Prestrain and cholinergic receptor-dependent differential recruitment of mechanosensitive energy loss and energy release elements in airway smooth muscle

Abstract

We tested the hypothesis that oscillatory airway smooth muscle (ASM) mechanics is governed by mechanosensitive energy loss and energy release elements that can be recruited by prestrain and cholinergic stimulation. We measured mechanical energy loss and mechanical energy release in unstimulated and carbachol-stimulated bovine ASM held at prestrains ranging from 0.3 to 1.0 L_o (reference length) and subjected to sinusoidal length oscillation at 1 hz with oscillatory strain amplitudes ranging from 0.1 to 1.5% L_o. We found that oscillatory ASM mechanics during sinusoidal length oscillation is governed predominantly by one class of nonlinear mechanosensitive energy loss element and one class of nonlinear mechanosensitive energy release element with differential mechanosensitivities to oscillatory strain amplitude. The greater mechanosensitivity of the energy loss element than energy release element may explain the bronchodilatory effect of deep inspiration. Prestrain, an important determinant of ASM responsiveness, differentially increased energy loss and energy release in unstimulated and carbachol-stimulated ASM. Cholinergic stimulation, an important cause of bronchoconstriction and airway inflammation, also differentially increased energy loss and energy release. When prestrain and cholinergic stimulation were combined, we found that prestrain and cholinergic stimulation synergistically increased energy loss and energy release by ASM. The relationship between recruitment of energy loss elements and recruitment of energy release elements was nonlinear, suggesting that energy loss and energy release elements are not coupled in ASM cells. These findings imply that large lung volume and cholinergic ASM activation would synergistically increase mechanical energy expenditure during inspiration and mechanical recoil of ASM during expiration.

NEW & NOTEWORTHY We report for the first time that oscillatory airway smooth muscle mechanics is governed predominantly by one class of nonlinear mechanosensitive energy loss element and one class of nonlinear mechanosensitive energy release element with differential mechanosensitivities to oscillatory strain amplitude. Prestrain and cholinergic stimulation synergistically and differentially recruit energy loss and energy release elements. The greater mechanosensitivity of the energy loss element than the energy release element may explain the bronchodilatory effect of deep inspiration.

INTRODUCTION

Airway smooth muscle (ASM) hyperresponsiveness is an important cause of obstructive lung diseases such as asthma (23). The conventional view of ASM dysfunction in asthma is that the abnormally high contractility of ASM causes airway narrowing in asthma. On the contrary, contractility, as measured by stress development and isotonic shortening velocity, of ASM isolated from asthmatic and nonasthmatic human subjects was not significantly different (11, 16). Instead, oscillatory mechanics of ASM derived from asthmatic and nonasthmatic subjects were significantly different. For example, length oscillation-induced force attenuation was lower, whereas passive stiffness was higher, in ASM derived from asthmatic subjects. The oscillatory mechanics of ASM is physiologically significant because ASM undergoes lengthening during inspiration and shortening during expiration, in parallel with an increase and decrease in lung volume during breathing cycles.

The oscillatory mechanics of ASM has been studied typically by investigating the effects of oscillatory strain/stress amplitude and frequency on the time courses of strain and stress. Prestrain, the static strain imposed on ASM before strain/stress oscillation is often controlled but not systematically investigated. Prestrain is a physiologically significant variable because prestrain imposed on ASM increases with lung volume and contributes to the decrease in airway resistance with lung volume (7, 10). Prestrain is an important determinant of ASM responsiveness to cholinergic receptor stimulation at multiple levels of cellular organization: phosphatidylinositol breakdown, intracellular Ca²⁺ concentration ([Ca²⁺]), myosin light chain phosphorylation, and force generation (3, 4, 30, 37). Recently, Al-Jumaily et al. (1) showed that a prestrain of 0.56 and 2% reference length (L_o) enhanced length oscillation-induced force reduction, while a prestrain of 4% did not. The range of prestrain investigated by Al-Jumaily et al. is small relative to the range of prestrain (30–100% L_o) that modulates ASM contractility (37). This study investigates the effects of prestrain and oscillatory strain on the oscillatory mechanics of ASM.

Analysis of data on oscillatory ASM mechanics has been performed by multiple approaches. Some studies described observations of force oscillation-induced muscle lengthening and length oscillation-induced force reduction in ASM without further analysis (6). One study modeled stress-strain data derived from oscillatory ASM mechanics empirically using empirical parameters without addressing mechanisms (2). The most common mechanistic approach to data analysis is modeling ASM as viscoelastic material using a linear model of viscoelasticity. For example, Fredberg and Stamenovic (14) and Fredberg et al. (13) calculated elastic modulus, loss modulus, and hysteresivity (loss modulus/elastic modulus) from stress/strain data derived from oscillatory ASM mechanics. A potential problem in this approach is the assumption of linearity because oscillatory ASM mechanics is known to be nonlinear.

