Figure 1.
Synaptically Driven Oscillations Optimize AP Precision In Vivo
(A) Schematic of the rodent olfactory receptor neuron (ORN) projection to a glomerulus in the olfactory bulb illustrating that oscillatory sensory input is coupled to the “sniff cycle” (inset, lower left). An example trace (top right) of a whole-cell recording from a representative mitral cell in a freely breathing mouse showing network-evoked oscillations in membrane potential due to background room-odor and overt odor (black line) stimulation. At the time indicated by the black horizontal bar, an overt odor stimulus (0.1% amyl acetate) evoked AP discharge. The simultaneously recorded thorax distention signal is shown directly underneath. Below an average trace is displayed, showing the subthreshold theta oscillation in the freely breathing preparation (traces averaged with respect to the thoracal breathing cycle [37]).
(B1 and B2) Average of subthreshold voltage traces showing that the inherent oscillatory membrane potential in the freely breathing animal can be abolished and reproduced in a tracheotomized preparation. Below are single example traces showing that continuous airflow through the nose removes the MPO (B1), whereas pulsed nasal airflow (triggered by the thorax signal) mimics the subthreshold oscillatory drive and controls spike timing (B2). The inset shows an example of an overt odor-evoked response in the tracheotomized preparation. From top to bottom: membrane voltage recording (scale bars are 20 mV and 500 ms), nasal suction, and odor valve opening. Odor presented was 10% hexanol. In the constant airflow case, positive constant current was injected to evoke approximately the same number of APs per thoracal breathing cycle.
(C) Overlapping histograms of AP times for continuous and pulsed airflow. Overlaid is the Gaussian fit of the pulsed airflow case (dashed red trace, n = 3 animals) and the freely breathing case ( n = 7, gray trace).
(D) AP precision was determined by combining respiration cycles with the same number of APs and quantified by measuring the average distance of each AP to the mean AP time. The mean distance (“AP jitter”) is measured relative to the thorax signal and plotted as a function of the number of APs per cycle. Pooled data from n = 3 cells showing AP precision for the oscillation (red) and nonoscillation case (black). Lower values of the jitter indicate higher precision (plotted is the mean ± SEM).
(E) AP precision data from the same experiments as in D, but normalized (gray lines) to the nonoscillation case for the first, second, third, and fourth AP within each oscillation cycle. Dashed line (red) is a linear fit to the oscillation data points. Note the jitter accumulation with AP number within an oscillation cycle for the synaptically driven oscillation.
Figure 2.
Current-Injection Evoked Oscillations Maintain Optimal AP Precision In Vitro
(A1) Experimental configuration for examining the impact of oscillations on AP precision in vitro. Under control conditions, mitral cells recorded in vitro received input current injected via the pipette consisting of known Poisson trains convoluted with EPSC-like waveforms and added noise (see Materials and Methods). In the oscillation condition, a sine wave was added to the control stimulus.
(A2) (Top) Single traces showing the voltage recorded under the two conditions in A1. Immediately below are rasters of AP discharge for ten repetitions (different random seeds for noise generation) for a single stimulus under control and oscillatory conditions. (Bottom) PSTH from the raster plots above. Spike trains were smoothed with a Gaussian filter (5 ms).
(A3) Autocorrelation of the PSTHs shown in A2.
(B) AP precision data from experiments as in A2, where AP jitter is normalized (gray line) to the nonoscillation case for the first, second, third, and fourth AP within each oscillation cycle. Dashed line (red) is a linear fit to the oscillation data points. Note that—as with the in vivo data (Figure 1E)—AP jitter accumulates with AP number within an oscillation cycle.
Figure 3.
Membrane Potential Hyperpolarization Recovers AP Precision
(A1) Five overlaid consecutive traces of the membrane voltage of a representative mitral cell in response to a long current injection that elicited an AP train of increasing imprecision. Red bars (above) indicate increasing AP jitter accumulation with time. (Right) Five voltage traces from the same cell where spiking is interrupted by 100-ms hyperpolarizing pulses, thus imitating oscillations with one, two, and three APs. Current pulse amplitude is 250 pA.
(A2) The mean ± SEM of the AP jitter from recordings with (red) and without (black) intermittent hyperpolarizing pulses plotted against AP number. Each data point is normalized to the jitter of the sixth spike. AP precision is fully preserved or recovered by the hyperpolarizing intervals ( n = 11).
(B1) Five overlaid consecutive traces of the membrane voltage of a representative CA1 pyramidal cell in response to a long current injection that elicited an AP train of increasing imprecision. Red bars (above) indicate increasing AP jitter accumulation with time. (Right) Five voltage traces from the same cell where spiking is interrupted by 100-ms hyperpolarizing pulses, thus imitating oscillations with one, two, and three APs. Current pulse amplitude is 300 pA.
(B2) The mean ± SEM of the AP jitter from recordings with (red) and without (black) intermittent hyperpolarizing pulses plotted against AP number. Each data point is normalized to the jitter of the sixth spike. AP precision is fully preserved or recovered by the hyperpolarizing intervals (CA1 pyramids, triangles, n = 5, left axis; and Purkinje neurons, squares, n = 3, right axis).
Figure 4.
