Mechanics and crossbridge kinetics of tracheal smooth muscle in two inbred rat strains

The aim of the study was to determine whether the nonspecific in vivo airway hyperresponsiveness of the inbred Fisher F‐344 rat strain was associated with differences in the intrinsic contractile properties of tracheal smooth muscle (TSM) when compared with Lewis rats. Isotonic and isometric contractile properties of isolated TSM from Fisher and Lewis rats (each n=10) were investigated, and myosin crossbridge (CB) number, force and kinetics in both strains were calculated using Huxley's equations adapted to nonsarcomeric muscles. Maximum unloaded shortening velocity and maximum extent of muscle shortening were higher in Fisher than in Lewis rats (∼46% and ∼42%, respectively), whereas peak isometric tension was similar. The curvature of the hyperbolic force/velocity relationship did not differ between strains. Myosin CB number and unitary force were similar in both strains. The duration of CB detachment and attachment was shorter in Fisher than in Lewis rats (∼−46% and −34%, respectively). In Fisher rats, these results show that inherited, genetically determined factors of airway hyperresponsiveness are associated with changes in crossbridge kinetics, contributing to an increased tracheal smooth muscle shortening capacity and velocity.

Asthma is characterised by chronic inflammatory disorders of the airways associated with increased airway responsiveness to various stimuli [1]. The mechanisms underlying nonspecific airway hyperresponsiveness (AHR) remain poorly understood. Although it is clear that airway smooth muscle (ASM) is the key effector of excessive airway narrowing in asthma, it remains unclear whether or not AHR is attributable to ASM abnormality [2,3]. The amount of ASM has been reported to be increased in human asthmatics [4][5][6] and in animal models of AHR [7]. However, recent stereological studies using axial airway sections at high resolution have provided no evidence of increased ASM in large airways of human asthmatics [8]. Marked differences in isotonic contractile properties of isolated ASM have been reported in human asthmatic [9], and in human- [10] and animal-sensitised [11][12][13][14] tissues. In these studies, isolated ASM was found to shorten more and faster in asthmatic and sensitised tissues than in controls without any differences in the ability to generate force. Taken together, these findings suggest functional changes resulting in increased ASM shortening capacity and velocity in hyperresponsive airways, without increases in the amount of ASM [8] or in ASM force production capacity. Potential mechanisms involved in such an increased ASM shortening capacity and velocity include reduced bronchial stiffness [9], decreased resistance to internal shortening [15], and increased myosin crossbridge (CB) cycling rate possibly related to an increased content of smooth-muscle myosin light-chain kinase (smMLCK) [16].
To study the direct contribution of ASM in the phenomenon of AHR, two complementary approaches are generally used in animals. First, various models dealing with passive or active sensitisation are used to investigate the acquired mechanisms involved in AHR. Second, models of spontaneous, nonspecific AHR can be used to study the inherited, genetically determined factors associated with AHR. To the best of the authors9 knowledge, ASM isotonic mechanical properties have never been studied in animal models of spontaneous genetically determined AHR. Two rat strains have been studied extensively because of marked differences in their spontaneous airway responsiveness, the Fisher F-344 strain and the Lewis strain. When compared with the Lewis strain, the Fisher strain exhibited greater airway responsiveness to various inhaled contractile agonists, such as methacholine [17] and 5-hydroxytryptamine [18,19]. This relative AHR was manifested by a shift in the dose/ response curve to the aerosolised agonist in both spontaneously breathing [17][18][19] and mechanically ventilated animals [20].
The aim of the present study was to determine whether the nonspecific in vivo AHR of the Fisher F-344 rat strain was associated with differences in the intrinsic contractile properties of tracheal smooth muscle (TSM) when compared with Lewis rats. Therefore, the mechanical properties of isolated TSM of inbred Fisher and Lewis rats were studied, focusing on isotonic parameters (extent and velocity of shortening), and the hypothesis of whether potential, inherited, genetically determined mechanical differences could be attributed to differences in myosin CB interactions was tested.

