title: The determination of the instantaneous velocity of axonally transported organelles from filmed records of their motion.
abstract: A computational procedure is described for obtaining reproducible, low noise estimates of the instantaneous velocity of axonally transported organelles. Axonally transported organelles were detected in myelinated nerve fibers from Xenopus laevis by dark-field microscopy. The motion of the organelles was recorded on motion picture film at 3 frames/s, and the position of organelles travelling in the retrograde direction was obtained as a pair of x (axial) and y (transverse) coordinates at each 0.33-s interval. THe trend in organelle movement with time was calculated for each of the series of x and y coordinates by linear regression. This trend was removed from the measurements of x and y to yield sets of trend-free displacements. The trend yielded a measure of the mean velocity of the organelle in each of the two orthogonal directions. Power spectra of the deviations in x and y about the trend were calculated. For 133 particles studied, 99% of the power in the trend-free deviations occurred at frequencies below 0.3 Hz. The peak power in the x and y deviations occurred at a frequency of 0.1 Hz or less. Positional deviations about the trend were treated with a discrete 21-term differentiating filter that attenuated frequencies above 0.3 Hz. Instantaneous velocities for the organelles were obtained by adding the result of the band-limited differentiation to the appropriate estimates of mean velocity. The 21-term method was compared with a commonly used 2-term approximation to a differentiator and was shown to produce velocity estimates with about one order of magnitude less error. Estimates of organelle velocity obtained with the 21-term method indicate that saltatory particle motion may be viewed either as a smooth variation of particle velocity with respect to time or as an irregular, or discontinuous, variation of velocity with respect to particle position.
mesh_terms: D000818:Animals; D001370:Axonal Transport; D066298:In Vitro Techniques; D008433:Mathematics; D008954:Models, Biological; D009068:Movement; D010781:Photography; D012044:Regression Analysis; D014982:Xenopus laevis