Effect of muscle length on cross-bridge kinetics in intact cardiac trabeculae at body temperature

The main function of the heart is to pump blood to meet the demands of the body. This pumping activity depends on cardiac muscle contraction, which, in turn, depends on the interaction of sarcomeric thick and thin filaments, which form cross-bridges that generate force. Consequently, the pumping capability of the heart is determined by the number of cross-bridges capable of generating force and the rate at which they cycle through unbound, weakly bound, and strongly bound (force-generating) states (Hanft et al., 2008; McDonald, 2011). Therefore, alterations in either of these two factors can affect cardiac function.

The Frank–Starling law of the heart—as ventricular volume (corresponding to muscle length) increases, the heart intrinsically strengthens—describes a well-known cardiac regulatory mechanism. Although increased muscle length generally results in improved force development, in parallel with a prolonged time to peak (TTP) force and a slowing of relaxation time (Allen and Kentish, 1985; Monasky et al., 2008, 2010), it is unclear whether changes in muscle length per se affect cross-bridge kinetics. Some previous studies found that cross-bridge cycling kinetics decreased with increased sarcomere length (Adhikari et al., 2004; Stelzer and Moss, 2006; Korte and McDonald, 2007), whereas others found that sarcomere length has no effect on the rate of cross-bridge cycling (Hancock et al., 1993; Edes et al., 2007). These previous studies, however, were performed using permeabilized cardiac preparations, sub-physiological temperatures, or both. Data obtained under physiological temperature and in intact muscle preparations might help resolve this discrepancy and clarify the effects of muscle length on cross-bridge kinetics.

Various laboratory techniques have been used to study cross-bridge cycling, including Edman’s slack test, actomyosin ATPase activity, rate of tension redevelopment, and sinusoidal perturbation (Ruf et al., 1998; Wannenburg et al., 2000; Brixius et al., 2003). Of these, the rate of tension redevelopment (k_tr) (Brenner and Eisenberg, 1986) has been the most widely adopted approach. This technique assesses the rate at which force redevelops after a rapid slack–stretch maneuver has disconnected all cross-bridges. The k_tr protocol has been used by many investigators and has provided valuable information with regard to quantifying the kinetic steps in thick and thin filament interactions. However, intact cardiac preparations do not normally produce tetanic (fused) contractions, even at very high stimulation rates (Slabaugh et al., 2012). This makes measuring k_tr, which requires a stable level of Ca²⁺ activation, very difficult. The few studies that measured k_tr in preparations with intact membranes (Hancock et al., 1993; Baker et al., 1998; Hannon et al., 2001) combined high frequency stimulation with irreversible SR poisoning (using cyclopiazonic acid or ryanodine) to maintain stable Ca²⁺ concentrations, an approach that is constrained to low (nonphysiological) temperatures. Our goal here was to design a protocol that allows repeated assessment of k_tr in intact cardiac trabeculae at physiological body temperature. We found that this could be done reliably and reproducibly by using K⁺ contractures, a technique that leads to depolarization of the muscle, causing an influx of calcium into the cytoplasm that produces a tetanus-like steady-state contraction. We then used this method to show that an increase in cardiac muscle length leads to a decrease in k_tr.

For the first part of the study, we assessed three muscles from rabbit hearts. Rabbits were anesthetized using 50 mg/kg sodium pentobarbital, delivered intravenously (into the lateral ear vein). However, we used rats for most experiments. Male brown Norway rats (∼3 mo old and weighing 250 g; n = 11) were anesthetized intraperitoneally with 50 mg/kg sodium pentobarbital. The chest wall was opened by means of bilateral thoracotomy, and the heart was injected with 1,000 U heparin. In all cases, the heart was rapidly removed and perfused via the ascending aorta with Krebs–Henseleit solution containing (mM) 137 NaCl, 5 KCl, 10 glucose, 20 NaHCO₃, 1.2 MgSO₄, 1.2 NaH₂PO₄, 0.25 CaCl₂, and 20 2,3-butanedione monoxime (BDM) (Bupha-Intr et al., 2009; Slabaugh et al., 2012). The BDM prevents contractions and minimizes cutting injury during dissection (Mulieri et al., 1989). The Krebs–Henseleit solution was equilibrated with 95% O₂/5% CO₂ resulting in a pH of 7.4. The right ventricle was opened, and thin nonbranched trabeculae (average dimensions of 159 ± 11–µm wide, 106 ± 7–µm thick, and 1.5 ± 0.1–mm long; n = 11; rat) were dissected leaving free ventricular wall at both ends. Muscles with a thickness of >150 µm were excluded from analysis to avoid the effects of core hypoxia (Raman et al., 2006).

