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Non-classical behavior: load fluctuations and dynamic equilibration of the muscle length
- Bronchospasm and its biophysical basis in airway smooth muscle

Load fluctuations are imposed continuously on airway smooth muscle and pulmonary vascular smooth muscle by the tidal action of breathing, and on muscular systemic arteries and arterioles by the pulsatile action of blood ejected from the heart. Smooth muscles in the urethra, urinary bladder, and gut are also subjected to periodic stretch. Accordingly, imposed fluctuations in muscle load seem to be a universal part of smooth muscle physiology.

It is well established that imposition of load fluctuations on smooth muscle inhibits development of active force and stiffness [80,98,120]. Although imposed load fluctuations induce important plastic changes in the cytoskeleton, as described later in this review [27,70], a major part of the force and stiffness inhibitions that are observed are attributable to direct effects of tidal stretch upon bridge dynamics [24,61,98].

Perturbed equilibria of myosin binding

In the case of airway smooth muscle, the effects of oscillatory loading were first addressed by Sasaki and Hoppin and later by Gunst and colleagues, who demonstrated that imposition of tidal changes in muscle length depresses active force [98,120-123]. Subsequent studies [24,98] showed that imposed fluctuations of muscle length about a fixed mean length cause depression of muscle force and muscle stiffness (averaged over the stretch cycle); imposed length fluctuations also cause augmentation of the specific rate of ATP utilization and the hysteresivity (related to the muscle viscosity and an index of bridge cycling rate, as described below [105]. Thus, from both a mechanical and a metabolic point of view, the perturbed state is a hot or a melted state of the muscle [23,24,61,94]. Imposed force fluctuations about a fixed mean distending force systematically bias the airway smooth muscle toward lengthening; this phenomenon is called fluctuation-driven muscle lengthening [24]. Although tidal stretches smaller than 1% of muscle length produce only trivial mechanical effects, tidal stretches in the range of amplitudes expected during quiet tidal breathing (about 3% of muscle length) produce force inhibition that is equipotent with concentrations of isoproterenol in the range 10-7 to 10-5 M [99]. Molfino et al. showed in humans that brief cessation of tidal breathing causes the cross-sectional area of central airways to decrease by about half under the influence of baseline smooth muscle tone, and when tidal breathing is resumed the airway promptly dilates [124]. Taken together, these findings suggest that quiet tidal breathing is as effective in relaxing airway smooth muscle as is a potent relaxing agonist.

Importantly, there is increasing evidence that the potent bronchodilating response to periodic stretch and deep inspirations is impaired in asthma, and that this impairment may be the proximal cause of the loss of the plateau of the dose-response curve and the resulting morbidity of the disease [81,84,86,87,125,126]. There exists also a bronchoprotective effect of deep inspirations; deep inspirations prior to agonist challenge have been shown to blunt the subsequent contractile response [127-131]. It has been suggested that the bronchoprotective effect of deep inspirations are even more important than the bronchodilating response, and it too is profoundly impaired in asthma.

Lung inflations strain airway smooth muscle with each breath, and these periodic mechanical strains are transmitted to the myosin head and cause it to detach from the actin filament much sooner than it would have in isometric circumstances. This premature detachment profoundly reduces the duty cycle of myosin, typically by as much as 50–80% of its unperturbed isometric steady-state value, and depresses total numbers of bridges attached and active force to a similar extent. Of the full isometric force generating capacity of the muscle, therefore, only a small fraction ever comes to bear on the airway during tidal breathing, even when the muscle is activated maximally. Since bridge cycling is strongly perturbed by the imposed tidal stretches over time the number of myosin attachment and detachment events come into a dynamic balance. To distinguish it from the state that prevails in static loading conditions, this state has been called a perturbed equilibrium of myosin binding [24,61].

In pathological circumstances the tidal strains acting on myosin can become compromised, however. For example, in the chronically inflamed airway the peribronchial adventitia thickens [8,9,132]; this thickening decreases tidal muscle strains and thereby permits myosin binding to approach an unperturbed binding equilibrium. In doing so, the muscle would then generate the full complement of isometric force appropriate to the stimulus. Any factor that lessens peribronchial stress will decrease the force fluctuations impinging upon the muscle, including inflammatory thickening of the lamina reticulosa, thickening of the peribronchial adventitia, loss of lung elastic recoil, breathing at low lung volumes, and failure to take deep breaths [18,21,22,75,133-135]; in addition, Colebatch and colleagues found evidence of increased rigidity of airways in asthmatic subjects [136]. If any of these factors pertain, then the perturbed equilibrium of myosin binding can collapse toward a static binding equilibrium. For example, if for any reason the muscle should stretch a bit less, then fewer bridges would be perturbed. Because more attached bridges working in parallel are harder to break than fewer, the muscle would then become stiffer still and therefore stretch even less, and so on. Ultimately this process reaches the limit in which the muscle may become so stiff that the physiological forces acting on it are insufficient to stretch the muscle appreciably, leaving the muscle stuck at its static equilibrium length [23,24,61]. Compared with the perturbed state, this statically equilibrated contractile state is also characterized by slow bridge cycling and a small rate of ATP utilization per bridge attached or per unit force developed [24]. So from both the mechanical and the metabolic point of view, it would appear to be a cold or 'frozen' contractile state. The muscle could be said to be statically equilibrated and frozen in the latch state.

This point of view leads to the hypothesis that airway hyperresponsiveness is associated with the failure of the underlying perturbed binding equilibrium to sustain itself, and an ensuing collapse of myosin binding kinetics to the binding equilibrium that pertains in static conditions and latch [23]. Clearly, this constellation of factors points towards dynamic instability, as described below.

Dynamic muscle instabilities

It is a well-established empirical fact that within any given lung or lung segment the response of airways to contractile agonists is always accompanied by 1) extreme heterogeneity of the response and 2) sensitivity of the response to the amplitude of the tidal volume and the magnitude of the load fluctuation [36,100,137-142]. It has been speculated that the observation of a smoothly graded decline of tests of lung functions (such as lung resistance) with progressively increasing doses of contractile agonist might be better explained by progressive changes in number of open airways accommodating gas flow rather than by some smoothly changing reduction in the airway caliber of each [138]. Indeed, the heterogeneity of the response is so extensive that peripheral airways have sometimes been thought of as being partitioned into only two quantum-like states, as it were, either open wide or almost closed entirely, with virtually no intermediate state [138,143,144]. Several plausible factors have been invoked to try to account for this profound heterogeneity of the contractile response, including intrinsic inhomogeneities in airway structure, muscle amounts, muscle sensitivity to agonist, and nonuniformity of agonist delivery [36,79,145].

Anafi and Wilson considered the narrowing of an airway containing activated airway smooth muscle subject to load fluctuations as would occur during breathing [146,147]. Their mathematical analysis shows that in some circumstances such an airway must become unstable. Of course, the generic idea that airways can be unstable is not at all new [148], but the analysis of Anafi and Wilson identified a new class of airway instability that is intrinsically dynamic and, in particular, is rooted in the response of airway smooth muscle to imposed load fluctuations.

To appreciate the potential importance of this muscle instability, we imagine a lung in which there are a large number of airways that are all operating in parallel and that are in every regard identical. The airway smooth muscle is activated uniformly and subjected to identical load fluctuations caused by the tidal action of breathing. Even though inter-regional differences are infinitesimally small at the outset, any small perturbation would be amplified by the processes described above. And as the differences grow the amplification grows. When the process eventually becomes dynamically equilibrated, the airways will be seen to have partitioned themselves between only two states in order to accommodate the total flow-one state effectively wide open and the other nearly closed. The analysis of Anafi and Wilson and that of Fredberg and colleagues [24] address overlapping but different aspects of airway narrowing; although the relationship between these perspectives remains somewhat unclear, airway smooth muscle in the closed airways might be expected to correspond to the static or 'frozen' state, and muscle in the open airways might be expected to correspond to a 'melted' state with an underlying perturbed equilibrium of myosin binding. Changes in tidal volume would affect the number of airways in each state.

In the healthy lung during spontaneous breathing, tidal volume and associated force fluctuations acting on airway smooth muscle may be large enough to keep almost all units in the open/melted state and out of jeopardy of closure. But if tidal volumes were compromised, or deep inspirations were prohibited, or transmission of force fluctuations to the airway smooth muscle were to become compromised, then a larger fraction of units would be expected to be found in the closed/frozen state. Therefore, this picture would seem to be able to explain in one stroke both a profound heterogeneity of the airway response and its sensitivity to tidal volume.

This insight on instability of smooth muscle dynamics does not preclude important contributions from intrinsic heterogeneities that exist amongst airways, of course. The Anafi-Wilson instability is attractive, though, because it shows that it is not necessary to postulate intrinsic airway heterogeneity of any kind in order to account for both a profound heterogeneity of the airway response and its sensitivity to tidal volume.

Deep Inspirations

Jensen and colleagues [149] followed the earlier studies of Fish [84], Lim et al. [86], and then Skloot [87] to show in normal individuals challenged with nonspecific contractile agonists that a single deep inspiration (DI) causes a prompt and dramatic decrease in airway resistance (Raw) followed by a slow return of Raw to the level observed prior to the DI. By contrast, in individuals with severe asthma a single DI causes a prompt but only modest decrease in Raw followed by rapid return of Raw to the level observed prior to the DI. The findings in challenged normal individuals are consistent with disruption of cross bridges as described above. In the asthmatic, however, it is plausible that bridges were stretched, but not enough to disrupt an appreciable fraction of the acto-myosin bonds. Immediately following the deep inspiration, the rapid recovery of Raw to pre-DI levels could reflect either a rapid elastic recoil of the stretched muscle, or an altered cytoskeletal remodeling response to the DI (described below), or reattachment of bridges that were disrupted, but at a rate that is faster than that observed in healthy individuals.

The crucial role of tidal loading of the ASM was further demonstrated by Mitzner and Brown in an ingenious use of high resolution CT in a dog model in which one lung was ventilated while the other was held isovolumic [150]. Compared to the lung undergoing cyclic volume changes, the isovolumic hung was found to be both hyperresponsive and refractory to the bronchodilating effects of a subsequent deep inspiration.

In order to better understand these processes and, especially, the impact of inflammatory remodeling processes upon ASM shortening and acute airway narrowing, Mijailovich and colleagues [151] developed a computational model which, unlike previous attempts [13,16,21], took into account explicitly molecular dynamics of myosin and the ability of load fluctuations associated with tidal breathing and periodic deep inspirations to perturb myosin binding. Results for a generation 10 airway reveal hyperreactive airways in asthma and COPD, as was found by others using static muscle models (Fig. 1). However, this model of molecular dynamics expresses two additional phenomena that the static model does not. The first is induction of hypersensitivity – a shift of the dose-response curve to the left – which arises from myosin binding dynamics and their interaction with a fluctuating load. As noted above, mechanisms responsible for hypersensitivity vs. hyperreactivity had been though to be distinct whereas, by contrast, this result shows that myosin binding dynamics in the setting of a fluctuating mechanical load can elicit both. Compared to the case of the asthmatic airway, in the case of the normal airway the action of tidal loading upon myosin binding dynamics is sufficient to inhibit airway narrowing until the level of muscle activation is relatively large. The second phenomenon is what would appear to be a discontinuous or unstable response: with an increasing degree of muscle activation (agonist dose) there arises a value beyond which, when the airway does begin to narrow, it does so precipitously.

Taken together, these non-classical behaviors support the notion that activated airway smooth muscle is typically melted by the tidal action of breathing and, therefore, muscle length is dynamically equilibrated. Nonetheless, in pathological circumstances, as described below, muscle can become frozen in the latch state.

Clinical manifestations

In practical terms, specific instances in which elevated rates of bridge cycling might come into play include the differences in airway responsiveness that have been observed between normal versus allergen sensitized muscle, between certain animal strains and, in some species, between mature versus immature animals [68,142,152-156]. This rationale leads us to a plausible mechanism by which the rate of bridge cycling and its regulation may be reasonably thought to bear upon the prevalence of childhood asthma and its changes with lung maturation and allergic status.

Although far from explaining these phenomena in their entirety, the perturbed equilibrium hypothesis may help to tie together still other loose ends (Fig. 2). According to that hypothesis, greater contractile responses are favored whenever the force fluctuations acting on the airway become compromised, not only when the peribronchial adventitia undergoes cytokine-driven inflammatory thickening, but also when the lung loses elastic recoil, or tidal lung expansion becomes diminished. These instances bring immediately to mind not only asthma, but also emphysema, normative aging, restrictive disorders of the chest wall, obesity, and cervical spinal cord injury, each of which is known to be associated with a predisposition for airway hyperresponsiveness or asthma [157-163]. Reduced amplitude of force fluctuations may come into play similarly in asthma exacerbations that occur during sleep (nocturnal asthma) [164,165] and during late pregnancy [166,167] where, in both circumstances, functional residual capacities are diminished [168,169], suggesting in turn diminished lung recoil and smaller load fluctuations acting upon the airway smooth muscle [24,94]. Moreover, it is clear that when inflammatory remodeling of the airway does occur, the perturbed equilibrium hypothesis predicts that the resulting predisposition for airway hyperresponsiveness might persist long after the inflammation itself is resolved [46,170]. And finally, perturbed equilibria might also help to explain why the obstructive response in exercise-induced asthma typically begins only after cessation of the exercise, when tidal volumes have declined to resting levels.

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