Spatial and temporal characteristics of the fish lateral line detection

The object of investigation in this thesis is the fish canal lateral line organ (CLLO). The canal lateral line organ is distributed on the head (cephalic lateral line) and laterally along the body of the fish (trunk lateral line). The function of the CLLO is to detect water vibrations produced in the immediate surroundings of the fish by other swimming objects such as prey, a mate or a school of the same species. The main topic of this thesis focuses on: a) the temporal characteristics of the functioning of the CLLO, such as time delay and time resolution of detection by the CLLO; b) the spatial characteristics of the functioning of the CLLO, such as cues for discerning the position of an object (localisation) and the spatial resolution of detection by the CLLO. The canal lateral line organ in ruffe is a narrow canal below the skin or the scales of the fish. The sensory units of lateral line organs are neuromasts, groups of mechano-sensory hair cells. In the ruffe (Gymnocephalus cernuus), the subject of experimental investigation in this thesis, neuromasts in the supra-orbital canal were investigated (Ø < 1 mm). The neuromasts in the cephalic CLLO were chosen due to their substantial size (Ø ~ 500 µm) and large number of hair cells (~ 2000). Neuromasts possess a gelatinous cupula which slides over the hair cells and reflects their mechanical properties. The canal has pores between subsequent neuromasts, enabling the exchange of fluid with the surroundings of the fish. Chapter 2 describes the setup and function of a Laser Interferometer Microscope (LIM) used as a displacement detection apparatus in the measurements described in Chapters 3 and 4. The LIM is based on the standard technique of laser interferometry and adapted to the particular purpose of measuring nanometer-scale displacements along the optical axis as well as at right angles to it. The LIM can be used in two modes: the referential and the differential. The differential mode is suited to measurements of the velocities or displacements of an object vibrating in the horizontal plane. Two laser beams with parallel optical polarisation and a frequency shift of 400 kHz are directed such that they interfere on the object of which the motion is to be measured. The interference beam reflected by the object is imaged onto a photo-multiplier, from which the electrical signal is both frequency- and phase-demodulated, enabling simultaneous measurements of the velocity and displacement of the object. The referential mode is suited to measurements of the displacements and velocities of an object vibrating along the optical axis. In this mode only one laser beam is reflected from the object, while the second beam, the reference beam, also with a frequency shift of 400 kHz travels directly through the microscope. The reflected and referential beams interfere on the photo-multiplier. The output of the demodulator simultaneously gives the displacement and velocity of the measured object vibrating in the vertical plane. The LIM used in our experiments enabled the measurement of displacement with an accuracy as small as 1.5 nm and velocity with an accuracy of approximately 0.6 µm/s (signal-to-noise = 1). The temporal characteristics of the lateral line are investigated in Chapters 3 and 4. Impulse responses of the cupula in the cephalic CLLO were measured and investigated for the first time (Chapter 3). In general, the canal fluid dynamics combined with the cupular dynamics impose the condition that the outside water acceleration is proportional to the displacement of the cupula. However, when the canal is exposed by removing the skin above the cupula being measured, and when a small vibrating stimulus sphere is placed in the canal in front of the cupula, then the cupular displacement is proportional to the velocity of the water surrounding the cupula. Therefore, a stimulus consisting of a step-displacement of the sphere was used, causing a step-displacement of the fluid surrounding the cupula and hence an impulse velocity. The displacement responses of the cupula to such stimuli are thus velocity impulse responses, revealing information about the time delay and the temporal resolution of the neuromasts. The displacements of the cupula were measured using the LIM in its differential mode. The impulse responses of the cupula resembled damped oscillations of which the initial phase follows the displacement of the fluid flowing past it. The time delay of such a response was within the accuracy of the time measurement (< 0.1 ms). The inertial fluid forces, which are associated with the high frequency content of a step, are shown to cause a cupula to instantaneously respond to the fluid step displacement without delay and with the same displacement as the local fluid. The cupula oscillated with a resonance frequency calculated to be fr= 121 ±56 Hz and with a quality factor Q = 1.8 ± 0.5. These values were in good agreement with those obtained using the control technique of sinusoidal stimuli combined with modelling of the data, where the resonance frequency and quality factor of the same cupula were estimated to be fr= 128 ± 60 Hz and Q = 1.7 ± 0.3, respectively. The relaxation time-constant of the impulse responses was determined to be τ = 4.4 ± 2.7 ms, reflecting the time that a cupula needs to recover to its equilibrium position after a displacement step. The main conclusion of this chapter is that the hydrodynamics of the peripheral lateral line organ does not impose a limit on the time resolution of detection by the cupula at the onset of a step displacement of the water. The temporal characteristics of the cupular dynamics are further investigated in Chapter 4. The influence of the mechano-transduction of the underlying hair cells to the timing of the impulse responses was studied by measuring the impulse responses of the cupula to fluid displacement steps with increasing magnitude. The displacement of the cupula is transferred into a deflection of the hair bundles, which are the sensory organelles of the hair cells. Their deflection causes opening of mechano-electrical transducer channels, which influence the overall stiffness of the hair bundle by decreasing it while the channels are opening. Previous investigations of the copular displacement induced by a series of sinusoidal fluid displacements revealed that the nonlinear mechanics of the cupula causes a shift in resonance frequency. Our measurements were in a good agreement with those studies, with an overall frequency shift of 12 ±6 Hz over the whole range of stimulus magnitudes. Furthermore, we examined the extent of the influence of the non-linearities on the timing characteristics of the cupula. The period of the damped oscillation changes with increasing magnitude of the stimulus such that it first increases (when the amplitude of the copular displacement falls in the operational range of the mechano-transducer channels) and then decreases again. The total change in the period of oscillation is of the order of 1 ms for a period that was originally ≈ 8 ms. This change in period is small when compared to the relaxation time of the cupula, estimated earlier to be approximately 5 ms. The variation in the resonant frequency of the cupula imposed by the non-linearities is small compared to the variation in the resonant frequency of the cupula among different fish (60 Hz). Thus, the main conclusion is that the cupular non-linearities do not impose significant constraints on the temporal resolution of lateral line detection. Spatial characteristics of the CLLO are examined in Chapter 5. Previous studies showed that information on the distance of a vibrating source is represented in the overall pressure gradient (the so-called excitation pattern) which is detected by an array of neuromasts in the lateral line canal. However, a precise description, together with a quantitative interpretation of such patterns that allows a reconstruction of the location and vibration direction of the source, has not been given so far. In order to quantitatively interpret these excitation patterns along a lateral line array in terms of the position and direction of vibration of a source, we measured the extracellular receptor potentials (ERPs) for a single neuromast that were induced by a dipole source of which the position was changed in the horizontal plane. It is shown in Chapter 5 that the excitation patterns have characteristic shapes that are linearly scaled by a distance parameter $d$, which is equal to the shortest distance between the source and the lateral line. As a result, the excitation patterns can be described by a family of wavelet functions with the scale factor, d, together with a shift factor, b, which is the position of the source along the lateral line. The wavelet transform of a 1-D excitation pattern is shown to reconstruct a 2-D map of the dipole source. Several algorithms are discussed that could potentially be used by a fish to decode lateral line excitation patterns in order to localise a source and its axis of vibration. The related accuracy and the operational range of the source position detection of this decoding were determined. The length of the lateral line array, L, which is obviously limited by the body length of the fish, imposes an upper bound on the detection range of L/square root(2). The accuracy of the source location detection is limited by the inter-neuromast distance Dn. Therefore, the lower limit of the source detection distance is fixed at 2Dn.