Sensitivity of the airway smooth muscle in terms of force, shortening and stiffness

Eight pig tracheal strips were stimulated to contract with log increments of methacholine from 10 -8 to 10 -5 M. For each strip, the concentration-response was repeated four times in a randomized order to measure isometric force, isotonic shortening against a load corresponding to either 5 or 10 % of a reference force, and average force, stiffness, elastance and resistance over one cycle while the strip length was oscillating sinusoidally by 5 % at 0.2 Hz. For each readout, the logEC50 was calculated and compared. Isotonic shortening with a 5 % load had the lowest logEC50 (-7.13), yielding a greater sensitivity than any other contractile readout (p < 0.05). It was followed by isotonic shortening with a 10 % load (-6.66), elastance (-6.46), stiffness (-6.46), resistance (-6.38), isometric force (-6.32), and average force (-6.30). Some of these differences were significant. For example, the EC50 with the average force was 44 % greater than with the elastance (p = 0.001). The methacholine sensitivity is thus affected by the

With in vitro preparations of airway smooth muscle, isometric force is by far the most studied contractile readout.An entrenched conviction is that sensitivity measured in isometric conditions applies to in vivo physiology.Yet, isometric force does not typically exist in vivo.As smooth muscle force develops, the muscle shortens and the airway constricts, and in so doing, it rather adds to the passive recoil force of the airway wall, which is continuously distended because the surrounding attached parenchyma is stretched by the negative pressure of the pleural cavity (Lambert et al., 1993;Oliver et al., 2007).The actual meaning of isometric force on airway and lung mechanics is thus uncertain, and the sensitivity to methacholine deduced from isometric force measurements may well differ from the one affecting lung mechanics.
Many contractile readouts other than isometric force can be measured in vitro (Chin et al., 2010;Ijpma et al., 2015Ijpma et al., , 2020;;Noble et al., 2007;Gazzola et al., 2016;Fredberg et al., 1997).They include, inter alias, shortening, stiffness, elastance, resistance, and the ability to relax in response to a bronchodilator.Each contractile readout is potentially relevant to understanding the lung response to an inhaled spasmogen (Bossé and Paré, 2013).The contractile readouts being measured in a given experimental setting are often context-dependent and are often restricted to one per study.Comparison between studies are also difficult because different preparations (e.g., tracheal strips, bronchial rings, precision-cut lung slices, isolated cells,…) from different species are used in distinct experimental settings (Chin et al., 2010;Ijpma et al., 2015Ijpma et al., , 2020;;Noble et al., 2007;Gazzola et al., 2016;Fredberg et al., 1997;Donovan et al., 2015;Ma et al., 2002;An et al., Fig. 1.Concentration-response of porcine tracheal strips in the isometric condition.A representative force trace is shown in A. For each tracheal strip, the maximal force at each methacholine concentration (purple asterisks) and the force near the end of each methacholine concentration (short green line) were collected.Concentration-response curves were then constructed.The ones constructed with the maximal force are shown in B and the ones constructed with the end isometric force are shown in C. The individual curves and their mean are shown on the left and right panels, respectively.n = 8. 2016; Harvey et al., 2013;Mailhot-Larouche and Bossé, 2019).
Herein, the changes in several contractile readouts in response to incremental concentrations of methacholine were monitored on porcine tracheal smooth muscle strips to directly compare sensitivity between contractile readouts.More precisely, the concentration of methacholine causing half of the maximal response (EC50) was measured and was used as a surrogate for sensitivity.A lower EC50 means an increased sensitivity because it typically implies that the whole concentrationresponse curve is shifted to the left and that not only the response is observed at lower concentrations but that any percentage of the maximal response also typically occurs at lower concentrations.We hypothesized that the sensitivity of the airway smooth muscle to methacholine depends on by the contractile readout being measured.

Porcine tracheal smooth muscle strips
Tracheas from eight pigs were obtained from a local abattoir (Boucherie Alphonse Côté, Sainte-Eulalie, Canada).The trachea was excised after death and immersed into 4 • C Krebs solution (pH 7.4, 111.9 mM NaCl, 5.0 mM KCl, 1.0 mM KH 2 PO 4 , 2.1 mM MgSO 4 , 29.8 mM NaHCO 3 , 11.5 mM glucose, 2.9 mM CaCl 2 ), in which it was kept during transportation and until further processing.One smooth muscle strip from each trachea was isolated and mounted vertically in a 40-mL organ bath at in situ length in 37 • C Krebs solution and underwent a period of preconditioning as previously described (Gazzola et al., 2020).Indomethacin at 10 -6 M was also added during the entire experiment to avoid spontaneous prostanoids-mediated contractions.

