Figure 3.

Complementary Tuning of Na⁺ and K⁺ Conductances Enhances AP Energy Efficiency in PV⁺-BC Axons

(A) Top: Na⁺ current (I_Na) and corresponding conductance (g_Na) evoked by an AP waveform in an axonal membrane patch 102 μm from the soma. Black line indicates a monoexponential function fit to the decay phase of g_Na. Bottom: summary graph of the g_Na decay time constant. Filled circles, individual data points in 28 axonal recordings, box chart indicates the median and distribution of data points.

(B) Top: Na⁺ current (I_Na, blue) evoked by an AP waveform superimposed on the K⁺ current (I_K, red) recorded from the same outside-out patch (102 μm from the soma) to illustrate the delay (δ) between the onset of Na⁺ current and K⁺ current. Bottom: summary graph of the delay. Filled circles, individual data points in 8 axonal recordings, box chart indicates the median and distribution of data points. Traces in (A) and (B) are from the same recording.

(C) Top: K⁺ current (I_K) and corresponding conductance (g_K) evoked by an AP waveform in an axonal membrane patch (81 μm from the soma). Black line indicates a monoexponential function fit to the decay phase of g_K. Bottom: summary graph of the g_K decay time constant. Filled circles, individual data points in 8 axonal recordings, box chart indicates the median and distribution of data points.

(D) Simulation of APs in a hybrid model, in which experimentally determined conductance traces were introduced into a computational model by a threshold trigger mechanism (Alle et al., 2009). Top: structure of the axon cable used for simulations. For further model parameters, see Method Details. Bottom: plot of normalized g_Na and g_K versus time (average from 8 axonal recordings; error bars indicate SEM). Individual conductance values were normalized to peak value for each cell, averaged, and normalized to the peak of the average trace to account for slight differences in peak time.

(E) Propagation of the AP along the axon. Traces represent membrane potential at 5 equally spaced axonal sites. Note that the model predicts fast AP propagation.

(F) Overlay of experimentally recorded AP (blue) and simulated AP (green) in the center of the cable. Peak conductance values (g_Na and g_K) and threshold in the model were varied to provide the best fit to experimental observations. Both traces were vertically aligned by subtracting the membrane potential before the AP and horizontally aligned by subtracting the AP peak time. Weight factors for t_peak − 250 μs ≤ t ≤ t_peak + 500 μs set to 1, and to 0.2 otherwise. Note that measured and simulated traces were in good agreement.

(G) Summary graph of AP peak amplitude (left) and half-duration (right). Note that the model accurately reproduced the experimental observations. Data points representing individual experimentally recorded APs and corresponding simulated APs were connected by lines. NS indicates p = 0.23 and 0.36, respectively.

(H) Summary graph of total Na⁺ charge, relative to the theoretical minimum.

Whiskers in box charts indicate the 5^th and 95^th percentile of data points, and the box itself indicates median, first quartile, and third quartile of the data points.