An electrokinematic theory of muscle contraction

Muscle active force-length curve explained by an electrophysical model of interfilament spacing

The active isometric force-length relation (FLR) of striated muscle sarcomeres is central to understanding and modeling muscle function. The mechanistic basis of the descending arm of the FLR is well explained by the decreasing thin:thick filament overlap that occurs at long sarcomere lengths. The mechanistic basis of the ascending arm of the FLR (the decrease in force that occurs at short sarcomere lengths), alternatively, has never been well explained. Because muscle is a constant-volume system, interfilament lattice distances must increase as sarcomere length shortens. This increase would decrease thin and thick-filament electrostatic interactions independently of thin:thick filament overlap. To examine this effect, we present here a fundamental, physics-based model of the sarcomere that includes filament molecular properties, calcium binding, sarcomere geometry including both thin:thick filament overlap and interfilament radial distance, and electrostatics. The model gives extremely good fits to existing FLR data from a large number of different muscles across their entire range of measured activity levels, with the optimized parameter values in all cases lying within anatomically and physically reasonable ranges. A local first-order sensitivity analysis (varying individual parameters while holding the values of all others constant) shows that model output is most sensitive to a subset of model parameters, most of which are related to sarcomere geometry, with model output being most sensitive to interfilament radial distance. This conclusion is supported by re-running the fits with only this parameter subset being allowed to vary, which increases fit errors only moderately. These results show that the model well reproduces existing experimental data, and indicate that changes in interfilament spacing play as central a role as changes in filament overlap in determining the FLR, particularly on its ascending arm.

An electrostatic mechanism of muscular contraction

The electrostatic mechanism proposed in the theory of muscular contraction propounded by Iwazumi is the force produced between an electric dipole and induced dipoles on a high dielectric rod. This force is similar to one between a short bar magnet and an iron rod. The force is always attractive and unidirectional and the rod orients itself to the direction pointing to the centre of the magnet. In muscle, the active cross-projection of myosin is analogous to the bar magnet, but an electric field is created by the dipole properties of myosin which are amplified during activation by the action of calcium ions and adenosine triphosphate. The filaments of actin are analogous to the iron rod. Detailed mathematical application of this principle to the array of filaments found in muscle, with incorporation of the troponin/tropomyosin complex, yields a complete theory of muscular contraction which provides explanations for many as yet unexplained phenomena, and provides a set of specific predictions for test.

Stretch of contracting muscle fibres: evidence for regularly spaced active sites along the filaments and enhanced mechanical performance

Single frog skeletal muscle fibres were stretched during fused tetanic contractions. The force increase during stretch exhibited a breakpoint at a mean critical length change of 16.6 nm per half sarcomere that was independent of stretch velocity and sarcomere length. The early decaying extra force after stretch (component 2) was removed by a small quick release, leaving a longer lasting component (component 3). The amplitude of release required increased with time up to the angle in the force record during stretch, was constant for the remainder of the stretch and decreased with time after the end of stretch; it was consistently less than the critical amplitude of stretch (above). Component 3 occurred at sarcomere lengths above 2.3 microns and was amplitude dependent. The final force after stretch was usually higher than the isometric force at the starting length of the stretch. Non-uniformity as a cause of this component was examined by (a) laser diffraction studies which showed sarcomere stretch at all locations and (b) 0.6-0.7 mm long segments along the entire fibre which all elongated during stretch. After stretch the sarcomeres and segments were significantly more stable than during control isometric tetani. Segments which were clamped by a servo system demonstrated component 3. Shortening during contraction followed by stretch back to the starting length led to nearly as much force enhancement as stretch alone, suggesting that component 3 is not due to a passive elastic element recruited during activation. An increase in temperature decreased components 1 (velocity dependent force during stretch) and 2 but increased component 3. The critical length features of component 2 suggest a cross-bridge mechanism. However, the sarcomere length dependence of all components differs from that of isometric force and from predictions based on filament overlap.

