff. Since kon has been reported to be diffusion-limited20 and therefore is constant, affinity may be determined chiefly by koff.) 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 koff 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 ktr 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 control8 9 10 when differences in temperature were taken into account. ktr, 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, kact is similar to ktr 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 kact, ktr, 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 αα-myosin heavy chains), whereas in guinea pig V2 and V3 myosins (αβ- and ββ-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% α-myosin heavy chains (ie, mostly V1 myosin), whereas guinea pig contained only 40% to 50% α-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 ktr, 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 ktr, kact, 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+ activation4 5 and thus would have little effect on the maximum values of ktr and kact, 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⇑).
kact and ktr Are Ca2+ Dependent
The values of kact and ktr 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 ktr in cardiac muscle. Hancock and colleagues7 8 reported no change in ktr when Ca2+ was varied in intact7 and skinned8 cardiac muscles, whereas a Ca2+ dependence of ktr was observed by other groups using rat skinned trabeculae9 and myocytes.10 11 In the present study, we confirm that ktr is increased as [Ca2+] rises. Possible reasons why Hancock and colleagues7 8 reached the opposite conclusion have been discussed elsewhere5 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 ktr. Our results (Figure 4⇑) show the importance of defining the optimal holding period for ktr measurements. Although we found that ktr 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 ktr is greater in fast skeletal than in slow skeletal fibers.6 The significance of the Ca2+ dependence of ktr (and kact) remains to be clarified: as with previous studies, our finding that ktr and kact are Ca2+ dependent could support Brenner’s kinetic model,2 in which Ca2+ regulates force by increasing fapp, 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 ktr or kact. This similarity is difficult to reconcile with any of the models for the Ca2+ dependence of ktr. From the kinetic model,2 the rate constant of force change after a sudden alteration of [Ca2+] should equal f′app+gapp, where f′app is the new fapp at the final [Ca2+] level, and gapp 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 ktr measurements, and the maximum relaxation rate should correspondingly be substantially smaller than the maximum kact or ktr. 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 kact or ktr (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 Pi 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 Pi 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 ktr but may be explained if a reversal of the crossbridge working stroke contributes to relaxation.
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.
- © 1998 American Heart Association, Inc.
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