AP collision experiment. (A) The ventral nerve cord (VNC) of an earthworm is positioned on a series of transverse, single-ended electrodes to excite and monitor APs. 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. (B) Photograph of the recording chamber with a white thread to illustrate the position of the VNC. (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 collision is captured in the recording line at y-position 0 mm, while orthodromic propagation is at the top and antidromic propagation is at the bottom. (D) The peak amplitude as a function of the distance to the collision. Examples of four sweeps at three positions along the nerve cord. 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 flows 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) Model predictions of the discharge (q(x)) generated by AP annihilation and released around the collision site. (D) 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.

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 at a bouton of a neuron terminal (upper neuron in 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

Comparison of experimental data from Blot and Barbour (2014) on modulation of Purkinje cell activity (grey lines) with our RTM model predictions (red lines with two different τ) and the TM model prediction (blue) for two different geometries and physiological properties of the source neuron (e.g. the Basket cell). (A) source neuron with bouton (size 2 µm) and all segments in our calculation with same physiology (excitable). (B) source neuron with bouton as well but last segments, corresponding to 15 µm inactivated (non-excitable, e.g. no switch from resting state to excited state).

Experiment details

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

Model parameters

For all models, we used the measured propagation velocity vp (14.9 m/s) and the width of the collision, which is described by λ⋆ (1.8 mm) in the TM and RTM model, in order to adjust the parameters ri and cm. For the HH model, we used literature values describing the different channels, their conductivities and time constants. For the TM model, we used the value of g⋆ as given by Tasaki and Matsumoto (2002). In order to compare the TM and the RTM with the HH model, we adjusted g⋆ such that the extracellular potential of the AP is comparable. Although the predicted amplitudes of the extracellular potentials are very different, the products ricm are very similar and in good agreement with literature values (see Tasaki and Matsumoto (2002)).

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

Grey crosses show the maximal negative deflection of the extra-cellular 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.