The myoplasmic fixed charges of the barnacle muscle fiber and the free Ca2+ concentration

An experimental model was recently developed to measure the myoplasm density of fixed charges (Caillé J.P. (1979) Biochim. Biophys. Acta 585, 300-313). The effect of ATP, Mg2+ and Ca2+ suggests that the myoplasmic thermodynamically effective charge density (phi X) decreases during muscular contraction. In order to determine if this reduction was due to either ATP, Mg2+ or Ca2+, the phi X dependence on those substances was studied. The results indicated that the addition of MgCl2 (2 mM) reduced phi X by 10 to 30% depending on the water content of the myoplasm. A reduction of phi X was also observed with the addition of (10(-4) M) Ca2+, but the presence of ATP was necessary for this reduction to occur. Finally when EGTA was added to the external solution in order to control the level of free Ca2+, an important reduction of phi X (40%) was observed for a pCa equal to 5.7 (water content 76.1 +/- 0.3 ml/100 g). These results allowed a correlation between the reduction of the myoplasmic fixed charges and the turning on of the contractile machinery.

The mechanism for the promotion of tenderness in meat during the post-mortem process: a review

The post-mortem changes in the chemical composition and structure of striated muscle have been reviewed on the basis of various concepts that emerged from the studies of different investigators to explain the course of tenderization of meat during aging. These concepts include the changes in the sarcoplasmic proteins, myofibrillar proteins (such as complete dissociation of actomyosin, partial dissociation of actomyosin, cleavage of disulfide linkages, depolymerization of F-actin filaments, cleavage of myosin filaments, disorganization of Z-bands and the troponin-tropomyosin complex), sarcolemma, connective tissue elements (collagen fibrils, ground substance), and the protein-ion relationship of the muscle cells (more strictly, syncytia). The experimental evidence for and against each of the views is discussed critically in the light of certain fundamentals of biophysical chemistry and biochemistry. Finally, an alternative hypothesis has been presented based on the differential effect of the post-mortem formation of lactic acid (H+ ion concentration) on the intra- and extracellular components of muscle and the possible role of lysosomal cathepsins. Consequently, a series of biophysical, biochemical, and ultrastructural changes seem to account for the mechanism by which meat becomes tender during the aging process.

Distributed representations for actin-myosin interaction in the oscillatory contraction of muscle

In this paper we suggest and test a specific hypothesis relating the attachment-detachment cycle of cross bridges between actin (I) and myosin (A) filaments to the measured length-tension dynamics of active insect fibrillar flight muscle. It is first shown that if local A-filament strain perturbs the rate constants in the cross-bridge cycle appropriately, then exponentially delayed tension changes can follow imposed changes of length; the latter phenomenon is sufficient for the work-producing property of fibrillar muscle, as measured with small-signal forcing of length and at low Ca(2+) concentration, and possibly for related effects described recently in frog striated muscle. It is not clear a priori that the above explanation of work production by fibrillar muscle will remain tenable when the viscoelastic complexity of the heterogeneous sarcomere is taken into account. However, White's (1967) recent mechanical and electron microscope study of the passive dynamics of glycerinated fibrillar muscle has produced a model of the distributed viscoeleastic structure sufficiently explicit that alternative schemes for cross-bridge force generation in this muscle can now be tested more critically than previously. Therefore, we derive and solve third-order partial-differential equations which relate local interfilament shear forces associated with the perturbed cross-bridge cycles to the over-all length-tension dynamics of an idealized sarcomere. We then show (a) that the starting hypothesis can account approximately for the small-signal dynamics of glycerinated muscle in the work-producing state over two decades of frequency and (b) that the rate constants for cross-bridge formation and breakage, restricted solely by fitting of the model to the mechanical data, determine a cycling rate of cross bridges in the model compatible with recent measurements of ATP hydrolysis rate vs. stretch in this muscle. Finally, the formulation is extended tentatively to the large-signal nonlinear case, and shown to compare favorably with previous suggestions for the origin of the work-producing dynamics of fibrillar flight muscle.