INTRODUCTION

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The cardinal features of asthma are reversible airway obstruction, airway hyperresponsiveness, and airway inflammation. In asthma, the key effector of acute airway narrowing is airway smooth muscle; as the muscle surrounding the airway shortens, the airway lumen narrows. Explanations of acute airway narrowing that are currently available in the literature rest on the idea that airway smooth muscle length is determined by a balance of two static forcesthe isometric steady-state force generated by the muscle in balance with the passive reaction force developed by the load against which the muscle shortens (1). The muscle load is set by elasticity of the airway wall, tethering of the airway to the lung parenchyma, and the state of lung inflation. This conceptual framework has become a useful guide for experimental investigation of airway obstruction and hyperresponsiveness because it points to the key factors that determine the static equilibrium length toward which activated airway smooth muscle would tend if given enough time.

The search for the mechanical origin of excessive airway narrowing in asthma focused initially on the muscle. Abnormality of the muscle cannot be ruled out based on the available evidence, but viable muscle isolated from the airways of asthmatic patients is difficult to obtain, and the few studies reported thus far, when taken together, have failed to demonstrate conclusively that airway hyperresponsiveness can be attributed to hypersensitivity of the muscle to nonspecific bronchoconstrictors or to excess capacity for isometric force generation (6). In order to explain excessive airway narrowing, therefore, attention then turned to the muscle load and how that load might become diminished in inflammatory airway disease (1- 5). At present, however, the specific inflammatory changes in the muscle or its load that might account for excessive airway narrowing remain uncertain (7). Even more puzzling is the emerging realization that the cardinal features of asthma are associated with one another only loosely (7, 8). The conceptual difficulty in understanding the relationship between airway obstruction, airway hyperresponsiveness, and inflammation in asthma may be traceable in part to the fact that asthma comprises a variety of distinct pathobiological processes, and is likely a collection of diverse phenotypes (7).

These phenotypes share as their common downstream effector the actin-myosin interaction within airway smooth muscle, and any factor that appreciably modulates this interaction would therefore modulate the extent of the organ-level response. If so, then this article provides what may be a major missing piece of this puzzle. Our results suggest that if the binding of myosin to actin is the molecular motor that drives muscle shortening, then the mechanical disruption of that binding by force fluctuations (caused by the action of tidal breathing) acts to disengage the level of the contractile response from the level of the contractile stimulus. We offer evidence to suggest that it may be the dysfunction of this process, rather than the motor, its static load, or its level of stimulation, that accounts for many aspects of excessive airway narrowing. This line of thinking leads naturally to previously unanticipated determinants of muscle length, especially the muscle stiffness and the rate of myosin cycling, and provides what may prove to be a mechanistic framework linking at least some facets of what had seemed previously to be unrelated hyperresponsiveness phenotypes. In this article we address the relationship between muscle length and tidal loading, the molecular basis of this relationship, and its implications in acute airway narrowing.

	METHODS

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Force Fluctuations

We used an in vitro system in which muscle length (L) was the dependent variable while the force distending the muscle and its variations in time were the controlled independent variables. Bovine tracheal smooth muscle was mounted in a muscle bath (Krebs-Heinseleit solution, 37° C, aerated with 95% O₂-5% CO₂, pH of 7.3 to 7.5) and set to optimal length (Lo), where active force was maximal (Fo). The muscle was then contracted isotonically (at 0.32 Fo) with acetylcholine (maintained at 10⁴ M) and allowed to shorten for 120 min, by which time the static equilibrium length was clearly established. To simulate the effects of tidal breathing, we then superposed upon that steady distending force a sinusoidal force fluctuation of amplitude F (2 F peak-to-peak) with zero mean, at a frequency of 0.2 Hz, and measured the resulting incremental changes of muscle length that accumulated progressively over the course of many tidal cycles. We also measured the resulting tidal changes of muscle length, amplitude L (2 L peak-to-peak), that occurred within each tidal event and that were phasic with tidal changes in the muscle load;  is L/Lo expressed as a percent. From the tidal force and length fluctuations we computed muscle stiffness, E (a measure of the slope of the force-length loop and an index of the number of actin-myosin interactions), and muscle hysteresivity,  (a measure of the fatness of that loop and, like unloaded shortening velocity, an index of the rate of turnover of those interactions [9, 10]).