Tracheal smooth muscle preparation
Experiments were conducted with highly inbred male rats obtained from Charles River (Sulzfeld, Germany). Care of animals conformed to the recommendations of the Helsinki convention and the study was approved by the authors9 institution (INSERM, France). Ten adult Fisher F-344 rats (means ¡ SEM weight 208 ¡ 12 g) and 10 adult Lewis rats (weight 215¡14 g; p=0.71) were studied after being housed at a conventional animal facility where all animals had free access to food and water. At the time of the experiment, the investigator was not aware of which strain was Fisher or Lewis. For each animal, experiments were performed on TSM obtained from a tracheal ring consisting of four segments. The ring was opened with a dorsal midline section through the cartilage in order to obtain a strip of the posterior membranous portion of the trachea. The epithelium was not removed. The strip was then vertically suspended in a 100 mL organ bath containing a Krebs-Henseleit solution, bubbled with 95% oxygen/5% carbon dioxide and maintained at 37uC, pH 7.4. The lower end of the strip was held by a stationary clip at the bottom of the bath, while the upper extremity was held in a spring clip linked to an electromagnetic lever system [21,22]. Supramaximal electrical field stimulation (EFS; 30 V?cm -1 , 50 Hz AC, 3 ms pulse duration, 12 s train duration) was applied every 4 min by means of two platinum electrodes arranged in parallel on either side of the muscle preparation. Mechanical experiments were conducted after a 1-h equilibration period.

Mechanical parameters, force/velocity relationship
Mechanical parameters were recorded at optimal initial muscle length (L0) over the load continuum [21,22]. According to the conventional afterloaded technique, 8-10 EFS-elicited contractions were performed against increasing loads, from zero-load up to the fully isometric contraction. Maximum unloaded shortening velocity (Vmax; L0?s -1 ), using the zero-load clamp technique [23], maximum shortening velocity at the preload required to obtain L0 (Vc,max; L0?s -1 ) and maximum extent of shortening at preload (DL; %L0) were measured. Peak isometric force (F0; mN) was also measured and normalised per cross-sectional area to obtain peak isometric tension (P0; mN?mm -2 ). For each contraction, peak shortening velocity (V) was plotted against total isotonic load normalised per cross-sectional area (P). Data from the force/velocity curve were fitted according to HILL9s [24] hyperbolic equation, -a and -b being the asymptotes of the hyperbola, and G being the curvature of the hyperbola. At the end of the study, cross-sectional area (mm 2 ) was calculated from the ratio of muscle weight (mg) to muscle length at L0 (mm), assuming a muscle density of 1 [25]. Mean crosssectional area did not differ between groups (1.17¡0.12 mm 2 in Fisher versus 0.94¡0.08 mm 2 in Lewis, p=0.12).

Calculation of myosin crossbridge number, force and kinetics
HUXLEY9s [26] original equations constitute the most widely accepted mathematical model of muscle contraction.
This model provides an informative system for estimating the number, unitary force and kinetics of myosin CB in living striated muscles. An adaptation of these equations to nonsarcomeric muscles, such as smooth muscles, was recently developed [27]. This approach allows calculation of the unitary force per CB (P0; pN), the number of CB per mm 2 at peak active tension (Y610 9 ), mean CB velocity during power stroke (v0; mm?s -1 ), total duration of the CB cycle (tc; ms), the rate of adenosine triphosphatase (ATPase) activity (kcat, with kcat=1/tc) and duration of CB attachment (1/f1; ms) and detachment (1/g2; ms), where f1 represents peak value of attachment rate constant and g2 represents peak value of detachment rate constant (another constant of detachment being termed g1; fig. 1).
In fact, if h is termed the molecular step size (h=11 nm in ASM) [28,29], it can be seen from HUXLEY9s [26] manuscript, that w=(f1zg1)h/2 and that it is assumed that w=b and G= g2/(f1zg1). If w is termed the mechanical work of a single CB (w=3.8610 -20 J) [26,30], e is termed the free energy required to split one adenosine triphosphate (ATP) molecule (e=5.1610 -20 J) [26,30], and l is termed the length between two actin binding sites (l=36 nm) [31], then the following is obtained: P0~w ð4Þ For each TSM, the number, force and kinetics of CB were calculated by substituting the measured values of the force/ velocity relationship (namely Vmax, a, b, G) in the seven

Pi release
Step 5 ADP release g2 ATP Step 1 Detachment step Step 2 ATP hydrolysis f1 Step 3 Attachment step Step 4 Power stroke is triggered by the release of the inorganic phosphate (Pi; step 4) and occurs after adenosine triphosphate (ATP) hydrolysis (step 2) and attachment of the myosin head to the actin filament (step 3). Myosin rapidly dissociates from actin (step 1) after adenosine diphosphate (ADP) release (step 5). g2: peak value of detachment rate constant; f1: peak value of attachment rate constant. above-mentioned equations (for details see Appendix [26,27,32]).

