Hull MJ , Soffe SR , Willshaw DJ , Roberts A .

Biotechnology and Biological Sciences Research Council , Medical Research Council

	Fig 1. The hatchling tadpole CNS and a population of electrically coupled neurons (dINs).(A) Side view of a hatchling Xenopus laevis tadpole 48 hours after fertilisation. (B) Top view diagram of the tadpole showing skin, swimming muscles, and CNS with hindbrain and spinal cord. The CNS region able to generate swimming rhythm when isolated (green) contains a population of ~30 dIN neurons (brown) on each side. (C) Side view of the hindbrain and spinal cord showing diagrammatic recording electrodes (1 and 2) and tracings of two filled dINs (from [29]) with somata and short dendrites. dIN-1 has only a descending axon (arrowhead). dIN-2 also has an ascending axon (arrow). The intertwining of the axons can be seen (arrowheads). (D) Electrical coupling was shown using simultaneous voltage recordings from two dINs. Hyperpolarising current injection into either dIN (bars) caused a small voltage deflection in the other (arrowheads; from [29]). (E) Diagram of part of the dIN column with descending axons leaving the somata and intermingling where axo-axonic gap junctions could lie.
	Fig 2. A passive population model of descending interneurons in the hindbrain and rostral spinal cord and their gap junctions.(A) dIN morphology was approximated as four sections each modelled as a cylinder or tapered cylinder, one for the soma, two for the hillock and one for the axon (not to scale). (B) The somata of the dINs form a rostral-caudal column (light: circles = somata) each with a descending axon (lines). In this example, there is a single gap junction (dark vertical line) between a pair of dINs {i, j}. (C, D) Two layout schemes for generating gap junctions between two axons were tried, to evaluate their effects on coupling coefficients: (C) A gap junction could occur with a certain probability at a fixed point along the axon of the more caudal dIN; (D) A gap junction could occur with a certain probability at any location within a defined region of the axon of the more caudal dIN.
	Fig 3. The effects of different parameters on the coupling coefficients measured between neurons in a passive population model.In (A-C) a single parameter is varied (two values are shown) and the coupling between model neurons at different distances was measured for 100 generated networks for comparison with the coupling between pairs of dINs measured experimentally (shown by dots in each graph; [29]). The notched grey bars show the median and 25% to 75% quartiles of the model coupling coefficient at each distance. The lines represent the 5% to 95% percentiles. Starting parameters (see text): Ri = 80 Ωcm, RGJ = 600 MΩ, min-dist = 20 μm, max-dist = 70 μm, glk = 0.25 mS cm-2 and axon diam = 0.4 μm. In each case the visual match to experiments is better in the left column than in the right column. (A) RGJ reduced from 600 to 300 MΩ or increased to 900 MΩ. (B) Axon diameter increased from 0.4 to 0.6 μm or reduced to 0.2 μm. (C) Minimum distance from the caudal soma was reduced from 30 to 10 μm or increased to 40 μm. The parameters min-dist and max-dist correspond to the left and right-hand edges of the GJ distribution step in Fig 2D respectively. When gap junctions were distributed closer to the somata of the neurons, the coupling was stronger (in part because there are more gap-junctions in the network in total).
	Fig 4. Gap junction distribution and coupling coefficients between dINs.(A) The chosen layout of gap junctions in the column of 30 dINs (somata red circles spaced 10 μm apart) with descending axons (red lines). Blue dots represent one side of a gap junction (hemichannel), which connects to another gap junction at the same position along the column (x axis). (B) Direct and indirect dIN to dIN coupling: directly coupled neurons (blue dots); indirectly coupled via the axon of another neuron (yellow dots); coupled via more than 3 axons (empty square). (C) Histogram of gap junction distributions along the axons of dINs. In order to get good coupling between dINs, we found that gap junctions needed to form close to the somata. (D) Comparison of the coupling coefficients between pairs of dINs measured experimentally (red circles; [29]) and in the model (as in Fig 3).
	Fig 5. Effects of uniform changes in densities of channels on model dIN membrane excitability, firing and action potential propagation.(A) Current was injected into a single dIN in a population model of 30 dINs electrically coupled via axo-axonic gap junctions. (B, C) When the membrane excitability is low, model dINs reliably fire a single action potential at the onset of current injection (B) but would not reliably conduct action potentials along their axons (C). (D, E) With increased excitability, the model neurons fire repetitively to higher levels of current injection and (E) action potential propagation could be reliable. (C, E) Action potential propagation in the model was tested by recording the voltage in the soma and at 20 points along the axon (20 μm spacing) of a random neuron in the network. A short current pulse injected into the soma is used to initiate an action potential (first trace). (F, G). Rebound firing was investigated using short hyperpolarising step current pulses during a longer depolarising step current injection. (The values for these traces were (B, C, F): Mca = 0.5, Mna = 1.0, Mkf = 1.0, Mks = 1.5, and Mlk = 0.5 and (D, E, G): Mca = 1.0, Mna = 1.5, Mkf = 0.5, Mks = 0.5, and Mlk = 0.5).
	Fig 6. Responses of final active dIN model to current injections and comparison to physiological recordings.(A) In response to increasing levels of step current injection (top), the model neuron soma has a firing threshold of ~80 pA (red), and fires a single action potential, even in response to currents of 3 times the threshold (blue). (B) Rebound spikes to negative current steps (expanded in bottom traces) during depolarisation in model neurons (thin blue line) and whole-cell recordings (thick grey line; from Dr Wen-Chang Li, unpublished).
	Fig 7. Effects of electrical coupling on firing properties of single stimulated dINs.(A) Diagram of network of 30 electrically coupled dINs where injection of 200 ms step current at increasing levels (red, green, blue) into a single dIN reliably produces only a single spike. (B) When gap junctions were removed, the injected dIN fires repetitively.
	Fig 8. The effects of electrical coupling on firing of a population of 30 electrically coupled dINs.(A) Current is injected into all the electrically coupled dINs. (B) Even at threshold, the whole population fires repetitively, and in synchrony. (C) Raster plots of spike times show that as the number of gap junctions in the network was reduced, neurons still fired repetitively but synchronisation decreased. (D) Firing becomes desynchronised with 0% gap junction coupling. (E) Current-frequency curve for a dIN in the electrically coupled network. (100% gap junction coupling, equal current injected into all dINs). (F) When the dIN network with 100% coupling is synchronously active, a raster plot of every fourth dIN shows spikes recorded in the soma (circles) propagate reliably for 1500 μm along the axon (crosses; network setup identical to B).
	Fig 9. The effects of electrical coupling on recruitment of dINs by synaptic excitation following head skin stimulation.(A) 20 sensory pathway tIN interneurons produce glutamate EPSPs in the dINs in a pattern based on recorded responses to head skin touch (see Methods). (B) Without dIN electrical coupling, more individual dINs are recruited as the stimulus is increased. (C) With electrical coupling, there is a step recruitment of the whole dIN population. A ‘Level of Stimulation’ of 100 is defined as one that will reliably initiate swimming measured experimentally (see Methods).

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