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.     

Velocity transients and viscoelastic resistance to active shortening in cat papillary muscle.

When isotonic force steps were applied to activated papillary muscles, the velocity was almost never constant. Early rapid shortening associated with the step persisted for 2-7 ms after the step ends. The early rapid shortening is attributed to lightly damped series elastic recoil and velocity transients of the contractile elements. In most steps, the subsequent velocity declines progressively with shortening, and most of the decline in velocity can be accounted for by compression of a viscoelastic element in parallel with the contractile elements. To demonstrate this, the time course of isotonic velocity was compared with a model in which the force-velocity characteristics of the contractile element were assumed to be constant, and the decline in velocity was due to increasing compression of the viscoelastic element. This model predicted the observed results except that the predicted velocities rose progressively above the measured values for steps to light loads applied late in the twitch, and fell below the velocity trace for heavy loads applied early in the twitch. These deviations would occur if rapid shortening caused deactivation late in the twitch, and if activation were rising early in the twitch. A conditioning step applied to the muscle during the rise of force depressed both isometric force and maximum velocity measured at the peak of force; isometric force was more depressed with later conditioning steps than with earlier steps, while maximum velocity was depressed by about the same extent with both early and late steps. This difference between the effects on isometric force and maximum velocity are explained by a combination of deactivation and viscoelastic load.     

The biophysics and biochemistry of smooth muscle contraction.

In this review the biophysics and biochemistry of smooth muscle contraction are dealt with. We describe a new model for the study of bronchial smooth muscle, which facilitates study of cellular contractile mechanisms. A new concept emerging is that study of steady-state mechanical parameters such as maximal isometric force (Po) velocity is inadequate because two types of crossbridges (normally cycling (NBR) and latch) seem to be sequentially active during smooth muscle contraction. Thus quick-release techniques are required to characterize the force-velocity properties of the two types of bridges. Pathophysiological processes that affect the muscle's shortening ability seem to affect the early NBRs only. With respect to maximal shortening capacity of the smooth muscle, the role of loading is very important. The differences between isotonic, elastic, and viscous loading are considerable. Ultimately, the time course and magnitude of loading should exactly resemble that operative in vivo. Once again, it is the characteristic of loading in the early phase of contraction that is crucial, as most of the shortening in smooth muscle occurs early in the contraction. While the maximum force developed by smooth muscle per unit cross-sectional area is the same as for striated muscle, the velocity is 50 times less. The properties of the series and parallel elastic elements of smooth muscle are described. The latter, when in compression mode, acts as an internal resistance to shortening and probably limits it. Isotonic relaxation has therefore not been studied in smooth muscle. We have developed a shortening parameter that is independent of the load on the muscle and of the initial length of the muscle's contractile element. We report the novel observation that isotonically relaxing smooth muscle reactivates itself, resulting in terminal slowing of the relaxation process. With respect to the biochemistry of smooth muscle contraction, contractile (actin isoforms, myosin heavy and light chains and their isoforms), regulatory (calmodulin-4 Ca2+, myosin light chain kinase, myosin light chain and its phosphorylation, tropomyosin, caldesmon, and calponin), and cytoskeletal (chiefly desmin and vimentin) proteins are discussed. While the kinase activates the contractile system, caldesmon and calponin modulate the activity downward. The cytoskeletal proteins desmin, vimentin, and alpha-actinin could constitute the muscle cell's internal resistor.     

A dynamic model of smooth muscle contraction

A dynamic model of smooth muscle contraction is presented and is compared with the mechanical properties of vascular smooth muscle in the rat portal vein. The model is based on the sliding filament theory and the assumption that force is produced by cross-bridges extending from the myosin to the actin filaments. Thus, the fundamental aspects of the model are also potentially applicable to skeletal muscle. The main concept of the model is that the transfer of energy via the cross-bridges can be described as a 'friction clutch' mechanism. It is shown that a mathematical formulation of this concept gives rise to a model that agrees well with experimental observations on smooth muscle mechanics under isotonic as well as isometric conditions. It is noted that the model, without any ad hoc assumptions, displays a nonhyperbolic force-velocity relationship in its high-force portion and that it is able to maintain isometric force in conditions of reduced maximum contraction velocity. Both these findings are consistent with new experimental observations on smooth muscle mechanics cannot be accounted for by the classical Hill model.     