Statistical analysis
All data are expressed as mean ¡ SEM. Statistical comparisons between groups were carried out by using an unpaired t-test. For the force/velocity curves, a correlation coefficient (r) between measured values of force and velocity and the model estimate was used to test the accuracy of the hyperbolic fit. The correlation between two variables was calculated by linear regression using the least-squares method. A pv0.05 was considered statistically significant.

Force/velocity relationship of tracheal smooth muscle in rats
In both strains, the force/velocity relationship was accurately fitted by a hyperbola: the r value between experimental data and Hill9s model was 0.993 ¡ 0.001 and 0.997 ¡ 0.001 in Fisher and Lewis rats, respectively. As shown in table 1, parameter b (which has units of velocity) was higher in Fisher than in Lewis rats. Conversely, parameter a (which has units of tension) was similar in both strains, as was the G curvature of the hyperbolic force/velocity relationship (table 1). Figure 4 shows representative force per mm 2 /velocity curves in Fisher and Lewis TSM.

Myosin crossbridge number, force and kinetics
P0 and the number of CB at peak active tension (Y6 10 9 ) are depicted in figure 5. No significant differences were observed between Fisher and Lewis rats. There were no strain differences in mean CB velocity during power stroke (v0=0.249¡0.040 mm?s -1 in Fisher and v0=0.246 ¡ 0.046 mm?s -1 in Lewis rats, p=0.95). There was no correlation between the Vmax and v0 (r 2 =0.056, p=0.32). There was a weak correlation between P0 of the muscle strip and P0 (r 2 =0.223, pv0.05; fig. 6a). Figure 6b shows that there was a strong linear relationship between P0 of the muscle strip and Y.

Discussion
The major findings of the present study are that: 1) the higher genetically determined spontaneous nonspecific AHR of the Fisher rat strain is associated with higher shortening capacity and velocity of isolated TSM when compared with Lewis; 2) myosin CB kinetics differ between strains; 1/g2 and, to a lesser extent, 1/f1 is shorter in Fisher than in Lewis rats, and 3) P0 and the unitary force per CB were similar in both strains, although F0 was higher in Fisher than in Lewis rats.
Data are presented as mean¡SEM. L0: optimal initial muscle length; -a and -b: the asymptotes of the hyperbola; G: the curvature of the hyperbola. n=10 for both. *: pv0.05.

Validation of the animal models
Both Fisher and Lewis are anatomically well-characterised strains of inbred rats [33]. When compared with Lewis, Fisher rats are known to exhibit higher airway responsiveness to various inhaled contractile agonists, such as methacholine [17] or 5-hydroxytryptamine [18,19]. In vivo, this relative AHR is manifested by a shift in the dose/response curve to the aerosolised agonist in both spontaneously breathing [17][18][19] and mechanically ventilated animals [20]. In the present study,   in vivo airway responsiveness was not measured in either rat strain. It cannot be excluded therefore that minor differences in airway responsiveness could occur between the rats used in this study and data from the literature. In vitro, the ASM of these two rat strains exhibits marked differences; while isolated TSM develops similar isometric force at baseline in both strains [17], the TSM of Fisher rats has been shown to be more responsive to cumulative concentrations of carbachol [34] or serotonin [35] than the Lewis strain. Lung explants have recently been used to show that this innate relative hyperresponsiveness of the Fisher strain was not restricted to the trachea but extended throughout the airway tree [19,36]. These studies also provided evidence that Fisher rat airways could exhibit a greater capacity for airway narrowing than Lewis. Taken together, these studies support the hypothesis that the relative nonspecific AHR found in the Fisher strain could be related to differences in the intrinsic contractile properties of the ASM [19].