NADH Fluorimetry

The rate of total adenosine triphosphate (ATP) usage was measured by quantifying the rate of -nicotinamide adenine denucleotide (NADH) consumption as previously described (10). In brief, canine tracheae were obtained from mongrel dogs. A muscle bundle was isolated, mounted in the apparatus, and set to its optimal length using stimulation with acetylcholine. It was then chemically skinned by perfusing it for 20 min with 10% triton X-100 in relaxing solution at 25° C [Na₂ATP 2.5 mM, ethylene glycol-bis(-aminoethyl ether), N,N,N',N'-tetraacetic acid (EGTA) 7.8 mM, imidazole 83 mM, phosphoenol pyruvate (PEP) 5 mM, NADH 0.2 mM, lactate dehydrogenase (LDH) 140 U/ml, pyruvate kinase (PK) 100 U/ml, and calmodulin 5 µM, pH 7.1]. Tissues were then perfused with relaxing solution (without triton X-100) to remove the detergent. The rate of total ATP usage was measured by quantifying the rate of NADH consumption using an instrument obtained commercially (Scientific Instruments, Germany). When ATP is hydrolyzed, ATP is regenerated from adenosine diphosphate (ADP) and PEP by the enzyme PK. This reaction is coupled to the oxidation of NADH to nicotinamide adenine dinucleotide (NAD⁺) and the reduction of pyruvate to lactate; these reactions are catalyzed by LDH. For each mole of ADP produced, one mole of NADH (the fluorescent compound) is oxidized (i.e., consumed) to NAD⁺ (a nonfluorescent compound). Thus, the rate of decrease of NADH fluorescence intensity is proportional to the rate of ATP usage. The perfusion cuvette was flushed for 7 s with fresh solution containing the constituents necessary to couple ATP hydrolysis to NADH consumption. Flushing the cuvette with fresh solution caused an abrupt increase in NADH fluorescence. The rate of decline in NADH fluorescence between solution changes (over an 8-s period during which perfusion was stopped) is proportional to the rate of ATP usage during that time. NADH fluorescence was determined for known concentrations of NADH before each experiment, so that the amount of NADH consumed during the 8-s period can be calculated and used to quantify the rate of ATP usage (µM of ATP used per second).

HHM Theory

There is a good deal of controversy surrounding the mechanisms that regulate the rate of myosin cycling in smooth muscle, but the prevailing concept is the latch hypothesis of Hai and Murphy (11). We assessed the relationship between load fluctuations and actomyosin dynamics based upon a computational analysis of the latch mechanism of cycling rate regulation integrated explicitly into the sliding filament theory of muscle contraction of Huxley (15). This synthesis, which we refer to as HHM theory (for Huxley, Hai, and Murphy), is expressed in a system of four coupled partial differential equations that govern conservation of each of the relevant myosin species, which in vector form becomes

(1)

The operator D/Dt is the material derivative  / t  v(t) / x, and v(t) is the velocity of the actin relative to the myosin filament and is traditionally taken to be positive during muscle shortening. Each of the four components of the vector n(x,t) corresponds to the population fraction of myosin in one of its four states (M, Mp, AMp, AM; where A denotes actin, M myosin, and Mp phosphorylated myosin), which vary both in time, t, and in space, x, where x is the position of the myosin head relative to the backbone of its myosin filament. In this analysis, these species follow the latch regulatory scheme of Hai and Murphy (12) as shown:

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The four-by-four rate transition matrix T(x, t) describes the probability of transitions between these four states, and how these probabilities vary with position of the myosin head. These probabilities are important because, with each tidal stretch, the myosin head may traverse regions that tend to favor attachment events and others that tend to favor detachment events; the latter dominate where x is large and also where x is negative (15). The elements of the four-by-four rate transition matrix T(x, t) include both the position-independent transitions between M and Mp and between AM and AMp (phosphorylation and dephosphorylation events driven by the action of kinases and phosphatases) and the position-dependent transitions between Mp and AMp and between M and AM (attachment and detachment of myosin and actin). As such, T(x, t) governs the transduction of chemical events into mechanical events and, importantly, the converse. To set T(x, t) we used the rate functions reported by Hai and Murphy after adapting them to include the rate constant g₃ described by Zahalak (16) to increase the rate of detachment in the region x > h, where h is the range for nonzero probability of attachment (15). After taking the strain of the contractile element to be 36% of the overall strain (to account for the series elastic component [17]), h to be 15.6 nm, and effective sarcomere spacing s to be 2.2 µ (12), there remained no free parameters. n(x,t) was computed from Equation 1 by numerical means described subsequently and, in turn, the population fraction of myosin in each of the four pools, muscle force, length, stiffness, hysteresivity, and the rate of utilization of ATP were computed from n(x,t). Although two-state approximations have been previously reported (12, 18), this is the first analysis of the explicit four-state HHM latch regulatory system.

