Contribution of the Axon Initial Segment to Action Potentials Recorded Extracellularly

Sodium distribution within the neuron. Color scale shows the channel conductance per membrane area. Left, Physiological Na_v model. Right, Reduced Na_v model. A, Full morphology. B, Zoom into the soma and the initial segments of the axon. C, Concentrations of two different types of sodium channels (Na_v1.2 and Na_v1.6) in the AIS (at 0 μm, AIS is attached to the soma; 69.90 μm is its far end). Note that in both models, the density of Na_v1.2 channels in the soma is 500 pS/μm², while there are no Na_v1.6 channels.

Action potentials in two different locations: soma (orange) and distal end of AIS (blue). The AP is shown both in the time domain (left) and in a phase-plot (right). A, Physiological Na_v model. B, Reduced Na_v model.

Extracellular potentials (right) measured at different locations (white dots within the black rectangle, left) for the physiological Na_v model (red) and reduced Na_v model (green). Calibrations: A, 2 μV; B, 30 μV. The y-scale is adjusted in each panel separately for better visualization of the EAPs. A, Full morphology. B, Zoom in to the soma and initial part of the axon. The distal end of the AIS is marked with a red circle (A, B).

Maximum peak-to-peak amplitude of the EAP calculated in the different places of the field. A, Full morphology imposed on the maximum peak-to-peak amplitude (heatmap; colorbar on the right) in the physiological Na_v model (left) and reduced Na_v model (right). The EAPs with the highest peak-to-peak amplitudes are obtained in the somatic region of the neuron (dark red color in heat map; see also Fig. 6 for a zoom-in). B, Dotted lines show the axes along which subpanels a–e are calculated. Soma is centered at the position (0 μm, 0 μm). B, Maximum peak-to-peak potential normalized to the largest value of the potential for each model separately: the physiological Na_v model (red) and reduced Na_v model (green). The potential is given in the logarithmic scale. a, Signal recorded in the vertical axis passing through the soma. b, Signal recorded in the horizontal axis passing 200 μm above the soma. c, Signal recorded in the horizontal axis passing through the soma. d, Signal recorded in the horizontal axis passing through the AIS. e, Signal recorded in the horizontal axis passing through 200 μm below the soma. Arrows point to the area occupied by a dendrite, which creates a sharp peak in the measured extracellular potential.

Comparison of peak-to-peak amplitude in physiological and reduced Na_v models. A, Zoom-in to the maximum peak-to-peak amplitude of the EAP (shown as a heatmap; colorbar is on the right-hand side) generated by the physiological Na_v model (left) and reduced Na_v model (right). The peak-to-peak amplitude around AIS (red circles, distal end) is higher in the model with axonal initiation (physiological Na_v model). B, C, Difference between normalized peak-to-peak amplitudes (heatmap; colorbar on the right) of the EAP obtained from physiological and reduced Na_v models: the zoomed-in view (B) and full morphology (C).

EAP at different time points in the physiological Na_v model (left) and reduced Na_v model (right). A, Intracellular APs in the soma (orange) and in the end of the AIS (blue). Dotted vertical lines show at which time points B–D are recorded. B–D, Extracellular potentials (colormap; see the colorbar on the right, red is positive and blue is negative) and electrical current (arrows) at different times of APs plotted for around the whole morphology (left) and around the soma–AIS region (right). B–D, Recordings were made as follows: at 0.15 ms before the peak of the AP in the AIS (B), at the peak of the AP in the AIS (C), and 0.4 ms after the peak of the AP in the AIS (D). In the physiological Na_v model, the AP initiates in the AIS (red circles) giving rise to a dipolar potential (AIS negative, soma positive; C, left), which later reverses in polarity (AIS positive, soma negative; D, left). In contrast, the reduced Na_v model produces a large dipole that encompasses the axon, soma, and proximal dendrites (soma–dendrites dipole).

Extracellular potentials calculated from the soma–axon model with the AIS at three different distances: 0 μm from the soma (blue), 20 μm from the soma (green), and 45 μm from the soma (orange). A, Calculation of EAP amplitude in a simplified soma–AIS model. The drawing represents the cell body (white rectangle) and the axon (black) with the AIS at different locations (color coded). The location of the measurement points along horizontal (black dots) and vertical axes (gray stars). B, C, Peak-to-peak amplitude of the EAP along the soma–AIS axis (B, black dots in A show the recording locations) and vertically to the axon (B, gray stars in A) in a double-logarithmic scale. Color lines correspond to different positions of the AIS (see color code in A). Insets show example profiles of AIS amplitudes obtained in full morphologic model (compare Fig. 5B) along the respective axes. The decay of far-field potential with horizontal distance is well approximated with a power law, r^k. The exponent, k, estimated from the slope of linear fit to the log-transformed potential, and the log distance is close to −2 along the horizontal axis (B, the value of k estimated for each model is given in the legend). The k exponent can be even smaller than −2 for vertical axis (C) due to the dependence of the extracellular potentials on the angle from the dipole axis (Fig. 9, θ).

Dipole model consisting of a current sink (red) and a current source (blue) separated by d. The point of measurement represents a possible recording location where extracellular potential, V_ext, is recorded. For the far-field approximation to hold the distance from the dipole r should be much larger than the distance between the sink and source (d). See text for more detail. I is current intensity, σ is extracellular medium conductivity, and θ is the angle measured from the dipole axis.

Dependence of axial current peak-to-peak amplitude on the soma–AIS distance in the soma–axon model. A, Axial current passing from the axon to the soma during the action potential, aligned to the peak of somatic AP (which is at 0.5 ms). B, The maximum of the axial current vs the distance of the AIS end proximal to the soma in double-logarithmic scale. The red line shows the fitted function (which is a linear function in double-logarithmic scale).