Long anisotropic absolute refractory periods with rapid rise times to reliable responsiveness

Refractoriness is a fundamental property of excitable elements, such as neurons, indicating the probability for re-excitation in a given time lag, and is typically linked to the neuronal hyperpolarization following an evoked spike. Here we measured the refractory periods (RPs) in neuronal cultures and observed that an average anisotropic absolute RP could exceed 10 ms and its tail is 20 ms, independent of a large stimulation frequency range. It is an order of magnitude longer than anticipated and comparable with the decaying membrane potential time scale. It is followed by a sharp rise-time (relative RP) of merely ∼1 md to complete responsiveness. Extracellular stimulations result in longer absolute RPs than solely intracellular ones, and a pair of extracellular stimulations from two different routes exhibits distinct absolute RPs, depending on their order. Our results indicate that a neuron is an accurate excitable element, where the diverse RPs cannot be attributed solely to the soma and imply fast mutual interactions between different stimulation routes and dendrites. Further elucidation of neuronal computational capabilities and their interplay with adaptation mechanisms is warranted.

Figure 1

The experimental setup and measurements of the RP using pairs of intracellular stimulations. (a) Left: A microelectrode array (MEA) consisting of 60 electrodes combined with a patch-clamp pipette (orange) (see Sec. 4 for details). Right: A scheme of a patched neuron, which can be extracellularly stimulated via its two dendrites (purple and green electrodes) and intracellularly via the patch-clamp pipette (orange). (b) An intracellular recorded evoked spike by intracellular stimulation without visible hyperpolarization. (c) Similar to (b), but with extracellular stimulation. (d) A scheme of the first type of experiments where two intracellular stimulations separated by increasing $\mathrm{\Delta }t$ is given to a patched neuron. (e) Neuronal responses to the stimulation scheduling in (d) with stimulations amplitudes close to the neuronal intracellular threshold (750 pA intensity, 3 ms duration), where $\mathrm{\Delta }t=\left[4,5.4\right]$ ms with increments of 0.1 ms, with vanishing RRP under experimental resolution. (f) Histogram of the ARP obtained from $n=14$ experiments as in (e) (see also Supplemental Material [13]). (g) The same neuron in (e) but with strong intracellular stimulations amplitudes (1200 pA intensity, 3 ms duration), $\mathrm{\Delta }t=\left[3,6.8\right]$ ms with increments of 0.2 ms, with vanishing RRP under experimental resolution.

Figure 2

Measurements of the RP using combinations of intra- and extracellular stimulations. (a) A scheme of the second type of experiments where a neuron is stimulated intracellularly and then stimulated extracellularly after $\mathrm{\Delta }t$. (b) Results of (a) using $\mathrm{\Delta }t=\left[8,12.9\right]$ ms with an increment of 0.1 ms (gray color lines represent no responses to the second extracellular stimulations, as the neuron is in the ARP). Extracellular stimulations were given with 380 mV amplitude, 0.2 ms duration. Intracellular stimulations were given with 1200 pA intensity, 3 ms duration. (c) Probability for an evoked spike in (b) using sliding average over three consecutive $\mathrm{\Delta }t$ [the responses in the range [8.9,9.4] are 101101, where 1 (0) stands for spike (no spike), respectively], RRP $=0.5\mathrm{ms}$. (d) Results of (a) for another neuron with $\mathrm{\Delta }t=\left[3,27.5\right]$ ms with increments of 0.5 ms, indicating ARP larger than 20 ms and negligible RRP (gray color lines represent small depolarization to the second extracellular stimulations, as the neuron is in the ARP). Extracellular stimulations were given with 900 mV amplitude, 2 ms duration. Intracellular stimulations were given with 800 pA intensity, 3 ms duration. (e) Histogram of the ARP obtained from $n=18$ experiments of type 2 (see text and Supplemental Material). (f) A scheme of the third type of experiments where a neuron is stimulated from the same extracellular electrode by pairs of stimulations separated by increasing $\mathrm{\Delta }t$. (g) Results of (f) using $\mathrm{\Delta }t=\left[9,13.9\right]$ ms with increments of 0.1 ms. Extracellular stimulations were given with 400 mV amplitude, 0.2 ms duration. (h) Probability for an evoked spike in (g) using sliding average over five consecutive $\mathrm{\Delta }t$ in the range $\mathrm{\Delta }t=\left[9.8,11.1\right]$ ms (the responses were 10000100101101), RRP $=1.3\mathrm{ms}$. (i) Histogram of the ARP obtained from $n=11$ experiments of type 3 (see text and Supplemental Material).

Figure 3

The ARP as a function of the stimulation frequency, measured by pairs of extracellular stimulations from the same electrode. The patched neuron was stimulated twice using an extracellular electrode, at a time lag $\mathrm{\Delta }t=\left[3,27.5\right]$ ms with increments of 0.5 ms. The neuronal responses are presented for stimulation frequencies of 0.5, 2, 4, 8, 12, 15, and 20 Hz. Results indicate that the ARP is around 5.9 ms and with negligible RRP under the experimental resolution, independent of the stimulation frequency. Gray color lines represent no responses to the second extracellular stimulations, as the neuron is in the ARP. Extracellular stimulations were given with 900 mV amplitude, 0.2 ms duration. Population behavior is presented in Supplemental Material Fig. S1.

