On the potential role of lateral connectivity in retinal anticipation

Abstract

We analyse the potential effects of lateral connectivity (amacrine cells and gap junctions) on motion anticipation in the retina. Our main result is that lateral connectivity can—under conditions analysed in the paper—trigger a wave of activity enhancing the anticipation mechanism provided by local gain control (Berry et al. in Nature 398(6725):334–338, 1999; Chen et al. in J. Neurosci. 33(1):120–132, 2013). We illustrate these predictions by two examples studied in the experimental literature: differential motion sensitive cells (Baccus and Meister in Neuron 36(5):909–919, 2002) and direction sensitive cells where direction sensitivity is inherited from asymmetry in gap junctions connectivity (Trenholm et al. in Nat. Neurosci. 16:154–156, 2013). We finally present reconstructions of retinal responses to 2D visual inputs to assess the ability of our model to anticipate motion in the case of three different 2D stimuli.

Retinal Processing: Insights from Mathematical Modelling

“…N can be real or complex, with a positive or a negative real part. In the case where W B A and W A B commute, it is actually possible to explicitly compute the eigenvalues and the eigenvectors and obtain conditions for stability (all eigenvalues have real negative part) and real/complex eigenvalues [45]. If we further assume that W B A and W A B have no zero eigenvalues, the sign constraints on these matrices imply that L (n) is invertible for all n. This is what we are going to assume from now.…”

“…Here, this is a desensitization when activated by a steady illumination [72], mediated by a rise in intracellular calcium Ca 2+ , at the origin of a feedback inhibition thus preventing prolonged signalling of the ON B cell [44,73]. It can be modelled as follows [42,44,45]. Each B cell has a dimensionless activity variable a B i obeying the differential equation:…”

“…Gain control at the level of B cells and RG cells induces retinal anticipation. When combined with A cells' lateral connectivity or gap junctions' connectivity, it results in a wave of activity ahead of the propagating stimulus (e.g., a moving bar) for specific ranges of parameters (characteristic times of cells response, weight intensities) as studied in [45].…”

“…In this paper, I address these problems with the help of two models. The first, presented in Section 2.1, grounded on biology and e.g., the papers [42][43][44][45] mimics the Bipolar-Amacrine-Ganglion cells network and is used, in Sections 3.1 and 3.2, to make progress in elucidating problem 1. I first show how one can obtain an explicit form for the kernel (1) featuring the A cells lateral connectivity.…”

Unraveling neural coding of dynamic natural visual scenes via convolutional recurrent neural networks

“…[26][27][28] In addition, the retina, known as an efficient encoder, can anticipate motion with recurrent connections. 29 The RGCs can be connected laterally by electric synapses, i.e., gap junctions [30][31][32][33] or specific amacrine cells. The lateral connection allows the retina to detect the differential motion of the object and background, 34 while specific asymmetric connectivity of the amacrine cells helps the RGCs show direction selectivity.…”