Analytical solution to isometric mechanogram of hill’s model of striated muscle

The two-element muscle model considered consists of a contractile element defined by a hyperbolic force-velocity relation connected in series with an “exponential spring”. Differential equations for the isometrically developed force during a tetanic contraction and the corresponding contractile element shortening velocity are derived and their stability is investigated. Analytical solutions to both equations are obtained. Two numerical examples are given, the second chosen to illustrate pressure-induced hypertrophy of a cardiac muscle.     

Some proposals in cardiac muscle mechanics and energetics

Based on A. V. Hill's three-component model, mechanical properties of the contractile element (CE), such as velocity and tension, were determined as muscle shortening and loads in quick-release or afterloaded isotonic contraction. The method is applicable for studying cardiac mechanics, to obtain force-velocity data of the same CE length at varous afterloads. Analysis of the energetics of cardiac muscle was based on simulation studies of cardiac mechanics (Wong 1971, 1972). By proper derivation, the conventional contractile element work (CEW) was found to be a minor energy determinant. The tension-time integral and tension-independent heat (Ricchiuti and Gibbs, 1965) represent energy utilization for activation and maintenance of tension, the primary energy determinant.     

Slowing of velocity during isotonic shortening in single isolated smooth muscle cells. Evidence for an internal load

In single smooth muscle cells, shortening velocity slows continuously during the course of an isotonic (fixed force) contraction (Warshaw, D.M. 1987. J. Gen. Physiol. 89:771-789). To distinguish among several possible explanations for this slowing, single smooth muscle cells were isolated from the gastric muscularis of the toad (Bufo marinus) and attached to an ultrasensitive force transducer and a length displacement device. Cells were stimulated electrically and produced maximum stress of 144 mN/mm2. Cell force was then reduced to and maintained at preset fractions of maximum, and cell shortening was allowed to occur. Cell stiffness, a measure of relative numbers of attached crossbridges, was measured during isotonic shortening by imposing 50-Hz sinusoidal force oscillations. Continuous slowing of shortening velocity was observed during isotonic shortening at all force levels. This slowing was not related to the time after the onset of stimulation or due to reduced isometric force generating capacity. Stiffness did not change significantly over the course of an isotonic shortening response, suggesting that the observed slowing was not the result of reduced numbers of cycling crossbridges. Furthermore, isotonic shortening velocity was better described as a function of the extent of shortening than as a function of the time after the onset of the release. Therefore, we propose that slowing during isotonic shortening in single isolated smooth muscle cells is the result of an internal load that opposes shortening and increases as cell length decreases.     

Interaction between series compliance and sarcomere kinetics determines internal sarcomere shortening during fixed-end contraction

The interaction between contractile force and in-series compliance was investigated for the intact skeletal muscle-tendon unit (MTU) of Rana pipiens semitendinosus muscles during fixed-end contraction. It was hypothesized that internal sarcomere shortening is a function of the length-force characteristics of contractile and series elastic components. The MTUs (n=18) were dissected, and, while submerged in Ringer's solution, muscles were activated at nine muscle lengths (-2 to +6 mm relative to optimal length in 1 mm intervals), while measuring muscle force and sarcomere length (SL) by laser diffraction. The MTU was clamped either at the bone (n=6), or at the proximal and distal ends of the aponeuroses (n=6). Muscle fibers were also trimmed along with aponeuroses down to 5-20 fibers and identical measurements were performed (n=6). The magnitude of shortening decreased as MTU length increased. The magnitude of shortening ranged from -0.08 to 0.3 microm, and there was no significant difference between delta SL as a function of clamp location. When aponeuroses were trimmed, sarcomere shortening was not observed at L(0) and longer. These results suggest that the aponeurosis is the major contributor to in-series compliance. Results also support our hypothesis but there also appear to be other factors affecting internal sarcomere shortening. The functional consequence of internal sarcomere shortening as a function of sarcomere length was to skew the muscle length-tension relationship to longer sarcomere lengths.     

