Mathematical description of geometric and kinematic aspects of smooth muscle plasticity and some related morphometrics

Chronic anal fissure: morphometric analysis of the anal canal at 3.0 Tesla MR imaging

OBJECTıVE: To compare the morphometric data relating to the muscular structures of the anal canal, in patients with chronic anal fissure and in control group, examined at a 3.0 Tesla MR system.

SUBJECTS AND METHODS

Forty-seven consecutive patients with chronic anal fissure and randomly selected 40 patients who had no claims for perianal disease during their life time were included in the study. T2-weighted sagittal, high-resolution (HR) T2-weighted, and contrast-enhanced fat-suppressed T1-weighted oblique axial and oblique coronal images were retrospectively analyzed by two observers in consensus. Thickness of sphincteric muscles, anal canal length, anorectal angle, thickness of anococcygeal ligament, depth of Minor triangle, width between subcutaneous sphincters, vascularity of posterior commissure, visibility of posterosuperior projection of external sphincter, and angle between the distal anal canal and posterosuperior projection of external sphincter (H angle) in patients and in controls were compared and analyzed using t test, Mann-Whitney U test, and Spearman correlation.

RESULTS

The patients with chronic anal fissure had longer anal canal (51.50 mm ± 0.91 vs. 44.11 mm ± 0.71; p = 0.000), thicker internal anal sphincter muscle at mid-anal level (4.18 ± 0.15 vs. 3.39 ± 0.07; p = 0.007), and wider space between subcutaneous external sphincters (11.39 ± 0.50 vs. 6.89 ± 0.22; p = 0.000). In patients, there was a positive correlation between H angle and external sphincter thickness at proximal (r = 0.347; p = 0.021), middle (r = 0427; p = 0.000), and distal (r = 0.518; p = 0.000)) levels of the anal canal. CONCLUSıON: 3.0 Tesla MR imaging provides detailed information about the morphometric changes in the anal sphincter muscles in patients with chronic anal fissure.

Smooth muscle function and myosin polymerization

Smooth muscle is able to function over a much broader length range than striated muscle. The ability to maintain contractility after a large length change is thought to be due to an adaptive process involving restructuring of the contractile apparatus to maximize overlap between the contractile filaments. The molecular mechanism for the length-adaptive behavior is largely unknown. In smooth muscle adapted to different lengths we quantified myosin monomers, basal and activation-induced myosin light chain (MLC) phosphorylation, shortening-velocity, power-output and active force. The muscle was able to generate a constant maximal force over a 2-fold length range when it was allowed to go through isometric contraction/relaxation cycles after each length change (length adaptation). In the relaxed state myosin monomer concentration and basal MLC phosphorylation decreased linearly, while in the activated state activation-induced MLC phosphorylation and shortening-velocity/power-output increased linearly with muscle length. The results suggest that recruitment of myosin monomers and oligomers into the actin filament lattice (where they form force-generating filaments) occurs during muscle adaptation to longer length with the opposite occurring during adaptation to shorter length.

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.

Accumulating evidence for increased velocity of airway smooth muscle shortening in asthmatic airway hyperresponsiveness

It remains unclear whether airway smooth muscle (ASM) mechanics is altered in asthma. While efforts have originally focussed on contractile force, some evidence points to an increased velocity of shortening. A greater rate of airway renarrowing after a deep inspiration has been reported in asthmatics compared to controls, which could result from a shortening velocity increase. In addition, we have recently shown in rats that increased shortening velocity correlates with increased muscle shortening, without increasing muscle force. Nonetheless, establishing whether or not asthmatic ASM shortens faster than that of normal subjects remains problematic. Endobronchial biopsies provide excellent tissue samples because the patients are well characterized, but the size of the samples allows only cell level experiments. Whole human lungs from transplant programs suffer primarily from poor patient characterization, leading to high variability. ASM from several animal models of asthma has shown increased shortening velocity, but it is unclear whether this is representative of human asthma. Several candidates have been suggested as responsible for increased shortening velocity in asthma, such as alterations in contractile protein expression or changes in the contractile apparatus structure. There is no doubt that more remains to be learned about the role of shortening velocity in asthma.

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.