Another mechanistic approach to data analysis is the inclusion of force-velocity relationships and cross-bridge mechanisms in modeling strain-stress data derived from oscillatory ASM mechanics. Using this approach, Bates and Lauzon (8) showed that interaction between contractile apparatus and connective tissue could explain the nonlinear stress-strain relationships of ASM during strain-stress oscillation. By combining Huxley’s sliding filament model and Hai and Murphy’s latch model of smooth muscle contraction, Mijailovich et al. (27) showed that mechanical disruption of cross-bridge cycling by oscillatory strain/stress could explain stress-strain relationships during strain/stress oscillation in ASM. A potential problem in these modeling approaches is the uncertain identity and validity of model parameters and assumptions.

We have previously taken a novel energetics approach to studying the oscillatory mechanics of ASM by calculating rebound resilience, the ratio of mechanical energy release after unloading/mechanical energy absorption during loading of ASM (21). Rebound resilience is a concept in materials engineering for quantifying the recoil energy of material during unloading relative to energy absorption during loading (35). Rebound resilience of a purely viscous material is zero, whereas rebound resilience of a purely elastic material is 1. A major strength of this energetics approach is that it does not require the assumption of linearity and is therefore applicable to both linear and nonlinear material. Rebound resilience is useful for explaining the high-frequency oscillation of asynchronous flight muscles during insect flight, when stretch-induced delayed muscle activation enables oscillation of the flight muscle in resonance with oscillation of the thorax (18). For oscillatory ASM mechanics, rebound resilience is the ratio of mechanical recoil energy by ASM during shortening divided by the mechanical energy input exerted on ASM during lengthening (21). High rebound resilience of ASM would enhance airway closure during expiration and limit expiratory flow, and vice versa. We have previously found that oscillatory strain decreased rebound resilience in ASM, whereas prestrain and cholinergic stimulation increased rebound resilience of ASM (21). In the analysis of oscillatory ASM mechanics, mechanical energy absorption during loading equals the sum of mechanical energy loss and mechanical energy release (Fig. 1A). Accordingly, rebound resilience can be expressed as 1/(1 + energy loss/energy release), as shown in Fig. 1B. In this study, we postulate that oscillatory mechanics of ASM cells is governed by mechanosensitive energy loss element(s) and mechanosensitive energy release element(s) that dissipate and liberate energy as a function of oscillatory strain. Prestrain is an important determinant of ASM responsiveness to cholinergic receptor stimulation. Cholinergic stimulation of airway cells induces bronchoconstriction and promotes airway inflammation (22). We hypothesize that prestrain and cholinergic stimulation regulate oscillatory mechanics of ASM by recruiting mechanosensitive energy loss and mechanosensitive energy release elements. We tested the hypothesis by measuring energy loss and energy release in unstimulated and carbachol-stimulated bovine ASM held at different prestrains and subjected to sinusoidal length oscillation with different oscillatory strain amplitudes.

Fig. 1.

A: illustration of the calculation of energy loss (EL) by integrating the area within the length-force loop and the calculation of energy release (ER) by integrating the area under the shortening phase of the length-force loop. B: relationship between rebound resilience and the energy loss/energy release ratio based on the equation: rebound resilience = 1/(1 + energy loss/energy release).

MATERIALS AND METHODS

Preparation of ASM strips.

The dissection of ASM from bovine trachea has been described previously (21). Briefly, bovine tracheas were collected from a local slaughterhouse and transported to the laboratory in refrigerated (4°C) physiological salt solution (PSS) of the following composition (in mM): 140 NaCl, 4.7 KCl, 1.2 Na₂HPO₄, 2.0 MOPS (pH 7.4), 0.02 Na₂-EDTA, 1.2 MgSO₄, 1.6 CaCl₂, and 5.6 d-glucose. Adventitial and mucosal layers were carefully dissected away under a dissecting microscope. The remaining ASM layer was excised and placed in a petri dish. ASM strips, ~4 to 5 mm in width, were dissected along the direction of muscle fibers in the circumferential direction.

Sinusoidal length oscillation of ASM strips.

