Thermodynamic features of myosin filament suspensions: implications for the modeling of muscle contraction

The stiffness of myosin subfragment-1 changes with the physiological state of muscle

The anisotropy decay of the spin-labelled myosin subfragment-1, takes place with different rates depending on the physiological state of muscle: relaxation, isometric contraction and rigor. The decay is mostly explained by the rotation of myosin subfragment-1. This rotation is promoted by thermal energy and is opposed by the viscous and by the elastic reactions. A model is proposed that relates the amplitude of the rotation of myosin subfragment-1 to its stiffness. It is found that the amplitude of the rotation is inversely proportional to the stiffness assigned to the structure. It is concluded that, in relaxed myofibrils, the stiffness of myosin subfragment-1 is much lower than that in myosin subfragment-1 - F-actin. The consequences of this finding on modeling of muscle contraction are discussed.

Experimental basis of the hypotheses on the mechanism of skeletal muscle contraction

With time clever hypotheses may be accepted as "facts" without being supported by solid experimental evidence. In our opinion this happened with muscle contraction where pure suggestions still occupy the scene and delay the progress of the research. Among these suggestions are: 1. the believe that viscosity is irrelevant in the economy of muscle contraction, 2. the concept of the drag stroke, 3. some interpretations of the significance of the Huxley-Simmons manoeuvre, 4. the definition of the load as a force/cross-section without taking into consideration the possible, divergent effects of the infinite mass x acceleration couples. Technical questions are also raised since it is apparent that measuring equipments interfere with the measure itself.

Muscle mechanism: The acceleration of the load

The load (force/cross-section) determines the response of muscle power output, force and speed of contraction). The force is the product of the mass by the acceleration, thus the same force is generated by an infinite number of mass and acceleration couples and each one of these couples displays different physical and biological effects. Therefore, the load must be defined both by the mass and by the acceleration. Early muscle investigators were well aware of this situation as it is indicated by the work of Hill on the flexion of the arm against the "heavy fly-wheel". By making use of a model of sarcomere contraction we show here that the acceleration of the load is the first determinant of the time course of the process of generation of the isometric tension. We also propose that, in order to reproduce the rapid release, it is not necessary to invoke the presence of a distinct elastic element in the contractile machinery. It is sufficient to assume that the stiffness of the same machinery increases with the contractile force.

Skeletal muscle contraction. The thorough definition of the contractile event requires both load acceleration and load mass to be known

BACKGROUND

The scope of this work is to show that the correct and complete definition of the system of muscle contraction requires the knowledge of both the mass and the acceleration of the load.

RESULTS

The aim is achieved by making use of a model of muscle contraction that operates into two phases. The first phase considers the effects of the power stroke in the absence of any hindrance. In the second phase viscous hindrance is introduced to match the experimental speed and yield of the contraction. It is shown that, at constant force of the load, changing load acceleration changes the time course of the pre-steady state of myofibril contraction. The decrease of the acceleration of the load from 9.8 m.s(-2) to 1 m.s(-2) increases the time length of the pre-steady state of the contraction from a few microseconds to many hundreds of microseconds and decreases the stiffness of the active fibre.

CONCLUSIONS

We urge that in the study of muscle contraction both the mass and the acceleration of the load are specified.

Water and muscle contraction

The interaction between water and the protein of the contractile machinery as well as the tendency of these proteins to form geometrically ordered structures provide a link between water and muscle contraction. Protein osmotic pressure is strictly related to the chemical potential of the contractile proteins, to the stiffness of muscle structures and to the viscosity of the sliding of the thin over the thick filaments. Muscle power output and the steady rate of contraction are linked by modulating a single parameter, a viscosity coefficient. Muscle operation is characterized by working strokes of much shorter length and much quicker than in the classical model. As a consequence the force delivered and the stiffness attained by attached cross-bridges is much larger than usually believed.