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Figure 1. Overview of the tadpole spinal cord anatomy and the model’s 2D representation. (A) Diagram of a section of the tadpole CNS showing the main regions, including the neural canal surrounded by ependymal progenitor cells and the ventral floor plate, surrounded in turn by a layer of neuronal cell bodies. Lying outside the cell body layer is the marginal zone, in which most axons grow, and the dorsal tract which contains RB axons and is separated from the marginal zone by a column of sensory interneuron cell bodies (red line). Dorsally the marginal zone is bounded by a column of sensory RB neuron cell bodies (yellow line). (B) The CNS opened like a book along dorsal midline (dashed line in A) to show the two-dimensional modelling area.
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Table 1: Cell types and their corresponding colours.
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Figure 2. Schematic representation of the fasciculation/repulsion mechanism in the model. The solid orange line shows the direction of growth for the closest pioneer axon. This orange line is used to adjust the current growth angle of the follower axon shown by blue solid line. In case of fasciculation the current growth angle becomes closer to the growth angle of the pioneer axon. In case of repulsion the perpendicular dashed orange line is used to adjust the axon growth angle of the follower axon.
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Figure 3. Patterns of axons for dla neurons. (A) Pattern without fasciculation. (B) Pattern with a relatively weak fasciculation (spr=0.1) (C) Pattern with spr=0.5. showing multiple axon bundles. The four pioneer axons are shown in black. The initial point of axon growth is shown for each neuron by a magenta star.
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Figure 4. Patterns of primary sensory RB axons for different parameter values. (A) Primary RB axons without fasciculation; (B,C) Primary RB axons with sensitivity 0.1 and range 1 and 3 respectively; (D,E) Primary RB axons with sensitivity 0.5 and range 1 and 3 respectively. The initial point of axon growth is shown for each neuron by a magenta star.
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Figure 5. Patterns of sensory RB primary (yellow) and secondary (magenta) axons for different parameter values. Black lines show primary axons of pioneer neurons. (A) Primary and secondary RB axons without fasciculation; (B) Primary and secondary RB axons with sensitivity 0.1. (C) Primary and secondary RB axons with sensitivity 0.5. Note that while the primary axons (yellow) are equivalent to those shown in Fig. 4, the two figures are from different simulations, demonstrating the stochastic variability present in the model. Green stars show the initial point of the secondary axons.
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Figure 6. Full simulated spinal cord with all neuron types in the presence of fasciculation. (A) All axons in a fasciculated connectome with spr=sse=0.2,r=1
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, colour coded as in Table 1. (B) Zoom showing only axons on the left side of the body. Magenta and green stars show the initial point of the primary and secondary axon respectively. Note that the horizontal scale is the same in both figures.
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Figure 7. Patterns of axon growth for different neuron types with attraction, repulsion or neither. The left column shows axon patterns for RB (top) and cIN (bottom) cell types without fasciculation. The middle column shows axon patterns for the same cell types with fasciculation (sensitivity 0.2). The right column shows axon patterns for the same cell types in the case of repulsion (sensitivity â0.05). Primary axons are coloured according to Table 1, secondary axons are magenta and pioneer primary axons are black. Red horizontal lines indicate the boundaries of the marginal zone, and the dashed horizontal line in the bottom row corresponds to the ventral midline. cIN axons start on one side, cross the midline and then turn to grow longitudinally. Note that the horizontal scale is identical in all parts.
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Table 2: Number of synaptic connections (rounded average across 12 connectomes for each case) between different cell types on both sides, with and without fasciculation (first and second numbers respectively), as well as the percent change in synapse count that results from fasciculation. Each row gives the number of connections made by neurons of a particular type (first column) onto neurons of every other type. Dashes indicate pairs where there is a negligible number of connections (<50) in both cases. Green and red highlights show pairs with particularly large increases and decreases (respectively) in synapse counts. The core CPG network (dINs and cINs) is highlighted with a bold border.
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Figure 8. Fasciculation helps to constrain sensory axons to the dorsal tract when normal growth barriers do not perfectly block axon growth. Barriers (red lines) have 25âµm gaps at 25âµm intervals. Yellow lines show primary axons, magenta lines show secondary, black lines are pioneer primary axons. (A) With no fasciculation 24% of axon points are outside the marginal zone. (B) With fasciculation (s=0.2,r=1) 15% of axon points are outside the marginal zone.
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Figure 9. The effect of fasciculation on aIN axon trajectories. (A) Histogram comparing the dorso-ventral distribution of axons in the anatomical data used for optimization (solid line), optimized model output without fasciculation (dashed line) and model output with fasciculation sensitivity 0.1 (dotted line). (B,C) Example generated primary aIN axons for the sâ=â0 and sâ=â0.1 cases respectively. Magenta stars show positions where the axons begin growing.
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Figure 10. Reducing the number of synapses reduces the proportion of connectomes that can generate stable alternating patterns of MN spikes (swimming). A set of 24 connectomes (12 with fasciculation, 12 without) were modified to simulate the effect of reducing the synapse formation probability. Decreasing the probability (and therefore number of synapses) decreases the proportion of the 12 connectomes that can swim (s=0.2,r=1)
Each data point shows the average of Nâ=â12 connectome simulations.
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Figure 11. Fasciculation reduces mid-cycle dIN firing. (A) Simulation of a connectome with approximately 45,000 synapses and no fasciculation. A large number of dINs fire mid-cycle spikes at approximately the same time as neurons on the contralateral side of the body are active. Colour code as given in Table 1. (B) Reducing the number of synapses increases the number of dINs that fire mid-cycle spikes. For a given number of synapses, connectomes generated with fasciculation (s=0.2,r=1)
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have fewer mid-cycle dINs. (C) A dINâs spiking pattern depends on how many synapses it receives from other dINs. Neurons that receive little excitation (but not none) have a roughly 50% chance of firing mid-cycle spikes. Inactive dINs tend to receive a lot of excitatory input, but are unable to spike due to depolarisation blockade. Data from four connectomes with fasciculation and probability reduced to give approximately 50,000 synapses.
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