The computer-controlled lever system for length oscillation has been described previously (21). Briefly, one end of each ASM strip was tied to a stainless steel wire hook, which was attached to the arm of a lever (Aurora Scientific, Aurora, ON) for length oscillation, while the other end of the ASM strip was clamped to a length manipulator for adjusting prestrain muscle length before length oscillation.

Prior to length oscillation, ASM strips were adjusted to L_o at which isometric force development is maximal by the following procedure. Freshly dissected ASM strips were stretched to 12 g and incubated for 1 h in PSS bubbled with air at 37°C. Viability of ASM strips was tested by stimulating them for 3 min with K-PSS, a solution similar to PSS in composition except equimolar substitution of 105 mM NaCl by KCl. ASM strips were then equilibrated again in PSS for 1 h, during which ASM strips were gradually stretched to a length beyond L_o by stretching them to 12 g every 15 min. ASM strips were then adjusted to L_o by releasing them rapidly to 2.5 g, and then stimulated by K-PSS for 10 min. The active force (F_o) developed by each ASM strip in this contraction was recorded as maximal force for normalization of force development during sinusoidal length oscillations. The actual length of each ASM strip at L_o was measured using a caliper with 0.1-mm resolution for normalization of muscle length during sinusoidal length oscillations. After stimulation by K-PSS, ASM strips were allowed to relax in PSS for 1 h before further experimentation. Depending on the experiment, ASM strips were adjusted to 0.3, 0.7, or 1.0 L_o, and then either unstimulated or stimulated by 1 μM carbachol for 30 min before sinusoidal length oscillation. We have reported previously that carbachol-induced force development reaches steady state by 10 min after the addition of carbachol (3). Therefore, in this study, sinusoidal length oscillation was performed on carbachol-stimulated ASM during the steady-state phase of contraction.

Sinusoidal length oscillation of ASM strips was executed by a computer program that controls the electrical voltage sent to the length input port of the lever system at regular time intervals. Muscle length of ASM strips was then oscillated sinusoidally at 1 hz with oscillatory amplitudes at 0.1, 0.5, 1.0 or 1.5% L_o for 36 cycles. Data on position of the lever and the force exerted on the lever by ASM during sinusoidal length oscillation were collected by the computer at 100 hz. The lever position data, representing muscle length, were expressed as % L_o. The lever force data were expressed as fraction of F_o.

Data analysis.

We computed mechanical energy loss and mechanical energy release from the length and force time course data using IGOR Pro, version 6.0 (Wavemetrics, Lake Oswego, OR). First, we calculated the velocity of ASM lengthening and shortening by taking a time differential of the length data, as described previously (21). Second, we computed power input exerted on ASM during lengthening and power release by ASM during shortening by multiplying force and velocity at each time point. Third, we computed energy input during ASM lengthening and energy release during ASM shortening by integrating power input and power release with respect to time. Integrating power with respect to time for calculating energy input and energy release is equivalent to integrating force with respect to length, as shown in Fig. 1A. The integrated area during the lengthening phase represents energy input; the integrated area during the shortening phase represents energy release; and the integrated area within the loop represents energy loss, which is the difference between energy input and energy release.

Statistics.

Data are shown as means ± SE; n represents the number of tracheal rings. Student’s t-test was used for the comparison of two means (P < 0.05 considered significant). The dependencies of energy loss and energy release on oscillatory strain amplitude were analyzed by the power function with the calculation of a correlation coefficient.

RESULTS

Length-force relationships in unstimulated ASM during sinusoidal length oscillation.

Figure 2, A and B, shows representative length-force loops during sinusoidal length oscillation of unstimulated ASM held at prestrains ranging from 0.3 to 1.0 L_o and oscillated with relatively small oscillatory strain amplitudes (0.1 and 0.5% L_o). At a very low oscillatory strain amplitude (0.1% L_o), as shown in Fig. 2A, the length-force loop in unstimulated ASM during sinusoidal length oscillation appeared linear with very small loop areas. At each prestrain, force oscillates about a mean force that was prestrain dependent: lowest at 0.3 L_o and highest at 1.0 L_o. For example, mean force was ~0.01 F_o at 0.3 L_o and 0.22 F_o at 1.0 L_o. The dynamic modulus, as measured by the peak-to-peak slope of a length-force relationship, was also prestrain dependent: lowest at 0.3 L_o and highest at 1.0 L_o. Increasing oscillatory strain amplitude from 0.1 to 0.5% L_o, as shown in Fig. 2B, increased the loop area and dynamic modulus, but did not appear to change linearity of the length-force relationships.

Fig. 2.

