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Mechanisms of firing patterns in fast-spiking cortical interneurons.

Golomb D, Donner K, Shacham L, Shlosberg D, Amitai Y, Hansel D - PLoS Comput. Biol. (2007)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, Ben-Gurion University, Be'er-Sheva, Israel. golomb@bgu.ac.il

ABSTRACT
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.

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Voltage Traces and Firing Patterns of the Model Neuron in Response to a Noisy Current Step(A) Delayed tonic firing for θm = −24 mV, gd = 0.39 mS/cm2, Iapp = 3.35 μA/cm2.(B) Delayed stuttering for θm = −24 mV, gd = 1.8 mS/cm2, Iapp = 4.2 μA/cm2.(C) Delayed tonic firing for θm = −28 mV, gd = 0.39 mS/cm2, Iapp = 1.25 μA/cm2. In all three panels, the variance of the noise is D = 0.01 μA2 × ms/cm4. The time course of the mean applied current, Iapp, is also plotted. The membrane potentials during the delay periods are magnified in the panels on the right. Note the presence of subthreshold oscillations in (A) and (B). The peaks of these oscillations are denoted by the arrows.
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pcbi-0030156-g007: Voltage Traces and Firing Patterns of the Model Neuron in Response to a Noisy Current Step(A) Delayed tonic firing for θm = −24 mV, gd = 0.39 mS/cm2, Iapp = 3.35 μA/cm2.(B) Delayed stuttering for θm = −24 mV, gd = 1.8 mS/cm2, Iapp = 4.2 μA/cm2.(C) Delayed tonic firing for θm = −28 mV, gd = 0.39 mS/cm2, Iapp = 1.25 μA/cm2. In all three panels, the variance of the noise is D = 0.01 μA2 × ms/cm4. The time course of the mean applied current, Iapp, is also plotted. The membrane potentials during the delay periods are magnified in the panels on the right. Note the presence of subthreshold oscillations in (A) and (B). The peaks of these oscillations are denoted by the arrows.

Mentions: The probability of firing is always non-zero in the presence of noise. Hence, strictly speaking, the very definition of a delay in firing is ambiguous. This probability, however, is (exponentially) small in the limit of small noise. In practice, delays can still be observed in a clear manner in the model unless the noise is large. This is shown for both small (Figure 7A and 7B) and large (Figure 7C) Na+ window currents.


Mechanisms of firing patterns in fast-spiking cortical interneurons.

Golomb D, Donner K, Shacham L, Shlosberg D, Amitai Y, Hansel D - PLoS Comput. Biol. (2007)

Voltage Traces and Firing Patterns of the Model Neuron in Response to a Noisy Current Step(A) Delayed tonic firing for θm = −24 mV, gd = 0.39 mS/cm2, Iapp = 3.35 μA/cm2.(B) Delayed stuttering for θm = −24 mV, gd = 1.8 mS/cm2, Iapp = 4.2 μA/cm2.(C) Delayed tonic firing for θm = −28 mV, gd = 0.39 mS/cm2, Iapp = 1.25 μA/cm2. In all three panels, the variance of the noise is D = 0.01 μA2 × ms/cm4. The time course of the mean applied current, Iapp, is also plotted. The membrane potentials during the delay periods are magnified in the panels on the right. Note the presence of subthreshold oscillations in (A) and (B). The peaks of these oscillations are denoted by the arrows.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1941757&req=5

pcbi-0030156-g007: Voltage Traces and Firing Patterns of the Model Neuron in Response to a Noisy Current Step(A) Delayed tonic firing for θm = −24 mV, gd = 0.39 mS/cm2, Iapp = 3.35 μA/cm2.(B) Delayed stuttering for θm = −24 mV, gd = 1.8 mS/cm2, Iapp = 4.2 μA/cm2.(C) Delayed tonic firing for θm = −28 mV, gd = 0.39 mS/cm2, Iapp = 1.25 μA/cm2. In all three panels, the variance of the noise is D = 0.01 μA2 × ms/cm4. The time course of the mean applied current, Iapp, is also plotted. The membrane potentials during the delay periods are magnified in the panels on the right. Note the presence of subthreshold oscillations in (A) and (B). The peaks of these oscillations are denoted by the arrows.
Mentions: The probability of firing is always non-zero in the presence of noise. Hence, strictly speaking, the very definition of a delay in firing is ambiguous. This probability, however, is (exponentially) small in the limit of small noise. In practice, delays can still be observed in a clear manner in the model unless the noise is large. This is shown for both small (Figure 7A and 7B) and large (Figure 7C) Na+ window currents.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, Ben-Gurion University, Be'er-Sheva, Israel. golomb@bgu.ac.il

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus