Perturbed equilibria of myosin binding in airway smooth muscle: bond-length distributions, mechanics, and ATP metabolism

Adipose tissue in the small airways: How much is enough to drive functional changes?

Obesity is a contributing factor to asthma severity; while it has long been understood that obesity is related to greater asthma burden, the mechanisms though which this occurs have not been fully elucidated. One common explanation is that obesity mechanically reduces lung volume through accumulation of adipose tissue external to the thoracic cavity. However, it has been recently demonstrated that there is substantial adipose tissue within the airway wall itself, and that the presence of adipose tissue within the airway wall is related to body mass index. This suggests the possibility of an additional mechanism by which obesity may worsen asthma, namely by altering the behaviour of the airways themselves. To this end, we modify Anafi & Wilson's classic model of the bistable terminal airway to incorporate adipose tissue within the airway wall in order to answer the question of how much adipose tissue would be required in order to drive substantive functional changes. This analysis suggests that adipose tissue within the airway wall on the order of 1%-2% of total airway cross-sectional area could be sufficient to drive meaningful changes, and further that these changes may interact with volume effects to magnify the overall burden.

Use of human airway smooth muscle in vitro and ex vivo to investigate drugs for the treatment of chronic obstructive respiratory disorders

Isolated airway smooth muscle has been extensively investigated since 1840 to understand the pharmacology of airway diseases. There has often been poor predictability from murine experiments to drugs evaluated in patients with asthma or chronic obstructive pulmonary disease (COPD). However, the use of isolated human airways represents a sensible strategy to optimise the development of innovative molecules for the treatment of respiratory diseases. This review aims to provide updated evidence on the current uses of isolated human airways in validated in vitro methods to investigate drugs in development for the treatment of chronic obstructive respiratory disorders. This review also provides historical notes on the pioneering pharmacological research on isolated human airway tissues, the key differences between human and animal airways, as well as the pivotal differences between human medium bronchi and small airways. Experiments carried out with isolated human bronchial tissues in vitro and ex vivo replicate many of the main anatomical, pathophysiological, mechanical and immunological characteristics of patients with asthma or COPD. In vitro models of asthma and COPD using isolated human airways can provide information that is directly translatable into humans with obstructive lung diseases. Regardless of the technique used to investigate drugs for the treatment of chronic obstructive respiratory disorders (i.e., isolated organ bath systems, videomicroscopy and wire myography), the most limiting factors to produce high-quality and repeatable data remain closely tied to the manual skills of the researcher conducting experiments and the availability of suitable tissue.

A life off the beaten track in biomechanics: Imperfect elasticity, cytoskeletal glassiness, and epithelial unjamming

Textbook descriptions of elasticity, viscosity, and viscoelasticity fail to account for certain mechanical behaviors that typify soft living matter. Here, we consider three examples. First, strong empirical evidence suggests that within lung parenchymal tissues, the frictional stresses expressed at the microscale are fundamentally not of viscous origin. Second, the cytoskeleton (CSK) of the airway smooth muscle cell, as well as that of all eukaryotic cells, is more solid-like than fluid-like, yet its elastic modulus is softer than the softest of soft rubbers by a factor of 104-105. Moreover, the eukaryotic CSK expresses power law rheology, innate malleability, and fluidization when sheared. For these reasons, taken together, the CSK of the living eukaryotic cell is reminiscent of the class of materials called soft glasses, thus likening it to inert materials such as clays, pastes slurries, emulsions, and foams. Third, the cellular collective comprising a confluent epithelial layer can become solid-like and jammed, fluid-like and unjammed, or something in between. Esoteric though each may seem, these discoveries are consequential insofar as they impact our understanding of bronchospasm and wound healing as well as cancer cell invasion and embryonic development. Moreover, there are reasons to suspect that certain of these phenomena first arose in the early protist as a result of evolutionary pressures exerted by the primordial microenvironment. We have hypothesized, further, that each then became passed down virtually unchanged to the present day as a conserved core process. These topics are addressed here not only because they are interesting but also because they track the journey of one laboratory along a path less traveled by.

A dynamical model of TGF-β activation in asthmatic airways

Excessive activation of the regulatory cytokine transforming growth factor $\beta $ (TGF-$\beta $) via contraction of airway smooth muscle (ASM) is associated with the development of asthma. In this study, we develop an ordinary differential equation model that describes the change in density of the key airway wall constituents, ASM and extracellular matrix (ECM), and their interplay with subcellular signalling pathways leading to the activation of TGF-$\beta $. We identify bistable parameter regimes where there are two positive steady states, corresponding to either reduced or elevated TGF-$\beta $ concentration, with the latter leading additionally to increased ASM and ECM density. We associate the former with a healthy homeostatic state and the latter with a diseased (asthmatic) state. We demonstrate that external stimuli, inducing TGF-$\beta $ activation via ASM contraction (mimicking an asthmatic exacerbation), can perturb the system irreversibly from the healthy state to the diseased one. We show that the properties of the stimuli, such as their frequency or strength, and the clearance of surplus active TGF-$\beta $, are important in determining the long-term dynamics and the development of disease. Finally, we demonstrate the utility of this model in investigating temporal responses to bronchial thermoplasty, a therapeutic intervention in which ASM is ablated by applying thermal energy to the airway wall. The model predicts the parameter-dependent threshold damage required to obtain irreversible reduction in ASM content, suggesting that certain asthma phenotypes are more likely to benefit from this intervention.

Modeling and experimental approaches for elucidating multi-scale uterine smooth muscle electro- and mechano-physiology: A review

The uterus provides protection and nourishment (via its blood supply) to a developing fetus, and contracts to deliver the baby at an appropriate time, thereby having a critical contribution to the life of every human. However, despite this vital role, it is an under-investigated organ, and gaps remain in our understanding of how contractions are initiated or coordinated. The uterus is a smooth muscle organ that undergoes variations in its contractile function in response to hormonal fluctuations, the extreme instance of this being during pregnancy and labor. Researchers typically use various approaches to studying this organ, such as experiments on uterine muscle cells, tissue samples, or the intact organ, or the employment of mathematical models to simulate the electrical, mechanical and ionic activity. The complexity exhibited in the coordinated contractions of the uterus remains a challenge to understand, requiring coordinated solutions from different research fields. This review investigates differences in the underlying physiology between human and common animal models utilized in experiments, and the experimental interventions and computational models used to assess uterine function. We look to a future of hybrid experimental interventions and modeling techniques that could be employed to improve the understanding of the mechanisms enabling the healthy function of the uterus.

