Spatial frequency response of an anatomically reconstructed motor neuron model.

<p>(<b>A</b>). Morphology of a representative motor neuron. (<b>B</b>). Amplitude response (VA): the voltage attenuation data (VA_SD^AC(250 Hz) in the middle black dots) for the soma-to-dendrite AC signal with the fixed frequency, ω_f = 250 Hz, was superimposed on that for the DC signals in the same direction (VA_SD^DC(0) in the top gray dots) and in the opposite direction (VA_DS^DC(0) in the bottom gray dots) as a function of the path length (D_path) from the soma. Each data set was fitted with a single exponential function: e^−Dpath/η. The η values were 2678.7 for VA_SD^DC, 420.1 for VA_SD^AC and 225 for VA_DS^DC. (<b>C</b>). Phase response (Φ): the phase delay data (black dots) are shown as a function of D_path, fit with a cubic polynomial function (6.8*10⁻¹¹*D_path³–9.2*10⁻⁷ *D_path²–0.0018*D_path, gray line). Negative radian values indicate a phase lag with respect to the input signal. (<b>D</b>). The vector representation of distance dependent frequency response in the complex plane consisting of Imaginary (Im in the ordinate) and Real (Re in the abscissa) axes. The imaginary and real component of a vector pointing to the individual data points were calculated using Eq. (1) & (2) (Note: only the end point of the vector is shown; black dots). The distance and angle of the individual vectors from the origin correspond to the amplitude and phase response of the dendrites measured at the specific D_path in (<b>B</b>) and (<b>C</b>). The curve through the data was determined by the lines fit to data in panels (<b>B</b>) and (<b>C</b>), transformed by Eq. (1) & (2).