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Figure 1. The fast-inactivating spiking model of a tectal neuron. (A) The phase space of a system of two differential equations representing a spiking neuron, showing a sample trajectory in this space (black), two nullclines (purple and green), and the values involved in potential reset during spiking (Vspike in red, and Vreset in blue). (B) A typical response of a model neuron to a step current injection. (C) Spike-time rasters of four representative physiological neurons from Ciarleglio et al. (2015) as they spike in response to current clamp steps of amplitudes from 20 to 120 pA. (D) Voltage traces of four model neurons in response to current steps of amplitudes from 20 to 120 pA. Responses to 80 pA current step are highlighted. (E) Input-output curves, showing the number of spikes generated by neurons in response to current step injections of different amplitudes, for four representative spiking groups separately. Response curves of individual biological neurons from Ciarleglio et al. (2015) are shown in green, averages for biological neurons in blue, model neuron responses in black. (F) Distributions of first spike latencies (left) and first-to-second inter-spike intervals (right) during responses of biological neurons to step current injections of 100 pA, with similar values for model neurons superimposed on them (black dots).
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Figure 2. Network model, retinal inputs, and network responses. (A) The basic topology of the model network: a grid of retinal ganglion cells (RGCs) made a âblurredâ retinotopic projection to the tectal layer (black arrows), with recurrent connections within the tectal layer (red arrows). Different colors schematically show relative activation of RGCs and tectal cells during visual stimulus processing. (B) Three possible options for the recurrent intra-tectal connectivity: local (neurons are connected only to their neighbors); uniform (connections between any two neurons are equally probable); and scale-free (small-world network with highly connected hub cells). (C) Snapshots of RGC layer spiking, representing four visual stimuli: instantaneous full-field flash; randomly rearranged (scrambled) looming stimulus; linearly expanding looming stimulus (crash); and realistic non-linearly expanding looming stimulus. Each square shows a âstill frameâ from a dynamic response, taken in 250 ms increments after the stimulus onset (0 ms); with more recent spikes within each 250 ms window shown in lighter shades of gray. (D) Sample rasters of spiking responses in the tectum, generated for different recurrent connectivity profiles (rows), and different visual stimuli (columns). The horizontal axis presents model cell positions as distance from the 20 Ã 20 grid center; vertical axis shows spike latency; blue lines for crash and realistic stimuli show the theoretical time at which each tectal cell is directly engaged by the visual stimulus through the corresponding retinal cell. Cells of different spiking phenotypes are shown in different colors, from most spiky (red) to least spiky (dark blue).
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Figure 3. The summary statistics of spiking output in the tectum. (A) Averages (markers) and standard deviations (error bars) of the number of spikes per neuron generated by the tectum during responses to different visual stimuli, in models with different recurrent connectivity profiles (AâC), and in physiological data [D, data from Khakhalin et al. (2014) Figure 4]. Here âfâ stands for âflash,â âsâ for âscrambled,â âcâ for âcrash,â ârâ for realistic, and for physiological data âgâ stands for âgridâ (a stimulus that can be considered analogous to the âscrambledâ stimulus from the model); responses were respectively modeled or recorded for 2s after stimulus onset. Both in computational and biological experiments looming stimuli evoked stronger responses than an instantaneous flash (paired t-test p = 5eâ66, n = 400 for the model, p = 1eâ5, n = 56 in physiological experiments; significant after Bonferroni correction), while spatially disarranged stimuli evoked intermediate responses (B). The relative contribution of different neuronal spiking phenotypes to model responses, measured as the total number of spikes generated by all 10-spike (red), 5-spike (orange), 3-spike (light blue), and 1-spike (dark blue) neurons. Medium-spiking neurons were more involved in responses to slow than to fast stimuli (C). The median and inter-quartile ranges of first spike latencies during tectal responses to different stimuli, in model networks with different connectivity profiles (AâC), and in biological experiments (D), data from Khakhalin et al. (2014), not previously presented). The model successfully predicted typical latencies observed in physiological experiments (all pairwise comparisons between responses to different stimuli p < 1eâ6, paired t-test, significant after Bonferroni correction). (D) The average number of spikes generated by model neurons across all four visual responses correlated (r = 0.31) with their preference (Cohen d effect size) for looming stimuli (crashes) over flashes; regression line shown in red (E). A similar analysis for the physiological data from Khakhalin et al. (2014) verified this prediction, as spikier neurons preferred looming stimuli to flashes (r = 0.42).
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Figure 4. The effect of balance between recurrent and direct inputs to the tectum on stimulus selectivity (A). The total number of spikes (shown as pixels of different color, from black to white) generated in model networks with different strength of direct (horizontal axes) and recurrent (vertical axes) synaptic inputs, for different stimulus types (rows), and recurrent network topologies (columns) (B). The comparison of looming stimuli responses to full-field flash responses. Here color encodes the reliability (signed F-value) of getting a stronger total network response to either looming (red), or flash (blue) stimulus, for different strengths of direct (SR) and recurrent (ST) synaptic inputs. Networks with strong direct and recurrent synaptic inputs are selective for looming stimuli (red in the top right corner), while weakly connected networks are selective for full-field flashes (blue crescents in the left lower corner). This pattern is present, but less pronounced for fast looming stimuli, and in scale-free networks.
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Figure 5. Neuronal noise reduces selectivity to looming stimuli, and makes the balance of direct and recurrent inputs more important. (A) Selectivity charts in the (SR, ST) space for different connectivity profiles and two types of looming stimuli (columns), shown for different levels of spontaneous neural noise (rows). As the levels of noise increase (top to down across the panel), the areas of selectivity for looming stimuli become smaller. (B) The share of the parametric space selective to looming stimuli (with arbitrary threshold of F = 10), as a function of neural noise level, for two types of looming stimuli. The share of (SR, ST) combinations allowing looming stimuli detection goes down as noise levels increase, yet uniformly connected network (red) is less sensitive to background noise than either local (blue) or scale-free (green) networks.
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Figure 6. Effects of sensory experience on looming stimulus detection. (A) Compared to naïve networks shown in Figure 4, overstimulated networks spike more in response to fast stimuli (âflashâ and ârealisticâ looming), but not in response to slow âloomingâ stimuli. Color shows the total number of spikes generated by the network in response to a stimulus (B). Unlike naïve networks, overstimulated networks are not selective for slow looming stimuli (large blue areas in the first row), but retain selectivity for fast ârealisticâ looming stimuli (red areas in the second row) (C). In behavioral experiments, after prolonged strong visual stimulation tadpoles don't perform avoidance maneuvers in response to slow-moving objects (Mann-Whitney P = 0.003).
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