Muscles were mounted in a custom-made bath and connected to a force transducer (Scientific Instruments Heidelberg) on one end by means of two parallel hooks (to eliminate rotation movement artifacts) and to a linear motor (Scientific Instruments Heidelberg) (Xu et al., 2011a,b) on the other end. Vibrations associated with the movement of the motor and the flow of the superfusate were reduced by placing a small glass slide over the bath, and an electronic signaling anti-oscillation unit with an effective time constant faster than 1.2 ms was used to improve signal resolution (Scientific Instruments Heidelberg) (Xu et al., 2011a). The muscles were perfused with Krebs–Henseleit solution as described in the section above (without BDM and containing 2.0 mmol/L CaCl₂). The solutions were kept at a constant temperature of 37°C and equilibrated with 95% O₂/5% CO₂. Rat and rabbit muscles were stimulated at 4 and 1 Hz, respectively. The optimal lengths of the muscles were determined as described previously (Janssen et al., 2002). Clear striation patterns cannot always be observed with intact trabeculae preparations, but previous work (Rodriguez et al., 1992) has shown that optimal length (L_opt) corresponds to a sarcomere length of ∼2.2 µm, which is close to the sarcomere length at the end of diastole.

The rate of tension redevelopment was measured for each rat muscle at both the optimal length (L_opt) and at a shorter length, L₉₀ (90% of L_opt), close to the in vivo sarcomere length at the end of systole. To determine whether experimental order affected the results, we measured k_tr in the following order: L_opt→L₉₀→L_opt→L₉₀ in one subset of rat muscles (n = 6) and L₉₀→L_opt→L₉₀→L_opt in a second set (n = 5). The K⁺ contracture plateau (peak) allows for a steady-state equilibrium between calcium and force (Varian et al., 2006). Therefore, we performed all k_tr experiments when the muscles were under maximal force–inducing K⁺ contracture, conditions under which calcium concentration is 1 µM or higher, which is saturating for force in intact preparations (Varian et al., 2006, 2009; Monasky et al., 2010). After the muscles were maintained in Krebs–Henseleit solution for 15–20 min at either L_opt or L₉₀, we induced K⁺ contracture by switching to a solution containing (mM) 121.4 KCl, 20.6 NaCl, 10 glucose, 20 NaHCO₃, 1.2 MgSO₄, 1.2 NaH₂PO₄, and 6 CaCl₂. Once the K⁺ contracture started, the stimulation was turned off and the contracture was allowed to reach its plateau (maximum tension) phase. At this point the k_tr was determined, and the solution was rapidly switched back to Krebs–Henseleit buffer (inducing relaxation of the K⁺ contracture) and the electrical stimulation was restarted. Muscle length was then adjusted to L_opt or L₉₀ as appropriate, and the preparation was allowed to stabilize at the new length for 15–20 min, after which the K⁺ contracture and determination of k_tr protocol were repeated. A typical tracing of an entire K⁺ contracture containing a k_tr is given in Fig. 1 A for a muscle at L₉₀. An example of a k_tr tracing is given in Fig. 1 B. k_tr was determined through the following protocol: the muscle was rapidly shortened to 80% of its length during 1 ms (“slack” phase), maintained at this length for 10 ms, and then rapidly restretched to the original length during 1 ms. This maneuver disrupts cross-bridges, resulting in a decrease in force, followed by an exponential increase in force as the cross-bridges reattach (Brenner and Eisenberg, 1986; Campbell et al., 2003). Data were collected at a rate of 10 kHz.

All data were collected be means of a custom-made application in LabView (National Instruments). The cross-sectional areas of the muscles were used to normalize absolute force measurements to reduce variations among muscles of different diameter. The rate of tension redevelopment (k_tr) was obtained by fitting the force redevelopment curve following the slack–restretch maneuver to the equation F = F_max · (1 − e^ktr(t)) + F_initial (in which F = force, F_max = maximal force, and F_initial = initial force) using a nonlinear least-squares fitting method (Kemmer and Keller, 2010). Fitting a double exponential did not significantly improve the fit. Additionally, the half-time of force redevelopment, t_1/2, was determined by linear transformation of the data and used for calculation of k_tr, where k_tr = ln(2) · (t_1/2)⁻¹. The differences between multiple groups were analyzed via two-way ANOVA with a significance threshold of P < 0.05. The differences between k_tr calculated by monoexponential curve fit and linear transformation were determined by paired Student’s t test with a significance threshold of P < 0.05. The data are presented as mean ± SEM.

