Mechanisms of firing patterns in fast-spiking cortical interneurons.
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In contrast, when the Na(+) window current is large, the neuron always fires tonically.We propose that the variability in the response of cortical FS neurons is a consequence of heterogeneities in their gd and in the strength of their Na(+) window current.We report experimental results from intracellular recordings supporting this prediction.
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Affiliation: Department of Physiology, Ben-Gurion University, Be'er-Sheva, Israel. golomb@bgu.ac.il
ABSTRACT
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Cortical fast-spiking (FS) interneurons display highly variable electrophysiological properties. Their spike responses to step currents occur almost immediately following the step onset or after a substantial delay, during which subthreshold oscillations are frequently observed. Their firing patterns include high-frequency tonic firing and rhythmic or irregular bursting (stuttering). What is the origin of this variability? In the present paper, we hypothesize that it emerges naturally if one assumes a continuous distribution of properties in a small set of active channels. To test this hypothesis, we construct a minimal, single-compartment conductance-based model of FS cells that includes transient Na(+), delayed-rectifier K(+), and slowly inactivating d-type K(+) conductances. The model is analyzed using nonlinear dynamical system theory. For small Na(+) window current, the neuron exhibits high-frequency tonic firing. At current threshold, the spike response is almost instantaneous for small d-current conductance, gd, and it is delayed for larger gd. As gd further increases, the neuron stutters. Noise substantially reduces the delay duration and induces subthreshold oscillations. In contrast, when the Na(+) window current is large, the neuron always fires tonically. Near threshold, the firing rates are low, and the delay to firing is only weakly sensitive to noise; subthreshold oscillations are not observed. We propose that the variability in the response of cortical FS neurons is a consequence of heterogeneities in their gd and in the strength of their Na(+) window current. We predict the existence of two types of firing patterns in FS neurons, differing in the sensitivity of the delay duration to noise, in the minimal firing rate of the tonic discharge, and in the existence of subthreshold oscillations. We report experimental results from intracellular recordings supporting this prediction. Related in: MedlinePlus |
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Mentions: We now turn to the dynamics of the full system. Let us assume that the neuron is at rest (Iapp = 0) and that the inactivation variable b is equal to brest (brest = 0.5 in the example of Figures 2C and 5A). At time t = 0, a current step is applied and Iapp is raised abruptly (e.g., 3.35 Î¼A/cm2 in Figure 5Aâ€“5C and 1.25 Î¼A/cm2 in Figure 5Dâ€“5F). The evolution of the membrane potential of the neuron, V, right after the step onset is driven first by the dynamics of the fast subsystem with b âˆ¼ brest (Figures 5A and 5D). The membrane depolarizes rapidly, the current Id starts to inactivate, and the variable b decreases. During this process, which occurs on the slow time scale of Ï„b, the state of the neuron follows the fixed point of the fast subsystem adiabatically, for the applied current Iapp. In particular, the membrane potential of the neuron is V(t) âˆ¼ VFP(b(t)), and the slow variable b continues to decrease as long as bâˆž(VFP(b(t))) < b (Equation 17). If the equation bâˆž(VFP(b)) = b has a solution, b*, for which the fixed point of the fast subsystem is stable, b stops evolving when it reaches that value. In that case, the state of the neuron converges to a stable fixed point where it does not fire action potentials. This situation, which happens when Iapp is small, is depicted in Figure 6A and 6B. The value b* decreases with Iapp. The largest value of Iapp for which the fixed point is stable is determined by the equationor by the equation bâˆž(VFP(bSN; Iapp)) = bSN for small and large window INa, respectively. For larger values of Iapp, a solution of the equation bâˆž(VFP(b)) = b exists only for a b value for which the fixed point of the fast subsystem is unstable (Figure 5C and 5F). As a result, b keeps decreasing until it crosses the bifurcation of the fast subsystem (b = bHopf or b = bSN). When this happens, V starts to diverge from VFP(b) and the neuron fires action potentials. The patterns of firing following the delay can also be assessed using the fastâ€“slow analysis as we will explain below. |
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Affiliation: Department of Physiology, Ben-Gurion University, Be'er-Sheva, Israel. golomb@bgu.ac.il