Networks of interneurons with fast and slow gamma-aminobutyric acid type A (GABAA) kinetics provide substrate for mixed gamma-theta rhythm - PubMed (original) (raw)

Networks of interneurons with fast and slow gamma-aminobutyric acid type A (GABAA) kinetics provide substrate for mixed gamma-theta rhythm

J A White et al. Proc Natl Acad Sci U S A. 2000.

Abstract

During active exploration, hippocampal neurons exhibit nested rhythmic activity at theta ( approximately 8 Hz) and gamma ( approximately 40 Hz) frequencies. Gamma rhythms may be generated locally by interactions within a class of interneurons mediating fast GABA(A) (GABA(A,fast)) inhibitory postsynaptic currents (IPSCs), whereas theta rhythms traditionally are thought to be imposed extrinsically. However, the hippocampus contains slow biophysical mechanisms that may contribute to the theta rhythm, either as a resonance activated by extrinsic input or as a purely local phenomenon. For example, region CA1 of the hippocampus contains a slower class of GABA(A) (GABA(A,slow)) synapses, believed to be generated by a distinct group of interneurons. Recent evidence indicates that these GABA(A,slow) interneurons project to the GABA(A, fast) interneurons that contribute to hippocampal gamma rhythms. Here, we use biophysically based simulations to explore the possible ramifications of interneuronal circuits containing separate classes of GABA(A,fast) and GABA(A,slow) interneurons. Simulated interneuronal networks with fast and slow synaptic kinetics can generate mixed theta-gamma rhythmicity under restricted conditions, including strong connections among each population, weaker connections between the two populations, and homogeneity of cellular properties and drive. Under a broader range of conditions, including heterogeneity, the networks can amplify and resynchronize phasic responses to weak phase-dispersed external drive at theta frequencies to either GABA(A,slow) or GABA(A,fast) cells. GABA(A, slow) synapses are necessary for this process of amplification and resynchronization.

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Figures

Figure 1

Figure 1

Interconnections between two classes of inhibitory interneurons. (a) Slow IPSC evoked in a SR interneuron by SL-M stimulation. The slow IPSC was completely blocked by 40 μM bicuculline. Also shown is the averaged fast spontaneous IPSC from the same cell for comparison. Magnitudes are normalized for comparative purposes. (b) Suggested interneuronal circuitry in region CA1. Solid lines show established connections. Dashed lines show hypothetical connections. GABAA,fast and GABAA,slow cells are so-named because of the kinetics of their postsynaptic effects.

Figure 2

Figure 2

Autonomous theta-gamma oscillations in networks with mixed GABAA kinetics. (a) Raster plots for a network containing 50 GABAA,fast (Bottom) and 50 GABAA,slow (Top) neurons. CVI = the coefficient of variation (ratio of standard deviation to mean) of the level of dc current drive given to the population of cells. Increasing CVI implies increasing heterogeneity in drive. (b and c) Population histograms for (b) GABAA,slow and (c) GABAA,fast cells, generated from the spike trains in a. (d) Magnitude spectra of the histograms of the GABAA,fast cells. The theta (4–12 Hz) and gamma (30–80 Hz) frequency bands are marked. Model specifications: mean values of applied current = 5 μA/cm2 for GABAA,fast cells and 3 μA/cm2 for GABAA,slow cells. In addition to randomly distributed mean currents, time-dependent current noise (normally distributed, σ = 5 μA/cm2) was added to each cell independently. Cells were all-to-all coupled with coupling conductances (in mS/cm2): Gfast,fast = 0.04, Gfast,slow = 0, Gslow,slow = 0.08, Gslow,fast = 0.04.

Figure 3

Figure 3

Dependence on theta and gamma frequencies on synaptic kinetics and applied current. (a) Normalized periods of theta and gamma rhythms from autonomously oscillating, noiseless networks, plotted vs. τA,fast, the time constant of decay of GABAA,fast synapses. Parameter values other than τA,fast and noise level were the same as in Fig. 2. Control values of τA,fast, theta period, and gamma period are 9, 143, and 26 ms, respectively. (b) Normalized periods of theta and gamma rhythms vs. τA,slow, the time constant of decay of GABAA,slow synapses. Parameter values other than τA,slow and noise level were the same as in Fig. 2. Control values of τA,slow, theta period, and gamma period are 50, 143, and 26 ms, respectively. (c) Frequencies of theta and gamma rhythms plotted vs. _I_app, the amount of current delivered to each cell in the simulated network. Also plotted is the ratio (γ/θ) of the gamma frequency to theta frequency. All parameters other than _I_app and noise level were the same as in Fig. 2.

Figure 4

Figure 4

Networks with weak 8-Hz, oscillatory drive show robust theta-gamma activity. Each group of two plots shows population histograms for GABAA,slow (upper plots) and GABAA,fast (lower plots) cells. The average stimulus for each cell is shown schematically above the top two panels. For t < 0, all cells in the network are driven with constant current. For t > 0 (note the tick mark on the x axis), a small 8-Hz component (magnitude 2 μA/cm2) is added to the drive of the GABAA,slow cells. CVI = coefficient of variation (ratio of standard deviation to mean) in dc current drive. σϕ = the standard deviation of the phase of the small 8-Hz input. Both current levels and phases were normally distributed. Model specifications: mean values of applied current = 7 μA/cm2 for GABAA,fast cells, 4.5 μA/cm2 for GABAA,slow cells. Mean values were perturbed with coefficient of variation CVI as before. Time-dependent current noise (normally-distributed, σ = 7 μA/cm2) was added to each cell independently. Cells were all-to-all coupled with coupling conductances (in mS/cm2): Gfast,fast = 0.04, Gfast,slow = 0.03, Gslow,slow = 0.06, Gslow,fast = 0.06.

Figure 5

Figure 5

Frequency spectra of networks with oscillatory drive. Magnitude spectra of histograms of the GABAA,fast cells, arranged in the same order as in Fig. 4. Spectra were derived from fast Fourier transforms (see Materials and Methods) of data traces in Fig. 4 for t > 0.

Figure 6

Figure 6

GABAA,slow synapses are necessary for theta-gamma responses to weak periodic drive. Model parameters as in Figs. 4 and 5 for control simulations (filled symbols). Vector strengths measure the degree to which the GABAA,slow cells synchronize at the stimulus frequency. (a) Vector strengths (means ± σ; n = 5) in response to normally distributed phases of sinusoidal input (σϕ = standard deviation). Solid squares and diamonds indicate delivery of the 8-Hz input to the GABAA,slow and GABAA,fast cells of the control network, respectively. Open symbols indicate responses of a network in which the postsynaptic responses driven by GABAA,slow cells have been transformed into GABAA,fast responses. Vector strengths are measured in the population of formerly GABAA,slow cells. For open circles (error bars too small to resolve), the new network had maximal conductances as in the control case. Open triangles indicate a network with uniform GABAA,fast kinetics in which values of synaptic conductance have been scaled up to preserve the area of the postsynaptic response, and thus leave the average amount of inhibition at a given firing rate unchanged from the control case. (b) Vector strengths in GABAA,slow cells, measured in response to uniformly distributed phases of 8-Hz input to GABAA,slow (squares) or GABAA,fast cells (diamonds).

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