The transfer functions of sensory intensity in the nervous system

Color discrimination thresholds vary throughout color space in a reef fish (Rhinecanthus aculeatus)

Animal use color vision in a range of behaviours. Visual performance is limited by thresholds, which are set by noise in photoreceptors and subsequent neural processing. The receptor noise limited (RNL) model of color discrimination is widely used for modelling color vision and accounts well for experimental data from many species. In one of the most comprehensive tests yet of color discrimination in a non-human species, we using Ishihara-style stimulus patterns to examine thresholds for 21 directions at five locations in color space for the fish Rhineacanthus aculeatus. Thresholds matched RNL model predictions most closely for stimuli near to the the achromatic point, but exceeded predictions (indicating a decline in sensitivity) with distance from this point. Thresholds were also usually higher for saturation than for hue differences. These changes in color threshold with color space location and direction may give insight into photoreceptor non-linearities and post-receptoral mechanisms of color vision in fish. Our results highlight the need for a cautious interpretation of the RNL model - especially for modelling colours that differ from one another in saturation (rather than hue), and especially for highly saturated colours distant from the achromatic point in colour space.

A variational approach to behavioral and neuroelectrical laws

Variational methods play a fundamental and unifying role in several fields of physics, chemistry, engineering, economics, and biology, as they allow one to derive the behavior of a system as a consequence of an optimality principle. A possible application of these methods to a model of perception is given by considering a psychophysical law as the solution of an Euler-Lagrange equation. A general class of Lagrangians is identified by requiring the measurability of prothetic continua on interval scales. The associated Hamiltonian (the energy of the process) is tentatively connected with neurophysiological aspects. As an example of the suggested approach a particular choice of the Lagrangian, that is a sufficient condition to obtain classical psychophysical laws, while accounting for psychophysical adaptation and the stationarity of neuronal activity, is used to explore a possible relation between a behavioral law and a neuroelectrical ,response based on the Naka-Rushton model.

Sensory recoding via neural synchronization: integrating hue and luminance into chromatic brightness and saturation

If neural spike trains carry information in the frequency and timing of the spikes, then neural interactions--such as oscillatory synchronization--that alter spike frequency and timing can alter the encoded information. Using coupled oscillator theory, we show that synchronization-based processing can be used to integrate sensory information, resulting in new second-order sensory percepts signaled by the compromise frequency of the coupled system. If the signals to be coupled are nonlinearly compressed, the coupled system behaves as if it signals the product or ratio of the uncoupled signals, e.g., chromatic brightness can be signaled by the compromise frequency of coupled neurons responding to hue and luminance, and chromatic saturation can be signaled by the coupled frequency of neurons responding to hue and brightness, with a power- (Stevens's) law scaling like that observed psychophysically. These emergent properties of coupled sensory systems are intriguing because multiplicative processing and power-law scaling are fundamental aspects of sensory processing.

Comparing and unifying slope estimates across psychometric function models

The psychometric function relating stimulus intensity to response probability generally presents itself as a monotonically increasing sigmoid profile. Two summary parameters of the function are particularly important as measures of perceptual performance: the threshold parameter, which defines the location of the function over the stimulus axis (abscissa), and the slope parameter, which defines the (local) rate at which response probability increases with increasing stimulus intensity. In practice, the psychometric function may be modeled by a variety of mathematical structures, and the resulting algebraic expression describing the slope parameter may vary considerably between different functions fitted to the same experimental data. This variation often restricts comparisons between studies that select different functions and compromises the general interpretation of slope values. This article reviews the general characteristics of psychometric function models, discusses three strategies for resolving the issue of slope value differences, and presents mathematical expressions for implementing each strategy.

Physiological development of the kitten's retina: an ERG study

The physiological development of the retina was followed by recording ERGs and OPs from kittens of different ages. We found that different properties of the retina attain adult values at different ages: the b-wave elicited by higher stimulus intensities became adultlike by five to seven weeks while the b-waves elicited by lower stimulus intensities required another 3-5 weeks; the implicit time for the b-waves elicited by the full intensity stimulus attained adult values by 10 weeks of age; and the oscillatory potentials did not become adultlike until 18 weeks of age. The physiological development of the ERG was related to the development of the photoreceptors and the ganglion cells as well as to the morphological development of the second order neurons. It was concluded that the physiological development, as the morphological development, proceeds in three stages: an initial slow phase during which the late receptor potential and the b-waves are first recorded; a second rapid phase, during which the amplitude of the b-waves and OPs increase rapidly; and a third slow differentiation phase during which the final development of the properties of the retina are attained.

Quantitative studies of stimulus coding in first-order vibrissa afferents of rats. 2. Adaptation and coding of stimulus parameters

Mechanosensory neurons are often classified as either rapidly adapting or slowly adapting. We examined response decay (adaptation) during constant deflection of the vibrissae with quantitative, repeatable, ad hoc measures. We found that first-order vibrissa-activated neurons of the fifth ganglion exhibit a variety of adaptation rates that appear to be distributed continuously between the rapidly and slowly adapting extremes. Also, adaptation rate is influenced markedly by stimulus magnitude. We found no evidence for a dichotomy within the more slowly adapting neurons on the basis of discharge regularity. Threshold tuning curves were used to evaluate vibration sensitivity. Both the best frequencies and 1:1 discharge thresholds for sinusoidal stimulation ranged over two orders of magnitude and were continuously distributed. First-order vibrissa-activated afferents exhibit a broad variety of response patterns to constant-velocity stimulation. The pattern of discharge varied both as a function of time during constant-velocity (ramp) deflection and as a function of stimulus velocity. Although information about the parameters of a stimulus may be conveyed by any of several features of the response pattern, it appears that few if any neurons function as "pure" encoders of any particular stimulus parameter. We examined quantitatively the relationship between discharge rate and both velocity and amplitude of vibrissa deflection with the aid of a computer-based curve-fitting procedure. We found that about half the observed rate-level functions were best described by a power function; the remainder were best fit by a logarithmic function. The parameters of the best-fitting functions varied widely and continuously, emphasizing further the diversity of coding properties of the rat's vibrissa afferents. Rate-level curves for stimulus magnitude generally exhibited saturation; some were nonmonotonic. None were described adequately by either a logarithmic function or a power function.