Mechanical output of the cat soleus during treadmill locomotion: in vivo vs in situ characteristics

To study the mechanical output of skeletal muscle, four adult cats were trained to run on a treadmill and then implanted under sterile conditions and anesthesia with a force transducer on the soleus tendon and EMG electrodes in the muscle belly. After a two-week recovery period, five consecutive step cycles were filmed at treadmill speeds of 0.8, 1.3 and 2.2 m s-1. Locomotion data in vivo included individual muscle force, length and velocity changes and EMG during each step cycle. Data for an average step cycle at each speed were compared to the force-velocity properties obtained on the same muscle under maximal nerve stimulation and isotonic loading conditions in situ. Results indicate that the force and power generated at a given velocity of shortening during late stance in vivo were greater at the higher speeds of locomotion than the force and power generated at the same shortening velocity in situ. Strain energy stored in the muscle-tendon unit during the yield phase in early stance is felt to be a major contributor to the muscle's enhanced mechanical output during muscle shortening in late stance.     

Pharmacological modulation of the mechanical response of airway smooth muscle to length oscillation

Shen, X., M. F. Wu, R. S. Tepper, and S. J. Gunst. Pharmacological modulation of the mechanicalresponse of airway smooth muscle to length oscillation.J. Appl. Physiol. 83(3): 739-745, 1997.Stretch and retraction of the airways caused by changes in lungvolume may play an important role in regulating airway reactivity. Westudied the effects of different pharmacological stimuli on airwaysmooth muscle to determine whether the muscle behavior during lengthoscillation can be modulated pharmacologically and to evaluate the roleof different activation mechanisms in determining its behavior duringthe oscillation. Active force decreased below the static isometricforce during the shortening phase of length oscillation, resulting inan overall depression of force during the length oscillation cycle.This pattern of response was unaffected by the contractile stimulus orlevel of activation, suggesting that it was caused by a mechanism that is independent of the level of activation of cross bridges. The normalized area of the length-force hysteresis loop (hysteresivity) differed depending on the stimulus used for contraction. Effects ofdifferent stimuli on hysteresivity were not correlated with theireffects on isotonic shortening velocity or isometric force, suggestingthat the pharmacological modulation of the behavior of airway smoothmuscle during length oscillation at these amplitudes cannot beaccounted for by the effects on the cross-bridge cycling rate.

     

A calcium-driven mechanochemical model for prediction of force generation in smooth muscle

A new model for the mechanochemical response of smooth muscle is presented. The focus is on the res- ponse of the actin–myosin complex and on the related generation of force (or stress). The chemical (kinetic) model describes the cross-bridge interactions with the thin filament in which the calcium-dependent myosin phosphorylation is the only regulatory mechanism. The new mechanical model is based on Hill’s three-component model and it includes one internal state variable that describes the contraction/relaxation of the contractile units. It is characterized by a strain-energy function and an evolution law incorporating only a few material parameters with clear physical meaning. The proposed model satisfies the second law of thermodynamics. The results of the combined coupled model are broadly consistent with isometric and isotonic experiments on smooth muscle tissue. The simulations suggest that the matrix in which the actin–myosin complex is embedded does have a viscous property. It is straightforward for implementation into a finite element program in order to solve more complex boundary-value problems such as the control of short-term changes in lumen diameter of arteries due to mechanochemical signals.     