A multiscale sliding filament model of lymphatic muscle pumping

The lymphatics maintain fluid balance by returning interstitial fluid to veins via contraction/compression of vessel segments with check valves. Disruption of lymphatic pumping can result in a condition called lymphedema with interstitial fluid accumulation. Lymphedema treatments are often ineffective, which is partially attributable to insufficient understanding of specialized lymphatic muscle lining the vessels. This muscle exhibits cardiac-like phasic contractions and smooth muscle-like tonic contractions to generate and regulate flow. To understand the relationship between this sub-cellular contractile machinery and organ-level pumping, we have developed a multiscale computational model of phasic and tonic contractions in lymphatic muscle and coupled it to a lymphangion pumping model. Our model uses the sliding filament model (Huxley in Prog Biophys Biophys Chem 7:255-318, 1957) and its adaptation for smooth muscle (Mijailovich in Biophys J 79(5):2667-2681, 2000). Multiple structural arrangements of contractile components and viscoelastic elements were trialed but only one provided physiologic results. We then coupled this model with our previous lumped parameter model of the lymphangion to relate results to experiments. We show that the model produces similar pressure, diameter, and flow tracings to experiments on rat mesenteric lymphatics. This model provides the first estimates of lymphatic muscle contraction energetics and the ability to assess the potential effects of sub-cellular level phenomena such as calcium oscillations on lymphangion outflow. The maximum efficiency value predicted (40%) is at the upper end of estimates for other muscle types. Spontaneous calcium oscillations during diastole were found to increase outflow up to approximately 50% in the range of frequencies and amplitudes tested.

Flexibility of microstructural adaptations in airway smooth muscle

The airway smooth muscle undergoes an elastic transition during a sustained contraction, characterized by a gradual decrease in hysteresivity caused by a relatively greater rate of increase in elastance than resistance. We recently demonstrated that these mechanical changes are more likely to persist after a large strain when they are acquired in dynamic versus static conditions; as if the microstructural adaptations liable for the elastic transition are more flexible when they evolve in dynamic conditions. The extent of this flexibility is undefined. Herein, contracted ovine tracheal smooth muscle strips were kept in dynamic conditions simulating tidal breathing (sinusoidal length oscillations at 5% amplitude) and then subjected to simulated deep inspirations (DI). Each DI was straining the muscle by either 10%, 20%, or 30% and was imposed at either 2, 5, 10, or 30 min after the preceding DI. The goal was to assess whether and the extent by which the time-dependent decrease in hysteresivity is preserved following the DI. The results show that the time-dependent decrease in hysteresivity seen pre-DI was preserved after a strain of 10%, but not after a strain of 20% or 30%. This suggests that the microstructural adaptations liable for the elastic transition withstood a strain at least twofold greater than the oscillating strain that pertained during their evolution (10% vs. 5%). We propose that a muscle adapting in dynamic conditions forges microstructures exhibiting a substantial degree of flexibility.NEW & NOTEWORTHY This study confirms that airway smooth muscle undergoes an elastic transition during a sustained contraction even when it operates in dynamic conditions simulating breathing at tidal volume. It also demonstrates that the microstructural adaptations liable for this elastic transition withstand a strain that is at least twice as large as the oscillating strain that pertains during their evolution. This degree of flexibility might be an asset with major significant impact for a tissue such as the airway smooth muscle that displays an everchanging shape due to breathing.

An in silico study examining the role of airway smooth muscle dynamics and airway compliance on the rate of airway re-narrowing after deep inspiration

Deep inspirations are a widely studied topic due to their varied effectiveness as a bronchodilator in asthmatic and non-asthmatic patients. Specifically, they are known to be effective at reversing bronchoconstriction in non-asthmatic patients but may fail to prevent bronchoconstriction in asthmatic patients. Inspired by a recent study on the effect of deep inspirations on the rate of re-narrowing of an isolated airway, we investigate whether the latch-bridge dynamics of smooth muscle cross-bridge theory, coupled with non-linear compliance of the airway wall, can account for the reported results: namely that only the rate of renarrowing after DI is sensitive to the interval between deep inspirations, while other measures are unaffected. We develop and present length- and pressure-controlled protocols which mimic both the experiments performed in the study, as well as simulate in vivo conditions respectively. Both protocols are simulated and show qualitative agreement with the results reported by the experiments, suggesting that latch-bridge dynamics coupled with airway wall non-compliance may be sufficient to explain these results. Moreover pressure- and length-controlled protocols show important differences which should be considered when designing in vitro experiments to mimic in vivo conditions.

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

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.

The Aftermath of Bronchoconstriction

Asthma is characterized by chronic airway inflammation, airway remodeling, and excessive constriction of the airway. Detailed investigation exploring inflammation and the role of immune cells has revealed a variety of possible mechanisms by which chronic inflammation drives asthma development. However, the underlying mechanisms of asthma pathogenesis still remain poorly understood. New evidence now suggests that mechanical stimuli that arise during bronchoconstriction may play a critical role in asthma development. In this article, we review the mechanical effect of bronchoconstriction and how these mechanical stresses contribute to airway remodeling independent of inflammation.

Mitigation of airways responsiveness by deep inflation of the lung

Stretching activated strips of airway smooth muscle (ASM) significantly affects both active force and stiffness due to a temporary reduction of the proportion of cycling myosin cross bridges that are bound to their actin binding sites. For the same reason, stretch applied to ASM in situ by a deep inflation (DI) of the lungs is one of the most potent means of reversing bronchoconstriction. When the DI is sufficiently large, however, and is applied while bronchoconstriction is in the process of developing, the subsequent depression in airway resistance is more persistent than can be attributed simply to temporary detachment of ASM cross bridges. In the present study, we use a computational model to demonstrate that this DI-induced ablation of airway responsiveness can be explained by a dose-dependent reduction in the number of cross bridges available to bind to actin when the ASM in the airway wall is stretched above a critical threshold strain and that this disruption of the contractile apparatus recovers over an order of magnitude longer time scale than that of the simple reattachment of unbound cross bridges. NEW & NOTEWORTHY The mechanisms by which deep inflation of the lung reverse bronchoconstriction and affect subsequent airway responsiveness have important potential implications for asthma, yet remain controversial. This study uses computational modeling to posit a mechanism by which sufficiently vigorous inflations applied during active bronchoconstriction not only transiently reverse bronchoconstriction, but also reduce subsequent airways responsiveness for a period of time. Fitting the model to published data in mice supports this notion.

A Distribution-Moment Approximation for Coupled Dynamics of the Airway Wall and Airway Smooth Muscle

Asthma is fundamentally a disease of airway constriction. Due to a variety of experimental challenges, the dynamics of airways are poorly understood. Of specific interest is the narrowing of the airway due to forces produced by the airway smooth muscle wrapped around each airway. The interaction between the muscle and the airway wall is crucial for the airway constriction that occurs during an asthma attack. Although cross-bridge theory is a well-studied representation of complex smooth muscle dynamics, and these dynamics can be coupled to the airway wall, this comes at significant computational cost-even for isolated airways. Because many phenomena of interest in pulmonary physiology cannot be adequately understood by studying isolated airways, this presents a significant limitation. We present a distribution-moment approximation of this coupled system and study the validity of the approximation throughout the physiological range. We show that the distribution-moment approximation is valid in most conditions, and we explore the region of breakdown. These results show that in many situations, the distribution-moment approximation is a viable option that provides an orders-of-magnitude reduction in computational complexity; not only is this valuable for isolated airway studies, but it moreover offers the prospect that rich ASM dynamics might be incorporated into interacting airway models where previously this was precluded by computational cost.