The rate transition matrix is:

(2)

where

(3)

The position-dependent rate constants f_p1, g_p1, and g₁ were chosen to match Murphy's position-independent state transition constants k₃, k₄, and k₇, respectively, when the former are integrated over all x. The other time constants, namely g_p2, g_p3, and g₂, g₃ are in the same proportion to g_p1 and g₁, respectively, as in Huxley (15) and Zahalak (16). The numerical parameter values used in simulations were: k₁ = k₆ = 0.35 s¹ for 5 s followed by 0.060 s¹ afterwards (assuming 70% activation with respect to Hai and Murphy µ (12); k₂ = k₅ = 0.1 s¹; k₄ = 0.11 s¹; k₃ = 4 k₄ = 0.44 s¹; k₇ = 0.005 s¹; f_p1 = 0.88, g_p1 = 0.22, g_p2 = 4.4, and g_p3 = 0.66 s¹; g₁ = 0.01, g₂ = 0.2, and g₃ = 0.03 s¹. Changes of filament overlap with changes of muscle length were set such that the static length-tension relationship in the vicinity of the static equilibrium length was approximated by a straight line with force equal to zero at 15% Lo and equal to Fo at Lo.

We followed the approach of Piazzesi and Lombardi (19) and used the method of characteristics and an iterative scheme to secure the evolving solution (17). The instantaneous forces were computed from the first spatial moments of the attached cross bridge state number distributions AMp(x,t), and AM(x,t) integrated over all x. The rate of ATP consumption was summed from the four rate processes, each computed by trapezoidal integration over all x.

	RESULTS AND DISCUSSION

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Fluctuation-driven Muscle Lengthening

When F was increased from 0% to 4% or 8% of Fo, the instantaneous muscle length simply oscillated about the static equilibrium length, and the mean muscle length over the cycle remained close to that length (Figure 1A). But when F was increased to 16% or more, the muscle then substantially lengthened and became progressively less stiff and more hysteretic (Figures 1 and 2). Although the muscle was at all times supporting the same mean load component (0.32 Fo), the dynamic equilibrium length to which the muscle equilibrated systematically exceeded the static equilibrium length (Figures 1A and 2A). Force fluctuations (with zero mean) systematically biased airway smooth muscle length.

View larger version (18K): [in this window] [in a new window]   Figure 1.   Evolution of mechanical properties of a representative muscle during contraction against a steady force component of 0.32 Fo upon which is superimposed force fluctuations (0.2 Hz) of graded amplitude F. (A) Mean muscle length over each force cycle. (B) Loop stiffness (percentage of maximal isometric value). (C ) Hysteresivity (dimensionless). (D) Tidal length change;  is L/Lo expressed as percent. Force fluctuations are seen to drive the contractile state away from static equilibrium conditions.

View larger version (15K): [in this window] [in a new window]   Figure 2.   Pooled observations (filled circles, n = 6; error bars denote SD between muscle strips, drawn in only one direction for clarity) and expected (solid lines, predicted from HHM theory) values for (A) dynamic equilibrium muscle length versus force fluctuation amplitude. (B) Loop stiffness (percentage of maximal isometric value). (C  ) Hysteresivity (dimensionless). (D) Tidal length change;  is L/Lo expressed as percent. *Significant differences from static equilibrium length, p < 0.01. Open triangles denote state after force fluctuations were reduced from a higher value (32%) back to 8%.

If the amplitude of the tidal force fluctuation was subsequently reduced from 32% back to 8% of Fo, the muscle reshortened, but the new equilibrated length was substantially greater than the prior length in identical loading conditions (Figures 1A and 2A [triangle]). Therefore, the force fluctuation amplitude necessary to maintain the muscle at that new length was smaller than that required to break through initially and attain that length. Conversely, if the force fluctuations were kept at 8% or less throughout the contractile event, the muscle remained close to the static equilibrium length, as if it were stuck at that length. The dynamic equilibrium length was determined by the tidal loading dynamics and, importantly, by the history of the tidal loading dynamics.