Length-force loops during sinusoidal length oscillation of unstimulated airway smooth muscle (ASM) strips at the following oscillatory strain amplitudes: 0.1% reference muscle length at which isometric force development is maximal (L_o; A), 0.5% L_o (B), 1% L_o (C), and 1.5% L_o (D). Each length-force loop represents data from 1 representative experiment. In each experiment, unstimulated ASM strips were held at the following prestrains: 0.3 L_o (green), 0.7 L_o (red), and 1.0 L_o (blue).

At moderate oscillatory strain amplitude (1.0% L_o), as shown in Fig. 2C, length-force loops during sinusoidal length oscillation of unstimulated ASM remained prestrain dependent, but became nonlinear with clearly defined loop areas. In Fig. 2C, during sinusoidal length oscillation with an oscillatory strain amplitude at 1% L_o, the length-force loop area of unstimulated ASM held at 0.3, 0.7, and 1.0 L_o were 0.19, 0.26, and 0.47, respectively. The dynamic modulus, as measured by the peak-to-peak slope of a length-force relationship, was clearly prestrain dependent: lowest at 0.3 L_o and highest at 1.0 L_o. Increasing oscillatory strain amplitude to 1.5% L_o, as shown in Fig. 2D, increased both the loop areas and dynamic modulus.

Dependencies of mechanical energy loss and mechanical energy release on oscillatory strain amplitude in unstimulated ASM.

For each length-force loop during sinusoidal length oscillation of unstimulated ASM at a given oscillatory amplitude, as shown in Fig. 2, we calculated mechanical energy loss from the area within the length-force loop and mechanical energy release from the area under the lower portion of the length-force loop, as illustrated in Fig. 1. We repeated the experiments and calculated the mean ± SE of energy loss and energy release by unstimulated ASM for each prestrain (0.3, 0.7, and 1.0 L_o) and each oscillatory strain amplitude (0.1, 0.5, 1.0, or 1.5% L_o). As shown in Fig. 3A, for each prestrain (0.3, 0.7, or 1.0 L_o), energy loss by unstimulated ASM increased nonlinearly with oscillatory strain amplitude. Each energy loss-oscillatory amplitude relationship was well fitted by a power function: Energy Loss = A × (Oscillatory Amplitude)^B. The square of the correlation coefficient (R²) of the fits shown in Fig. 3A ranged from 0.989 to 0.991. As shown in Fig. 3B, energy release by unstimulated ASM also increased nonlinearly with oscillatory strain amplitude for each prestrain (0.3, 0.7, or 1.0 L_o). Each energy release-oscillatory amplitude relationship was also well fitted by a power function: Energy Release = C × (Oscillatory Amplitude)^D. The square of the correlation coefficient (R²) of the fits shown in this figure ranged from 0.928 to 0.990.

Fig. 3.

Dependencies of energy loss (A) and energy release (B) on oscillatory strain amplitude in unstimulated ASM strips held at the following prestrains: 0.3 L_o (triangles), 0.7 L_o (squares), and 1.0 L_o (circles). L_o is the reference muscle length at which isometric force development is maximal. Symbols represent means (n = 3); vertical lines represent SE. Curves represent power function fits to data: energy loss = A × (oscillatory strain amplitude)^B and energy release = C × (oscillatory strain amplitude)^D. Values of proportionality coefficients (A and B) and exponents (B and D) are shown in Table 1.

Table 1 shows the coefficients (A and C) and exponents (B and D) of the power functions for energy loss-oscillatory strain and energy release-oscillatory strain relationships during sinusoidal length oscillation of unstimulated ASM at each prestrain (0.3, 0.7, and 1.0 L_o). As shown in Table 1, for the energy loss-oscillatory strain relationship in unstimulated ASM, coefficient A changed substantially with prestrain; for example, coefficient A increased by ninefold from 318 at 0.3 L_o to 2,807 at 1.0 L_o. In comparison, values of exponent B were relatively invariant with prestrain. Exponent B at 0.3, 0.7, and 1.0 L_o were 1.57, 1.83, and 1.66, respectively. The coefficient of variation (standard deviation/mean) of these values was <7%.

Table 1.

Coefficient and exponent of power functions for relating energy loss and energy release to oscillatory amplitude

	Energy Loss = A × (Oscillatory Amplitude)B
	Coefficient A		Exponent B
Prestrain	Unstimulated	Carbachol	Unstimulated	Carbachol
0.3 Lo	318	3,775	1.57	1.69
0.7 Lo	3,176	26,558	1.83	1.81
1.0 Lo	2,807	47,495	1.66	1.88

	Energy Release = C × (Oscillatory Amplitude)D
	Coefficient C		Exponent D
Prestrain	Unstimulated	Carbachol	Unstimulated	Carbachol
0.3 Lo	5	56	0.67	0.66
0.7 Lo	28	986	0.78	0.75
1.0 Lo	362	4,729	0.80	0.86

L_o is the reference muscle length at which isometric force development is maximal. Coefficients and exponents in this table were derived from modeling data shown in Figs. 3 and 5.