Transient stretch induces cytoskeletal fluidization through the severing action of cofilin

With every deep inspiration (DI) or sigh, the airway wall stretches, as do the airway smooth muscle cells in the airway wall. In response, the airway smooth muscle cell undergoes rapid stretch-induced cytoskeletal fluidization. As a molecular mechanism underlying the cytoskeletal fluidization response, we demonstrate a key role for the actin-severing protein cofilin. Using primary human airway smooth muscle cells, we simulated a DI by imposing a transient stretch of physiological magnitude and duration. We used traction microscopy to measure the resulting changes in contractile forces. After a transient stretch, cofilin-knockdown cells exhibited a 29 ± 5% decrease in contractile force compared with prestretch conditions. By contrast, control cells exhibited a 67 ± 6% decrease ( P < 0.05, knockdown vs. control). Consistent with these contractile force changes with transient stretch, actin filaments in cofilin-knockdown cells remained largely intact, whereas actin filaments in control cells were rapidly disrupted. Furthermore, in cofilin-knockdown cells, contractile force at baseline was higher and rate of remodeling poststretch was slower than in control cells. Additionally, the severing action of cofilin was restricted to the release phase of the transient stretch. We conclude that the actin-severing activity of cofilin is an important factor in stretch-induced cytoskeletal fluidization and may account for an appreciable part of the bronchodilatory effects of a DI.

Inter-airway structural heterogeneity interacts with dynamic heterogeneity to determine lung function and flow patterns in both asthmatic and control simulated lungs

Asthma is a disease involving both airway remodelling (e.g. thickening of the airway wall) and acute, reversible airway narrowing driven by airway smooth muscle contraction. Both of these processes are known to be heterogeneous, and in this study we consider a new theoretical model which considers the interactions of both mechanisms: structural heterogeneity (variation in airway remodelling) and dynamic heterogeneity (emergent variation in airway narrowing and flow). By integrating both types of inter-airway heterogeneity in a full human lung geometry, we are able to draw several insights regarding the mechanisms underlying observed ventilation heterogeneity. We show that: (1) bimodal ventilation distributions are driven by paradoxical contraction/dilation patterns for airways of all sizes; (2) structural heterogeneity differences between asthmatic and control subjects significantly influences resulting lung function, and observed ventilation heterogeneity patterns; and (3) individual airway dilation probabilities are uncorrelated with prior airway remodelling of that airway.

Modeling the Actin.myosin ATPase Cross-Bridge Cycle for Skeletal and Cardiac Muscle Myosin Isoforms

Modeling the complete actin.myosin ATPase cycle has always been limited by the lack of experimental data concerning key steps of the cycle, because these steps can only be defined at very low ionic strength. Here, using human β-cardiac myosin-S1, we combine published data from transient and steady-state kinetics to model a minimal eight-state ATPase cycle. The model illustrates the occupancy of each intermediate around the cycle and how the occupancy is altered by changes in actin concentration for [actin] = 1-20K_m. The cycle can be used to predict the maximal velocity of contraction (by motility assay or sarcomeric shortening) at different actin concentrations (which is consistent with experimental velocity data) and predict the effect of a 5 pN load on a single motor. The same exercise was repeated for human α-cardiac myosin S1 and rabbit fast skeletal muscle S1. The data illustrates how the motor domain properties can alter the ATPase cycle and hence the occupancy of the key states in the cycle. These in turn alter the predicted mechanical response of the myosin independent of other factors present in a sarcomere, such as filament stiffness and regulatory proteins. We also explore the potential of this modeling approach for the study of mutations in human β-cardiac myosin using the hypertrophic myopathy mutation R453C. Our modeling, using the transient kinetic data, predicts mechanical properties of the motor that are compatible with the single-molecule study. The modeling approach may therefore be of wide use for predicting the properties of myosin mutations.

Airway Bistability Is Modulated by Smooth Muscle Dynamics and Length-Tension Characteristics

Airway closure has important implications for lung disease, especially asthma; in particular, the prospect of bistability between open and closed (or effectively closed) airway states has been thought to play a prominent role in airway closure associated with the formation of clustered ventilation defects in asthma. However, many existing analyses of closure consider only static airway equilibria; here we construct, to our knowledge, a new model wherein airway narrowing and closure dynamics are modulated by coupling the airway to cross-bridge models of airway smooth muscle dynamics and force generation. Using this model, we show that important qualitative features of airway pressure-radius hysteresis loops are highly dependent on both airway smooth muscle dynamics, and the length-tension relationship. Furthermore, we show that two recent experimental results from intact bronchial segments are both expressions of the same phenomenon: that a monotonically increasing length-tension relationship, with sharply higher tension at longer lengths, is needed to drive the observed changes in low-compliance regions of the baseline pressure-radius curve. We also explore the potential implications of this finding for airway closure in coupled airway models.

The actin regulator zyxin reinforces airway smooth muscle and accumulates in airways of fatal asthmatics

Bronchospasm induced in non-asthmatic human subjects can be easily reversed by a deep inspiration (DI) whereas bronchospasm that occurs spontaneously in asthmatic subjects cannot. This physiological effect of a DI has been attributed to the manner in which a DI causes airway smooth muscle (ASM) cells to stretch, but underlying molecular mechanisms-and their failure in asthma-remain obscure. Using cells and tissues from wild type and zyxin-/- mice we report responses to a transient stretch of physiologic magnitude and duration. At the level of the cytoskeleton, zyxin facilitated repair at sites of stress fiber fragmentation. At the level of the isolated ASM cell, zyxin facilitated recovery of contractile force. Finally, at the level of the small airway embedded with a precision cut lung slice, zyxin slowed airway dilation. Thus, at each level zyxin stabilized ASM structure and contractile properties at current muscle length. Furthermore, when we examined tissue samples from humans who died as the result of an asthma attack, we found increased accumulation of zyxin compared with non-asthmatics and asthmatics who died of other causes. Together, these data suggest a biophysical role for zyxin in fatal asthma.

Superimposed pressure oscillations: An alternative to treat airway hyperresponsiveness in an acute sensitized airways mouse model

The main driving mechanism during an asthma attack is the hyper-constrictions of airway smooth muscle (ASM), which reduces the airway lumen and makes normal breathing difficult. In spite of some noticeable side effects, bronchodilator drugs such as salbutamol are used to alleviate these symptoms by inducing temporary relaxation of the contracted ASM. In vitro studies have shown that mechanical oscillation can induce relaxation in isolated contracted ASM obtained from healthy subjects but not from asthmatics. To date, little is known about in vivo ASM behaviours, in particular in asthmatic subjects. This in vivo study aims at determining the effect of various superimposed pressure oscillation (SIPO) patterns (different to those occurring during normal breathing) on sensitized airways during an ACh challenge (mimicking an asthmatic attack) and comparing it with the effect of a widely studied broncho-relaxant drug, Isoproterenol (ISO). The study shows that superimposed pressure oscillation in the range of 5-15Hz induces approximately 50% relaxation on pre-constricted sensitized airways in vivo; however, this behaviour was not observed at 20Hz. Our finding suggests that mechanical oscillation, particularly SIPO, may act as a bronchodilator and achieve ASM relaxation.

