Extended Data Fig. 5 |. Computer simulation of branch point failure and rescue by GABA.

a, Model of a 3D reconstructed proprioceptive afferent, drawn to scale, except myelinated branch lengths all shortened an order of magnitude. Double line segments are myelinated (white) and the rest unmyelinated. Adapted from anatomical studies of Walmsley²⁵. Nodes are indicated with a green dot, and ventrally projecting terminal boutons indicated with a yellow dot. As in our axons of Fig. 1, branch points were always at nodes. GABA_A receptors of equal conductance (nS) were placed at each node and associated branch points, and total dorsal columns (dc) depolarization from phasically activating these receptors is shown in inset. The branch lengths (L) and computed space constants (λ_S) are indicated in gray boxes for each segment of the afferent, the latter computed from subthreshold current injections into each segment. From left to right the gray boxes are for segments spanning from the dorsal columns (dc) to N0, N0 to N1, N1 to N5, N1 to N4, N4 to B2 and N5 to B1. Average space constant was λ_S = 91 μm, similar to in other axons³⁹. b, Responses to simulated dorsal root (DR) stimulation (0.1 ms pulse, 2 nA, at black arrows) computed at various downstream branch points (nodes) and terminal boutons in the spinal cord, with resting potential indicated by thin dashed line (−82 mV). A sodium spike propagated to the branch point at node N1, but failed to invade into the downstream branches, leaving nodes N2 and N3 with only a passive depolarization from the N1 spike (failure potential, FP). Further downstream nodes and terminals experienced vary little depolarization during this failure (N5, B1 and B2). In this case the GABA conductance was set to zero (g_GABA = 0, control), simulating a lack of GABA tone. Note that only the nodes beyond the parent branch at node N1 failed due to the conductance increases in large daughter branches to nodes N2 and N3 that drew more current than node N1 could provide (shunting conductances). Node 3 is particularly interesting as it does not itself branch, though a neighbouring node has a small branch, both contributing to the overall conductance and related failure, and Node 2 has two adjacent branches contributing to its conductance. Other branch points with relatively smaller conductance increases (N0, simpler branching) did not fail to conduct spikes. Generally speaking, if the upstream node of a parent branch cannot provide enough current to activate the nodes of its daughter branches then spikes fail, and this is especially likely with multiple sequential branch points, like in N1 – N2. However, failure even occurs at daughter nodes than themselves lack branches (N3), so GABA receptors are useful in aiding spikes at unbranched nodes. c, As seen experimentally, nodal GABA_A receptor activation to produce PAD prior to the DR stimulation (~ 10 ms prior; as in Fig. 4f) rescued spikes from failing to propagate. That is, with GABA_A receptors placed just at nodes and associated branch points a weak phasic activation of these receptors (conductance g_GABA = 0.6 – 1.5 μS per node shown) rescued conduction down the branch to node N2, with full nodal spikes seen at the distal node N4 and the terminal bouton B2 (DR stimulation at peak of PAD, detailed in (g) with black arrows indicating DR stimulation timing). A larger GABA receptor activation (2.4 nS) additionally rescued spike conduction down the branch to node N3, with full spike conduction to the distal node N5 and the terminal bouton B1. Note that increasing GABA conductance sped up the arrival of distal spikes (e.g. at N4 and B2), by up to 1 ms, suggesting substantial variation in sensory transmission times induced by GABA, as we see experimentally. Also note that this nodal GABA depolarized the nodes (N1 – N3) relative to rest (thin dashed line), thus assisting spike initiation. In contrast, nodal GABA did not depolarize the terminal boutons (B1 and B2), consistent with our recent direct recordings from terminals¹⁵. Sensitivity analysis revealed similar results with a wide range of sodium channel and GABA receptor conductances, though increasing sodium conductance sufficiently prevented failure all together (like in Extended Data Fig. 10f). Interestingly, when we put GABA receptors only at node N2 (or at the unmyelinated bouton immediately above N2) then the spike propagating though N2 to the terminal bouton B2 was rescued with the same GABA conductance (0.6 μS) as in the main simulation (c). Likewise with GABA receptors only at node N3 and nowhere else, then the spike was rescued at that node N3 (at 2.4 μS, as in c). d, When instead we removed all nodal GABA receptors and instead place them on terminal boutons (near B1 and B2, yellow, with equivalent total conductance, 2.4 μS condition), then activating them did not rescue the spike propagation failure, since the associated depolarization of nodes is too attenuated at the failure point (N1-N3; no change from resting potential). The GABA receptors did depolarize the terminal boutons (B1 and B2, thick dashed lines) substantially relative to the resting potential (thin dashed lines), but this depolarization was sharply attenuated in more proximal nodes (N1–3). e, Reduction of spike height (shunt) and speeding of spike onset with increasing GABA conductance at a non-failing node (N1; model with nodal and not terminal bouton GABA conductances, c), consistent with actual recordings from axons in Fig. 3d and Extended Data Fig. 8a. f-h, PAD recorded at the dorsal columns (dc) during conditions in (b-d), respectively, as experimentally recorded dorsal PAD. A phasic GABA induced depolarization (PAD) was generated by changing GABA conductances, g_GABA, as detailed in Methods, and GABA receptor location varied as in (c-d). DRs were stimulated at the peak of this PAD in (c-d). Note that nodal (g) but not terminal (h) GABA_A receptors caused a visible depolarization (PAD) at the dc, due to less electrotonic attenuation over a shorter distance to the dc.