A Theory on Non-Constant Frequency Decompositions and Applications

Formation of a stable polarity axis underlies numerous biological processes. Here, using high-resolution imaging and complementary mathematical modeling we find that cell polarity can be established via the spatial coordination of opposing membrane trafficking activities: endocytosis and exocytosis. During polarity establishment in budding yeast, these antagonistic processes become apposed. Endocytic vesicles corral a central exocytic zone, tightening it to a vertex that establishes the polarity axis for the ensuing cell cycle. Concomitantly, the endocytic system reaches an equilibrium where internalization events occur at a constant frequency. Endocytic mutants that failed to initiate periodic internalization events within the corral displayed wide, unstable polarity axes. These results, predicted by in silico modeling and verified by high resolution in vivo studies, identify a requirement for endocytic corralling during robust polarity establishment.

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Effects of activation frequency and force on low-frequency fatigue in human skeletal muscle

Journal of Applied Physiology ◽

10.1152/jappl.1999.86.4.1337 ◽

1999 ◽

Vol 86 (4) ◽

pp. 1337-1346 ◽

Cited By ~ 44

Author(s):

Stuart A. Binder-Macleod ◽

David W. Russ

Keyword(s):

Healthy Subjects ◽

Human Skeletal Muscle ◽

Low Frequency ◽

Variable Frequency ◽

Activation Pattern ◽

Constant Frequency ◽

Mean Frequency ◽

Before And After ◽

Low Frequency Fatigue ◽

Force Time

No comparison of the amount of low-frequency fatigue (LFF) produced by different activation frequencies exists, although frequencies ranging from 10 to 100 Hz have been used to induce LFF. The quadriceps femoris of 11 healthy subjects were tested in 5 separate sessions. In each session, the force-generating ability of the muscle was tested before and after fatigue and at 2, ∼13, and ∼38 min of recovery. Brief (6-pulse), constant-frequency trains of 9.1, 14.3, 33.3, and 100 Hz and a 6-pulse, variable-frequency train with a mean frequency of 14.3 Hz were delivered at 1 train/s to induce fatigue. Immediately postfatigue, there was a significant effect of fatiguing protocol frequency. Muscles exhibited greater LFF after stimulation with the 9.1-, 14.3-, and variable-frequency trains. These three trains also produced the greatest mean force-time integrals during the fatigue test. At 2, ∼13, and ∼38 min of recovery, however, the LFF produced was independent of the fatiguing protocol frequency. The findings are consistent with theories suggesting two independent mechanisms behind LFF and may help identify the optimal activation pattern when functional electrical stimulation is used.

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