As shown in Table 1, for the energy release-oscillatory strain relationship in unstimulated ASM, coefficient C changed substantially with prestrain; for example, coefficient C increased by 72-fold from 5 at 0.3 L_o to 362 at 1.0 L_o. In comparison, exponent D remained relatively constant with prestrain. Exponent D at 0.3, 0.7, and 1.0 L_o were 0.67, 0.78, and 0.80, respectively. The coefficient of variation of these values was <8%.

Length-force relations in carbachol-stimulated ASM during sinusoidal length oscillation.

Figure 4, A and B, shows representative length-force loops during sinusoidal length oscillation of carbachol-stimulated ASM held at prestrains ranging from 0.3 to 1.0 L_o and oscillated with relatively small oscillatory strain amplitudes (0.1 and 0.5% L_o). As shown in Fig. 4A, at very low oscillatory strain amplitude (0.1% L_o), the length-force relationship in carbachol-stimulated ASM during sinusoidal length oscillation was prestrain dependent and appeared linear with very little hysteresis (loop area). At each prestrain, force oscillates about a mean force that was prestrain dependent: lowest at 0.3 L_o and highest at 1.0 L_o. For example, mean force was ~0.02 F_o at 0.3 L_o and 1.5 F_o at 1.0 L_o. These values of mean force in carbachol-stimulated ASM were higher than the corresponding values in unstimulated ASM (Fig. 2). The dynamic modulus, as measured by the peak-to-peak slope of a length-force relationship, also appeared to be prestrain dependent: lowest at 0.3 L_o and highest at 1.0 L_o. Increasing oscillatory strain amplitude to 0.5% L_o, as shown in Fig. 4B, increased hysteresis and the dynamic modulus, and caused the length-force relationship to become nonlinear.

Fig. 4.

Sinusoidal length oscillation of carbachol-stimulated ASM at the following oscillatory strain amplitudes: 0.1% L_o (A), 0.5% L_o (B), 1.0% L_o (C), and 1.5% L_o (D). L_o is the reference muscle length at which isometric force development is maximal. Each length-force loop represents data from 1 representative experiment. In each experiment, carbachol-stimulated ASM were held at the following prestrains: 0.3 L_o (green), 0.7 L_o (red), and 1.0 L_o (blue).

At moderate oscillatory strain amplitude (1.0% L_o), as shown in Fig. 4C, length-force loops during sinusoidal length oscillation of carbachol-stimulated ASM was prestrain dependent and appeared nonlinear with noticeable hysteresis. In Fig. 4C, during sinusoidal length oscillation with an oscillatory strain amplitude at 1% L_o, the length-force loop area of carbachol-stimulated ASM held at 0.3, 0.7, and 1.0 L_o were 1.3, 5.7, and 7.5, respectively. Comparison between length-force loop areas in unstimulated ASM (Fig. 2C) and carbachol-stimulated ASM (Fig. 4C) indicates prestrain and cholinergic receptor dependencies of energy loss in ASM during sinusoidal length oscillation. The dynamic modulus, as measured by the peak-to-peak slope of a length-force relation, was clearly prestrain-dependent: lowest at 0.3 L_o and highest at 1.0 L_o. Increasing oscillatory strain amplitude to 1.5% L_o, as shown in Fig. 4D, increased both hysteresis and the dynamic modulus.

Dependencies of mechanical energy loss and mechanical energy release on oscillatory strain amplitude in carbachol-stimulated ASM.

