Search

Subthreshold solutions of the Hodgkin-Huxley equations are considered here by means of the linearized forms of these equations. An asymptotic theory is obtained, based on dimensional analysis and scaling arguments. Explicit expressions for the crest speed are obtained and are shown to be in good agreement with experiment, with computation, and with an exact asymptotic value which is also obtained here.

A procedure is given for the comparison of nerve impulse data with model predictions. This method utilizes information in the nerve impulse train that is ignored by the post-stimulus-onset histogram and thereby gives an improved signal-to-noise ratio. Comparison of observed responses in the Limulus retina with predictions derived from a detailed model gives good agreement.

We have analyzed the responses of cat retinal ganglion cells to luminosity gratings that are modulated in time by a sum of sinusoids. A judicious choice of the component temporal frequencies permits a separation of the linear and second-order nonlinear components. Y cell responses show harmonic generation and intermodulation distortion over a wide frequency range. These nonlinear components predominate over the linear components for certain types of spatial stimuli. Nonlinear components in X cells are greatly diminished in comparison. The character of the nonlinear responses provides strong constraints on prospective models for the nonlinear pathway of the Y cell.

In an optic nerve fiber of the compound eye of the horseshoe crab, Limulus, the time course of a train of nerve impulses discharged in response to illumination reflects the interplay of excitatory and inhibitory influences. Responses to sinusoidally modulated excitation and inhibition, as a function of frequency, were measured separately and in combination. A simple linear superposition of the separate frequency responses properly accounts for the composite frequency response for both synchronous and asynchronous modulation of the excitatory and inhibitory influences. In general, the effect on the frequency response of increasing the delay of the inhibitory influence is progressively to shift the maximum amplitude to lower frequencies and gradually to produce pronounced maxima and minima in both the amplitude and phase.