Three-dimensional stochastic model of actin-myosin binding in the sarcomere lattice

The effect of molecule tethering in three-dimensional (3-D) space on bimolecular binding kinetics is rarely addressed and only occasionally incorporated into models of cell motility. The simplest system that can quantitatively determine this effect is the 3-D sarcomere lattice of the striated muscle, where tethered myosin in thick filaments can only bind to a relatively small number of available sites on the actin filament, positioned within a limited range of thermal movement of the myosin head. Here we implement spatially explicit actomyosin interactions into the multiscale Monte Carlo platform MUSICO, specifically defining how geometrical constraints on tethered myosins can modulate state transition rates in the actomyosin cycle. The simulations provide the distribution of myosin bound to sites on actin, ensure conservation of the number of interacting myosins and actin monomers, and most importantly, the departure in behavior of tethered myosin molecules from unconstrained myosin interactions with actin. In addition, MUSICO determines the number of cross-bridges in each actomyosin cycle state, the force and number of attached cross-bridges per myosin filament, the range of cross-bridge forces and accounts for energy consumption. At the macroscopic scale, MUSICO simulations show large differences in predicted force-velocity curves and in the response during early force recovery phase after a step change in length comparing to the two simplest mass action kinetic models. The origin of these differences is rooted in the different fluxes of myosin binding and corresponding instantaneous cross-bridge distributions and quantitatively reflects a major flaw of the mathematical description in all mass action kinetic models. Consequently, this new approach shows that accurate recapitulation of experimental data requires significantly different binding rates, number of actomyosin states, and cross-bridge elasticity than typically used in mass action kinetic models to correctly describe the biochemical reactions of tethered molecules and their interaction energetics.

Systems-level airway models of bronchoconstriction

Understanding lung and airway behavior presents a number of challenges, both experimental and theoretical, but the potential rewards are great in terms of both potential treatments for disease and interesting biophysical phenomena. This presents an opportunity for modeling to contribute to greater understanding, and here, we focus on modeling efforts that work toward understanding the behavior of airways in vivo, with an emphasis on asthma. We look particularly at those models that address not just isolated airways but many of the important ways in which airways are coupled both with each other and with other structures. This includes both interesting phenomena involving the airways and the layer of airway smooth muscle that surrounds them, and also the emergence of spatial ventilation patterns via dynamic airway interaction. WIREs Syst Biol Med 2016, 8:459-467. doi: 10.1002/wsbm.1349 For further resources related to this article, please visit the WIREs website.

Systems physiology of the airways in health and obstructive pulmonary disease

Fresh air entering the mouth and nose is brought to the blood-gas barrier in the lungs by a repetitively branching network of airways. Provided the individual airway branches remain patent, this airway tree achieves an enormous amplification in cross-sectional area from the trachea to the terminal bronchioles. Obstructive lung diseases such as asthma occur when airway patency becomes compromised. Understanding the pathophysiology of these obstructive diseases thus begins with a consideration of the factors that determine the caliber of an individual airway, which include the force balance between the inward elastic recoil of the airway wall, the outward tethering forces of its parenchymal attachments, and any additional forces due to contraction of airway smooth muscle. Other factors may also contribute significantly to airway narrowing, such as thickening of the airway wall and accumulation of secretions in the lumen. Airway obstruction becomes particularly severe when these various factors occur in concert. However, the effect of airway abnormalities on lung function cannot be fully understood only in terms of what happens to a single airway because narrowing throughout the airway tree is invariably heterogeneous and interdependent. Obstructive lung pathologies thus manifest as emergent phenomena arising from the way in which the airway tree behaves a system. These emergent phenomena are studied with clinical measurements of lung function made by spirometry and by mechanical impedance measured with the forced oscillation technique. Anatomically based computational models are linking these measurements to underlying anatomic structure in systems physiology terms. WIREs Syst Biol Med 2016, 8:423-437. doi: 10.1002/wsbm.1347 For further resources related to this article, please visit the WIREs website.

Nonlinear compliance modulates dynamic bronchoconstriction in a multiscale airway model

The role of breathing and deep inspirations (DI) in modulating airway hyperresponsiveness remains poorly understood. In particular, DIs are potent bronchodilators of constricted airways in nonasthmatic subjects but not in asthmatic subjects. Additionally, length fluctuations (mimicking DIs) have been shown to reduce mean contractile force when applied to airway smooth muscle (ASM) cells and tissue strips. However, these observations are not recapitulated on application of transmural pressure (PTM) oscillations (that mimic tidal breathing and DIs) in isolated intact airways. To shed light on this paradox, we have developed a biomechanical model of the intact airway, accounting for strain-stiffening due to collagen recruitment (a large component of the extracellular matrix (ECM)), and dynamic actomyosin-driven force generation by ASM cells. In agreement with intact airway studies, our model shows that PTM fluctuations at particular mean transmural pressures can lead to only limited bronchodilation. However, our model predicts that moving the airway to a more compliant point on the static pressure-radius relationship (which may involve reducing mean PTM), before applying pressure fluctuations, can generate greater bronchodilation. This difference arises from competition between passive strain-stiffening of ECM and force generation by ASM yielding a highly nonlinear relationship between effective airway stiffness and PTM, which is modified by the presence of contractile agonist. Effectively, the airway at its most compliant may allow for greater strain to be transmitted to subcellular contractile machinery. The model predictions lead us to hypothesize that the maximum possible bronchodilation of an airway depends on its static compliance at the PTM about which the fluctuations are applied. We suggest the design of additional experimental protocols to test this hypothesis.

Static and dynamic stress heterogeneity in a multiscale model of the asthmatic airway wall

Airway hyperresponsiveness (AHR) is a key characteristic of asthma that remains poorly understood. Tidal breathing and deep inspiration ordinarily cause rapid relaxation of airway smooth muscle (ASM) (as demonstrated via application of length fluctuations to tissue strips) and are therefore implicated in modulation of AHR, but in some cases (such as application of transmural pressure oscillations to isolated intact airways) this mechanism fails. Here we use a multiscale biomechanical model for intact airways that incorporates strain stiffening due to collagen recruitment and dynamic force generation by ASM cells to show that the geometry of the airway, together with interplay between dynamic active and passive forces, gives rise to large stress and compliance heterogeneities across the airway wall that are absent in tissue strips. We show further that these stress heterogeneities result in auxotonic loading conditions that are currently not replicated in tissue-strip experiments; stresses in the strip are similar to hoop stress only at the outer airway wall and are under- or overestimates of stresses at the lumen. Taken together these results suggest that a previously underappreciated factor, stress heterogeneities within the airway wall and consequent ASM cellular response to this micromechanical environment, could contribute to AHR and should be explored further both theoretically and experimentally.

