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

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.

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.

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.

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.

Length adaptation of smooth muscle contractile filaments in response to sustained activation

Airway and bladder smooth muscles are known to undergo length adaptation under sustained contraction. This adaptation process entails a remodelling of the intracellular actin and myosin filaments which shifts the peak of the active force-length curve towards the current length. Smooth muscles are therefore able to generate the maximum force over a wide range of lengths. In contrast, length adaptation of vascular smooth muscle has attracted very little attention and only a handful of studies have been reported. Although their results are conflicting on the existence of a length adaptation process in vascular smooth muscle, it seems that, at least, peripheral arteries and arterioles undergo such adaptation. This is of interest since peripheral vessels are responsible for pressure regulation, and a length adaptation will affect the function of the cardiovascular system. It has, e.g., been suggested that the inward remodelling of resistance vessels associated with hypertension disorders may be related to smooth muscle adaptation. In this study we develop a continuum mechanical model for vascular smooth muscle length adaptation by assuming that the muscle cells remodel the actomyosin network such that the peak of the active stress-stretch curve is shifted towards the operating point. The model is specialised to hamster cheek pouch arterioles and the simulated response to stepwise length changes under contraction. The results show that the model is able to recover the salient features of length adaptation reported in the literature.

Airway compliance and dynamics explain the apparent discrepancy in length adaptation between intact airways and smooth muscle strips

Length adaptation is a phenomenon observed in airway smooth muscle (ASM) wherein over time there is a shift in the length-tension curve. There is potential for length adaptation to play an important role in airway constriction and airway hyper-responsiveness in asthma. Recent results by Ansell et al., 2015 (JAP 2014 10.1152/japplphysiol.00724.2014) have cast doubt on this role by testing for length adaptation using an intact airway preparation, rather than strips of ASM. Using this technique they found no evidence for length adaptation in intact airways. Here we attempt to resolve this apparent discrepancy by constructing a minimal mathematical model of the intact airway, including ASM which follows the classic length-tension curve and undergoes length adaptation. This allows us to show that (1) no evidence of length adaptation should be expected in large, cartilaginous, intact airways; (2) even in highly compliant peripheral airways, or at more compliant regions of the pressure-volume curve of large airways, the effect of length adaptation would be modest and at best marginally detectable in intact airways; (3) the key parameters which control the appearance of length adaptation in intact airways are airway compliance and the relaxation timescale. The results of this mathematical simulation suggest that length adaptation observed at the level of the isolated ASM may not clearly manifest in the normal intact airway.

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.

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.

Development and maintenance of force and stiffness in airway smooth muscle

Airway smooth muscle (ASM) plays a central role in the excessive narrowing of the airway that characterizes the primary functional impairment in asthma. This phenomenon is known as airway hyper-responsiveness (AHR). Emerging evidence suggests that the development and maintenance of ASM force involves dynamic reorganization of the subcellular filament network in both the cytoskeleton and the contractile apparatus. In this review, evidence is presented to support the view that regulation of ASM contraction extends beyond the classical actomyosin interaction and involves processes within the cytoskeleton and at the interfaces between the cytoskeleton, the contractile apparatus, and the extracellular matrix. These processes are initiated when the muscle is activated, and collectively they cause the cytoskeleton and the contractile apparatus to undergo structural transformation, resulting in a more connected and solid state that allows force generated by the contractile apparatus to be transmitted to the extracellular domain. Solidification of the cytoskeleton also serves to stiffen the muscle and hence the airway. Oscillatory strain from tidal breathing and deep inspiration is believed to be the counter balance that prevents hypercontraction and stiffening of ASM in vivo. Dysregulation of this balance could lead to AHR seen in asthma.

Force maintenance and myosin filament assembly regulated by Rho-kinase in airway smooth muscle

Smooth muscle contraction can be divided into two phases: the initial contraction determines the amount of developed force and the second phase determines how well the force is maintained. The initial phase is primarily due to activation of actomyosin interaction and is relatively well understood, whereas the second phase remains poorly understood. Force maintenance in the sustained phase can be disrupted by strains applied to the muscle; the strain causes actomyosin cross-bridges to detach and also the cytoskeletal structure to disassemble in a process known as fluidization, for which the underlying mechanism is largely unknown. In the present study we investigated the ability of airway smooth muscle to maintain force after the initial phase of contraction. Specifically, we examined the roles of Rho-kinase and protein kinase C (PKC) in force maintenance. We found that for the same degree of initial force inhibition, Rho-kinase substantially reduced the muscle's ability to sustain force under static conditions, whereas inhibition of PKC had a minimal effect on sustaining force. Under oscillatory strain, Rho-kinase inhibition caused further decline in force, but again, PKC inhibition had a minimal effect. We also found that Rho-kinase inhibition led to a decrease in the myosin filament mass in the muscle cells, suggesting that one of the functions of Rho-kinase is to stabilize myosin filaments. The results also suggest that dissolution of myosin filaments may be one of the mechanisms underlying the phenomenon of fluidization. These findings can shed light on the mechanism underlying deep inspiration induced bronchodilation.

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.