Myosin Crossbridge, Contractile Unit, and the Mechanism of Contraction in Airway Smooth Muscle: A Mechanical Engineer's Perspective

Abstract

Muscle contraction is caused by the action of myosin motors within the structural confines of contractile unit arrays. When the force generated by cyclic interactions between myosin crossbridges and actin filaments is greater than the average load shared by the crossbridges, sliding of the actin filaments occurs and the muscle shortens. The shortening velocity as a function of muscle load can be described mathematically by a hyperbola; this characteristic force-velocity relationship stems from stochastic interactions between the crossbridges and the actin filaments. Beyond the actomyosin interaction, there is not yet a unified theory explaining smooth muscle contraction, mainly because the structure of the contractile unit in smooth muscle (akin to the sarcomere in striated muscle) is still undefined. In this review, functional and structural data from airway smooth muscle are analyzed in an engineering approach of quantification and correlation to support a model of the contractile unit with characteristics revealed by mathematical analyses and behavior matched by experimental observation.

Keywords: force-velocity relationship; length-force relationship; muscle contraction; myosin filament polymerization.

Fig. 1

A schematic depiction of a smooth muscle contractile unit consisting of a side-polar myosin filament with crossbridges on each side of the filament possessing opposite polarity, sandwiched by two actin filaments attached to dense bodies on one end. The double arrows indicate the direction of actin filament sliding relative to the myosin filament during active muscle shortening.

Fig. 2

A two-state model for the cycle of the actomyosin interaction. D, detached state; A, attached state. f_APP and g_APP are the apparent attachment and detachment rates.

Fig. 3

A model of the contractile filament lattice illustrating the relationship between force generated by a contractile unit and the length of the overlap between myosin and actin filaments (L_overlap). An assumption associated with the model is that the force generated by a contractile unit is directly proportional to the overlap length. A: A change in L_overlap due to shortening of a contractile unit from L_overlap1 to L_overlap2. B: The model predicts a linear relationship between force and L_overlap.

Fig. 4

Length–force relationship of airway smooth muscle (solid line with open circles) compared with that of skeletal muscle (gray lines). Lengths are expressed as fractions of the muscle's in situ length dessignated as a reference length (L_ref); forces are expressed as fractions of the muscle's maximal isometric force (F_max). Modified from Seow (2016, Introduction to Smooth Muscle Mechanics: Length-Force Relationship and Length Adaptation, Friesen Press, Victoria, BC, pp. 109–131) with permission.

Fig. 5

(a) Mathematical simulation of the time course of an isotonic contraction in smooth muscle. Shortening starts at time zero from a reference length (L_ref) toward a final length (L_i) with a time constant (−mK/[K + F_i]) defined by Eq. (19). (b) Experimental data from an isotonic quick-release (circles) fitted with an exponential equation (Eq. (19)) after taking into account the viscoelastic recoil associated with the isotonic quick-release (solid line). Modified from Ref. [25] with permission.

Fig. 6

(a) Length distribution of airway smooth muscle myosin filaments. The dashed line is a simple exponential fit to the data (open circles). Modified from Ref. [26] with permission. (b) Myosin filaments within an actin-filament lattice. The single continuous myosin filament shown in Fig. 3(a) is reproduced here as segments of filaments of different lengths lined up end-to-end to accommodate the observation of filament length distribution shown in panel (a).