Following these tidal loading maneuvers, the isometric force generation capacity of the muscle was not compromised, retaining 85% or more of the initial capacity. Therefore, fluctuation-driven lengthening was not accounted for by muscle injury or fatigue. Rather, the muscle attained different modes of steady-state operation, and could be made to switch between these modes by alteration of the history of the dynamic loading. As such, the contractile state was conditionally stable.

Perturbed Equilibria of Myosin Binding

Quantitive analysis of HHM theory indicated that in isometric unactivated muscle, 100% of the myosin is found in the unphosphorylated unattached pool (M), but this pool becomes rapidly depleted with stimulus onset (Figure 3). It is replaced by population of the Mp pool, followed closely by population of the AMp pool which, taken together, correspond to the early phosphorylation transient (20). The AM pool is the last to become populated. The steady-state binding equilibrium in isometric muscle corresponds to what Hai and Murphy referred to as the latch state, and is seen to comprise slowly cycling latch bridges (AM) in a slight preponderance over rapidly cycling cross bridges (AMp), although this partitioning varies with the level of muscle activation. However, imposition of rather modest sinusoidal changes of muscle length (L = 4% Lo, about mean length fixed at Lo for t > 180 s) upsets this isometric binding equilibrium, and causes it to adapt rapidly to a perturbed equilibrium characterized by many fewer attached bridges. Together with alterations in the spatial binding distributions along the actin filament (not shown), these changes are consistent with inhibition of force and stiffness caused by imposed tidal changes in muscle length (Figure 4), and in this regard are similar to the mechanism of force depression caused by imposed length fluctuations in skeletal muscle (21). Among these remaining attached species, however, the perturbed equilibrium is seen to comprise rapidly cycling cross bridges in a slight preponderance over slowly cycling latch bridges, although this partitioning varies with the tidal stretch amplitude. In addition, with imposed length fluctuations each of these attached species progresses through its cycle more rapidly than in static conditions. Taken together, these results suggest higher bridge cycling rates on average, and are consistent with tidal stretch-induced augmentation of both hysteresivity and the rate of ATP utilization.

View larger version (30K): [in this window] [in a new window]   Figure 3.   Computational results from HHM theory. (A) Evolution of the rate of ATP utilization. (B) Evolution of myosin state populations, where each represents the integral of one of the components of n(x,t) integrated over all x and averaged in time over the stretch cycle on a cycle-by-cycle basis. The system was activated by a step increase in free calcium at t = 0 for 5 s (k1 = k6 = 0.35/s), followed by a reduction to constant level (k1 = k6 = 0.06/s). The conditions depicted approximate isometric muscle by using very small  (0.5%) for t  180 s, whereafter  was increased to 4%. Notice that tidal stretches of physiological amplitude push the myosin state population far away from static binding equilibrium.

View larger version (27K): [in this window] [in a new window]   Figure 4.   Observed (symbols, n = 5, SD, f = 0.33 Hz) and predicted (solid lines, HHM theory) for steady-state force averaged over the stretch cycle (red ), stiffness (purple), and hysteresivity (green) in maximally activated tracheal smooth muscle held at a mean length of Lo and subjected to imposed length fluctuations L about Lo. Data were obtained from (23) renormalized to 100% when  = 0.25%. For data,  corresponds to L/Lo expressed as percent; for theory,  corresponds to the peak-to-peak length change per effective sarcomere times the effective sarcomere spacing (s) expressed as percent. As the amplitude of length fluctuations,  , is increased, the muscle undergoes a fluctuation-driven change of state from a stiff, low-viscosity, solid-like phase to a compliant, high-viscosity, liquid-like phase. Therefore, these data represent a sequence of nonequilibrium states and, taken together, comprise a nonequilibrium phase transition (63).

Measurements of changes in the rate of ATP hydrolysis caused by tidal changes of muscle length reinforce this interpretation. Simultaneously with measurement of mean force, stiffness, and hysteresivity, we used NADH-linked fluorimetry to measure the rate of ATP utilization in the detergent-skinned canine tracheal smooth muscle fiber bundles that were maximally activated by increasing the concentration of free calcium from 10⁹ to 10⁵ M (10, 22). Once the muscle had attained a steady-state contractile response, the amplitude of the tidal length change (fluctuating about Lo) was suddenly increased from 0.5 to 4% of Lo. The induced changes in mean force, stiffness, and hysteresivity paralleled those observed in intact muscle. The total rate of ATP hydrolysis did not change significantly, whereas the specific rate of ATP utilization (i.e., rate of ATP utilization per bridge attached, using muscle stiffness as an index of the latter) increased by 2.9 ± 0.3 fold (p < 0.00001, n = 10).