Influence of dispersion in myosin filament orientation and anisotropic filament contractions in smooth muscle

A new constitutive model for the biomechanical behaviour of smooth muscle tissue is proposed. The active muscle contraction is accomplished by the relative sliding between actin and myosin filaments, comprising contractile units in the smooth muscle cells. The orientation of the myosin filaments, and thereby the contractile units, are taken to exhibit a statistical dispersion around a preferred direction. The number of activated cross-bridges between the actin and myosin filaments governs the contractile force generated by the muscle and also the contraction speed. A strain-energy function is used to describe the mechanical behaviour of the smooth muscle tissue. Besides the active contractile apparatus, the mechanical model also incorporates a passive elastic part. The constitutive model was compared to histological and isometric tensile test results for smooth muscle tissue from swine carotid artery. In order to be able to predict the active stress at different muscle lengths, a filament dispersion significantly larger than the one observed experimentally was required. Furthermore, a comparison of the predicted active stress for a case of uniaxially oriented myosin filaments and a case of filaments with a dispersion based on the experimental histological data shows that the difference in generated stress is noticeable but limited. Thus, the results suggest that myosin filament dispersion alone cannot explain the increase in active muscle stress with increasing muscle stretch.

Adaptation of the length-active tension relationship in rabbit detrusor

Studies have shown that the length-tension (L-T) relationships in airway and vascular smooth muscles are dynamic and can adapt to length changes over a period of time. Our prior studies have shown that the passive L-T relationship in rabbit detrusor smooth muscle (DSM) is also dynamic and that DSM exhibits adjustable passive stiffness (APS) characterized by a passive L-T curve that can shift along the length axis as a function of strain history and activation history. The present study demonstrates that the active L-T curve for DSM is also dynamic and that the peak active tension produced at a particular muscle length is a function of both strain and activation history. More specifically, this study reveals that the active L-T relationship, or curve, does not have a unique peak tension value with a single ascending and descending limb, but instead reveals that multiple ascending and descending limbs can be exhibited in the same DSM strip. This study also demonstrates that for DSM strips not stretched far enough to reveal a descending limb, the peak active tension produced by a maximal KCl-induced contraction at a short, passively slack muscle length of 3 mm was reduced by 58.6 +/- 4.1% (n = 15) following stretches to and contractions at threefold the original muscle length, 9 mm. Moreover, five subsequent contractions at the short muscle length displayed increasingly greater tension; active tension produced by the sixth contraction was 91.5 +/- 9.1% of that produced by the prestretch contraction at that length. Together, these findings indicate for the first time that DSM exhibits length adaptation, similar to vascular and airway smooth muscles. In addition, our findings demonstrate that preconditioning, APS and adaptation of the active L-T curve can each impact the maximum total tension observed at a particular DSM length.

Airway mechanics and methods used to visualize smooth muscle dynamics in vitro

Contraction of airway smooth muscle (ASM) is regulated by the physiological, structural and mechanical environment in the lung. We review two in vitro techniques, lung slices and airway segment preparations, that enable in situ ASM contraction and airway narrowing to be visualized. Lung slices and airway segment approaches bridge a gap between cell culture and isolated ASM, and whole animal studies. Imaging techniques enable key upstream events involved in airway narrowing, such as ASM cell signalling and structural and mechanical events impinging on ASM, to be investigated.

Biophysical basis for airway hyperresponsiveness

Airway hyperresponsiveness is the excessive narrowing of the airway lumen caused by stimuli that would cause little or no narrowing in the normal individual. It is one of the cardinal features of asthma, but its mechanisms remain unexplained. In asthma, the key end-effector of acute airway narrowing is contraction of the airway smooth muscle cell that is driven by myosin motors exerting their mechanical effects within an integrated cytoskeletal scaffolding. In just the past few years, however, our understanding of the rules that govern muscle biophysics has dramatically changed, as has their classical relationship to airway mechanics. It has become well established, for example, that muscle length is equilibrated dynamically rather than statically, and that in a dynamic setting nonclassical features of muscle biophysics come to the forefront, including unanticipated interactions between the muscle and its time-varying load, as well as the ability of the muscle cell to adapt (remodel) its internal microstructure rapidly in response to its ever-changing mechanical environment. Here, we consider some of these emerging concepts and, in particular, focus on structural remodeling of the airway smooth muscle cell as it relates to excessive airway narrowing in asthma.