Smooth muscle molecular mechanics in airway hyperresponsiveness and asthma

Asthma is a respiratory disorder characterized by airway inflammation and hyperresponsiveness associated with reversible airway obstruction. The relative contributions of airway hyperresponsiveness and inflammation are still debated, but ultimately, airway narrowing mediated by airway smooth muscle contraction is the final pathway to asthma. Considerable effort has been devoted towards identifying the factors that lead to the airway smooth muscle hypercontractility observed in asthma, and this will be the focus of this review. Airway remodeling has been observed in severe and fatal asthma. However, it is unclear whether remodeling plays a protective role or worsens airway responsiveness. Smooth muscle plasticity is a mechanism likely implicated in asthma, whereby contractile filament rearrangements lead to maximal force production, independent of muscle length. Increased smooth muscle rate of shortening via altered signaling pathways or altered contractile protein expression has been demonstrated in asthma and in numerous models of airway hyperresponsiveness. Increased rate of shortening is implicated in counteracting the relaxing effect of tidal breathing and deep inspirations, thereby creating a contracted airway smooth muscle steady-state. Further studies are therefore required to understand the numerous mechanisms leading to the airway hyperresponsiveness observed in asthma as well as their multiple interactions.     

Structure-function correlation in airway smooth muscle adapted to different lengths

Airway smooth muscle is able to adapt and maintain a nearly constant maximal force generation over a large length range. This implies that a fixed filament lattice such as that found in striated muscle may not exist in this tissue and that plastic remodeling of its contractile and cytoskeletal filaments may be involved in the process of length adaptation that optimizes contractile filament overlap. Here, we show that isometric force produced by airway smooth muscle is independent of muscle length over a twofold length change; cell cross-sectional area was inversely proportional to cell length, implying that the cell volume was conserved at different lengths; shortening velocity and myosin filament density varied similarly to length change: increased by 69.4% ± 5.7 (SE) and 76.0% ± 9.8, respectively, for a 100% increase in cell length. Muscle power output, ATPase rate, and myosin filament density also have the same dependence on muscle cell length: increased by 35.4% ± 6.7, 34.6% ± 3.4, and 35.6% ± 10.6, respectively, for a 50% increase in cell length. The data can be explained by a model in which additional contractile units containing myosin filaments are formed and placed in series with existing contractile units when the muscle is adapted at a longer length. muscle contraction; myosin filaments; ATPase activity; electron microscopy     

Sensitized airway smooth muscle plasticity and hyperreactivity: a review

To help elucidate the mechanisms underlying asthmatic bronchospasm, the goal of our research has been to determine whether airway smooth muscle (ASM) hyperreactivity was the responsible factor. We reported that in a canine model of asthma, the shortening capacity (DeltaLmax) and velocity (Vo) of in vitro sensitized muscle were significantly increased. This increase was of sufficient magnitude to account for 75% narrowing of the in vivo airway, but maximal isometric force was unchanged. This last feature has been reported by others. Under lightly loaded conditions, ASM completes 75% of its isotonic shortening within the first 2 s. Furthermore, 90% of the increased shortening of ragweed pollen-sensitized ASM (SASM), compared with control (CASM), is complete within the first 2 s. The study of shortening beyond this period will apparently not yield much useful information, and studies of isotonic shortening should be focused on this interval. Although both CASM and SASM showed plasticity and adaptation with respect to isometric force, neither muscle type showed a difference in the force developed in these phases. During isotonic shortening, no evidence of plasticity was seen, but the equilibrated SASM showed increased DeltaLmax and Vo of shortening. Molecular mechanisms of changes in Vo could result from changes in the kinetics of the myosin heavy chain ATPase. Motility assay, however, showed no changes between CASM and SASM in the ability of the purified myosin molecule (SF1) to translocate a marker actin filament. On the other hand, we found that the state of activation of the ATPase by phosphorylation of smooth muscle myosin light chain (molecular mass 20,000 Da) was greater in the SASM. This would account for the increased Vo. Investigating the signalling pathway, we found that whereas [Ca2+]i increased in both isometric and isotonic contraction, there was no significant difference between CASM and SASM. The content and activity of calmodulin were also not different between the 2 muscles. Nevertheless, we did find that content and total activity of smooth muscle myosin light chain kinase (smMLCK) and the abundance of its message were greater; this would explain the increased MLC20 phosphorylation. The binding affinity between Ca2+ and calmodulin and between 4 Ca2+ calmodulin and smMLCK remains to be studied. We conclude that SASM shows increased isotonic shortening capacity and velocity. It also shows increased content and total activity of smMLCK, which is consistent with the increased shortening. Plasticity produced by oscillation is not seen in the shortening muscle, although it is seen with respect to force development. It did not modulate the behaviour of the sensitized muscle.     