Mechanical contractile properties of tracheal smooth muscle
To the best of the authors9 knowledge, no data are available concerning the isotonic contractile properties of isolated TSM of the Fisher and the Lewis strains. The first aim of the present study therefore was to characterise the contractile properties of isolated TSM in both strains, with particular attention paid to isotonic parameters. Vmax was found to be higher in Fisher than in Lewis rats ( fig. 2), as were DL and Vc,max ( fig. 3). These results corroborate previous findings from sensitised dogs [11,12], guinea-pigs [13], mice [14] and human bronchi [10], which all demonstrated that isolated ASM of sensitised tissue is able to shorten more and faster than ASM of controls. The results could also explain, at least in part, the previous findings reported in lung explants from Fisher and Lewis rats [19,36].
In ASM, two methods are usually used to elicit the force/ velocity relationship; conventional afterloaded isotonic contractions or quick releases applied 2 s after the onset of isometric contractions. Since force/velocity characteristics were first described in canine TSM by STEPHENS et al. [37], the best way of eliciting the force/velocity relationship has been a subject of discussion. In a preliminary study, the Vmax elicited with the afterloaded technique did not differ from the one measured with the quick-release technique [38] in both rat strains. It was also found that experimental data were accurately fitted by a hyperbolic curve, with no obvious deviation of velocities at high load, contrary to results previously reported in dogs [39]. The force/velocity relationship has never been studied in the ASM of rats. Interspecies differences may explain, at least in part, the differences observed between the present data and previous reports in canine TSM. As a hyperbola accurately fitted the current experimental data, the modified equation described by WANG et al. [39] was not used. Using the classic HILL [24] equation, parameter b of the equation was higher in Fisher than in Lewis rats, whereas parameter a did not differ between strains (table 1). This result was in agreement with the higher shortening capacity and velocity in Fisher compared with Lewis rats. The G curvature was also found to be similar in both strains (table 1). Similar results have been reported in sensitised canine TSM when compared with controls [11]. In striated muscles, the curvature of the force/velocity relationship has been found to be linked to the myothermal economy of force generation: the more curved Hill9s hyperbola (i.e. the higher G), the greater the economy of force generation [30,40]. Assuming that the fundamental properties of myosin CB do not strikingly differ between smooth and striated muscles [26], the present results suggest similar energetic cost of force generation in Fisher and Lewis TSM.
In this study, there were no strain differences in the P0 developed by isolated electrically stimulated TSM, although F0 was higher in Fisher than in Lewis rats ( fig. 2). In mechanical studies, it is usual to report the results of isometric tension rather than isometric force, as differences in cross-sectional area may interfere with results of force. This was clearly the case in this study. These results are in agreement with those reported previously in the same strains [17] and in animal models of nongenetically determined AHR [10][11][12][13][14].

