Figure 10. Effects of changing the presynaptic firing rate on synchrony and postsynaptic oscillations in a feed-forward SNr neuron pair.

(A) Tuning curve for presynaptic firing rate (FR) versus applied current, $I_{APP}$. Dashed line indicates the baseline firing rate (10.5 Hz) with no applied current. (B) Histograms of the input phase in the postsynaptic neuron under baseline conditions ($I_{APP}=0pA/pF$). (C1–C4) Input phase histograms for different presynaptic firing rates (9.76 Hz, 10.15 Hz, 10.91 Hz, 11.26 Hz from left to right). $E_{GABA}$ ranges are not the same in all panels. Regions of phase slipping (PS) and phase advancing (PA) oscillations are each indicated by a solid horizontal bar. Example oscillations in input phase (D1–D4) and postsynaptic firing rate (E1–E4) at specific values of $E_{GABA}$ for different presynaptic firing rates highlighted in red for the corresponding D panels. Notice that the PA oscillations in C1-2 and D1-2 result in periodic increases in the postsynaptic firing rate in E1-2 whereas PS oscillations in C3-4 and D3-4 result in periodic decreases in firing rate in E3-4.

Figure 10—figure supplement 1. The relationship between $E_{GABA}$ and phase locking and the emergence of slow oscillations are maintained at least up to in vivo SNr firing rates.

(A) Relationship between applied current ($I_{APP}$) and the firing rate of an isolated SNr model neuron. (B) Example voltage trace for a simulated neuron firing at 33.0 Hz with $IAPP=0.8pA/pF$. (C) Histograms of input phase in the two SNr neurons with unidirectional (feed forward) connectivity as a function of $E_{GABA}$. Oscillations occur for $E_{GABA}\le -57mV$ and strict phase locking for $E_{GABA}>-57mV$. (D) Example plot showing slow oscillations in the phase of the presynaptic neuron at which the postsynaptic spike occurs (input phase) over time. (E) Example slow oscillations in the instantaneous firing rate of the postsynaptic neuron. $E_{GABA}=-60mV$ in panels D and E.

Figure 10—figure supplement 2. Effect of increasing noise on SNr phase relationships as a function of $E_{GABA}$.

(A) Dependence of CV (blue) and firing rate (red) of model SNr neuron on applied noise amplitude. (B) Example voltage trace at the highest level of added Gaussian noise ($0.6pA/pF$) and $CV=0.1$. (C) Relationships between $E_{GABA}$ and input phase distributions for increasing Gaussian noise: (C1) $0.2pA/pF$, (C2) $0.4pA/pF$, and (c3) $0.6pA/pF$. (D–E) Example slow oscillations in the input phase (D1–D3) and the post synaptic firing rate (E1–E3). $E_{GABA}$ values in the example traces are indicated by red histograms in the corresponding panel in (C). (F1) Example power spectrum curves in the 0–3 Hz range with 0.0, 0.2, 0.4, and 0.6 pA/pf of Gaussian noise and $E_{GABA}=-60mV$. In each case, results shown are remaining power after subtraction of the mean power in the 3–4 Hz range. (G) Area of the power spectrum peak as a function of $E_{GABA}$ and applied Gaussian noise. (H) CV in the postsynaptic neuron as a function of $E_{GABA}$ and added Gaussian noise. Note that postsynaptic CVs exceed those reported in the literature when we take a noise amplitude of 0.6 pA/pf, suggesting that this value may be excessive.

Figure 10—figure supplement 3. Effect of synaptic delay on the relationship between $E_{GABA}$ and presynaptic/postsynaptic phase locking.

(A–C) Examples of synaptic delays of increasing magnitude: 0 mS, 1.6 mS, and 8.6 mS, respectively. (D) Histogram of input phase in the postsynaptic neuron as a function of $E_{GABA}$ and varying delay duration. Notice that delays do not strongly effect the neurons’ spiking relationship.

Figure 10—figure supplement 4. Relationship between postsynaptic firing properties as a function of $E_{GABA}$ and varying degrees of synchrony between two presynaptic neurons.

(A) Characterization of the varying degrees of presynaptic synchrony defined by the parameter presynaptic offset. The presynaptic offset is the phase difference between the first (red) and second (blue) presynaptic neuron. (B and C) Effect of varying presynaptic offset on postsynaptic (B) firing rate and (C) coefficient of variation (CV). (D1–D6) Input phase histograms for synaptic inputs in the postsynaptic neuron from the first presynaptic neuron as a function of the presynaptic offset and $E_{GABA}$. (E1–E6) Power spectrum in the post synaptic neurons as a function of the presynaptic offset and $E_{GABA}$.

Figure 10—figure supplement 5. Relationship between postsynaptic firing properties as a function of $E_{GABA}$ and varying degrees of synchrony between three presynaptic neurons.

(A) Characterization of the varying degrees of presynaptic synchrony defined by the parameter presynaptic offset. The presynaptic offset is the phase difference between the first (red),second (green) and third (blue) presynaptic neuron. (B and C) Effect of varying presynaptic offset on postsynaptic (B) firing rate and (C) coefficient of variation (CV). (D1–D6) Input phase histograms for synaptic inputs in the postsynaptic neuron from the first presynaptic neuron as a function of the presynaptic offset and $E_{GABA}$. (E1–E6) Power spectrum in the post synaptic neurons as a function of the presynaptic offset and $E_{GABA}$.

Figure 10—figure supplement 6. Relationship between postsynaptic firing properties as a function of $E_{GABA}$ and varying degrees of synchrony between four presynaptic neurons.

(A) Characterization of the varying degrees of presynaptic synchrony defined by the parameter presynaptic offset. The presynaptic offset is the phase difference between the first (red),second (green),third (blue) and fourth (purple) presynaptic neuron. (B and C) Effect of varying presynaptic offset on postsynaptic (B) firing rate and (C) coefficient of variation (CV). (D1–D6) Input phase histograms for synaptic inputs in the postsynaptic neuron from the first presynaptic neuron as a function of the presynaptic offset and $E_{GABA}$. (E1–E6) Power spectrum in the post synaptic neurons as a function of the presynaptic offset and $E_{GABA}$.

Figure 10—figure supplement 7. Effects of varying $E_{GABA}$ on post synaptic dynamics in the three-neuron motif where neuron 1 projects to neuron 2 and neuron 3 and neuron 2 projects to neuron 3 (motif number 10 from Song et al., 2005).

(A) Phase difference between the two presynaptic neurons (cell 1 and cell 2) as a function of $E_{GABA}$. (B) Firing rate and coefficient of variation (CV) in the postsynaptic neuron (cell 3) as a function of $E_{GABA}$. (C) Input phase histograms for synaptic inputs in the postsynaptic neuron from the first presynaptic neuron as a function of $E_{GABA}$. (D) Power spectrum in the postsynaptic neuron as a function of $E_{GABA}$. (E1 and E2) Example traces of the input phase relationship between the postsynaptic neuron and the first presynaptic neuron. The value of $E_{GABA}$ is indicated to the left of each trace.