Smooth muscle in human bronchi is disposed to resist airway distension

Studying airway smooth muscle (ASM) in conditions that emulate the in vivo environment within which the bronchi normally operate may provide important clues regarding its elusive physiological function. The present study examines the effect of lengthening and shortening of ASM on tension development in human bronchial segments. ASM from each bronchial segment was set at a length approximating in situ length (Linsitu). Bronchial tension was then measured during a slow cyclical strain (0.004Hz, from 0.7Linsitu to 1.3Linsitu) in the relaxed state and at graded levels of activation by methacholine. In all cases, tension was greater at longer ASM lengths, and greater during lengthening than shortening. The threshold of methacholine concentration that was required for ASM to account for bronchial tension across the entire range of ASM lengths tested was on average smaller by 2.8 logs during lengthening than during shortening. The length-dependency of ASM tension, together with this lower threshold of methacholine concentration during lengthening versus shortening, suggest that ASM has a greater ability to resist airway dilation during lung inflation than to narrow the airways during lung deflation. More than serving to narrow the airway, as has long been thought, these data suggest that the main function of ASM contraction is to limit airway wall distension during lung inflation.

Biphasic force response to iso-velocity stretch in airway smooth muscle

Airway smooth muscle (ASM) in vivo is constantly subjected to oscillatory strain due to tidal breathing and deep inspirations. ASM contractility is known to be adversely affected by strains, especially those of large amplitudes. Based on the cross-bridge model of contraction, it is likely that strain impairs force generation by disrupting actomyosin cross-bridge interaction. There is also evidence that strain modulates muscle stiffness and force through induction of cytoskeletal remodeling. However, the molecular mechanism by which strain alters smooth muscle function is not entirely clear. Here, we examine the response of ASM to iso-velocity stretches to probe the components within the muscle preparation that give rise to different features in the force response. We found in ASM that force response to a ramp stretch showed a biphasic feature, with the initial phase associated with greater muscle stiffness compared with that in the later phase, and that the transition between the phases occurred at a critical strain of ∼3.3%. Only strains with amplitudes greater than the critical strain could lead to reduction in force and stiffness of the muscle in the subsequent stretches. The initial-phase stiffness was found to be linearly related to the degree of muscle activation, suggesting that the stiffness stems mainly from attached cross bridges. Both phases were affected by the degree of muscle activation and by inhibitors of myosin light-chain kinase, PKC, and Rho-kinase. Different responses due to different interventions suggest that cross-bridge and cytoskeletal stiffness is regulated differently by the kinases.

A biomechanical model for fluidization of cells under dynamic strain

Recent experiments have investigated the response of smooth muscle cells to transient stretch-compress (SC) and compress-stretch (CS) maneuvers. The results indicate that the transient SC maneuver causes a sudden fluidization of the cell while the CS maneuver does not. To understand this asymmetric behavior, we have built a biomechanical model to probe the response of stress fibers to the two maneuvers. The model couples the cross-bridge cycle of myosin motors with a viscoelastic Kelvin-Voigt element that represents the stress fiber. Simulation results point to the sensitivity of the myosin detachment rate to tension as the cause for the asymmetric response of the stress fiber to the CS and SC maneuvers. For the SC maneuver, the initial stretch increases the tension in the stress fiber and suppresses myosin detachment. The subsequent compression then causes a large proportion of the myosin population to disengage rapidly from actin filaments. This leads to the disassembly of the stress fibers and the observed fluidization. In contrast, the CS maneuver only produces a mild loss of myosin motors and no fluidization.

Adaptation of active tone in the mouse descending thoracic aorta under acute changes in loading

Arteries can adapt to sustained changes in blood pressure and flow, and it is thought that these adaptive processes often begin with an altered smooth muscle cell activity that precedes any detectable changes in the passive wall components. Yet, due to the intrinsic coupling between the active and passive properties of the arterial wall, it has been difficult to delineate the adaptive contributions of active smooth muscle. To address this need, we used a novel experimental-computational approach to quantify adaptive functions of active smooth muscle in arterial rings excised from the proximal descending thoracic aorta of mice and subjected to short-term sustained circumferential stretches while stimulated with various agonists. A new mathematical model of the adaptive processes was derived and fit to data to describe and predict the effects of active tone adaptation. It was found that active tone was maintained when the artery was adapted close to the optimal stretch for maximal active force production, but it was reduced when adapted below the optimal stretch; there was no significant change in passive behavior in either case. Such active adaptations occurred only upon smooth muscle stimulation with phenylephrine, however, not stimulation with KCl or angiotensin II. Numerical simulations using the proposed model suggested further that active tone adaptation in vascular smooth muscle could play a stabilizing role for wall stress in large elastic arteries.

Effectiveness of a load-imposing device for cyclic stretching of isolated human bronchi: a validation study

Background

Mechanical ventilation may induce harmful effects in the airways of critically ill patients. Nevertheless, the effects of cyclic stretching caused by repetitive inflation-deflation of the bronchial compartment have not been well characterized in humans. The objective of the present study was to assess the effectiveness of a load-imposing device for the cyclic stretching of human bronchi.

Methods

Intact bronchial segments were removed from 128 thoracic surgery patients. After preparation and equilibration in an organ bath, bronchi were stretched repetitively and cyclically with a motorized transducer. The peak force imposed on the bronchi was set to 80% of each individual maximum contraction in response to acetylcholine and the minimal force corresponded to the initial basal tone before stretching. A 1-min cycle (stretching for 15 sec, relaxing for 15 sec and resting for 30 sec) was applied over a time period ranging from 5 to 60 min. The device's performance level was assessed and the properties of the stretched bronchi were compared with those of paired, non-stretched bronchi.

Results

Despite the intrinsic capacities of the device, the targets of the tension adjustments remained variable for minimal tension (156–178%) while the peak force set point was unchanged (87–115%). In the stretched bronchi, a time-dependent rise in basal tone (P <.05 vs. non-stretched) was apparent after as little as 5 min of cyclic stretching. The stretch-induced rise in basal tone continued to increase (P <.01) after the stretching had ended. Only 60 min of cyclic stretching was associated with a significant (P <.05) increase in responsiveness to acetylcholine, relative to non-stretched bronchi.

Conclusions

Low-frequency, low-force, cyclic loading of human bronchi is associated with elevated basal tone and acetylcholine responsiveness. The present experimental model is likely to be a useful tool for future investigations of the bronchial response to repetitive stress during mechanical ventilation.

Modeling the impairment of airway smooth muscle force by stretch

Imposed length changes of only a small percent produce transient reductions in active force in strips of airway smooth muscle (ASM) due to the temporary detachment of bound cross-bridges caused by the relative motion of the actin and myosin fibers. More dramatic and sustained reductions in active force occur following large changes in length. The Huxley two-state model of skeletal muscle originally proposed in 1957 and later adapted to include a four-state description of cross-bridge kinetics has been widely used to model the former phenomenon, but is unable to account for the latter unless modified to include mechanisms by which the contractile machinery in the ASM cell becomes appropriately rearranged. Even so, the Huxley model itself is based on the assumption that the contractile proteins are all aligned precisely in the direction of bulk force generation, which is not true for ASM. The present study derives a coarse-grained version of the Huxley model that is free of inherent assumptions about cross-bridge orientation. This simplified model recapitulates the key features observed in the force-length behavior of activated strips of ASM and, in addition, provides a mechanistically based way of accounting for the sustained force reductions that occur following large stretch.

