Constants underlying frequency changes in biological rhythmic movements

Abstract

When an animal increases or decreases the frequency of its limb motions, how should the transformation in timing be characterized? It has been hypothesized that the transformation is adiabatic, even though the biological conditions are nonconservative and non-rate-limited (Kugler and Turvey 1987). An adiabatic transformation requires that the rhythmic system's action (energy/frequency) and entropy production remain time-invariant throughout the transformation. The non-conservative adiabatic hypothesis was evaluated through an experiment on human rhythmic hand movements. On each trial, a subject began at a prescribed frequency and then, over a 30 s interval, increased (or decreased) the frequency continuously at will. For each subject, on each increasing and decreasing trial, cycle kinetic energy was a linear function of cycle frequency with a negative energy intercept. By the adiabatic hypothesis, the slope of the function defines the constant action and the intercept defines the constant dissipation — changes in cycle frequency incur no changes in energy dissipated per cycle. Slopes and intercepts were correlated suggesting a common basis for the two constants, and the variety of cycle amplitude-cycle duration relations were in agreement with the nonmonotonic, nonlinear space-time function predicted by the hypothesis. The possibilities of addressing aspects of the data through (a) muscle modeled as a continuum of Kelvin bodies with a continuous relaxation spectrum, and (b) various classes of autonomous differential equations, were discussed. Most importantly, the discussion focused on the puzzling independence of energy cost and speed exhibited by locomoting animals differing in morphology, physiology, size, and taxa. It was suggested that the independence may reflect a very general principle — adiabatic transformability of biological movement systems.