A. Siemienski

Unit for Biophysics of Motion, PE Academy, Wroclaw, Poland

Muscle force gradation occurs through varying the number of active motor units and the rate at which the active motor units generate action potentials. As the force exerted by a muscle increases, new motor units are recruited and remain active until the force declines. This happens in a set sequence with slow-contracting, fatigue-resistant motor units being recruited first and fast-contracting, fatigue-sensitive motor units being recruited last.

The purpose of this work is to show that the phenomenon of orderly motor-unit recruitment can be interpreted as following from a teleological design principle of minimisation of energy consumption within a muscle.

The problem of minimisation of metabolic energy consumption within a muscle is formulated in terms of the theory of optimal control based on the following assumptions:

Fig. 1. Muscle tension vs. Ca⁺⁺-ion concentration (adsorption isotherm).

• energy consumption within a muscle is directly related to the amount of ATP used
• regulation of muscle fibre tension is accomplished by the sarcoplasmic reticulum by means of an active ATP-consuming Ca⁺⁺-ion pump
• non-linear relationship between Ca⁺⁺-ion concentration and muscle tension follows the shape of an adsorption isotherm (Fig.1.)
• specific tensions of slow and fast muscle fibres are about the same [2]
• slow-twitch fibres use less ATP per unit force generated than the fast-twitch fibres [1]

Fig. 2. shows a solution of the optimisation problem for a muscle consisting of a uniform pool of five types of muscle fibres with different contraction speeds. Muscle units are recruited in an orderly manner, starting with the slowest ones. Muscle force increase is due to both motor-unit recruitment and rate coding, the extent of the latter depending on fibre composition of a particular muscle.

Fig. 2. Orderly recruitment pattern in an optimal intra-muscular force distribution.

Taking into account the non-linear excitation characteristics of muscle fibres leads to orderly recruitment patterns in energy optimal intra-muscular force distributions. The emerging order appears to be in a qualitative agreement with that observed experimentally.

1. Billeter, R., Hoppeler, H. In: Strength and Power in Sport, Komi, P.V. (Ed.), Blackwell Scientific Publications, 39-63, 1992.

2. Lucas, S.M., Ruff, R.L., Binder, M.D. Exp. Neurology, 95, 142-154, 1987.

1. Siemienski, PE Acad., Paderewskiego 35, 51-612 Wroclaw, Poland

Fax: (4871)482281, Email: as@awf.wroc.pl