Airway smooth muscle in asthma: linking contraction and mechanotransduction to disease pathogenesis and remodelling

Asthma is an obstructive airway disease, with a heterogeneous and multifactorial pathogenesis. Although generally considered to be a disease principally driven by chronic inflammation, it is becoming increasingly recognised that the immune component of the pathology poorly correlates with the clinical symptoms of asthma, thus highlighting a potentially central role for non-immune cells. In this context airway smooth muscle (ASM) may be a key player, as it comprises a significant proportion of the airway wall and is the ultimate effector of acute airway narrowing. Historically, the contribution of ASM to asthma pathogenesis has been contentious, yet emerging evidence suggests that ASM contractile activation imparts chronic effects that extend well beyond the temporary effects of bronchoconstriction. In this review article we describe the effects that ASM contraction, in combination with cellular mechanotransduction and novel contraction-inflammation synergies, contribute to asthma pathogenesis. Specific emphasis will be placed on the effects that ASM contraction exerts on the mechanical properties of the airway wall, as well as novel mechanisms by which ASM contraction may contribute to more established features of asthma such as airway wall remodelling.

Phenotype, endotype and patient-specific computational modelling for optimal treatment design in asthma

Understanding and treatment of asthma is significantly complicated by the heterogeneous spectrum of phenotypes associated with the disease. Recent advances in phenotype classification promise more targeted therapies, but these categories are based on constellations of largely external measurements and are not necessarily indicative of underlying pathophysiology. We propose that computational modelling is a valuable tool that allows the disease spectrum to be decomposed not into phenotypes but rather into groups organized by underlying dysfunction, referred to by some authors as endotypes. By breaking down the asthmatic spectrum in this way, therapies can be targeted more directly to the underlying defects. This would be not only an important improvement in its own right, but also an important step toward the ultimate goal of patient-specific modelling.

Emergence of airway smooth muscle mechanical behavior through dynamic reorganization of contractile units and force transmission pathways

Airway hyperresponsiveness (AHR) in asthma remains poorly understood despite significant research effort to elucidate relevant underlying mechanisms. In particular, a significant body of experimental work has focused on the effect of tidal fluctuations on airway smooth muscle (ASM) cells, tissues, lung slices, and whole airways to understand the bronchodilating effect of tidal breathing and deep inspirations. These studies have motivated conceptual models that involve dynamic reorganization of both cytoskeletal components as well as contractile machinery. In this article, a biophysical model of the whole ASM cell is presented that combines 1) crossbridge cycling between actin and myosin; 2) actin-myosin disconnectivity, under imposed length changes, to allow dynamic reconfiguration of "force transmission pathways"; and 3) dynamic parallel-to-serial transitions of contractile units within these pathways that occur through a length fluctuation. Results of this theoretical model suggest that behavior characteristic of experimentally observed force-length loops of maximally activated ASM strips can be explained by interactions among the three mechanisms. Crucially, both sustained disconnectivity and parallel-to-serial transitions are necessary to explain the nature of hysteresis and strain stiffening observed experimentally. The results provide strong evidence that dynamic rearrangement of contractile machinery is a likely mechanism underlying many of the phenomena observed at timescales associated with tidal breathing. This theoretical cell-level model captures many of the salient features of mechanical behavior observed experimentally and should provide a useful starting block for a bottom-up approach to understanding tissue-level mechanical behavior.

Complexity and emergent phenomena

Complex biological systems operate under non-equilibrium conditions and exhibit emergent properties associated with correlated spatial and temporal structures. These properties may be individually unpredictable, but tend to be governed by power-law probability distributions and/or correlation. This article reviews the concepts that are invoked in the treatment of complex systems through a wide range of respiratory-related examples. Following a brief historical overview, some of the tools to characterize structural variabilities and temporal fluctuations associated with complex systems are introduced. By invoking the concept of percolation, the notion of multiscale behavior and related modeling issues are discussed. Spatial complexity is then examined in the airway and parenchymal structures with implications for gas exchange followed by a short glimpse of complexity at the cellular and subcellular network levels. Variability and complexity in the time domain are then reviewed in relation to temporal fluctuations in airway function. Next, an attempt is given to link spatial and temporal complexities through examples of airway opening and lung tissue viscoelasticity. Specific examples of possible and more direct clinical implications are also offered through examples of optimal future treatment of fibrosis, exacerbation risk prediction in asthma, and a novel method in mechanical ventilation. Finally, the potential role of the science of complexity in the future of physiology, biology, and medicine is discussed.

Mechanical and structural plasticity

Excessive narrowing of the airways due to airway smooth muscle (ASM) contraction is a major cause of asthma exacerbation. ASM is therefore a direct target for many drugs used in asthma therapy. The contractile mechanism of smooth muscle is not entirely clear. A major advance in the field in the last decade was the recognition and appreciation of the unique properties of smooth muscle--mechanical and structural plasticity, characterized by the muscle's ability to rapidly alter the structure of its contractile apparatus and cytoskeleton and adapt to the mechanically dynamic environment of the lung. This article describes a possible mechanism for smooth muscle to adapt and function over a large length range by adding or subtracting contractile units in series spanning the cell length; it also describes a mechanism by which actin-myosin-actin connectivity might be influenced by thin and thick filament lengths, thus altering the muscle response to mechanical perturbation. The new knowledge is extremely useful for our understanding of ASM behavior in the lung and could provide new and more effective targets for drugs aimed at relaxing the muscle or keeping the muscle from excessive shortening in the asthmatic airways.

Can tidal breathing with deep inspirations of intact airways create sustained bronchoprotection or bronchodilation?

Fluctuating forces imposed on the airway smooth muscle due to breathing are believed to regulate hyperresponsiveness in vivo. However, recent animal and human isolated airway studies have shown that typical breathing-sized transmural pressure (Ptm) oscillations around a fixed mean are ineffective at mitigating airway constriction. To help understand this discrepancy, we hypothesized that Ptm oscillations capable of producing the same degree of bronchodilation as observed in airway smooth muscle strip studies requires imposition of strains larger than those expected to occur in vivo. First, we applied increasingly larger amplitude Ptm oscillations to a statically constricted airway from a Ptm simulating normal functional residual capacity of 5 cmH2O. Tidal-like oscillations (5-10 cmH2O) imposed 4.9 ± 2.0% strain and resulted in 11.6 ± 4.8% recovery, while Ptm oscillations simulating a deep inspiration at every breath (5-30 cmH2O) achieved 62.9 ± 12.1% recovery. These same Ptm oscillations were then applied starting from a Ptm = 1 cmH2O, resulting in approximately double the strain for each oscillation amplitude. When extreme strains were imposed, we observed full recovery. On combining the two data sets, we found a linear relationship between strain and resultant recovery. Finally, we compared the impact of Ptm oscillations before and after constriction to Ptm oscillations applied only after constriction and found that both loading conditions had a similar effect on narrowing. We conclude that, while sufficiently large strains applied to the airway wall are capable of producing substantial bronchodilation, the Ptm oscillations necessary to achieve those strains are not expected to occur in vivo.