Concerns have persisted in the literature regarding the validity of the theories advanced by Huxley and by Hai and Murphy. Despite these concerns, the single integrated theory (HHM) leads to several quantitative predictions, each of which is seen to be accurate. Stretch-induced changes of muscle force, stiffness, hysteresivity (Figure 4, solid lines), and specific rate of ATP utilization computed from HHM theory are for the most part indistinguishable from those determined experimentally, both in terms of the threshold levels and the magnitudes of the effects. With the exception of one telling discrepancy that we discuss below (Figure 2A, triangle), the same can be said of fluctuation-driven muscle lengthening. On this basis we were persuaded that these diverse mechanical and metabolic effects of tidal loading may be largely accounted for by a single mechanismperturbed equilibria of myosin binding. Compared with isometric binding equilibrium, these perturbed states are characterized by diminished bridge numbers and augmented rate of bridge turnover.

As a consequence of the law of mass action, individual myosin molecules randomly sample each myosin pool and, in the isometric steady state, the net flux into each pool is zero and the population of each is time-invariant. A binding equilibrium prevails, therefore, but requires for its maintenance continuous energy consumption associated with ongoing hydrolysis of ATP (Figure 3). Accordingly, the isometric steady state is far away from thermodynamic equilibrium and, in that sense, is sustained by a nonequilibrium chemical reaction (thermodynamic equilibrium in muscle corresponds to the rigor state). To the degree that the binding equilibrium that pertains in isometric conditions is already pushed far away from thermodynamic equilibrium by the hydrolytic activity of myosin on ATP, force or length fluctuations are seen to push the system even farther from thermodynamic equilibrium. This is evidenced by even higher rates of bridge cycling and specific ATP utilization (Figure 3A), and higher hysteresivity (10, 23) compared with static conditions (Figure 1C, Figure 4). In this regard, fluctuation-driven lengthening of airway smooth muscle seems to fall into the broader class of nonequilibrium phenomena described recently by Astumian (24) in which energy supplied by external force fluctuations (with zero mean) can systematically bias probabilistic binding events in a way that produces unidirectional transport of material and sustained departures from equilibrium. In the particular case of fluctuation-driven muscle lengthening, these biases are embodied within the attachment and detachment rate functions that comprise T(x,t).

Analysis of T(x,t) and its role in Equation 1 indicates that the extent of fluctuation-driven lengthening and the extent to which the underlying myosin binding is upset depend not only upon the amplitude of the force fluctuation, but also upon the time over which the load is cycled in relation to the reciprocals of operative reaction rates embodied in T(x,t). That is to say, tidal fluctuations in muscle load can come so fast compared with the rate of bridge cycling that the isometric binding equilibrium (i.e., the latch state) is never attained. This perspective of the airway as an intrinsically dynamic system (25, 26) stands in contrast with the classical view of airway lumen narrowing and its underlying premises of static forces and isometric binding equilibrium, where time is not a factor.

The quantitative agreement between HHM theory and experiment (Figures 2 and 4) also contrasts with recent reports attributing most of the force inhibition caused by periodic changes of muscle length to nonbridge mechanisms. These mechanisms include plastic remodeling of the focal adhesion complex and/or the cytoskeletal (CSK) network (27). But HHM theory seems to explain force and stiffness inhibition, hysteresivity augmentation (Figure 4) and fluctuation-driven lengthening (as the tidal loads increase in amplitude, Figure 2, circles); this degree of agreement suggests a dominant role for bridge mechanisms. Importantly, though, steady-state solutions from HHM theory were not able to account for muscle length as force fluctuation amplitude was decreased, and therefore bridge mechanisms cannot account for the effect of history evident in Figure 2A (triangle). This discrepancy may provide an important clue concerning the largely unexplored interrelationship between bridge versus nonbridge mechanisms and the history of tidal loading. (The effect of load history evident in Figure 1 is consistent with heterogeneity of dynamics at the level of sarcomere, called sarcomere popping, that has been noted in striated muscle [30].) In the studies reported here, perturbed equilibrium was a precondition for plastic remodeling events that followed.