Figure 4

Anisotropic properties of the ARP, using pairs of extracellular stimulations from two different extracellular electrodes with distinct spike wave forms. (a) A scheme of the fourth type of experiments, a patched neuron is stimulated using two different extracellular electrodes (purple and green) separated by increasing $\mathrm{\Delta }t$. (b) The two extracellular electrodes experimentally generate two distinct intracellular measured spike wave forms. (c) Results of (a), where the stimulation from the green electrode is given $\mathrm{\Delta }t$ before the purple electrode, $\mathrm{\Delta }t=\left[1,25.5\right]$ ms with increments of 0.5 ms and vanishing RRP under the experimental resolution (gray color lines represent small depolarization to the second extracellular stimulations, as the neuron is in the ARP). (d) Similar to (c), but the stimulation from the purple electrode is given before the stimulation from the green electrode, $\mathrm{\Delta }t=\left[4,28.5\right]$ ms with increments of 0.5 ms and vanishing RRP under te expeprimental resolution. All extracellular stimulations were given with 900 mV amplitude, 0.2 ms duration.

Figure 5

Anisotropic properties of the ARP, using pairs of extracellular stimulations from two different extracellular electrodes (green and purple) with similar spike waveforms. (a) Top: A scheme of the stimulation scheduling from an extracellular electrode (green), where a pair of stimulations is separated by increasing $\mathrm{\Delta }t$. Bottom: The responses of the patched neuron, with vanishing RRP under experimental resolution. (b) Similar to (a), where stimulations are given from the purple electrode and with vanishing RRP under experimental resolution. (c) Similar to (a), where the stimulation from the purple electrode is given before the stimulation from the green electrode, with vanishing RRP under experimental resolution. (d) Similar to (a), the stimulation from the green electrode is given before the stimulation from the purple electrode. In all panels $\mathrm{\Delta }t=\left[2.5,27\right]$ ms with increments of 0.5 ms and with vanishing RRP under experimental resolution. Gray color lines represent small depolarization or no responses to the second extracellular stimulations, as the neuron is in the ARP. All extracellular stimulations were given with 900 mV amplitude, 2 ms duration.

Figure 6

The effect of different amplitudes and temporal ordering of intra- and extracellular stimulations on the ARP and neuronal outputs. (a) Neuronal responses to strong intracellular stimulations amplitudes, where two intracellular stimulations separated by increasing $\mathrm{\Delta }t$ are given to a patched neuron [the same type of experiment presented in Fig. 1], where $\mathrm{\Delta }t=\left[1,8\right]$ ms with increments of $0.5$ ms and with vanishing RRP under experimental resolution (gray color lines represent no responses to the second intracellular stimulations, as the neuron is in the ARP). Intracellular stimulations were given with 1300 pA intensity, 0.5 ms duration. (b) Responses of the same neuron in (a) using stimulation scheduling where the neuron is stimulated from the same extracellular electrode by pairs of stimulations separated by increasing $\mathrm{\Delta }t$ [the same type of experiment presented in Fig. 2], where $\mathrm{\Delta }t=\left[4,26\right]$ ms, with increments of 1 ms and with vanishing RRP under experimental resolution (gray color lines represent no responses to the second extracellular stimulations, as the neuron is in the ARP). Extracellular stimulations were given with 900 mV amplitude, 1 ms duration. (c) The same neuron as in Fig. 2, stimulated by pairs of a strong intracellular stimulation given $\mathrm{\Delta }t$ after an extracellular one with an amplitude close to its threshold, $\mathrm{\Delta }t=[-6,-1.1]$ ms, with increments of 0.1 ms, where the neuronal response latency of an extracellular stimulation is ∼2 ms (see Sec. 4) and with vanishing RRP under experimental resolution. Extracellular stimulations were given with 500 mV amplitude, 0.2 ms duration. Intracellular stimulations were given with of 1200 pA intensity, 3 ms duration. (d) The second type of experiment, where the neuron is stimulated by pairs of an extracellular stimulation given $\mathrm{\Delta }t$ after an intracellular one [Fig. 2], with stimulation amplitude of 730 mV $\left({\mathrm{d}}_1\right)$ and 900 mV $\left({\mathrm{d}}_2\right)$, both durations are 0.2 ms (Sec. 4) and with vanishing RRP under experimental resolution. $\left({\mathrm{e}}_{\mathbf{1}}\right)$ A scheme of a perceptron with arbitrary synchronous input and set of weights resulting in two possible outputs, spike or no spike. $\left({\mathrm{e}}_{\mathbf{2}}\right)$ Similar to $\left({\mathrm{e}}_{\mathbf{1}}\right)$ but with equal weights which are grouped into short and long delays, representing two dendrites, and with three possible stimulation amplitudes (color coded): $A_s$, strong stimulation much above the threshold, $A_{Th}^{+}$ and $A_{Th}^{-}$ close to the threshold from above and below, respectively. Spike timings and ARPs are represented by red arrows and yellow strips, respectively. The ARP is longer after an evoked spike resulted from $A_{Th}^{+}$ (third output), where the dashed red arrow represents a response failure, no spike.