Protocol
For each strip, a concentration-response with methacholine was repeated four times under four different contractile conditions in a randomized order.Each time, four concentrations of methacholine were added in log increments from 10 -8 to 10 -5 M. One contractile condition was isometric, meaning that the length of the strip was held fixed during the entire concentration-response.During the isometric condition, the concentrations of methacholine were added at 5-min intervals and both the maximal force over the 5 min and the force near the end of the 5 min were recorded at each concentration.The latter was more precisely calculated 10 s before the administration of the subsequent concentration of methacholine using an average over 1 s (thus 100 data points of isometric force, as the sampling frequency was 100 Hz).Two other contractile conditions were isotonic, meaning that the load impeding smooth muscle shortening was held fixed.Two loads were tested, corresponding to 5 and 10 % of the reference force.The latter was obtained at the end of the preconditioning period.It is more precisely the force generated in response to an optimal electrical-field stimulation (it nearly represents the highest force that the muscle can generate).During isotonic conditions, the concentrations of methacholine were added at 8min intervals and the maximal shortening was recorded at each methacholine concentration.The other contractile condition was during cyclical motion, meaning that the length of the tracheal strips was continuously fluctuating before and during the concentration-response.More precisely, the length of tracheal strips was sinusoidally oscillating by 5 % (trough-to-peak) at 0.2 Hz, mimicking the strain the smooth muscle undergoes in vivo due to tidal volume breathing.During the oscillatory condition, the concentrations of methacholine were added at 5-min intervals and several contractile readouts were deduced at each methacholine concentration, including peak force, average force, stiffness, elastance and resistance.How they were calculated is described below.
The order to which each strip was exposed to the four concentrationresponses was randomized using a 4×4 Latin square, which was repeated twice for a sample size of eight.The Latin square was uniform, meaning that each strip was subjected to all four concentrationresponses and each concentration-response occurred only once at a particular order at every four experiments.The Latin square was also balanced, meaning that the number of times a given concentrationresponse occurred before or after all the other ones happened only once every four experiments.

Data analyses
During the concentration-response in condition of cyclical motion, five contractile readouts were measured.The first one is peak force, representing the maximal force recorded at each methacholine concentration during one of the sinusoidal peaks in length.The other four contractile readouts were calculated over 5 s, specifically from trough to trough in the sine wave with the peak force.The second readout is average force, representing the average of all data points of force (500 of them, as the sampling frequency was again at 100 Hz) of the sine wave with the peak force.The third contractile readout is stiffness, representing the change in force over the change in length during the sine wave with the peak force.The last two are elastance and resistance.Since ASM tissue is innately non-linear (Ito et al., 2006;Bates and Lauzon, 2005), they were calculated using analytical tools applicable to both linear and non-linear systems (Fredberg and Stamenovic, 1989).The method was described in detail by others (Fredberg et al., 1993).Briefly, it consists of measuring the area between the ascending and the descending limbs of the force-length loops, which is then used to sequentially deduce resistance, the phase angle, hysteresivity and elastance.Put it simply, the phase angle quantifies the extent by which the resistive forces contribute to the total (elastic + resistive) forces.It has been described in more details in two original papers (Fredberg and Stamenovic, 1989;Fredberg et al., 1993), as well as in a recent review where it is explained more simply (Bossé, 2022).A representative force trace at 10 -6 M of methacholine is shown in A, together with a zoomed trace (inset) showing three cycles that include the peak cycle (green).For each tracheal strip, the peak force at each methacholine concentration (purple asterisks) were collected.From the cycle with the peak force (green traces), several contractile readouts were calculated, including average force, stiffness, elastance and resistance.Concentration-response curves were then constructed for each of these readouts and are shown in B to F. The individual curves and their mean are shown on the left and right panels, respectively.n = 8.
• R = 4 A/πω(ε 2 ), where R is resistance, A is area of the loop, ω is angular frequency and ε is strain.• ϕ = arcsin ωεR/ΔF, where ϕ is the phase angle and F is force.
For each contractile readout, the log EC50 was calculated.More precisely, a log(methacholine) vs. response with three parameters (top, bottom and EC50) was fitted by the least square method to each concentration-response of each tracheal strip for each contractile readout.Individual results, together with means ± standard deviations are presented.A repeated measures ANOVA was then used to compare the logEC50 between contractile readouts, which was followed by a Tukey multiple comparisons test to compare each contractile readout with each other.Statistical analyses were performed using Prism 10 (Version 10.1.1,GraphPad Software, San Diego, CA) and p≤0.05 was deemed significant.