Bronchospasm and Airway Hyperresponsiveness

The provocative length fluctuation amplitude L required to cause active force or muscle stiffness to fall by half, or hysteresivity to double, is about 3% of Lo (Figure 4). This compares with amplitudes that occur during spontaneous breathing, which are believed to range from 4% of Lo during quiet tidal breathing at rest, to 12% during a sigh, and up to 25% for a maximal inspiration from functional residual capacity to total lung capacity (23). Accordingly, the physiological range of tidal length change in healthy individuals during bronchial provocation would correspond to the part of the stretch-effect relationships where force and stiffness are profoundly inhibited, hysteresivity is augmented, and the contractile state is dynamically determined (Figure 4). Thinking in terms of imposed force fluctuations, rather than imposed length fluctuations, the range of tidal force fluctuations to which airway smooth muscle is exposed in situ spans the critical force amplitude threshold^* (between 8 and 16% of Fo for maximally activated muscle, Figure 2A). Although the estimate is rough, it seems that quiet tidal breathing is perched just beyond the brink of the force threshold, and deep inspirations surely exceed it. The implications of exceeding the threshold are not small; using conservative estimates, the extent of fluctuation-driven lengthening evident in Figure 2A translates into increases of airway lumen area of more than fourfold, and decreases of airways resistance of more than 20-fold relative to static equilibrium conditions. Accordingly, the point of view that the length of airway smooth muscle during acute airway narrowing is determined by a balance of static forces, and by an isometric binding equilibrium of myosin, would seem to be no longer tenable.

Consideration of airway smooth muscle as a part of a conditionally stable dynamic system, by contrast, reveals a richer range of phenomena, including the possibility that healthy individuals subjected to maximal bronchial provocation may systematically exceed the force fluctuation threshold referred to previously, while individuals with spontaneous asthmatic obstruction fail to do so. We reason as follows.

Tidal lung inflation and airway reactivity are organ-level mechanical events, whereas fluctuation-driven muscle lengthening is rooted in the molecular dynamics of actomyosin. To integrate perspectives spanning such widely disparate scales, we require a middle range theory of airway responsiveness, sketched in Figure 5, in which actomyosin kinetics are characterized by their rough macroscopic correlates: the muscle stiffness E (bridge numbers) and the hysteresivity  (bridge cycling rate).

View larger version (9K): [in this window] [in a new window]   Figure 5.   A middle range theory of airway responsiveness linking organ-level and molecular level events. Because it causes the stiffness (E) to decrease, tidal stretch acts as its own catalyst. (See text.) The self-perpetuating dynamic disengages the level of response (force or shortening) from the level of the stimulus.

The central feature of this arrangement is that tidal muscle stretch acts as its own catalyst; the more the muscle stretches, the easier it becomes to stretch (indicated by decreasing stiffness as  shifts to the right along the x axis in Figure 4). For the same reason, the more myosin binding is disrupted the more susceptible it becomes to further disruption (31). As a result, fluctuation-driven lengthening (Figures 1A and 2A) is maintained by a self-reinforcing dynamic process, and plastic remodeling of the CSK may follow. As such, perturbed equilibria of myosin binding are seen to disengage the magnitude of the contractile response from the level of the contractile stimulus, and to profoundly attenuate that response (Figures 1 and 4), much as stepping on the clutch pedal in an automobile disengages the wheels from the motor. However, should the force fluctuation amplitude somehow become compromised, then the self-reinforcing spiral of events described previously might not be triggered, and the muscle would remain so stiff that it would be virtually frozen at its static equilibrium length. Both behaviors are evident in Figures 1 and 2.

This mechanism is just a proposal and is far from being demonstrated in the intact human lung. Nonetheless, it follows logically and has rather interesting implications. In particular, it points to determinants of muscle length that could not have been anticipated based upon analysis of a system at a static equilibrium, or passing through a sequence of static equilibrium states. For example, greater contractile response would be predicted whenever the force fluctuations acting on the airway become compromised, as would be expected when the peribronchial adventitia or reticular basement membrane undergoes cytokine-driven inflammatory thickening (2, 7), or the lung loses elastic recoil, or tidal lung expansion becomes diminished. These instances bring immediately to mind asthma, emphysema, restrictive disorders of the chest wall, obesity, nocturnal asthma, breathing at low lung volumes, and cervical spinal cord injury, each of which is known to be associated with a predisposition for airway hyperreactivity (32- 40). Perturbed equilibria might also help to explain why the obstructive response in exercise-induced asthma typically begins only after cessation of the exercise. Moreover, when inflammatory remodeling of the airway does occur, this mechanism might bear upon the question of how a predisposition for airway hyperresponsiveness can persist long after the inflammation itself is resolved.