The eye of the soldier beetle Chauliognathus pulchellus (Cantharidae)

The soldier beetle eye is unusual in having large optically isotropic corneal cones which project inwards from a thick isotropic cornea. Refraction is mainly at the corneal surface. Calculation shows that the first focal plane is near the tip of the cone, from which the optical pathway continues as a crystalline tract. At the distal end of the crystalline tract, 3 micrometer in diameter, the four cone cells enclose the proximal tip of the corneal cone; at the proximal end they enclose the distal tip of a long fused rhabdom rod. The eye is remarkable in that there are two classes of retinula cells; four cells contribute to the long thin axial rhabdom, 2 micrometer in diameter and 120 micrometer long, and the other four cells form two rounded rhabdoms, 10 x 4 micrometer in cross-section and 20 micrometer deep, which lie to one side of the optical axis. The physiological properties of individual retinula cells were measured by intracellular recording. The retinula cells are of three spectral types with peaks near 360, 450 and 520--530 nm. Except by the criterion of spectral sensitivity, the retinula cells sampled could not be sorted into more than one class. The measured value of the acceptance angle, near 3 degrees in the dark-adapted state, is consistent with the hypothesis that all sampled cells were of the anatomical type that participate in the central rhabdom rod. A calculation of the theoretical field size of individual retinula cells from measurments of refractive index and lens dimensions predicts that cells which participate in the central rhabdom will have acceptance angles near 3 degrees. The conclusion, therefore, is that only one anatomical type of cell has so far been sampled.

Stimulus-response functions of rapidly adapting mechanoreceptors in human glabrous skin area

1. Single unit impulses were recorded from the ulnar and median nerves of awake human subjects with tungsten electrodes inserted percutaneously in the upper arm.2. Forty-nine rapidly adapting mechanoreceptors with receptive fields in the glabrous skin area were studied. Thirty-nine units had small receptive fields with distinct borders (RA-receptors) while ten units had large fields with indistinct borders (PC-receptors).3. The afferent response to stimuli of varying indentation amplitude and velocity of indentation, was analysed.4. Amplitude thresholds varied from 0.05 to 1.65 mm for the RA-receptors. For the PC-receptors amplitude thresholds ranged from less than 0.05 to 1.95 mm.5. Velocity thresholds varied for the RA-receptors from 0.4 to 39.3 mm/sec, and for the PC-receptors from 0.5 to 19.6 mm/sec.6. The conduction velocities of the afferents were all in the A alpha-beta range. For the RA-receptors the conduction velocities ranged from 26 to 91 m/sec (mean = 55.3 +/- 3.4), and for PC-receptors the range was from 34 to 61 m/sec (mean = 46.9 +/- 3.6).7. The nerve impulse frequency as a function of indentation velocity was analysed for nineteen RA-receptors and four PC-receptors. A hyperbolic log tangent function of the type first introduced by Naka & Rushton (1966) in studies on S-potentials in the fish retina was found to be the best description of the stimulus-response function for sixteen RA-receptors and two PC-receptors. For the remaining units a pure logarithmic function was the best description. However, the logarithmic function may be, as found in the present study, a special case of the more general log tanh function.

Intensity coding in the frog retina. Quantitative relations between impulse and graded activity

The impulse discharge of single on-off neurons and a graded field potential, the proximal negative response (PNR), were simultaneously recorded with an extracellular microelectrode in the inner frog retina. Normalized amplitude-intensity functions for the on-response of the PNR and the neuron's post-stimulus time histogram (PSTH) were nearly coincident and typically showed a dynamic range spanning approximately 2 log units of intensity. Thus a nearly linear relation is found between the amplitude of the PNR and the neuron's PSTH. A neuron's PSTH amplitude and maximum instantaneous frequency of discharge were usually highly correlated, but occasional marked disparities indicate that temporal jitter of the first spike latency is an additional, relatively independent variable influencing PSTH amplitude. It typically changes by a factor of 20-30 over the intensity range. These and other findings have implications for the functional significance of the PNR and the PSTH, for a possible linear link between amacrine and on-off ganglion cells, and for a mechanism of intensity coding in which temporal jitter of latency exerts a major role.

Spectral sensitivity of the barnacle, Balanus amphitrite

The extracellular ocellar potential was used to evaluate the spectral sensitivity of the ocellus of the barnacle, Balanus amphitrite. Maximum relative sensitivity was at 530-540 nm. Studies with chromatic adapting lights suggest that the receptors contain a single photopigment. The spectra were relatively broader in the dark as compared to the light-adapted state. This effect was shown to be due to an increase in the slope of the amplitude-intensity function, caused by light adaptation. Studies of tapetal fluorescence and corneal transmission indicate little effect of the ocellar media on the determination of sensitivity.