Results
The results in the isometric condition are depicted in Fig. 1.As expected, the force rose with incremental concentrations of methacholine (Fig. 1A).Interestingly, the maximal force at each concentration was not maintained over time (Fig. 1A).Instead, the isometric force typically reached its highest value at a rate related to the methacholine concentration, and then receded (Fig. 1A).When the logEC50 was calculated using the maximal force at each methacholine concentration, it ranged from -6.87 to -5.95 M with a mean of -6.32 ± 0.28 M (Fig. 1B).When the logEC50 was calculated using the isometric force near the end of the 5 min of contraction at each methacholine concentration, it ranged from -6.89 to -6.08 M with a mean of -6.38 ± 0.28 M (Fig. 1C).The difference between the logEC50 with the maximal force and the end isometric force was not significant (p=0.96).
The results in isotonic conditions with a load corresponding to either 5 or 10 % of the reference force are depicted in Figs. 2 and 3, respectively.As expected, the shortening increased with incremental concentrations of methacholine (Fig. 2A & 3A).Interestingly, the maximal shortening at each concentration was mostly maintained over time (Fig. 2A & 3A).When the logEC50 was calculated using the shortening against a 5 % load, it ranged from -7.68 to -6.36 M with a mean of -7.13 ± 0.40 M (Fig. 2B).When the logEC50 was calculated using the shortening against a 10 % load, it ranged from -7.11 to -6.37 M with a mean of -6.66 ± 0.42 M (Fig. 3B).The logEC50 with the shortening against a 5 % load was lower than the one measured with the shortening against a 10 % load (p=0.03).
The results in the condition of cyclical motion are depicted in Fig. 4. As expected, all contractile readouts increased with incremental concentrations of methacholine.Similar to the isometric condition, the

Table 1
LogEC50 for contractile readouts measured during the condition of cyclical motion.

Readouts Range (M) Mean ± SD (M)
Peak force -6.93 to -5.70 -6.33 ± 0.41 Average force over the peak cycle -6.89 to -5.65 -6.30 ± 0.41 Stiffness during the peak cycle -7.14 to -5.86 -6.46 ± 0.43* † Elastance during the peak cycle -7.11to -5.84 -6.46 ± 0.42* † Resistance during the peak cycle -7.17 to -5.64 -6.38 ± 0.49 *Significantly different from the peak force (p<0.001)†Significantly different from the average force (p<0.001) L. Gélinas et al. maximal value for each contractile readout at each concentration was not maintained over time (Fig. 4A).Instead, they reached their highest value at a rate related to the methacholine concentration, and then receded (Fig. 4A).The range, mean and standard deviation of the logEC50 for the peak force, as well as for the average force, stiffness, elastance and resistance over the peak force cycle are shown in Table 1.Significant differences in logEC50 were observed with stiffness vs. peak force (p=0.003),stiffness vs. average force (p=0.003),elastance vs. peak force (p=0.002), and elastance vs. average force (p=0.001).
The logEC50s with all contractile readouts are depicted in Fig. 5.The repeated measures ANOVA was highly significant (p<0.0001).Apart from the significant differences stated above, the logEC50 with isotonic shortening against a 5 % load was significantly lower than the ones measured with all other contractile readouts (p<0.002), and the one with isotonic shortening against a 10 % load was significantly lower than the one measured with maximal isometric force (p=0.03).