Mechanism of partial adaptation in airway smooth muscle after a step change in length

The phenomenon of length adaptation in airway smooth muscle (ASM) is well documented; however, the underlying mechanism is less clear. Evidence to date suggests that the adaptation involves reassembly of contractile filaments, leading to reconfiguration of the actin filament lattice and polymerization or depolymerization of the myosin filaments within the lattice. The time courses for these events are unknown. To gain insights into the adaptation process, we examined ASM mechanical properties and ultrastructural changes during adaptation. Step changes in length were applied to isolated bundles of ASM cells; changes in force, shortening velocity, and myosin filament mass were then quantified. A greater decrease in force was found following an acute decrease in length, compared with that of an acute increase in length. A decrease in myosin filament mass was also found with an acute decrease in length. The shortening velocity measured immediately after the length change was the same as that measured after the muscle had fully adapted to the new length. These observations can be explained by a model in which partial adaptation of the muscle leads to an intermediate state in which reconfiguration of the myofilament lattice occurred rapidly, followed by a relatively slow process of polymerization of myosin filaments within the lattice. The partially adapted intermediate state is perhaps more physiologically relevant than the fully adapted state seen under static conditions, and it simulates a more realistic behavior for ASM in vivo.

Ultrastructural basis of airway smooth muscle contractionThis article is one of a selection of papers published in the Special Issue on Recent Advances in Asthma Research

The sliding filament theory of contraction that was developed for striated muscle is generally believed to be also applicable to smooth muscle. However, the well-organized myofilament lattice (i.e., the sarcomeric structure) found in striated muscle has never been clearly delineated in smooth muscle. There is evidence that the myofilament lattice in some smooth muscles, such as airway smooth muscle, is malleable; it can be reshaped to fit a large range of cell dimensions while the maximal overlap between the contractile filaments is maintained. In this review, some early models of the structurally static contractile apparatus of smooth muscle are described. The focus of the review, however, is on the recent findings supporting a model of structurally dynamic contractile apparatus and cytoskeleton for airway smooth muscle. A list of unanswered questions regarding smooth muscle ultrastructure is also proposed in this review, in the hope that it will provide some guidance for future research.

Adjustable passive length-tension curve in rabbit detrusor smooth muscle

Until the 1990s, the passive and active length-tension (L-T) relationships of smooth muscle were believed to be static, with a single passive force value and a single maximum active force value for each muscle length. However, recent studies have demonstrated that the active L-T relationship in airway smooth muscle is dynamic and adapts to length changes over a period of time. Furthermore, our prior work showed that the passive L-T relationship in rabbit detrusor smooth muscle (DSM) is also dynamic and that in addition to viscoelastic behavior, DSM displays strain-softening behavior characterized by a loss of passive stiffness at shorter lengths following a stretch to a new longer length. This loss of passive stiffness appears to be irreversible when the muscle is not producing active force and during submaximal activation but is reversible on full muscle activation, which indicates that the stiffness component of passive force lost to strain softening is adjustable in DSM. The present study demonstrates that the passive L-T curve for DSM is not static and can shift along the length axis as a function of strain history and activation history. This study also demonstrates that adjustable passive stiffness (APS) can modulate total force (35% increase) for a given muscle length, while active force remains relatively unchanged (4% increase). This finding suggests that the structures responsible for APS act in parallel with the contractile apparatus, and the results are used to further justify the configuration of modeling elements within our previously proposed mechanical model for APS.