A comparison of the mechanical behavior of the cat soleus muscle with a distribution-moment model

A state-variable model for skeletal muscle, termed the "Distribution-Moment Model," is derived from A. F. Huxley's 1957 model of molecular contraction dynamics. The state variables are the muscle stretch and the three lowest-order moments of the bond-distribution function (which represent, respectively, the contractile tissue stiffness, the muscle force, and the elastic energy stored in the contractile tissue). The rate equations of the model are solved under various conditions, and compared to experimental results for the cat soleus muscle subjected to constant stimulation. The model predicts several observed effects, including yielding of the muscle force in constant velocity stretches, different "force-velocity relations" in isotonic and isovelocity experiments, and a decrease of peak force below the isometric level in small-amplitude sinusoidal stretches. Chemical energy and heat rates predicted by the model are also presented.     

Force-velocity constants in smooth muscle: afterloaded isotonic and quick-release methods

In using pharmacologic stimuli, force-velocity (FV) curves are usually obtained by the method of quick release (QR) and redevelopment of shortening at peak tetanic tension; the advantage of the method being that the active state is at maximum. However, the QR may itself reduce the intensity of the active state and result in reduced values of FV constants. We tested this by delineating FV curves in canine tracheal smooth muscle using both conventional afterloaded isotonic contractions (ALI), and redevelopment of shortening after QR methods. For both these studies a supramaximal tetanizing electrical stimulus was used. The analysis of 11 experiments revealed that the latter method resulted in statistically significant reductions of all FV constants except for Po (maximum isometric tetanic tension). The means and standard errors for the sets of constants for the ALI and QR, respectively, are as follows: Vmax (maximum velocity of shortening) = 0.275 lo (optimal muscle length)/s +/- 0.024 (SE), and 0.216 lo/s + 0.023; a (hyperbolic constant with units of force) = 294 g/cm2 +/- 35 and 236 g/cm2 +/- 32; b (hyperbolic constant with units of velocity) = 0.059 lo +/- 0.004 and 0.039 lo/s +/- 0.005; a/Po = 0.214 +/- 0.028 and 0.182 +/- 0.026; and Po = 1.362 kg/cm2 +/- 0.106 and 1.294 kg/cm2 +/- 0.097. These data clearly show that the quick-release method for measuring force-velocity relationships in canine smooth muscle results in significant underestimates of muscle shortening properties.     

Internal viscoelastic loading in cat papillary muscle.

The passive mechanical properties of myocardium were defined by measuring force responses to rapid length ramps applied to unstimulated cat papillary muscles. The immediate force changes following these ramps recovered partially to their initial value, suggesting a series combination of viscous element and spring. Because the stretched muscle can bear force at rest, the viscous element must be in parallel with an additional spring. The instantaneous extension-force curves measured at different lengths were nonlinear, and could be made to superimpose by a simple horizontal shift. This finding suggests that the same spring was being measured at each length, and that this spring was in series with both the viscous element and its parallel spring (Voigt configuration), so that the parallel spring is held nearly rigid by the viscous element during rapid steps. The series spring in the passive muscle could account for most of the series elastic recoil in the active muscle, suggesting that the same spring is in series with both the contractile elements and the viscous element. It is postulated that the viscous element might be coupled to the contractile elements by a compliance, so that the load imposed on the contractile elements by the passive structures is viscoelastic rather than purely viscous. Such a viscoelastic load would give the muscle a length-independent, early diastolic restoring force. The possibility is discussed that the length-independent restoring force would allow some of the energy liberated during active shortening to be stored and released during relaxation.     