Of course, even with purely static muscle behavior a reduced static load implies reduced muscle length (2, 3, 39, 41, 42). But should it become destabilized and collapse to a statically determined length, the muscle that had been maintained dynamically at an elevated length (because it enjoys fluctuation-driven muscle lengthening) would have farther to fall. As such, the effect of connective tissue remodeling on muscle behavior might have two components, the dynamic component of which may be substantially amplified compared with the static component alone.

Similarly, greater contractile responses would be predicted in any circumstance that increases the intrinsic rate of bridge cycling; this is so because the faster the intrinsic reaction rate, the more difficult it is for force fluctuations to perturb the reaction and thereby maintain the dynamic steady state. Thus, perturbed equilibria lead naturally to the idea that excessive airway narrowing may not be a problem of the muscle being too strong, but rather too fast (26). Accordingly, this offers a plausible mechanism to explain a striking conundrum. Circumstances in which bridge cycling rate is increased have been consistently associated with airway hyperresponsiveness, even though isometric force generation capacity of the muscle is unchanged. Specific instances include differences in responsiveness between normal versus allergen-sensitized muscle, between certain animal strains and, in some species, between mature versus immature muscle (6, 43). Accordingly, this mechanism points to the importance in airway mechanics of the factors that are known to influence bridge cycling rates, including thin and thick filament regulatory proteins, the myosin isoform, and the factors that influence phosphorylation of 20 kD myosin regulatory light chain.

Taken together, these examples suggest that perturbed equilibria of myosin binding provide a logical hypothesis through which to consider a diverse group of respiratory diseases that are presently not well understood and that previously had not been thought to be related. Moreover, if the individual destabilizing factors noted previously should change in concert, as they undoubtedly do in inflammatory airway disease (7), this might explain how small changes in each which, if taken alone, might be inconsequential, taken collectively might be sufficient to destabilize the system and, in doing so, precipitate a collapse to static conditions and a disproportionately large decrement of airway function.

Finally, healthy individuals sigh spontaneously at the rate of about 10 times per hour (49, 50), and during bronchial provocation these deep inspirations act as a potent endogenous bronchodilating mechanism (51). To put the potency of this mechanism into perspective, to attain by purely pharmacological means the same degree of force inhibition as is demonstrated in Figure 4 requires extremely high concentrations of isoproterenol, in the range of 10⁷ to 10⁵ M. Spontaneous deep inspirations are the first line of defense against bronchospasm, therefore, and it may be fair to say that they are the most potent of all known bronchodilating agencies. (In the past, the teleological explanation for the desirability of involuntary sighs centered on the effect of lung inflation on the secretion and recruitment of surfactant to the alveolar gas-liquid interface.) While it is impossible to say that we could do without this endogenous bronchodilating mechanism, voluntary prohibition of sighs during bronchial provocation of nonasthmatic, nonallergic individuals has impressive adverse consequences (55, 59); voluntary prohibition of deep inspirations during bronchial provocation triggers asthmalike airway hyperresponsiveness and, once deep inspirations are reinstated, the subsequent impairment of the bronchodilating effects of those deep inspirations (55, 59). Inhalation of some of the most potent known bronchoconstrictors, such as leukotrienes LTC₄ and LTD₄, which are 3,000 to 10,000 times more potent than inhaled histamine, has substantially blunted responses unless deep inspirations are suppressed (60). During an asthmatic attack the frequency of these sighs increases (50), but to little effect (54); it has long been known that spontaneous asthmatic obstruction behaves as if it were caused by an intrinsic impairment of the bronchodilating effect of a deep inspiration (54, 56, 61, 62), although a mechanism to account for this impairment has been lacking.^* Because it is downstream of the inflammatory reaction itself, the interaction of myosin with actin cannot explain the root cause of airway hyperresponsiveness in asthma. Even so, a novel and attractive feature of perturbed equilibria and their conditional stability is that they put in place a mechanism with the potential to explain the potent dilating effect of deep inspirations in the healthy lung subjected to bronchial provocation, and the intrinsic impairment of that bronchodilating mechanism in the remodeled airway.