Energetics of contraction

Muscles convert energy from ATP into useful work, which can be used to move limbs and to transport ions across membranes. The energy not converted into work appears as heat. At the start of contraction heat is also produced when Ca(2+) binds to troponin-C and to parvalbumin. Muscles use ATP throughout an isometric contraction at a rate that depends on duration of stimulation, muscle type, temperature and muscle length. Between 30% and 40% of the ATP used during isometric contraction fuels the pumping Ca(2+) and Na(+) out of the myoplasm. When shortening, muscles produce less force than in an isometric contraction but use ATP at a higher rate and when lengthening force output is higher than the isometric force but rate of ATP splitting is lower. Efficiency quantifies the fraction of the energy provided by ATP that is converted into external work. Each ATP molecule provides 100 zJ of energy that can potentially be converted into work. The mechanics of the myosin cross-bridge are such that at most 50 zJ of work can be done in one ATP consuming cycle; that is, the maximum efficiency of a cross-bridge is ∼50%. Cross-bridges in tortoise muscle approach this limit, producing over 90% of the possible work per cycle. Other muscles are less efficient but contract more rapidly and produce more power.

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.

Protein osmotic pressure and cross-bridge attachment determine the stiffness of thin filaments in muscle ex vivo

The properties of some models of the actin filament are compared with those of the thin filament in muscle. The greater stiffness of thin filaments ex vivo with respect to F-actin in vitro is attributed to the effect of both protein osmotic pressure and the attached cross-bridges. By comparing the stiffness of thin filaments in vitro and in isometric and rigor muscles the stiffness of thin filaments in relaxed muscle is computed. The upper limit of thin filament stretching is deduced to approach approximately 10 nm microm(-1). It is also calculated that, on stretching by 2.02 nm of the fully non-overlapped thin filament or by 1.59 nm of the thin filament on isometric contraction, the energy released on the hydrolysis of one molecule of ATP is fully used up.

Cooperative behaviour of the elementary sarcomere units and the cross-bridge step size

We present a model of muscle contraction based on purely physical grounds and modulated by a parameter, k, related to the visco-elastic hindrances of the contractile apparatus. The model predicts a strong cooperation among sarcomere units and proposes that viscous hindrance is a fundamental component of the economy of the contraction. The concept of cross-bridge step size is also discussed and it is concluded that the step size is of various and probably undeterminable length.