PMC

Latency analysis from simultaneous axon and soma recordings. A1–A7: data from a representative dentate granule neuron. A1: the somatic membrane potential (V_m) during an action potential. Scale bar is 25 mV. A2: 1st derivative of the somatic membrane potential (dV/dt). Scale bar is 100 mV ms⁻¹. A3: 2nd derivative of the somatic membrane potential (d²V/dt²) exhibits 2 inflection points (indicated by the ↓ and +) occurring after the action potential threshold (- - -). Scale bar is 0.5 × 10⁶ mV ms⁻². A4: 3rd derivative of the membrane potential (d³V/dt³) is used as an aid to determine the first peak inflection on the d²V/dt² trace. Scale bar is 1 × 10¹⁰ mV ms⁻³. A5: axonally recorded extracellular signal at 280 μm from the soma. Scale bar is 10 pA. A6: 1st derivative of the axonal signal (dI/dt). Scale bar is 70 pA ms⁻¹. A7:. 2 latencies are indicated. Time 1 represents the time from the action potential threshold until the membrane potential reaches the 1st (nonstationary) inflection point of d²V/dt² (at the ↓). The nonstationary inflection in the 2nd derivative coincides with a 3rd derivative value that does not pass through 0 in A4 (↓). Time 2 represents the time from the action potential threshold until the peak in the 1st derivative in the axonal action potential signal (A6). B1–B4: data from a representative CA3 pyramidal neuron. B1: the CA3 somatic membrane potential (V_m) during an action potential. Scale bar is 25 mV. B2: 1st derivative of the somatic membrane potential (dV/dt). Scale bar is 100 mV ms⁻¹. B3: 2nd derivative of the somatic membrane potential (d²V/dt²) shows a waveform with 2 inflection points (indicated with ↓ and +) occurring after the action potential threshold (- - -). ··· through the 1st peak indicates a stationary inflection point in the 1st component. Scale bar is 0.5 × 10⁶ mV ms⁻². B4: 3rd derivative of the membrane potential (d³V/dt³) is used as an aid to determine the 2nd derivative stationary inflection point (3rd derivative = 0). Scale bar 1 × 10¹⁰ mV ms⁻³. C: a summary of time 1 from 31 paired recordings to show that the time between 1st threshold crossing and the development/invasion of the action potential into the axon hillock is not dependent on the axonal recording location. —, mean value for time 1 is 0.172 ± 0.004 ms; - - -, SE. D: a summary of time 2 from 31 paired recordings shows that the time between the 1st threshold crossing and the detection of the action potential in the axon ≤400 μm from the soma varied linearly with distance. Regression line (—) is plotted from 70 to 450 μm of axon recording distance (R² = 0.83). - - -, the 95% confidence bands of all possible straight lines through the data points. E: summary of the average conduction velocity over a distance of 400 μm from the soma on mossy fibers. Note the average conduction velocity is calculated from the velocity from the action potential initiation site to the axon recording site and the velocity from the action potential initiation site to the soma.

A, Three different action potentials during the rising phase. Vertical arrows depict the position of the threshold (left) and maximal slope (right). Inset, derivative of the action potential at the point indicated by the arrow. Note different time scale for the inset. B, Plot of the action potential maximal rising slope versus voltage threshold for all recorded action potentials (n = 633 spikes). The line is the best-fit line by the equation y(dV/dt) = −105.72 mV/ms – 7.38 ms⁻¹*x(V), R = −0.725, p<0.0001, two-tailed t test. C, bottom, sequence of action potentials discharged by the cell shown in A. Top, derivative (dV/dt) of the membrane potential (intra-TRN) for the trace at the bottom. Note variation in peak amplitude in the derivative. D, Plot of the action potential maximal rising slope versus the inter-spike interval for all recorded action potentials (n = 633 spikes). The line is the best-fit line by the exponential function y(dV/dt) = 327.43 mV/ms+68.5 mV/ms*exp (x(V)/164.66 ms), p<0.05, Kolmogorov-Smirnov test. Scale bars: A, spike, vertical 20 mV, horizontal 0.1 ms; derivative, vertical 50 mV/ms, horizontal 0.1 ms; C, dV/dt, vertical 200 mV/ms, horizontal 20 ms; intra-TRN, vertical 50 mV, horizontal 20 ms. Some portions of raw data (intracellular voltage recordings) from the cell in this figure have been used in previous publications (see ).

A, action potentials were calculated using a compartmental model for a length of axon incorporating the Hodgkin-Huxley equations. To simulate the effects of blocking K⁺ channels, the maximum K⁺ conductance in the terminal portion of the axon was reduced. B, prolonging action potential repolarization reduced the amplitude and slowed the time course of the negative component of the first derivative (dV/dt) of the action potential.

A, first action potentials evoked by cell depolarisation (400 pA) in control extracellular solution (continuous trace), after addition of TEA (4 mm; short dashed trace) and after addition of 4-AP (100 μM: long dashed trace). B, first action potentials evoked in another Purkinje cell by depolarisation (250 pA) in control extracellular solution (continuous trace), after addition of TEA (4 mm; short dashed trace) and after addition of 4-AP (100 μM: long dashed trace). C, first order time derivative of the same action potentials shown in A. D, first order time derivative of the same action potentials shown in B. Dotted lines in A and B are drawn at 0 mV; in C and D are drawn at 0 velocity.