AP collision experiment. (A) The ventral nerve chord (VNC) of an earthworm is positioned on a series of transverse, single-ended electrodes to excite and monitor APs. (B) Individual or two counter-propagating APs are generated by stimulating the nerve at the outermost electrodes. Some of the inner electrodes (C1, C2, C3) are used for recording, all other electrodes are grounded. Propagating APs generate biphasic electrical potential as sketched above C1 and C3 whereas colliding APs provoke an essentially unipolar peak (cf. C2). By variation of the delay between the opposing stimuli, the collision can be generated anywhere along the nerve between the stimulation electrodes. (C) Extracellular recording of propagating and colliding APs. A collision sweep experiment yields multiple recordings with varying distance between recording site and point of collision. The recording of a collision corresponds to the horizontal line in the middle, while orthodromic propagation is at the top and antidromic propagation is at the bottom. The recording was at a medial position. (D) The peak amplitude as a function of the distance to the collision. Examples of four recordings at three positions (C1, anterior; C2, medial; C3, posterior) along the nerve chord. As a guide to the eye, the data points are connected by a cubic spline (thin lines).

Figure 1—figure supplement 1. Raw Data

Figure 1—figure supplement 2. Fit of the collision width

The classical cable model. (A) A chain of identical RC circuits with conductivity gm, capacity cm and inner resistivity ri mimics the electric properties of the cellular membrane and connects the extracellular and intracellular space. The change of inner axial current Iax(x) is given by the transmembrane current density im(x) (Kirchhoff’s current law). (B) The propagating solution of the Tasaki-Matsumoto model. A boundary between a resting state and an excited state induces an axial current, that causes a propagation of the boundary. The axial current _ows in closed loops and returns within the resistive extracellular medium, causing an extracellular potential that travels with the current source along the neuron.

Comparison of experimental data (gray) with models (color, see legend). (A) Traces of Ve(t) from propagating APs. (B) Traces of Ve(t) at the collision site. (C) The extracellular discharge of annihilating APs, measured and calculated. The gray crosses are the experimental values from 4 recordings at 3 separate sites along the MGF, where each recording consists of up to 46 traces with varying delay times. (D) Different predictions about the discharge generated by AP annihilation and released around the collision site.

Examples of ephaptic coupling, calculated with the TM-model (blue) and the HH-model (green): (A) in a parallel target neuron when an AP is propagating in the source. (B,C) when the AP is annihilating (end-to-shaft geometry, similar to the Basket cell–Purkinje cell synapse). The source and target neurons are 1 μm in diameter and are separated by 1 μm (2000 compartments each, length 1 mm, bouton size 2 μm. The neurons are placed next to each other, that is to say the numeric point compartments are separated by 1 μm. Traces denote the target membrane potential next to the point of axon termination. The initial hyperpolarization effect may be followed by a subsequent depolarization, depicted by the RTM model (red) for different relaxation times. (D-F) Ephaptic coupling in an end-to-end synapse, illustrating the enhanced ephaptic coupling, due to enlarged neuron terminals (boutons). Here the source and target neurons are 100 nm in diameter (2000 compartments each, length 300 μm, bouton size 400 nm). The target neurons are 1/4 in length and N (500 compartments, length 75 μm). The TM model generates a distant depolarization. Traces in D and E show the membrane potential of the target at the point where the TM model provokes its maximal depolarization (corresponding to the peaks in F). Traces in F show the spatial profile of the membrane potential along the target, at the time of maximal depolarization (corresponding to the peaks in D, E).

Figure 4—figure supplement 1. More details of the end-shaft synapse simulation

Figure 4—figure supplement 2. More details of the end-end synapse simulation

Experiment details

Settings as well as measured velocity and width of each experiment.

Model parameters

The results from the fitting procedure ri are and cm, these values depend on the model that is used. For the model termed TMHH we adjusted the amplitude (amp.) of the TM model to match the HH model by choosing an appropriate g⋆. This lower value of g⋆ is also used for the RTM model. Internally the simulation uses a diameter of 80 μm, The rows vp and λ⋆ contain the result of the analytical expressions of the TM model. The expressions for vp and λ⋆ are coarse approximations for the RTM model, but do not apply to the HH model.

Complete raw data from experiment number 3 (out of 3).

Grey crosses show the maximal negative deflection of the extracellular potential from 88 recordings (C1, C2, C3 from 3 experiments). Grey dashed lines denote the Full width at half maximum (from channel C2 from all 3 experiments), which is used to fit the models. Continuous lines are the TM model (blue), RTM model (red) and HH model (green). For better comparison, the simulated curves are shifted to peak at −1 mV.

Simulation of target potential in an end-shaft synapse The y-axis denotes the position along the target where y = 0 refers to the target position next to the end of the source axon terminal.

Simulation of target potential in an end-end synapse The y-axis denotes the position along the target where y = 0 refers to the tip of the target at the synaptic gap. The color scale is cropped at −10 μV.