Li T et al. (2023), A model of decentralized vision in the sea urch...

ECB-ART-51534

iScience 2023 Apr 21;264:106295. doi: 10.1016/j.isci.2023.106295.

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A model of decentralized vision in the sea urchin Diadema africanum.

Li T , Kirwan J , Arnone MI , Nilsson DE , La Camera G .

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Sea urchins can detect light and move in relation to luminous stimuli despite lacking eyes. They presumably detect light through photoreceptor cells distributed on their body surface. However, there is currently no mechanistic explanation of how these animals can process light to detect visual stimuli and produce oriented movement. Here, we present a model of decentralized vision in echinoderms that includes all known processing stages, from photoreceptor cells to radial nerve neurons to neurons contained in the oral nerve ring encircling the mouth of the animals. In the model, light stimuli captured by photoreceptor cells produce neural activity in the radial nerve neurons. In turn, neural activity in the radial nerves is integrated in the oral nerve ring to produce a profile of neural activity reaching spatially across several ambulacra. This neural activity is readout to produce a model of movement. The model captures previously published data on the behavior of sea urchin Diadema africanum probed with a variety of physical stimuli. The specific pattern of neural connections used in the model makes testable predictions on the properties of single neurons and aggregate neural behavior in Diadema africanum and other echinoderms, offering a potential understanding of the mechanism of visual orientation in these animals.

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	Figure 1. Schematic illustration of the model nervous system(A) Schematic geometry of the animal. Left: 3D geometry. θ: latitudinal angle; φ: longitudinal angle. Right: transverse view of the animal cut above the ONR. The orange arcs indicate the distributions of PRCs on each ambulacrum (δ: half-width of the distribution). The green arcs indicate RN cells. The blue circle indicates eONR cells.(B) Cartoon of the network structure used in the model (only 2 ambulacra shown at the top, represented by purple rectangles). Red segments terminating in a circle indicate inhibitory connections, blue arrows indicate excitatory connections. From top to bottom, orange circles indicate groups of PRCs, green circles indicate groups of RN neurons, red circles indicate groups of iONR neurons, and blue circles indicate groups of eONR neurons. The rightmost sketch illustrates how the action of RN cells onto eONR cells results into an effective inhibition of the latter.
	Figure 6. Effect of acceptance angle and location of PRCs on the model’s spatial visionEach panel shows a heatmap of vmax, the maximal length of the population vector across initial orientations of the animal, for a given stimulus and a given pair of values for Δρ and δ. Each column shows the same stimulus for different arc widths of the target region (i.e., for different φstim, see Table S1), while each row shows the same φstim across different stimuli. If vmax<θp, the animal cannot detect the stimulus from any orientation. The red dotted line is the contour line where vmax=θp, while the black dotted line is the contour line where vmax=4. The white line is the collection of points with Δρ+2δ=60°. In each plot, Δρ ranged between 15° and 90° and δ ranged between 5° and 20°. Red stars mark the point (Δρ,δ)=(30°,15°), the parameter values used in the main simulations. DoG: Difference of Gaussians; FB: Flanked bar.
	Figure 2. Angular sensitivity curves and population vectors(A) Angular sensitivity curves of PRC fik(φ) (Equation 3 of STAR Methods with Δρ=30° and δ=15°). Each color represents an ambulacrum. The light shades represent the angular sensitivity curves of all PRCs (uniformly distributed with half-width δ in each ambulacrum). The darker lines are examples of single angular sensitivity curves (one example for each ambulacrum).(B) Plot of sigmoidal function S (Equation 2) used to model the output of RN and ONR neurons (here shown for the ONR neurons, β=4.5 and xc=−0.45; see Table 1). Note that activation of PRCs results in a reduced overall input x, reducing the output of RN cells (see the text).(C) Population vectors (readout of eONR cells, see Equation 11 of STAR Methods) for three stimuli: 40° bar, 29° DoG, and 69° DoG (from left to right). Each data point (red circle) corresponds to the tip of one population vector. Different population vectors were obtained by varying the orientation of the sea urchin with respect to the center of the stimulus (here, located at the top of the arena). All orientations (from 0° to 359°) are represented. The large blue circle is the threshold θp. If for a given orientation the population vector’s length exceeds θp, visual detection occurs and coherent motion is predicted along the direction of the population vector.(D) Examples of single population vectors among those in panel C for specific orientations (ψ) of the animal with respect to the center of the stimulus (see Figure S1).
	Figure 3. Experimental setting and stimuli(A) Behavioral experiment setting. The stimuli were attached on the outer wall of the arena. At the beginning of each trial, the animal was positioned at the center of the arena with a random orientation.(B) Examples of the six stimuli used in this work with φstim=40° (mathematical definitions in Table S1). The ink value of black and white is 1 and 0, respectively. Panel A adapted from ref.7
	Figure 4. Behavior: comparison of model with dataBehavior of model and Diadema africanum in the presence of 4 different stimuli.(A) Experimental results from the study by Kirwan et al.7 Each blue semicircle represents the final position of the animal at the end of one trial, while a full blue circle represents the final position of two animals. Although all animals reached the wall of the arena, final identical positions were stacked to show all the data. The stimuli used were a stimulus with uniform intensity in all directions (control; top left panel); a 29° DoG stimulus (top right); a 40° bar (bottom left); and a 69° DoG (bottom right; see Figure 3 and Table S1 for details about the stimuli). In each panel, the stimulus is shown on the outer wall of the arena (large circle). The red arrow at the center of the arena is a measure of aggregate directional movement across each cohort of subjects (see below).(B) Model results in simulations of the same tasks shown in panel A. Each blue circle corresponds to one predicted final position across a cohort of 100 animals with random initial orientations with respect to the center of the stimulus. Here, the final position was inferred from the population vector induced by the stimulus when the animal was at the center of the arena (see Figures 2C and 2D). In both panels, the red arrow at the center of each plot is circular mean vector of the final positions (see STAR Methods, Equation 14). The only significant circular mean vector was obtained with the 69° DoG stimulus: P=0.013 (V-test) and P=0.042 (Rayleigh test), in agreement with the analogous results of ref. 7 (P>0.5 for the remaining stimuli). Main parameters: Δρ=30°, δ=15°, θp=5 (see Table 1 for all other parameter values). Panel A adapted from ref.7
	Figure 5. Simulated trajectoriesSimulated trajectories of 100 bearings under control, 40° bar, 29° DoG, and 69° DoG stimuli. The outer circle represents the wall of the arena with the stimulus on it. Animals were placed at random orientations at the center of the arena and moved according to the behavioral model described in section “Model of visually induced movement”. The colored lines represent the trajectories covered by the center of each animal starting from the center of the arena and ending at the color-matched dot. The gray dots on the arena’s wall are the radial projections of the colored dots and represent the points where the animal’s body hits the wall. See Table 1 for model parameters.

References [+] :

Agca, Neurosensory and neuromuscular organization in tube feet of the sea urchin Strongylocentrotus purpuratus. 2011, Pubmed, Echinobase