A Three-Layer Network Model of Direction Selective Circuits in the Optic Tectum

Abstract

The circuit mechanisms that give rise to direction selectivity in the retina have been studied extensively but how direction selectivity is established in retinorecipient areas of the brain is less well understood. Using functional imaging in larval zebrafish we examine how the direction of motion is encoded by populations of neurons at three layers of the optic tectum; retinal ganglion cell axons (RGCs), a layer of superficial inhibitory interneurons (SINs), and periventricular neurons (PVNs), which constitute the majority of neurons in the tectum. We show that the representation of motion direction is transformed at each layer. At the level of RGCs and SINs the direction of motion is encoded by three direction-selective (DS) subtypes tuned to upward, downward, and caudal-to-rostral motion. However, the tuning of SINs is significantly narrower and this leads to a conspicuous gap in the representation of motion in the rostral-to-caudal direction at the level of SINs. Consistent with previous findings we demonstrate that, at the level of PVNs the direction of motion is encoded by four DS cell types which include an additional DS PVN cell type tuned to rostral-to-caudal motion. Strikingly, the tuning profile of this emergent cell type overlaps with the gap in the representation of rostral-to-caudal motion at the level of SINs. Using our functional imaging data we constructed a simple computational model that demonstrates how the emergent population of PVNs is generated by the interactions of cells at each layer of the tectal network. The model predicts that PVNs tuned to rostral-to-caudal motion can be generated via convergence of DS RGCs tuned to upward and downward motion and feedforward tuned inhibition via SINs which suppresses responses to non-preferred directions. Thus, by reshaping directional tuning that is inherited from the retina inhibitory inputs from SINs can generate a novel subtype of DS PVN and in so doing enhance the encoding of directional stimuli.

Keywords: direction selectivity; functional imaging; network model; retinal ganglion cell; tectum; zebrafish.

Figure 1

Functional characterization of DS SINs. (A) Diagram showing dorsal view of the retinotectal projection in zebrafish larvae. Retinal ganglion cells (in yellow) send projections contralaterally from the retina to the neuropil of the optic tectum where they arborize. Periventricular neurons (PVNs, in pink) project dendrites into the tectal neuropil. Unlike PVNs, Superficial inhibitory interneurons (SINs) (cyan) have cell bodies located in the most superficial tectal neuropil and extend broad monostratified arbors into the retinorecipient layers. (B) Responses of a single SIN expressing GCaMP5G to a drifting grating stimulus. Red arrows indicate direction of grating motion, yellow arrow indicates SIN cell body and blue arrow indicates SIN arbor. White dashed line indicates skin covering the tectum. (C) Example response of a single SIN tuned to 140° directed motion. Directions of motion eliciting significant responses are indicated by arrows. Inset shows response as a polar plot. (D) Cumulative histogram of preferred directions of all DS SINs. Fitting von-Mises curves (red lines, R² = 0.8) to the population histogram reveals three normally distributed, non-overlapping populations with population peaks centered at 9°, 157°, and 264°. Each population is color-coded according to preferred direction. (E) Normalized responses of direction selective SINs, color-coded according to subtype. Responses of individual cells are shown as colored lines, mean responses shown in black. (F) Polar plots showing normalized responses of each population; mean (solid line) and dashed (±1 SD). Mean DSI, tuning bandwidth (full width half max) and preferred direction of each population relative to the body axis of the fish are shown below each polar plot.

Figure 2

Comparison of direction-selectivity in the SIN, RGC and periventricular neuron (PVN) populations. (A) Cumulative histogram of preferred directions of all RGC voxels (n = 10,114 voxels from 29 larvae). Fitting von-Mises curves (red lines, R² = 0.99) to the population histogram reveals three normally-distributed, non-overlapping populations with population peaks centered at of 24°, 131°, and 256°. Each population is color-coded and the preferred direction of motion of each population relative to the body axis of the fish is shown in inset. (B) Polar plots showing normalized responses of each DS RGC subtype; mean (solid line) and dashed (±1 SD). Mean DSI, tuning bandwidth (full width half max) and preferred direction of each DS RGC subtype are shown below each polar plot. (C) Histogram of DS PVN preferred directions (n = 126 tectal neurons from 24 fish). Four normally distributed populations are present, with populations centered at 27°, 90°, 136°, and 268° (R² = 0.87). Note the emergent population of PVN tuned to 90° motion (yellow) that is absent from both RGCs and SINs. (D) Polar plots showing normalized responses of each DS PVN subtype; mean (solid line) and dashed (±1 SD). Mean DSI, tuning bandwidth (full width half max) and preferred direction of each subtype are shown below each polar plot. (E–H) Overlaid polar plots summarizing how direction of motion is encoded by RGCs (E), PVNs (F), and SINs (G). RGCs exhibit a tiled and triangular representation of directional space by three subtypes of DS RGC. In the SIN population the representation of motion is reshaped, leaving a gap at 90°. Directional space is represented by 4 subtypes of PVNs with preferred directions aligned with the cardinal axes. (H) Overlaying the polar plots of DS SINs with the emergent population of PVN reveals that the gap in the representation of motion in the rostral-to-caudal direction in the SIN population aligns with the emergent population of PVNs tuned to 90°.

Figure 3

Computational model of the direction selective tectal circuit. (A) Circuit motif showing a population of PVNs integrating input from two RGC populations and three SIN populations. Rounded arrowheads represent excitatory connections, flat arrowheads represent inhibitory connections, and pointed arrows indicate preferred stimulus direction. (B) Comparison between experimentally observed (colored) and simulated (black) normalized RGC tuning curves. (C) Normalized tuning curves of observed (colored) vs. simulated (black) SINs. (D) Normalized tuning curves of observed (colored) vs. simulated (black) PVN population tuned to rostral-to-caudal directed motion.

Figure 4

Contribution of SINs to stimulus tuning in simulated PVN populations. (A–E) PVN population tuning curves under various circuit perturbations, presented as polar plots with normalized data (left) and plots with unnormalized data (right). (F) Amplitude of PVN type P2 (the emergent population tuned to rostral-to-caudal directed motion) under simulated manipulations. (G) Tuning error of P2, defined as the absolute difference between the experimentally observed direction preference and the simulated direction preference. (H) FWHM bandwidth of P2 tuning curve. (I) DSI of P2.