Modelling airway smooth muscle passive length adaptation via thick filament length distributions

We present a new model of airway smooth muscle (ASM), which surrounds and constricts every airway in the lung and thus plays a central role in the airway constriction associated with asthma. This new model of ASM is based on an extension of sliding filament/crossbridge theory, which explicitly incorporates the length distribution of thick sliding filaments to account for a phenomenon known as dynamic passive length adaptation; the model exhibits good agreement with experimental data for ASM force-length behaviour across multiple scales. Principally these are (nonlinear) force-length loops at short timescales (seconds), parabolic force-length curves at medium timescales (minutes) and length adaptation at longer timescales. This represents a significant improvement on the widely-used crossbridge models which work so well in or near the isometric regime, and may have significant implications for studies which rely on crossbridge or other dynamic airway smooth muscle models, and thus both airway and lung dynamics.

The importance of synergy between deep inspirations and fluidization in reversing airway closure

Deep inspirations (DIs) and airway smooth muscle fluidization are two widely studied phenomena in asthma research, particularly for their ability (or inability) to counteract severe airway constriction. For example, DIs have been shown effectively to reverse airway constriction in normal subjects, but this is impaired in asthmatics. Fluidization is a connected phenomenon, wherein the ability of airway smooth muscle (ASM, which surrounds and constricts the airways) to exert force is decreased by applied strain. A maneuver which sufficiently strains the ASM, then, such as a DI, is thought to reduce the force generating capacity of the muscle via fluidization and hence reverse or prevent airway constriction. Understanding these two phenomena is considered key to understanding the pathophysiology of asthma and airway hyper-responsiveness, and while both have been extensively studied, the mechanism by which DIs fail in asthmatics remains elusive. Here we show for the first time the synergistic interaction between DIs and fluidization which allows the combination to provide near complete reversal of airway closure where neither is effective alone. This relies not just on the traditional model of airway bistability between open and closed states, but also the critical addition of previously-unknown oscillatory and chaotic dynamics. It also allows us to explore the types of subtle change which can cause this interaction to fail, and thus could provide the missing link to explain DI failure in asthmatics.

Effect of length oscillations on airway smooth muscle reactivity and cross-bridge cycling

Excessive airway narrowing due to airway smooth muscle (ASM) hyperconstriction is a major symptom in many respiratory diseases. In vitro imposition of length oscillations similar to those produced by tidal breathing on contracted ASM have shown to reduce muscle active forces, which is usually attributed to unconfirmed disruption of actomyosin cross-bridges. This research focuses on an in vitro investigation of the effect of mechanical oscillations on ASM reactivity and actomyosin cross-bridges. A computerized organ bath system was used to test maximally precontracted bovine ASM subjected to length oscillations at frequencies in the range of 10–100 Hz superimposed on tidal breathing oscillation. Using an immunofluorescence technique, two specific antibodies against the phospho-serine19 myosin light chain and the α-smooth muscle actin were used to analyze the colocalization between these two filaments. Data were processed using the plug-in “colocalization threshold” of ImageJ 1.43m software. The results demonstrate that both tidal and superimposed length oscillations reduce the active force in contracted ASM for a relatively long term and that the latter enhances the force reduction of the former. This reduction was also found to be frequency and time dependent. Additionally colocalization analysis indicates that length oscillations cause the detachment of the actomyosin connections and that this condition is sustained even after the cessation of the length oscillations.

A multi-scale approach to airway hyperresponsiveness: from molecule to organ

Airway hyperresponsiveness (AHR), a characteristic of asthma that involves an excessive reduction in airway caliber, is a complex mechanism reflecting multiple processes that manifest over a large range of length and time scales. At one extreme, molecular interactions determine the force generated by airway smooth muscle (ASM). At the other, the spatially distributed constriction of the branching airways leads to breathing difficulties. Similarly, asthma therapies act at the molecular scale while clinical outcomes are determined by lung function. These extremes are linked by events operating over intermediate scales of length and time. Thus, AHR is an emergent phenomenon that limits our understanding of asthma and confounds the interpretation of studies that address physiological mechanisms over a limited range of scales. A solution is a modular computational model that integrates experimental and mathematical data from multiple scales. This includes, at the molecular scale, kinetics, and force production of actin-myosin contractile proteins during cross-bridge and latch-state cycling; at the cellular scale, Ca²⁺ signaling mechanisms that regulate ASM force production; at the tissue scale, forces acting between contracting ASM and opposing viscoelastic tissue that determine airway narrowing; at the organ scale, the topographic distribution of ASM contraction dynamics that determine mechanical impedance of the lung. At each scale, models are constructed with iterations between theory and experimentation to identify the parameters that link adjacent scales. This modular model establishes algorithms for modeling over a wide range of scales and provides a framework for the inclusion of other responses such as inflammation or therapeutic regimes. The goal is to develop this lung model so that it can make predictions about bronchoconstriction and identify the pathophysiologic mechanisms having the greatest impact on AHR and its therapy.

Dilatation of the constricted human airway by tidal expansion of lung parenchyma

RATIONALE

In the normal lung, breathing and deep inspirations potently antagonize bronchoconstriction, but in the asthmatic lung this salutary effect is substantially attenuated or even reversed. To explain these findings, the prevailing hypothesis focuses on contracting airway smooth muscle and posits a nonlinear dynamic interaction between actomyosin binding and the tethering forces imposed by tidally expanding lung parenchyma.

OBJECTIVE

This hypothesis has never been tested directly in bronchial smooth muscle embedded within intraparenchymal airways. Our objective here is to fill that gap.

METHODS

We designed a novel system to image contracting intraparenchymal human airways situated within near-normal lung architecture and subjected to dynamic parenchymal expansion that simulates breathing.

MEASUREMENTS AND MAIN RESULTS

Reversal of bronchoconstriction depended on the degree to which breathing actually stretched the airway, which in turn depended negatively on severity of constriction and positively on the depth of breathing. Such behavior implies positive feedbacks that engender airway instability.

OVERALL CONCLUSIONS

These findings help to explain heterogeneity of airflow obstruction as well as why, in people with asthma, deep inspirations are less effective in reversing bronchoconstriction.

A three-dimensional chemo-mechanical continuum model for smooth muscle contraction

Based on two fields, namely the placement and the calcium concentration, a chemo-mechanically coupled three-dimensional model, describing the contractile behaviour of smooth muscles, is presented by means of a strain energy function. The strain energy function (Schmitz and Böl, 2011) is additively decomposed into a passive part, relating to elastin and collagen, and an active calcium-driven part related to the chemical contraction of the smooth muscle cells. For the description of the calcium phase the four state cross-bridge model of Hai and Murphy (Hai and Murphy, 1988) has been implemented into the finite element method. Beside three-dimensional illustrative boundary-value problems demonstrating the features of the presented modelling concept, simulations on an idealised artery document the applicability of the model to more realistic geometries.