For each length-force loop during sinusoidal length oscillation of carbachol-stimulated ASM at a given oscillatory strain amplitude, as shown in Fig. 4, we calculated mechanical energy loss from the area within the length-force loop and mechanical energy release from the area under the lower portion of the length-force loop, as illustrated in Fig. 1. We repeated the experiments and calculated the mean ± standard error of energy loss and energy release by carbachol-stimulated ASM for each prestrain (0.3, 0.7, and 1.0 L_o) and each oscillatory strain amplitude (0.1, 0.5, 1.0, or 1.5% L_o). As shown in Fig. 5A, energy loss by carbachol-stimulated ASM increased nonlinearly with oscillatory strain amplitude at each of the three prestrains (0.3, 0.7, and 1.0 L_o). Each energy loss-oscillatory amplitude relationship was fitted well by a power function: Energy Loss = A × (Oscillatory Amplitude)^B. The square of correlation coefficient (R²) of the fits shown in this figure ranged from 0.988 to 0.999. As shown in Fig. 5B, energy release by carbachol-stimulated ASM also increased nonlinearly with oscillatory strain amplitude at each of the three prestrains (0.3, 0.7, and 1.0 L_o). Each energy release-oscillatory amplitude relationship was fitted well by a power function in the form: Energy Release = C × (Oscillatory Amplitude)^D. The square of correlation coefficient (R²) of the fits shown in this figure ranged from 0.959 to 0.992.

Fig. 5.

Dependencies of energy loss (A) and energy release (B) on oscillatory strain amplitude in carbachol-stimulated ASM strips held at the following prestrains: 0.3 L_o (triangles), 0.7 L_o (squares), and 1.0 L_o (circles). Symbols represent means (n = 6); vertical lines represent SE. L_o is the reference muscle length at which isometric force development is maximal. Curves represent power function fits to data: energy loss = A × (oscillatory strain amplitude)^B and energy release = C × (oscillatory strain amplitude)^D. Values of proportionality coefficients (A and B) and exponents (B and D) are shown in Table 1.

Table 1 shows the coefficients (A and C) and exponents (B and D) of the power functions for energy loss-oscillatory strain and energy release-oscillatory strain relations during sinusoidal length oscillation of carbachol-stimulated ASM at each prestrain (0.3, 0.7, and 1.0 L_o). As shown in Table 1, for the energy loss-oscillatory strain relationship in carbachol-stimulated ASM, coefficient A changed substantially with prestrain; for example, coefficient A increased by 13- fold from 3,775 at 0.3 L_o to 47,495 at 1.0 L_o. In comparison, exponent B remained relatively invariant with prestrain. Exponent B at 0.3, 0.7, and 1.0 L_o were 1.69, 1.81, and 1.88, respectively. The standard deviation/mean ratio of these values was <5%.

As shown in Table 1, for carbachol-stimulated ASM, coefficient C changed substantially with prestrain; for example, coefficient C increased by 13-fold from 56 at 0.3 L_o to 4,729 at 1.0 L_o. In comparison, exponent D remained relatively constant with prestrain. Exponent D at 0.3, 0.7, and 1.0 L_o were 0.67, 0.75, and 0.86, respectively. The standard deviation/mean ratio of these values was <11%.

Predicted exponents of energy loss-oscillatory strain and energy release-oscillatory strain relationships for linear viscosity and elasticity.

As shown in Table 1, energy loss-oscillatory strain amplitude relationships for unstimulated and carbachol-stimulated ASM were well fitted by power functions with a relatively invariant exponent (B), ranging from 1.57 to 1.88. Energy release-oscillatory strain amplitude relationships for unstimulated and carbachol-stimulated ASM were well fitted by power functions with a relatively invariant exponent (D), ranging from 0.67 to 0.86. To determine whether these exponents are significantly different from the predicted exponents of energy loss-oscillatory strain and energy release-oscillatory strain relationships for linear viscous and elastic elements, we performed the following calculations.

We modeled linear viscosity by the equation: force = n(dx/dt), where n is a constant, x is strain, and t is time. We modeled sinusoidal length oscillation at a given prestrain and oscillatory amplitude by the following equation: x = L + Δxsin(ωt), where L is prestrain, Δx is oscillatory strain amplitude, and ω is angular frequency. The equation for force predicts that velocity (dx/dt) equals Δxωcos(ωt) and force equals nΔxωcos(ωt). Power equals force × velocity, which equals nΔx²ω²cos²(ωt). As shown in this calculation, at a given frequency, viscous power is a function of Δx². This equation predicts that viscous energy, an integral of power with respect to time, is also a function of Δx². Based on this analysis, energy loss during sinusoidal strain oscillation is expected to be proportional to (oscillatory strain amplitude)². That is, for linear viscosity, 2 is the expected value for exponent B in the power function for energy loss = A × (Oscillatory Amplitude)^B. As shown in Table 1, experimental values of exponent B for energy loss for unstimulated and carbachol-stimulated ASM ranged from 1.57 to 1.88. Statistical analysis using Student’s t-test indicated that experimental values of exponent B for ASM were significantly different from the predicted value of 2 for the linear viscous element (P < 0.05).