Myosin crossbridge number, force and kinetics
It has been suggested that the ultimate defect in AHR may be at the muscle cell level itself [14]. If so, it should concern structures, mechanisms or pathways involved in or resulting in higher capacity and velocity of muscle shortening. Several approaches have been used to investigate how myosin molecular motors work. Studies using in vitro motility assays [41] and high-resolution single-molecule experiments, such as the optical tweezers technique [42], have provided insights into interactions of elementary contractile proteins. Mathematical models of muscle mechanics provide an informative system for estimating the number, unitary force and kinetics of myosin CB in living muscle [26,43,44]. HUXLEY9s [26] formalism has been used in many mechanical, as well as biochemical muscle experiments, and can contribute to better understanding of CB interactions [32]. The use of Huxley9s equations has been applied to nonsarcomeric muscles, such as smooth muscles, allowing a calculation of CB number, unitary force and kinetics from experimental mechanical data [27]. This has been validated in ASM from several species, including the rat [27]. The reasons for applying Huxley9s model in the present study were the following: 1) Huxley9s model not only accounts for many macroscopic properties of muscle (force, velocity and heat production), but also relates these properties to its structural and biochemical properties; 2) according to Huxley9s model, force and shortening in muscle are generated by cyclic interactions of the myosin heads with specific sites on the thin filaments, with ATP hydrolysis providing the energy; 3) by using mechanical parameters (velocity, length, force) at the level of the entire muscle and at various load levels, Huxley9s theory infers the kinetics and number of CB. Thus, the use of Huxley9s formalism seemed to be an attractive way to test the hypothesis that inherited, genetically determined mechanical differences could be attributed to differences in CB interactions.
Beside the power stroke, two important steps occur during the CB cycle, i.e. the attachment and detachment of the myosin head from actin ( fig. 1). Attachment of myosin to actin occurs after ATP hydrolysis [45]. Myosin rapidly dissociates from actin after ADP release. Thereafter, one molecule of ATP binds to the nucleotide site of the myosin head (ATP-binding pocket). In this study, the attachment step was found to be shorter in Fisher than in Lewis rats ( fig. 7), and the detachment step was markedly shorter in Fisher than in Lewis rats ( fig. 7). A shorter detachment step could account, at least in part, for increased velocity of shortening at the muscle level. In fact, according to Huxley9s CB model [26], Vmax is proportional to the maximum value of g2; the higher Vmax, the higher g2, thus the lower 1/g2, i.e. the shorter the detachment step. Therefore, the detachment step is a crucial step in the determination of maximum shortening velocity in ASM. 1/g2, rather than tc, would thus strongly influence the shortening capacity of the whole muscle. Further studies are needed to investigate which structural, biochemical or mechanical factors influence g2 and, to a lesser extent, f1 in the Fisher strain. Potential candidates are as follows: 1) differences in the three-dimensional configuration of the ATP-binding pocket of the myosin head, or the presence of a seven amino acid insert near the ATP-binding pocket [42,46], or differences in the configuration of the actin-binding site; 2) higher expression of the smooth muscle-B isoform of the myosin heavy chain in Fisher trachea (the presence of this isoform has recently been reported in TSM of adult Fisher rats) [47]; 3) differences in the 20 kD regulatory light chains of myosin; 4) differences in the structure, content or activity of myosin light chain kinase, especially the smMLCK isoform [16]; 5) structural or functional differences in the calcium/calmodulin complex; and 6) differences in the activity of the Rho-associated kinase that can directly phosphorylate the 20 kD regulatory light chains of myosin independently of calcium [48]. However, it should be mentioned that increased intracellular calcium mobilisation has recently been described in Fisher rats when compared with Lewis rats [19], suggesting that calcium-dependent pathways are at least partly involved in the mechanisms underlying the nonspecific AHR of the Fisher strain.
Using Huxley9s equations adapted for smooth muscles [27], no interstrain differences were found between the number, unitary force and mean velocity of myosin CB at peak active tension. Moreover, no relationship was found between Vmax and v0. Therefore, greater velocity of muscle shortening observed in Fisher rats could not be attributed to higher velocity of CB during power stroke. Potential differences in tc were also sought but no such differences were found between Fisher and Lewis rats, indicating that higher velocity of shortening is not necessarily associated with a shorter time cycle.
In conclusion, the isotonic and isometric contractile properties of isolated tracheal smooth muscle of Fisher and Lewis inbred rat strains were analysed. The higher genetically determined spontaneous nonspecific airway hyperresponsiveness of the Fisher rat strain was associated with higher shortening capacity and velocity of tracheal smooth muscle when compared with Lewis rats, with no difference in the ability to produce isometric force. These mechanical differences were not attributed to differences in the number, unitary force or mean velocity of myosin crossbridge during power stroke. In contrast, differences in myosin crossbridge kinetics, i.e. shorter duration of crossbridge detachment and attachment in Fisher than in Lewis, may help explain the higher shortening capacity and velocity in Fisher rats. These results highlight the crucial role of the crossbridge itself in the phenomenon of innate greater airway responsiveness of the Fisher rat strain.

Appendix: Calculations
Using HUXLEY9s [26] manuscript, the authors first expressed the rate of total energy release (E 0 ) and the isotonic tension (PHux) as a function of velocity (V). Thus, E 0 is given as: The minimum rate of total energy release (E 0 o) occurs under isometric conditions (V=0 in equation 8), is equal to the product of a6b [24,26] and is given by: It can be deduced that: The isotonic tension PHux is given by equation 11 [26]: PHux,max is reached for V=0 and is assumed to be equal to total isometric tension (P0), which was experimentally determined. The mean unitary force per CB in isometric conditions is: P0~PHux,max=Y~w ' f1 f1zg1 Calculation of peak value of detachment rate constant (g2) As W=(f1zg1)h/2, W=b, G=g2/(f1zg1) [26] and Vmax=Gb, it is deduced that: g2~2 Vmax h As G=g2/(f1zg1) [26] and f1=Gg1, by solving the quadratic equation f1 2 zg1f1-g1g2=0, f1 as a function of g1 and g2 was obtained: f1~-g1z ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi g1 2 z4g1g2 p (3)