Time course of isotonic shortening and the underlying contraction mechanism in airway smooth muscle

Although the structure of the contractile unit in smooth muscle is poorly understood, some of the mechanical properties of the muscle suggest that a sliding-filament mechanism, similar to that in striated muscle, is also operative in smooth muscle. To test the applicability of this mechanism to smooth muscle function, we have constructed a mathematical model based on a hypothetical structure of the smooth muscle contractile unit: a side-polar myosin filament sandwiched by actin filaments, each attached to the equivalent of a Z disk. Model prediction of isotonic shortening as a function of time was compared with data from experiments using ovine tracheal smooth muscle. After equilibration and establishment of in situ length, the muscle was stimulated with ACh (100 μM) until force reached a plateau. The muscle was then allowed to shorten isotonically against various loads. From the experimental records, length-force and force-velocity relationships were obtained. Integration of the hyperbolic force-velocity relationship and the linear length-force relationship yielded an exponential function that approximated the time course of isotonic shortening generated by the modeled sliding-filament mechanism. However, to obtain an accurate fit, it was necessary to incorporate a viscoelastic element in series with the sliding-filament mechanism. The results suggest that a large portion of the shortening is due to filament sliding associated with muscle activation and that a small portion is due to continued deformation associated with an element that shows viscoelastic or power-law creep after a step change in force.

Myosin filament polymerization and depolymerization in a model of partial length adaptation in airway smooth muscle

Length adaptation in airway smooth muscle (ASM) is attributed to reorganization of the cytoskeleton, and in particular the contractile elements. However, a constantly changing lung volume with tidal breathing (hence changing ASM length) is likely to restrict full adaptation of ASM for force generation. There is likely to be continuous length adaptation of ASM between states of incomplete or partial length adaption. We propose a new model that assimilates findings on myosin filament polymerization/depolymerization, partial length adaptation, isometric force, and shortening velocity to describe this continuous length adaptation process. In this model, the ASM adapts to an optimal force-generating capacity in a repeating cycle of events. Initially the myosin filament, shortened by prior length changes, associates with two longer actin filaments. The actin filaments are located adjacent to the myosin filaments, such that all myosin heads overlap with actin to permit maximal cross-bridge cycling. Since in this model the actin filaments are usually longer than myosin filaments, the excess length of the actin filament is located randomly with respect to the myosin filament. Once activated, the myosin filament elongates by polymerization along the actin filaments, with the growth limited by the overlap of the actin filaments. During relaxation, the myosin filaments dissociate from the actin filaments, and then the cycle repeats. This process causes a gradual adaptation of force and instantaneous adaptation of shortening velocity. Good agreement is found between model simulations and the experimental data depicting the relationship between force development, myosin filament density, or shortening velocity and length.

Could an increase in airway smooth muscle shortening velocity cause airway hyperresponsiveness?

Airway hyperresponsiveness (AHR) is a characteristic feature of asthma. It has been proposed that an increase in the shortening velocity of airway smooth muscle (ASM) could contribute to AHR. To address this possibility, we tested whether an increase in the isotonic shortening velocity of ASM is associated with an increase in the rate and total amount of shortening when ASM is subjected to an oscillating load, as occurs during breathing. Experiments were performed in vitro using 27 rat tracheal ASM strips supramaximally stimulated with methacholine. Isotonic velocity at 20% isometric force (Fiso) was measured, and then the load on the muscle was varied sinusoidally (0.33 ± 0.25 Fiso, 1.2 Hz) for 20 min, while muscle length was measured. A large amplitude oscillation was applied every 4 min to simulate a deep breath. We found that: 1) ASM strips with a higher isotonic velocity shortened more quickly during the force oscillations, both initially (P < 0.001) and after the simulated deep breaths (P = 0.002); 2) ASM strips with a higher isotonic velocity exhibited a greater total shortening during the force oscillation protocol (P < 0.005); and 3) the effect of an increase in isotonic velocity was at least comparable in magnitude to the effect of a proportional increase in ASM force-generating capacity. A cross-bridge model showed that an increase in the total amount of shortening with increased isotonic velocity could be explained by a change in either the cycling rate of phosphorylated cross bridges or the rate of myosin light chain phosphorylation. We conclude that, if asthma involves an increase in ASM velocity, this could be an important factor in the associated AHR.

Remodeling of integrated contractile tissues and its dependence on strain-rate amplitude

Here we investigate the origin of relaxation times governing the mechanical response of an integrated contractile tissue to imposed cyclic changes of length. When strain-rate amplitude is held constant as frequency is varied, fast events are accounted for by actomyosin cross-bridge cycling, but slow events reveal relaxation processes associated with ongoing cytoskeletal length adaptation. Although both relaxation regimes are innately nonlinear, these regimes are unified and their positions along the frequency axis are set by the imposed strain-rate amplitude.

Contribution of Rho kinase to the early phase of the calcium-contraction coupling in airway smooth muscle

We investigated theoretically and experimentally the role of Rho kinase (RhoK) in Ca(2+)-contraction coupling in rat airways. Isometric contraction was measured on tracheal, extrapulmonary and intrapulmonary bronchial rings. Intracellular [Ca(2+)] was recorded in freshly isolated tracheal myocytes. Stimulation by carbachol (0.3 and 10 μm) and 50 mm external KCl induced a short-time, Hill-shaped contraction obtained within 90 s, followed by a sustained or an additional delayed contraction. Responses of [Ca(2+)](i) to acetylcholine consisted in a fast peak followed by a plateau and, in 42% of the cells, superimposed Ca(2+) oscillations. The RhoK inhibitor Y27632 (10 μm) did not alter the [Ca(2+)](i) response. Whatever the agonist, Y27632 did not modify the basal tension but decreased the amplitude of the short-duration response, without altering the additional delayed contraction. The Myosin Light Chain Phosphatase (MLCP) inhibitor calyculin A increased the basal tension and abolished the effect of RhoK. KN93 (Ca(2+)-calmodulin-dependent protein kinase II inhibitor) and DIDS (inhibitor of Ca(2+)-activated Cl(-) channels) had no influence on the RhoK effect. We built a theoretical model of Ca(2+)-dependent active/inactive RhoK ratio and subsequent RhoK-dependent MLCP inactivation, which was further coupled with a four-state model of the contractile apparatus and Ca(2+)-dependent MLCK activation. The model explains the time course of the short-duration contraction and the role of RhoK by Ca(2+)-dependent activation of MLCK and RhoK, which inactivates MLCP. Oscillatory and non-oscillatory [Ca(2+)](i) responses result in a non-oscillatory contraction, the amplitude of which is encoded by the plateau value and oscillation frequency. In conclusion, Ca(2+)-dependent but CaMK II-independent RhoK activation contributes to the early phase of the contractile response via MLCP inhibition.