Biophysical model for gamma rhythms in the olfactory bulb via subthreshold oscillations

Abstract

Gamma oscillations in the olfactory bulb can be produced as an interaction of subthreshold oscillations (STOs) in the mitral cells (MCs) with inhibitory granule cells (GCs). The mechanism does not require that the GCs spike, and we work in a regime in which the MCs fire at rates lower than the fast gamma rhythm they create. The frequency of the network is that of the STOs, allowing the gamma to be modulated in amplitude with only small changes in frequency. Gamma oscillations could also be obtained with spiking GCs, but only for GCs firing close to population rate. Our mechanism differs from the more standard description of the gamma oscillation, in which the the decay time of the inhibitory cells is critical to the frequency of the network.

Fig. 1.

Uncoupled MCs entrained by common inhibitory periodic input. (A) Percentage of open channels as a function of voltage for spiking (Left) and graded (Right) synaptic conductance. (B–D) Raster plots of the MC firing (Left) showing 450 ms of the 1,600-ms simulation. (Insets) The power spectrum, computed during the period of odor stimulation (1,000 ms), for the average MC voltages, which we define as our model spiking local field potential (sLFP). Two random MC voltages vs. time, with the inhibitory conductance overlaid (C and D), are shown on the right. (B) (Left) Raster plot for the population of MCs without common inhibition shows no synchronous activity in their firing. Simulated odor is introduced at t = 300 ms. The CI of the MC STOs is low but not zero. (Right) Voltage activity of two MCs from the population showing their mixed mode behavior of firing with STOs. (C) (Left) Raster plot for the MCs coupled to a single GCD. The raster plot after odor input becomes more coherent and the CI increases from 0.10 to 0.73. (Right) Voltage activity for two MCs are shown with the synaptic conductance from the GCD (red). The frequency of the inhibitory conductance coincides with that of the gamma rhythm of the MC voltage activity. (D) Population of MCs entrained by a periodic alpha function inhibitory stimulation. (Left) The raster plot shows rhythmic coherent firing of the MCs. (Right) Two MC voltages and the periodic input.

Fig. 2.

Periodic input can synchronize STOs. (A) Spiking currents are not necessary for sustaining the MC STOs. Voltages for two MCs are shown after removing all intrinsic currents except for the K_s and Na_P currents. (B) Periodic stimulation (red) strongly synchronizes STOs. The periodic stimulation has the same strength and frequency as in Fig. 1C but the synchronization of the STOs in this case is much stronger. (C) Decreasing the strength of the stimulation by half still roughly synchronizes the STOs. (D) Frequency of STOs depends on the intrinsic properties of the MCs. Increasing the time constant of the activation variable of the slow potassium current decreases the frequency of the STOs.

Fig. 3.

Sparsely connected population of MCs and GCDs can create fast gamma rhythm with frequency determined by the frequency of the STOs. (A) Sketch of the dendro-dendritic interaction between 100 MCs and 1,000 GCDs. (B) Raster plot showing the spiking activity of the MC population before the odor presentation (t < 300 ms) and after odor presentation (t > 300 ms). After odor is presented, population frequency (sLFP and snLFP) peaks at 72 Hz. (C) Two representative voltage activity traces for the GCDs in the GCD population. The solid line is the half activation value (−66 mV) of the graded synapse, and the dashed lines represent −66 ± 0.2 (see SI Appendix). (D) Power spectrum for the sLFP (blue) and nsLFP (green) are practically identical. (E) Power spectrum for the mean field of the GCD voltage shows that, as a population, the GCD activity oscillates at the same frequency as the MCs (compare with D).

Fig. 4.

External constant excitatory drive to GCDs decreases power of the sLFP with only a small change in frequency. (A) Raster plot (Left) and sLFP power (Right) show a clear gamma rhythm at (≈70 Hz) for the MC population. The mean field for the GCD subthreshold voltages (green) crosses into and out of the region of graded synaptic activation (black solid and dotted lines). The resultant mean GABAa conductance (red) is also modulated at frequency ≈70 Hz (power spectrum not shown). (B) If the GCDs receive too much drive, their voltages remain always above the graded synapse activation threshold and their conductance is almost constant. As a result the MC voltages receive almost constant inhibition incapable of producing a coherent rhythm. This is reflected in the low CI and weak power at the gamma frequency.

Fig. 5.

Rhythm frequency depends only mildly on decay time of inhibition. (A) Spiking inhibition with decay time 18 ms creates a slow rhythm (≈20 Hz) for the GCD and MC populations, as shown in raster plots (Left and Center) and power spectrum for the sLFP (Right). (B) Decreasing the decay time of inhibition 6-fold to 3 ms only increases the rhythm frequency to ≈30 Hz.