We modeled linear elasticity by the equation: force = kx, where k is a constant and x is strain. Energy stored and release by the elastic element during sinusoidal length oscillation equals the integral, ʃ force dx, or ʃ kx dx. During sinusoidal length oscillation with an oscillatory strain amplitude Δx about prestrain L, stored/released energy equals ʃ kx dx from x = L−Δx to L+Δx, which equals 2kΔx. Based on this analysis, energy release during sinusoidal strain oscillation is expected to be proportional to oscillatory strain amplitude. That is, for linear elasticity, 1 is the expected value for exponent D in the power function for energy release = C × (oscillatory amplitude)^D. As shown in Table 1, experimental values of exponent D for energy release for unstimulated and carbachol-stimulated ASM ranged from 0.66 to 0.86. Statistical analysis using Student’s t-test indicated that experimental values of exponent D for ASM were significantly different from the predicted value of 1 for linear elasticity (P < 0.05).

Coefficients of power functions for energy loss-oscillatory strain and energy release-oscillatory strain relationships.

As discussed in the last section, the relatively invariant exponents B and D of power functions for energy loss-oscillatory strain and energy release-oscillatory strain relationships characterize the mechanosensitivity of energy loss and energy release elements in ASM. We reason that coefficients A and C of power functions for energy loss-oscillatory strain and energy release-oscillatory strain relationships reflect the number of energy loss and energy release elements in ASM. As shown in Table 1, prestrain amplifies cholinergic recruitment of energy loss and energy release elements, as measured by coefficient A and coefficient C, respectively. For example, in response to cholinergic stimulation, the increment in coefficient A was 3,457 at 0.3 L_o but 44,688 at 1.0 L_o (Table 1). Similarly, in response to cholinergic stimulation, the increment in coefficient C was 51 at 0.3 L_o but 4,367 at 1.0 L_o. However, as shown in Fig. 6, the relationship between coefficient A and coefficient C was nonlinear and resembled saturation kinetics. At relatively low values, increases in coefficient A and coefficient C appeared proportional. At relatively high values, increase in coefficient A became disproportionally less than the increase in coefficient C.

Fig. 6.

A: relationship between coefficient A of the power function for energy loss and coefficient C of the power function for energy release. Symbols represent data from Table 1. Open symbols represent unstimulated ASM; closed symbols represent carbachol-stimulated ASM. Line represents the following equation of saturation kinetics: A = 55,000 × C/(C + 1,100).

DISCUSSION

Oscillatory ASM mechanics is an important determinant of airway diameter and therefore airway resistance during breathing cycles. In this study, we have taken a novel energetics approach to investigating oscillatory ASM mechanics by measuring and analyzing mechanical energy release and mechanical energy loss during sinusoidal length oscillation of ASM. Mechanical energy release by ASM represents the recoil energy of ASM during the expiratory phase of a breathing cycle. Mechanical energy loss by ASM represents the viscous energy that is lost between lengthening and shortening of ASM during a breathing cycle (12). This energetics approach is novel because it does not require the assumption of linearity or small oscillatory strain amplitude.

A major finding in this study is that oscillatory ASM mechanics during sinusoidal length oscillation is governed predominantly by one class of nonlinear mechanosensitive energy loss and one class of nonlinear mechanosensitive energy release elements, characterized by their unique dependencies on oscillatory strain amplitude in the form of power functions with relatively invariant exponents (Table 1). Energy loss by ASM equals A × (oscillatory strain amplitude)^B, where coefficient A is a function of prestrain and cholinergic stimulation, and exponent B is relatively invariant at 1.7 ± 0.1. Energy release by ASM equals C × (oscillatory strain amplitude)^D, where coefficient C is a function of prestrain and cholinergic stimulation, and exponent D is relatively invariant at 0.75 ± 0.07. The exponents B and D are relatively independent of prestrain and cholinergic stimulation and significantly different from expected values for linear viscosity and linear elasticity. To our knowledge, this is the first report that oscillatory ASM mechanics is governed predominantly by one class of nonlinear mechanosensitive energy loss element and one class of nonlinear mechanosensitive energy release element with differential mechanosensitivities to oscillatory strain amplitude. The observed larger exponent of the power function for energy loss than energy release predicts that increasing oscillatory strain amplitude will increase energy loss more than energy release, thereby increasing the energy loss/energy release ratio. This prediction explains our previously observed attenuating effect of oscillatory strain amplitude on rebound resilience of ASM, which is inversely related to the energy loss/energy release ratio (Fig. 1B) (21). This prediction may also explain the bronchodilatory effect of deep inspiration (5).