First, we compared k_tr in two species: the rat, which expresses the fast α-myosin isoform, and the rabbit, which expresses the slow β-myosin isoform. In Fig. 2 (A and B), we show traces of k_tr performed in a rabbit muscle. We obtained typical force tracings, similar to those described in permeabilized muscles at sub-physiological temperatures (Brenner and Eisenberg, 1986). Analyses of duplicate measurements showed that results were repeatable and reproducible (Fig. 2 C). k_tr is considerably slower (10.6 ± 1.2 s⁻¹; n = 3) in rabbit than in rat (27.7 ± 3.3 s⁻¹; n = 11; P < 0.01) under identical conditions (Fig. 2 D), indicating that the rate of k_tr at physiological temperature differs with different myosin isoforms.

Next, we investigated the effect of temperature on k_tr. We observed an increase in k_tr as temperature was increased from 27 to 37°C (n = 4 trabeculae, each from different rats), using a stimulation frequency of 1 Hz. We measured a Q10 in the range similar to that observed in permeabilized preparations (average Q10 of 2.2, ranging from 1.9 to 2.8; not depicted). The temperature dependence of our k_tr measurements supports the notion that k_tr in our experiments reflects cross-bridge cycling kinetics in a similar way as it does in permeabilized preparations at sub-physiological temperature.

Stretching the muscle from L₉₀ to L_opt resulted, as expected, in a significant increase in twitch tension (Fig. 3 A) from 17.0 ± 2.8 to 30.9 ± 3.3 mN/mm² (L₉₀ vs. L_opt, respectively; P < 0.05). In addition, at longer length, as expected (Janssen, 2010a,b), the TTP (Fig. 3 B), which measures the time it takes for maximal twitch tension to develop, was prolonged from 50.2 ± 1.7 ms at L₉₀ to 55.7 ± 2.2 ms at L_opt (P < 0.05). Similar results were observed for RT₅₀, which is the time from peak twitch force to 50% relaxation (Fig. 3 C), which increased from 30.2 ± 1.6 to 37.5 ± 1.5 ms (P < 0.05). The increase in muscle length resulted in an increase in the maximal tension obtained during the K⁺ contracture. The maximum (plateau) K⁺ contracture tension was 32.7 ± 5.1 mN/mm² at L₉₀ and 67.2 ± 6.6 mN/mm² for L_opt (Fig. 4 A). Maximum K⁺ contracture tension was not affected by time-dependent rundown; repeat measurements showed similar values (35.3 ± 8.0 mN/mm² for L₉₀ and 61.2 ± 7.0 mN/mm² for L_opt; P = 0.80). Maximum K⁺ contracture tension between L₉₀ and L_opt was significantly different (P < 0.05).

K_tr decreased as muscles were stretched from L₉₀ to L_opt (see example in Fig. 4 B). The average rate of tension redevelopment was 45.1 ± 7.6 s⁻¹ at L₉₀ and 27.7 ± 3.3 s⁻¹ at L_opt (Fig. 4 C). When k_tr for each length was measured a second time, the repeat k_tr measurements were 47.5 ± 9.2 s⁻¹ for L₉₀ and 27.8 ± 3.0 s⁻¹ for L_opt, indicating a high reproducibility (Fig. 4 C). K_tr was significantly different between the two lengths (P < 0.05), but similar between the initial and repeat measurements at each length, P = 0.84. Quantification of the k_tr data by linear transformation yielded values in close agreement and not significantly different from the above data (P > 0.4; not depicted). Finally, analysis of residual tension (F_res) after k_tr revealed a ratio of F_res to F_dev of 0.07 ± 0.05 at L₉₀, and this ratio was not significantly (ANOVA; P = 0.85) different from that at L_opt (0.09 ± 0.05).

We have developed a method for studying the effect of muscle length on cross-bridge cycling kinetics in intact cardiac trabeculae at physiological temperatures. We found that (a) it is feasible to assess in k_tr repeatedly in intact muscle preparations at physiological temperature using K⁺ contractures; and (b) under these conditions, an increase in rat muscle length leads to a decrease in k_tr.

We found effects of both different myosin isoforms and different temperature on cross-bridge kinetics similar to those described previously in permeabilized muscle at sub-physiological temperatures. k_tr for the α-myosin isoform was significantly faster than with the β isoform (Bottinelli et al., 1994; Herron et al., 2001), and increased temperature sped up k_tr (Hancock et al., 1996; de Tombe and Stienen, 2007). Given a Q10 of ∼2–3, the rate of tension redevelopment in our studies (up to 45–50 s⁻¹) would virtually be identical to six previously reported values (average of ∼9 s⁻¹ and range of 7–13 s⁻¹) for rats in skinned preparations at colder temperatures (Wolff et al., 1995; Hancock et al., 1996; Fitzsimons et al., 2001; Adhikari et al., 2004; Chen and Ogut, 2006; Chandra et al., 2007) and also be very close to those obtained in intact SR-poisoned cardiac trabeculae, where k_tr at normal calcium was ∼11 s⁻¹ (Baker et al., 1998).