Smooth muscle stiffness variation due to external longitudinal oscillations

This research focuses on an in vitro investigation of the stiffness changes of contracted airway smooth muscles (ASM) subjected to external longitudinal oscillations. ASM tissues were dissected from excised pig tracheas and stimulated by a chemical stimulus (acetylcholine, 10(-3) M) to produce maximum contractions. The tissues were then systematically excited with external oscillations. Various frequencies, amplitudes and durations were used in the experiments to determine stiffness changes in response to these variations. Force changes were recorded to reflect the muscle stiffness changes. Two stiffness definitions were used to quantify the results, dynamic stiffness to reflect variations during oscillation and static stiffness to reflect the net effect of oscillation. Under isometric contractions, these two stiffnesses were determined before, during and after oscillations. Incorporating an empirical stiffness equation, a two-dimensional finite element model (FEM) was developed to generalize the tissue responses to oscillation. The main outcomes from this work are: the dynamic stiffness has the tendency to decrease as the frequency and/or amplitude of external oscillation increases; the static stiffness has the tendency of decreasing with an increase in the frequency and/or amplitude of excitation until it reaches almost a constant value for frequencies at and above 25 Hz. The difference in the behavior of the dynamic and static stiffness changes may be attributed to the effect of elasticity and mass inertia that are involved in the dynamic motion. The findings of this research are in agreement with the hypothesis that oscillations exert a direct action on the contractile processes by causing an increased rate of actin-myosin detachments.

Smooth muscle length adaptation and actin filament length: a network model of the cytoskeletal dysregulation

Length adaptation of the airway smooth muscle cell is attributable to cytoskeletal remodeling. It has been proposed that dysregulated actin filaments may become longer in asthma, and that such elongation would prevent a parallel-to-series transition of contractile units, thus precluding the well-known beneficial effects of deep inspirations and tidal breathing. To test the potential effect that actin filament elongation could have in overall muscle mechanics, we present an extremely simple model. The cytoskeleton is represented as a 2-D network of links (contractile filaments) connecting nodes (adhesion plaques). Such a network evolves in discrete time steps by forming and dissolving links in a stochastic fashion. Links are formed by idealized contractile units whose properties are either those from normal or elongated actin filaments. Oscillations were then imposed on the network to evaluate both the effects of breathing and length adaptation. In response to length oscillation, a network with longer actin filaments showed smaller decreases of force, smaller increases in compliance, and higher shortening velocities. Taken together, these changes correspond to a network that is refractory to the effects of breathing and therefore approximates an asthmatic scenario. Thus, an extremely simple model seems to capture some relatively complex mechanics of airway smooth muscle, supporting the idea that dysregulation of actin filament length may contribute to excessive airway narrowing.

Models of contractile units and their assembly in smooth muscle

It is believed that the contractile filaments in smooth muscle are organized into arrays of contractile units (similar to the sarcomeric structure in striated muscle), and that such an organization is crucial for transforming the mechanical activities of actomyosin interaction into cell shortening and force generation. Details of the filament organization, however, are still poorly understood. Several models of contractile filament architecture are discussed here. To account for the linear relationship observed between the force generated by a smooth muscle and the muscle length at the plateau of an isotonic contraction, a model of contractile unit is proposed. The model consists of 2 dense bodies with actin (thin) filaments attached, and a myosin (thick) filament lying between the parallel thin filaments. In addition, the thick filament is assumed to span the whole contractile unit length, from dense body to dense body, so that when the contractile unit shortens, the amount of overlap between the thick and thin filaments (i.e., the distance between the dense bodies) decreases in exact proportion to the amount of shortening. Assembly of the contractile units into functional contractile apparatus is assumed to involve a group of cells that form a mechanical syncytium. The contractile apparatus is assumed malleable in that the number of contractile units in series and in parallel can be altered to accommodate strains on the muscle and to maintain the muscle's optimal mechanical function.

Myosin filament assembly in an ever-changing myofilament lattice of smooth muscle

A major development in smooth muscle research in recent years is the recognition that the myofilament lattice of the muscle is malleable. The malleability appears to stem from plastic rearrangement of contractile and cytoskeletal filaments in response to stress and strain exerted on the muscle cell, and it allows the muscle to adapt to a wide range of cell lengths and maintain optimal contractility. Although much is still poorly understood, we have begun to comprehend some of the basic mechanisms underlying the assembly and disassembly of contractile and cytoskeletal filaments in smooth muscle during the process of adaptation to large changes in cell geometry. One factor that likely facilitates the plastic length adaptation is the ability of myosin filaments to form and dissolve at the right place and the right time within the myofilament lattice. It is proposed herein that formation of myosin filaments in vivo is aided by the various filament-stabilizing proteins, such as caldesmon, and that the thick filament length is determined by the dimension of the actin filament lattice. It is still an open question as to how the dimension of the dynamic filament lattice is regulated. In light of the new perspective of malleable myofilament lattice in smooth muscle, the roles of many smooth muscle proteins could be assigned or reassigned in the context of plastic reorganization of the contractile apparatus and cytoskeleton.