Prestrain is an important determinant of dynamic mechanics of soft biological tissues (25, 29, 31, 34). In this study, we found that prestrain increased both energy loss and energy release by unstimulated and carbachol-stimulated ASM during sinusoidal length oscillation (Figs. 3 and 5; Table 1). This finding is consistent with results from linear analysis of oscillatory ASM mechanics indicating the enhancing effect of prestrain on the loss modulus and storage modulus in ASM (17). Findings from this study suggest that an increase in prestrain on ASM, typically associated with an increase in lung volume, would increase the energy cost of inspiration and increase ASM recoil during expiration. Cholinergic stimulation of airway cells induces bronchoconstriction and promotes airway inflammation (22). In this study, we found that cholinergic stimulation of ASM increased both energy loss and energy release during sinusoidal length oscillation (Figs. 3 and 5; Table 1). This finding is consistent with the observation from linear analysis of oscillatory ASM mechanics that cholinergic stimulation enhances the loss modulus and storage modulus in ASM (17). We have previously reported that cholinergic stimulation significantly increases rebound resilience in ASM (21), which is a function of the energy loss/energy release ratio. Results from this study imply that differential increases in energy loss and energy release with cholinergic stimulation result in the increase in rebound resilience. When prestrain and cholinergic stimulation were combined, we found that prestrain amplified the effect of cholinergic stimulation on energy loss and energy release. This observation suggests that prestrain and cholinergic stimulation synergistically increase energy loss and energy release by ASM during strain oscillation. A potential significance of this finding is that breathing at large lung volume in the presence of cholinergic ASM activation would substantially increase energy expenditure during inspiration and ASM recoil during expiration. The relationship between coefficient A of the power function for energy loss and coefficient C of the power function for energy release was nonlinear (Fig. 6), suggesting that energy loss and energy release elements are not coupled in ASM cells. This characteristic of ASM is different from that of lung tissues, which exhibit tight coupling between elastic and dissipative elements (28). One potential implication of this observation is that energy loss and energy release elements in ASM cells could be differentially recruited.

The observed relative invariance of exponents of power functions for energy loss-oscillatory strain amplitude and energy release-oscillatory strain amplitude relationships in ASM (Table 1) suggests that oscillatory ASM mechanics is governed predominantly by one class of energy loss element and one class of energy release element with differential and nonlinear mechanosensitivities to oscillatory strain amplitude. The identities of these energy loss and energy release elements are not known. The following analysis has led us postulate that actin cytoskeletal and actomyosin filaments are the functionally dominant energy loss and energy release elements in ASM cells. Actin cytoskeletal and actomyosin filaments are the major mechanical elements in cells (15, 24). We have previously reported that prestrain and cholinergic stimulation regulate cytoskeletal recruitment of actin- and integrin-binding proteins and activation of myosin cross bridges by myosin light chain phosphorylation in ASM (20, 21, 37). Myosin molecules interacting with actin filaments exhibit nonlinear elasticity and are the major determinant of length change-induced force transients in smooth muscle cells (19, 36). Cycling myosin cross bridges are capable of reattachment and doing external work by ATP hydrolysis, whereas, in comparison, actin cytoskeletal filaments consisting of mostly entangled and cross-linked proteins are less capable of doing external work (9, 26). This postulate predicts that actin cytoskeletal and actomyosin filaments are both necessary to explain oscillatory ASM mechanics. This prediction is consistent with the finding that contractility alone, as measured by isometric force and shortening velocity, is insufficient to explain oscillatory ASM mechanics (32, 33).

In summary, we report for the first time that oscillatory ASM mechanics is governed predominantly by one class of nonlinear mechanosensitive energy loss element and one class of nonlinear mechanosensitive energy release element with differential mechanosensitivities to oscillatory strain amplitude. The greater mechanosensitivity of the energy loss element than the energy release element may explain the bronchodilatory effect of deep inspiration. Prestrain and cholinergic stimulation synergistically and differentially recruit energy loss and energy release elements, with greater recruitment of energy release elements than energy loss elements, resulting in the downregulation of the energy loss/energy release ratio during sinusoidal length oscillation of ASM. This finding implies that breathing at large lung volume in the presence of cholinergic ASM activation would substantially increase energy expenditure during inspiration and ASM recoil during expiration.

GRANTS

This study was supported by National Institutes of Health Grant R56-HL-52714.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

C.-M.H. conceived and designed research; performed experiments; analyzed data; interpreted results of experiments; prepared figures; drafted manuscript; edited and revised manuscript; approved final version of manuscript.