Permeabilized or “skinned” preparations, which have typically been used to determine cross-bridge kinetics, have produced a wealth of critical knowledge. Although they are ideally suitable for highly controlled experiments on cross-bridge kinetics, these preparations are devoid of posttranslational modification machinery because membranous structures have been (partially) removed. This in turn may render inactive or altogether removes signaling kinases and phosphatases. However, posttranslational modification of contractile proteins is encountered under different conditions of preload, frequency, and β-adrenergic stimulation, and it has been proposed as a mechanism for altering cross-bridge cycling dynamics (Kranias and Solaro, 1982; de Tombe, 2003; Tong et al., 2004; Layland et al., 2005; Lamberts et al., 2007; Varian and Janssen, 2007; Ait Mou et al., 2008; Hidalgo et al., 2009; Varian et al., 2009; Monasky et al., 2010).

We used a modified K⁺ contracture protocol (Holubarsch, 1983; Varian et al., 2006; Varian and Janssen, 2007; Monasky et al., 2010) to reversibly “tetanize” intact cardiac trabeculae to assess cross-bridge kinetics at physiological temperature. This type of contracture induces a reversible steady-state force, without the need for compounds that interfere with SR calcium cycling (Hancock et al., 1993; Gao et al., 1994; Baker et al., 1998; Hannon et al., 2001), and can be repeated many times in the same muscle. The maximum tension developed during the K⁺ contracture did not change between duplicate measurements; this suggests that the maximal force generating capacity of myofilaments was not affected by a prior measurement per se, nor by the passage of time during the course of our analyses. Furthermore, we found that maximum tension at a given muscle length was independent of the order of length changes.

Although the relationship between muscle or sarcomere length and force development is well known (Allen and Kentish, 1985), the effect of sarcomere length on cross-bridge cycling rate remains controversial. We found that, when intact muscle length is reduced to 90% of optimal length, the rate of tension redevelopment was significantly accelerated. This is consistent with previous studies that used permeabilized cardiac preparations at sub-physiological temperatures (Adhikari et al., 2004; Stelzer and Moss, 2006; Korte and McDonald, 2007). However, other studies indicated that sarcomere length has no effect on rate of cross-bridge cycling (Hancock et al., 1993; Edes et al., 2007). The different results obtained in these studies could stem from various sources. First, they reflect experiments performed with different animal species or strains. Additionally, all but one (Hancock et al., 1993) of the past studies used permeabilized cardiomyocytes, which do not fully recapitulate intact myocardium. For instance, they do not have constant volume behavior when stretched; the interfilament spacing upon stretch may not reduce as much in skinned preparations compared with a similar stretch in intact muscle. Furthermore, many of these experiments were performed at a temperature range of 12–27°C, at which the behavior of many physiological processes may differ from that at mammalian physiological temperatures (∼37°C) (Little et al., 2012). Moreover, posttranslational modification of myofilament targets influences contractile properties, and the in situ status of posttranslational modifications may be (partially) lost with preparation of the muscle or myocyte for in vitro experimentation. As a result, assessment of cross-bridge cycling rate could thus be affected by preparation-induced or reduced levels of such modifications (Marston and de Tombe, 2008; Monasky et al., 2010). In addition, myofilament compliance may affect cross-bridge cycling rate (Martyn et al., 2002), and the presence of compliant structures, such as collagen and titin, in muscle preparations may render k_tr rates at different levels of force apparent rather than absolute. Finally, the residual tension could have an effect on the k_tr (Campbell, 2006; Campbell and Holbrook, 2007); however, residual tension was not significantly different in our studies and therefore could not have contributed to the lower k_tr observed at longer muscle lengths. At present, we do not have the necessary information and data to propose a molecular mechanism for the acceleration of k_tr we observed at shorter muscle lengths. However, others (Korte and McDonald, 2007) have proposed plausible mechanisms to explain this phenomenon. For instance, at longer muscle length, titin induces a strain on myosin-binding protein C, which in turn restrains the movement of myosin heavy chains, thus decreasing cross-bridge cycling rate (Korte and McDonald, 2007).

In conclusion, our work reveals that repeated k_tr measurements are feasible in intact myocardium at body temperature and that in intact muscle, k_tr decreases with increasing muscle length.

This study was partially supported by an Established Investigator Award from the American Heart Association National Center (grant 0740040N to P.M.L. Janssen) and by the National Institutes of Health (grant R01HL091986A2 to J.P. Davis and grant R01HL090749 to K.S. Campbell).

Richard L. Moss served as editor.