Mechanisms of mechanical strain memory in airway smooth muscle

We evaluated the hypothesis that mechanical deformation of airway smooth muscle induces structural remodeling of airway smooth muscle cells, thereby modulating mechanical performance in subsequent contractions. This hypothesis implied that past experience of mechanical deformation was retained (or "memorized") as structural changes in airway smooth muscle cells, which modulated the cell's subsequent contractile responses. We termed this phenomenon mechanical strain memory. Preshortening has been found to induce attenuation of both force and isotonic shortening velocity in cholinergic receptor-activated airway smooth muscle. Rapid stretching of cholinergic receptor-activated airway smooth muscle from an initial length to a final length resulted in post-stretch force and myosin light chain phosphorylation that correlated significantly with initial length. Thus post-stretch muscle strips appeared to retain memory of the initial length prior to rapid stretch (mechanical strain memory). Cytoskeletal recruitment of actin- and integrin-binding proteins and Erk 1/2 MAPK appeared to be important mechanisms of mechanical strain memory. Sinusoidal length oscillation led to force attenuation during oscillation and in subsequent contractions in intact airway smooth muscle, and p38 MAPK appeared to be an important mechanism. In contrast, application of local mechanical strain to cultured airway smooth muscle cells induced local actin polymerization and cytoskeletal stiffening. It is conceivable that deep inspiration-induced bronchoprotection may be a manifestation of mechanical strain memory such that mechanical deformation from past breathing cycles modulated the mechanical performance of airway smooth muscle in subsequent cycles in a continuous and dynamic manner.     

Modeling the oscillation dynamics of activated airway smooth muscle strips

When strips of activated airway smooth muscle are stretched cyclically, they exhibit force-length loops that vary substantially in both position and shape with the amplitude and frequency of the stretch. This behavior has recently been ascribed to a dynamic interaction between the imposed stretch and the number of actin-myosin interactions in the muscle. However, it is well known that the passive rheological properties of smooth muscle have a major influence on its mechanical properties. We therefore hypothesized that these rheological properties play a significant role in the force-length dynamics of activated smooth muscle. To test the plausibility of this hypothesis, we developed a model of the smooth muscle strip consisting of a force generator in series with an elastic component. Realistic steady-state force-length loops are predicted by the model when the force generator obeys a hyperbolic force-velocity relationship, the series elastic component is highly nonlinear, and both elastic stiffness and force generation are adjusted so that peak loop force equals isometric force. We conclude that the dynamic behavior of airway smooth muscle can be ascribed in large part to an interaction between connective tissue rheology and the force-velocity behavior of contractile proteins.     

The Effect of Shortening on the Time-Course of Active State Decay

The active state describes the force developed in a muscle when the contractile elements are neither lengthening nor shortening. Recently it was suggested that perturbations used to measure the active state also alter the time-course of the active state. The present research was undertaken to assess quantitatively the effect of two such perturbations, isotonic shortening and quick release, on the active state in frog sartorius muscle. Methods were developed which allowed the determination of active state points following periods of controlled isotonic shortening or quick release early in the contraction cycle. All experiments were carried out within the plateau region of the length-tension curve. Both isotonic shortening and quick release altered the active state decay. The active state force decreased as the extent of shortening or release was increased. For each 0.1 mm of isotonic shortening there was a 2% decrease in active state force. Quick release produced a larger decrement. From this data we conclude that the time-course of active state can be measured only in relative terms because it is altered by the motion which takes place in the contractile machine while the active state is being measured. This finding helps to resolve paradoxes in the literature relating to the time-course of the active state, calculated and experimentally determined isometric tetanic myograms, and the heat of shortening.