Discussion
This study was specifically designed to compare methacholine sensitivity between different contractile readouts within the same tissues.The results point to many statistically significant differences.This finding has not only implications in many experimental settings, but may also provide insights regarding the elusive role played by the airway smooth muscle on respiratory mechanics.The more sensitive contractile readouts are indeed more likely to be affected by a physiological range of contractile agonist concentrations and, thereby, more likely to influence airway wall and lung mechanics.
Unsurprisingly, the range of sensitivity between contractile readouts was modest.It was suspected that, upon activation, a contractile level sufficient to alter stiffness would be near to the one causing force development and shortening.This narrow range of logEC50, fluctuating between -7.13 and -6.30, was thus anticipated.Yet, it is still important to emphasize that the two extremes represent a 6.8-fold difference (7.4 ×10 -8 vs. 5.0 ×10 -7 M).It is thus possible that the lower spectrum of this range is physiologically relevant, while the higher spectrum may not.
The logical order of sensitivity, according to our opinion, should have been stiffness, together with its related contractile properties such as elastance and resistance, followed by force and shortening.Shortening is presumably the less desirable behavior of the airway smooth muscle in vivo as it would translate to airway constriction.It thus came as a surprise that shortening yielded a significantly greater sensitivity than any other contractile readout, at least under a low counteracting load.However, two important confounders need to be considered in our experimental settings.First, the shortening was done at low loads.This implies a substantial amount of shortening, and shortening can obviously not proceed infinitely.It is rather limited by physical constraints.Since the isotonic load was low, maximal (or near maximal) shortening could have been attained at low methacholine concentrations, therefore blocking (or limiting) further shortening by subsequent concentrations.This effect would shift the concentration-response curve to the left, thereby decreasing the EC50.Second, in our settings, the shortening can only be initiated once the load is attained.This can be seen in the inset of Figs. 2 and 3. Therefore, greater is the isotonic load, greater is the concentration required to initiate shortening.This effect shifts the concentration-response curve to the right, thereby increasing the EC50.The fact that sensitivity decreased with increasing load in our experiments supports this notion.Based on this trend, we surmised that by further increasing the load, the EC50 would have kept increasing.It is therefore possible that under physiological conditions with an auxotonic load (Oliver et al., 2010), the EC50 may surpass the ones observed for stiffness and force.More studies are clearly needed.
Perhaps the most relevant comparisons between contractile readouts are the ones measured in the same contractile condition.During cyclical motion, five different contractile readouts were measured, namely peak force, average force, stiffness, elastance and resistance.Both stiffness and elastance were more sensitive than both the peak force and the average force.This, at least, fits with the logical order of sensitivity stated above.As outlined in the Introduction, force development in vivo is very likely to cause shortening and airway narrowing.However, if the stiffening of the smooth muscle precedes force development (i.e., if it truly takes place at lower concentration), it would allow airways to resist dilation during breathing maneuvers without causing constriction.In turn, this would minimize dead space excursion during breathing, optimizing flow into the alveoli and maximizing gas exchange at every breath.Notably, it is worth mentioning that we and others have previously demonstrated that stiffness is more sensitive than force to methacholine (Gazzola et al., 2016;Ansell et al., 2013).In both cases, the difference was greater than the one reported herein, amounting to log differences.Since these studies were done with human bronchial rings and intact sheep airways (and not with strips that are mostly made of muscle), it is possible that this greater sensitivity to stiffness vs. force is amplified when the smooth muscle is surrounded by the other structural components of the airway wall.
Another interesting observation was that maximal isometric force at each methacholine concentration was not maintained while maximal shortening mostly was.It thus seems that even when the activation drive Fig. 5.A scatter plot showing the methacholine logEC50 calculated using different contractile readouts.For each readout, points are from individual tracheal strips and the grey horizontal bar is the mean.They are shown in order of sensitivity from left to right to facilitate comparison.A repeated measures ANOVA was conducted followed by a Tukey's multiple comparisons test to compare the logEC50 between contractile readouts.Asterisks indicate pairwise significant differences (*,** and *** are p<0.05,0.01 and 0.001, respectively).n = 8. decreases, the shortening can be maintained.This is consistent with a mounting literature on the molecular mechanisms governing airway smooth muscle contraction, showing that many evanescent structures can be erected to physically link the contractile machinery inside the cell with its plasmalemma, the extracellular matrix and the surrounding cells, which, at the tissue scale, efficiently works to maintain shortening passively (Zhang et al., 2015;Tang, 2018;Zhang and Gunst, 2019;Seow, 2013).It is also consistent with previous work, showing that the increase in respiratory system resistance caused by inhaled methacholine in humans is lasting longer than the time required for methacholine clearance (Chapman et al., 2014;Cartier et al., 1983).

Conclusion
This study demonstrates that, although all within the same log range, the sensitivity to methacholine is significantly affected by the contractile readout being measured.It was shown that direct comparisons between certain contractile readouts can be misleading and should thus be interpreted with caution.Yet, when measured within the same contractile condition, some readouts, such as stiffness, change in response to lower concentrations than others, such as force.This can be key elements to take into account when contemplating the role played by the airway smooth muscle in respiratory mechanics.

Fig. 2 .
Fig. 2. Concentration-response of porcine tracheal strips in the isotonic condition against a 5 % load.A representative length trace is shown in A. The force trace is also shown in the inset.For each tracheal strip, the maximal shortening at each methacholine concentration (purple asterisks) were collected.Concentration-response curves were then constructed and are shown in B. The individual curves and their mean are shown on the left and right panels, respectively.n = 8.

Fig. 3 .
Fig. 3. Concentration-response of porcine tracheal strips in the isotonic condition against a 10 % load.A representative length trace is shown in A. The force trace is also shown in the inset.For each tracheal strip, the maximal shortening at each methacholine concentration (purple asterisks) were collected.Concentration-response curves were then constructed and are shown in B. The individual curves and their mean are shown on the left and right panels, respectively.n = 8.