The Influence of Different Retinal Subcircuits on the Nonlinearity of Ganglion Cell Behavior

Abstract

Y-type retinal ganglion cells show a pronounced, nonlinear, frequency-doubling behavior in response to modulated sinewave gratings. This is not observed in X-type cells. The source of this spatial nonlinear summation is still under debate. We have designed a realistic biophysical model of the cat retina to test the influence of different retinal cell classes and subcircuits on the linearity of ganglion cell responses. The intraretinal connectivity consists of the fundamental feedforward pathway via bipolar cells, lateral horizontal cell connectivity, and two amacrine circuits. The wiring diagram of X- and Y-cells is identical apart from two aspects: (1) Y-cells have a wider receptive field and (2) they receive input from a nested amacrine circuit consisting of narrow- and wide-field amacrine cells. The model was tested with contrast-reversed gratings. First and second harmonic response components were determined to estimate the degree of nonlinearity. By means of circuit dissection, we found that a high degree of the Y-cell nonlinear behavior arises from the spatial integration of temporal photoreceptor nonlinearities. Furthermore, we found a weaker and less uniform influence of the nested amacrine circuit. Different sources of nonlinearities interact in a multiplicative manner, and the influence of the amacrine circuit is approximately 25% weaker than that of the photoreceptor. The model predicts that significant nonlinearities occur already at the level of horizontal cell responses. Pharmacological inactivation of the amacrine circuit is expected to exert a milder effect in reducing ganglion cell nonlinearity.

Responses of recurrent nets of asymmetric ON and OFF cells

“…Frequency doubling has been observed in many experimental studies of retinal ganglion cells responding to periodic illumination gratings (see [22] and references therein). These observations have also been reproduced computationally [21]. In [22], experiments were carried out in guinea pig retina, where both ON and OFF pathways are present.…”

“…In contrast, in regions of zero illumination, the activity of the ganglion cells oscillated at twice the temporal input frequency (labeled "F2" or "nonlinear" behavior). In [21], this phenomenon has been reproduced by a complex computational model of a retinal subcircuit in which frequency doubling, also called "second harmonic response", has been linked to photoreceptor nonlinearities and amacrine wide-field effects. The model, developed for the ON pathway because the data on the OFF pathway are more scarce, includes the properties of subtypes of photoreceptors, horizontal cells, bipolar cells, ganglion cells as well as two classes of amacrine cells: narrow field ("nested" amacrine cells) and wide field amacrine cells.…”

“…The setting of the experiment described in [22] and the work in [21] suggests that our model might be used to reproduce certain features of the observed dynamics. Those authors state that F2 nonlinear responses-qualitatively similar to our lateral frequency-doubling behavior-are due to the ganglion cell's "nonlinear" receptive field, which possesses quite distinct spatial summation properties in comparison to the more familiar center-surround "linear" receptive field.…”

“…The paper also presents novel results on a newly found discrepancy between the response of ON cells in the central region (i.e., where external forcing is applied) in ON/ON nets versus ON/OFF nets in the context of periodic input, and exposes the subtle role of asymmetry and of feedback in this effect and in frequency doubling in general. Finally, we study the response of ON/OFF nets to periodic gratings, i.e., periodic forcing in both space and time, and discuss how these results can shed light on certain aspects of frequency-doubling phenomena known to occur in the retina under conditions of periodic spatiotemporal illumination [21,22].…”

Analysis of the interaction between the retinal ON and OFF channels using CNN‐UM models

“…The measurements were repeated at different input frequencies and the filter characteristics were fitted to the measured sinusoid responses (temporal sinusoid measurements on bipolar cells [15]). The parameters of the nonlinear characteristics were calculated from the second-and third-order harmonic components of the responses to sinusoidal inputs (similar to [10]). …”