Inference of nonlinear receptive field subunits with spike-triggered clustering

Abstract

Responses of sensory neurons are often modeled using a weighted combination of rectified linear subunits. Since these subunits often cannot be measured directly, a flexible method is needed to infer their properties from the responses of downstream neurons. We present a method for maximum likelihood estimation of subunits by soft-clustering spike-triggered stimuli, and demonstrate its effectiveness in visual neurons. For parasol retinal ganglion cells in macaque retina, estimated subunits partitioned the receptive field into compact regions, likely representing aggregated bipolar cell inputs. Joint clustering revealed shared subunits between neighboring cells, producing a parsimonious population model. Closed-loop validation, using stimuli lying in the null space of the linear receptive field, revealed stronger nonlinearities in OFF cells than ON cells. Responses to natural images, jittered to emulate fixational eye movements, were accurately predicted by the subunit model. Finally, the generality of the approach was demonstrated in macaque V1 neurons.

Functional Organization of Midget and Parasol Ganglion Cells in the Human Retina

“…ON and OFF cells in the human retina exhibited two asymmetries in light response properties that were consistent with previous findings [13,16,22]. First, the RFs of ON parasol and midget cells were systematically larger than their OFF counterparts (Figs.…”

“…Second, human parasol cells exhibited nonlinear spatial summation that was asymmetric in ON and OFF cells, resembling previous findings in macaque parasol cells [22,34]. To quantify nonlinear spatial summation, a cascade model was fitted to the light responses of each cell, consisting of a first layer of several linear spatial subunits, followed by exponentiation and summation of subunit outputs, followed by a saturating nonlinearity that drives Poisson firing (Fig.…”

“…To characterize light responses of hundreds of recorded RGCs simultaneously, fine-grained white noise visual stimulation was performed, and the spike-triggered average (STA) stimulus was computed to identify the spatiotemporal receptive field (RF) of each cell [21]. The influence of nonlinear spatial summation on light responses was also examined with recently-developed analytical methods [22]. High-density electrical images [15,23] were used to reveal the average spatiotemporal properties of the spikes produced by each cell.…”

“…Model of spatial nonlinearity, in which the outputs of multiple spatially distinct subunits are exponentiated and then summed, followed by a final saturating nonlinearity, to produce light response. A recently-developed estimation procedure efficiently estimates the subunits, weights, and nonlinearity from the responses to a white noise stimulus [22]. A special case of this model, with one subunit, is a linear-nonlinear-Poisson cascade.…”

Linear and nonlinear chromatic integration in the mouse retina

“…Finally, many standard models of visual responses in retinal ganglion cells assume linear receptive fields and thus linear integration of visual signals. Yet, recent studies have emphasized the importance of incorporating nonlinear signal integration, in particular nonlinear spatial integration, to predict the responses of ganglion cells to natural stimuli (Heitman et al, 2016;Liu et al, 2017;Shah et al, 2020;Turner and Rieke, 2016;Turner et al, 2018). Commonly, such models are fitted to responses from achromatic (grayscale) stimuli, and it will be interesting to explore how to include nonlinear chromatic integration for predicting response to chromatic stimuli.…”