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First published online March 30, 2006
Journal of Experimental Biology 209, 1548-1559 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02140

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Source location encoding in the fish lateral line canal

Branislava uri-Blake and Sietse M. van Netten^*

University of Groningen, Neurobiophysics, Nijenborgh 4, 9747 AG Groningen, The Netherlands

View larger version (9K): [in a new window]   Fig. 1. Schematic representation of the experimental setup. The horizontal x,y-plane is defined by an x-axis parallel to the lateral line, along which the position is denoted by s, and a laterally directed y-axis. A neuromast at position s is stimulated by a sphere placed at distance r and angle with respect to the x-axis. The distance of the sphere from the y-axis is denoted by b, and the distance from the x-axis (lateral line) by d. The sphere vibrates (double-arrowed bold line) at an angle relative to the x-axis, which corresponds to an angle between the axis of vibration and the vector pointing to the sphere position (r). For clearness, the geometry is depicted in relation to the trunk lateral line system. Actual measurements were done on the cephalic lateral line system.

View larger version (20K): [in a new window]   Fig. 2. (A) The even dipole wavelet function, e, as a function of position along the lateral line, s, for two values of the source distance d (10 mm, solid line; 20 mm, broken line) as indicated. The shift factor b=0 mm. (B) The odd dipole wavelet function, o, for two values of the source distance d (10 mm, solid line; 20 mm, broken line) and with shift factor b=0 mm. D denotes the distance between the two extremes. (C) The linear combination of the even and odd wavelets for =8°, for two values of the source distance d (10 mm, solid line; 20 mm, broken line) and b=0 mm. S denotes the distance along the lateral line between the zero crossings (A,C).

View larger version (23K): [in a new window]   Fig. 3. (A) Stimulus signal as a function of time, with a frequency, f=65 Hz. (B) Extracellular receptor potential (ERP) of a neuromast as a function of time measured in response to the signal shown in A. (C) Spectrum of the ERP response depicted in B showing the amplitude components as a function of frequency. The component at twice the stimulus frequency (2f=130 Hz) clearly dominates the fundamental component (f=65 Hz) and is taken as the ERP amplitude. (D) Measured amplitude of the ERP (2f component) as a function of cupular displacement (data points taken from van Netten, 1987). The non-linear model (solid line) is given by Eqn 4, with fitted parameters g=37±3, n=1.7±0.2 and c=34±2. (E) ERP as a function of location along the lateral line s, simulated using the nonlinear function (Eqn 4) depicted in D, applied to the pressure gradient profile calculated from the linear combination of the wavelets shown in Fig. 2C (d=10 mm), corresponding to =8°. S denotes the distance between the zeros, and u is given by Eqn 4.

View larger version (16K): [in a new window]   Fig. 4. (A) Measured amplitude of extracellular receptor potentials (ERPs; circles) from a neuromast in the supraorbital lateral line of the ruffe. The sphere was moved along an axis parallel to the lateral line (x-axis) at a distance d=10 mm. This is referred to as an excitation pattern (see text). ERPs were fitted with the model given by Eqn 4 (solid line), describing the measured excitation patterns (b=–0.9±0.2 mm; d'=8.5±0.3 mm; =–9±3°). (B) Phase of ERPs.

View larger version (25K): [in a new window]   Fig. 5. Measured excitation patterns (circles) obtained from two cupulae (A,B) with model fits (solid lines) for three different distances, d, of the stimulus sphere along the y-axis. (A) Distances d from bottom to top are 7, 12 and 17 mm. (B) Distances d from bottom to top are 10, 15 and 20 mm. Broken lines in both panels are fairly well intersecting the zeros of the extracellular receptor potentials (ERPs) (indicated by crosses on the equidistant x-axes) and therefore illustrate the linear widening (S; Eqn 3a) of the excitation patterns with increasing distance d.

View larger version (16K): [in a new window]   Fig. 6. The distance d' obtained from the model (Eqn 4) fitted to the measured excitation patterns for N=9 neuromasts (various symbols) as a function of the real distance d. The thick solid line indicates the linear fit d'=Aavd+Bav, with parameters Aav=1.07±0.01 and Bav=–0.5±0.1 mm. For comparison, the broken line illustrates the case d'=d (A=1 and B=0 mm).

View larger version (63K): [in a new window]   Fig. 7. Continuous wavelet transforms (2D-contour maps) calculated using Eqn 5 from pressure gradient excitation profiles [f(s), red curves below each contour map] associated with one (A,B) or two (C,D) dipole sources. The column to the right of each contour map quantifies the contour colours. Pressure gradient profiles were obtained using a single wavelet function defined by Eqn 2c. For the case of two sources (C,D), the pressure gradient was determined as the sum of two individual wavelet functions. The white crosses in the contour maps indicate the positions of the dipole sources in x,y-space and correlate adequately with the maxima of the contour plots in b,d-space (A–C). If the sources are aligned with a fixed y-coordinate (D), the maxima seem to attract each other.