Student Theses and Dissertations

Date of Award


Document Type


RU Laboratory

Deans Office


limulus lateral eye, limulus retina, lateral inhibition, model-free linear theory, Hartline-Ratliff model, Weiner-Hopf theory


theory of linear systems analysis is developed in a form directly applicable to the treatment of the Limulus retina. The dynamics of the retina may conveniently be characterized by means of a spatiotemporal transfer function, which summarizes the response of the system to moving sinusoidal gratings ("analysis"). The response of the retina to an arbitrary stimulus may then be calculated by addition of the response to suitably weighted sinusoidal stimuli ("synthesis"). Responses were obtained from the in-situ retina by means of extracellular recording of impulse activity in single optic nerve fibers. Test ommatidia were chosen in the interior of the retina, to avoid asymmetries introduced by the edge of the retina. Stimuli which varied in both space and time were produced under computer control on the screen of a display oscilloscope, and were conveyed to the Limulus eye by means of a fiber-optic taper. Transfer functions were measured using counterphase modulation of cosine gratings according to a sum-of-sinusoids temporal signal, a procedure equivalent to the use of moving gratings, for ommatidia with symmetrical receptive fields. By means of these transfer functions, the responses of the Limulus eye to visual stimuli moving at various velocities were predicted in a parameter-free Fourier synthesis calculation. There was good agreement between these predictions and the measured responses to these stimuli. A quantitative model for the dynamic, integrative action of the Limulus retina is developed, based on the original formulation for the steady state given by the Hartline- Ratliff equations. The model comprises an excitatory generator potential, and dynamic processes of self and lateral inhibition. An explicit expression for the spatiotemporal transfer function is obtained in terms of transfer functions for the generator potential, self-inhibitory, and lateral-inhibitory transductions, and spatial transforms of the lateral inhibitory kernel and the point-spread characteristic of the experimental and physiological optics. Explicit functional forms for these component transductions are adopted. The parameters which occur in these expressions serve to incorporate information about the subcellular physiology of retinal neurons into the quantitative description of the function of the retina as a whole. Procedures are described for the estimation of these parameters from empirical transfer function data. Transfer functions calculated from the model on the basis of parameters obtained with these procedures show good agreement with the corresponding empirical transfer functions. The parameter values obtained in this way are, in general, quite consistent with the results of many more direct (and frequently more invasive) measurements reported in the literature. In particular, the inhibitory kernel, as determined from our transfer function measurements, shows a small crater in the vicinity of the test-ommatidium. The dynamical model can be used to describe the response of the retina in the vicinity of its boundary, as well as in the interior. An analysis, based on the "Wiener-Hopf technique," is given for the response of peripheral retinal neurons. The predictions derived from this theory were compared with experiment through the use of illumination patterns in which one half of the retina was kept in darkness, while the remaining half was presented with a moving stimulus. This procedure permitted the calibration of model transfer functions by means of methods appropriate only for interior ommatidia, while simulating the neural environment at the edge of a homogeneous retina. Significant differences between the responses to stimuli which moved toward and away from the simulated edge were observed experimentally, in good agreement with the predictions of the theory. Similar behavior was also observed at the actual anatomical boundary of the eye.


A thesis presented to the faculty of The Rockefeller University in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Permanent URL

Included in

Life Sciences Commons