The applicability of the white-noise method to the identificationof a nonlinear system is investigated. Subsequently, the methodis applied to certain vertebrate retinal neuronal systems and nonlinear,dynamic transfer functions are derived which describe quantitativelythe information transformations starting with the light-pattern stimulusand culminating in the ganglion response which constitutes the visually-derivedinput to the brain. The retina of the catfish, Ictaluruspunctatus, is used for the experiments.
The Wiener formulation of the white-noise theory is shown to beimpractical and difficult to apply to a physical system. A differentformulation based on crosscorrelation techniques is shown to be applicableto a wide range of physical systems provided certain considerationsare taken into account. These considerations include the time-invariancyof the system, an optimum choice of the white-noise input bandwidth,nonlinearities that allow a representation in terms of a small numberof characterizing kernels, the memory of the system and the temporallength of the characterizing experiment. Error analysis of the kernelestimates is made taking into account various sources of error suchas noise at the input and output, bandwidth of white-noise input andthe truncation of the gaussian by the apparatus.
Nonlinear transfer functions are obtained, as sets of kernels,for several neuronal systems: Light → Receptors, Light → Horizontal,Horizontal → Ganglion, Light → Ganglion and Light → ERG. The derivedmodels can predict, with reasonable accuracy, the system response toany input. Comparison of model and physical system performance showedclose agreement for a great number of tests, the most stringent ofwhich is comparison of their responses to a white-noise input. Othertests include step and sine responses and power spectra.
Many functional traits are revealed by these models. Someare: (a) the receptor and horizontal cell systems are nearly linear(small signal) with certain "small" nonlinearities, and become faster(latency-wise and frequency-response-wise) at higher intensity levels,(b) all ganglion systems are nonlinear (half-wave rectification), (c)the receptive field center to ganglion system is slower (latency-wiseand frequency-response-wise) than the periphery to ganglion system,(d) the lateral (eccentric) ganglion systems are just as fast (latencyand frequency response) as the concentric ones, (e) (bipolar response)= (input from receptors) - (input from horizontal cell), (f) receptivefield center and periphery exert an antagonistic influence on theganglion response, (g) implications about the origin of ERG, and manyothers.
An analytical solution is obtained for the spatial distributionof potential in the S-space, which fits very well experimental data.Different synaptic mechanisms of excitation for the external andinternal horizontal cells are implied.