Length adaptation of airway smooth muscle: a stochastic model of cytoskeletal dynamics

To account for cytoskeleton remodeling as well as smooth muscle length adaptation, here we represent the cytoskeleton as a two-dimensional network of links (contractile filaments or stress fibers) that connect nodes (dense plaques or focal adhesions). The network evolves in continuous turnover with probabilities of link formation and dissolution. The probability of link formation increases with the available fraction of contractile units, increases with the degree of network activation, and decreases with increasing distance between nodes, d, as 1/d(s), where s controls the distribution of link lengths. The probability of link dissolution decays with time to mimic progressive cytoskeleton stabilization. We computed network force (F) as the vector summation of link forces exerted at all nodes, unloaded shortening velocity (V) as being proportional to the average link length, and network compliance (C) as the change in network length per change in elastic force. Imposed deformation caused F to decrease transiently and then recover dynamically; recovery ability decreased with increasing time after activation, mimicking observed biological behavior. Isometric contractions showed small sensitivity of F to network length, thus maintaining high force over a wide range of lengths; V and C increased with increasing length. In these behaviors, link length regulation, as described by the parameter s, was found to be crucial. Concerning length adaptation, all phenomena reported thus far in the literature were captured by this extremely simple network model.

'Sarcomeres' of smooth muscle: functional characteristics and ultrastructural evidence

Smooth muscle cells line the walls of hollow organs and control the organ dimension and mechanical function by generating force and changing length. Although significant progress has been made in our understanding of the molecular mechanism of actomyosin interaction that produces sliding of actin (thin) and myosin (thick) filaments in smooth muscle, the sarcomeric structure akin to that in striated muscle, which allows the sliding of contractile filaments to be translated into cell shortening has yet to be elucidated. Here we show evidence from porcine airway smooth muscle that supports a model of malleable sarcomeric structure composed of contractile units assembled in series and in parallel. The geometric organization of the basic building blocks (contractile units) within the assembly and the dimension of individual contractile units can be altered when the muscle cells adapt to different lengths. These structural alterations can account for the different length-force relationships of the muscle obtained at different adapted cell lengths. The structural malleability necessary for length adaptation precludes formation of a permanent filament lattice and explains the lack of aligned filament arrays in registers, which also explains why smooth muscle is 'smooth'.

Cardiotrophin-1 alters airway smooth muscle structure and mechanical properties in airway explants

Induction of hypertrophy and inhibition of apoptosis may be important mechanisms contributing to increased airway smooth muscle (ASM) mass in asthma. Data from our laboratory indicate that cardiotrophin-1 (CT-1) induces hypertrophy and inhibits apoptosis in isolated human ASM cells. To determine whether these novel effects of CT-1 also occur in the airway tissue milieu and to determine whether structural changes are accompanied by functional changes, matched pairs of guinea pig airway explants were treated with or without CT-1 for 7 days, and structural features as well as isometric and isotonic contractile and relaxant mechanical properties were measured. CT-1 (0.2-5 ng/ml) increased both myocyte mass and extracellular matrix in a concentration-dependent fashion. CT-1 (10 ng/ml)-treated tissues exhibited a significant increase in passive tension at all lengths on day 7; at optimal length, passive tension generated by CT-1-treated tissues was 1.72 +/- 0.12 vs. 1.0 +/- 0.1 g for control. Maximal isometric stress was decreased in the CT-1-treated group on day 7 (0.39 +/- 0.10 kg/cm(2)) vs. control (0.77 +/- 0.15 kg/cm(2), P < 0.05). Isoproterenol-induced relaxant potency was reduced in CT-1-treated tissues, log EC(50) being -7.28 +/- 0.34 vs. -8.12 +/- 0.25 M in control, P < 0.05. These data indicate that CT-1 alters ASM structural and mechanical properties in the tissue environment and suggest that structural changes found in the airway wall in asthma are not necessarily associated with increased responsiveness.