Hyperpolarizations Maintain AP Precision by Minimizing Membrane Potential Variance
(A1) Schematic showing the experimental configuration and analysis parameters of the mitral cell membrane voltage recorded while varying the hyperpolarization period (Δt; 2 to 400 ms). AP jitter was created by injecting a depolarizing current pulse (150 to 250 pA for 100 ms) and estimated by calculating the standard deviation of the pre-AP time. The effect of the hyperpolarizing pulse on precision recovery was measured by determining the jitter of the AP immediately following the hyperpolarization pulse (post-AP) and comparing it to the control AP. The relationship between membrane potential at the beginning (Vmpre) and at the end (Vmpost) was determined by calculating the mean voltage over the first 250 μs and the last 100 μs of the nonspiking interval.
(A2) Two example traces of a 2-ms hyperpolarizing pulse with post-APs showing that depolarized (−48 mV) and hyperpolarized (−58 mV) potentials evoked early and late post-APs, respectively. The red ellipse highlights the variable membrane potential at the end of the hyperpolarizing pulse; red lines indicate the variable AP times of the post-AP that reflect post-AP jitter.
(A3) Representative voltage traces of APs for hyperpolarization intervals of 2, 6, 24, and 80 ms show a large variation in Vmpre (see also C); traces with the earliest and the latest prehyperpolarization AP are highlighted in black. Ten overlaid traces show the reduction in the variable membrane potential across the recovery period. The associated reduction in post-AP jitter is indicated by the red bars above the clipped APs.
(A4) Post-AP jitter as a function of the recovery interval (mean ± SEM, n = 4 cells). The data points were fitted with a single exponential (τ = 6.8 ms). The precision of the control AP is indicated by the dashed line. Inset: Correlation between the post-AP jitter and membrane potential variance at Vmpost ( R2 = 0.86).
(B) The correlation between Vmpre and Vmpost plotted as a function of the recovery interval ( n = 4). The graph is overlaid by the single exponential fit shown in A4 (red line). Inset: The Vmpre and Vmpost values are plotted for a 2-ms interval (filled circles) and compared to that for a 120-ms interval (open circles).
(C) (Top) Example traces showing the relationship between the pre-AP time (relative to the pulse onset) and Vmpre. (Below) A plot of Vmpre against pre-AP time for a single cell. A single AHP trace is superimposed on the graph.
(D1) Five consecutive traces from a mitral cell show spontaneous AP jitter relative to the same randomly chosen point in time (black) and the jitter of the AP (red) immediately following a precise AP (left). Cells were held at threshold by injecting constant current and the precise AP (pAP) was elicited by brief current injection (1,000 pA for 2 ms).
(D2) Population data from mitral cells ( n = 6), pyramidal neurons ( n = 5), and Purkinje neurons ( n = 3) showing the normalized jitter of ongoing APs and the AP immediately following the injected pAP (mean ± SEM, p < 0.001 in all cell types). Precision recovery is similar in the three cell types.
Figure 5.
Oscillation-Mediated AP Precision Permits Separation of Stimulus-Specific Spike Trains In Vitro
(A1) Stimuli (with the addition of randomly seeded noise, not shown) were evoked in CA1 pyramidal cells via the recording pipette in the absence and presence of an oscillation.
(A2) Example raster plots show ten repetitions for two different stimuli with and without MPOs.
(B) The normalized PSTH was calculated by averaging the ten smoothed (Gaussian filter; σ = 5 ms) spike trains shown in (A) and is plotted for stimulus 1 (green) and stimulus 2 (blue) separately (ordinate axis shown on left). Gray indicates the variance of the PSTH for stimulus 1 (SD of the ten [smoothed] repetitions shown in A2). Bar graphs show the overall AP precision for the entire stimulus period and both stimuli (ordinate axis far right).
(C1) A PSTH difference plot showing the difference between the mean PSTHs corresponding to the two stimuli normalized to the variance (red bars indicate where the two stimulus-evoked spike trains can be separated because the normalized PSTH difference is larger than 1, dashed line).
(C2) Population data showing temporal separation of all pairs of stimuli. Values given are the fraction of time the normalized PSTH difference was larger than 1 (e.g., red bars in C1, n = 7 cells, n = 77 stimulus pairs).
(C3 and C4) PSTH differences separated based on the amplitude of injected noise (low σ = 0.1–0.2 mV, n = 3 cells, 48 stimulus pairs; high σ = 0.3–0.5 mV, n = 4 cells, 29 stimulus pairs). Dotted line indicates chance level.
Figure 6.
Oscillations Boost Stimulus Discrimination by Optimizing AP Precision
(A1) Scheme showing the template-matching discrimination analysis: Spike trains of repetition A are correlated to trains from repetition B. Correlation coefficients are ranked and the rank of the correct match indicates level of discrimination: Examples shown are perfect (stimulus 1, highest correlation coefficient between 1A and 1B → rank 1) and near-perfect (stim. 3, second-highest correlation coefficient for 3A and 3B → rank 2).
(A2) Stimulus discrimination plotted as the mean rank for the ten most separable stimulus sets from a single CA1 cell in vitro under control (no oscillation) and oscillation conditions ( p < 10−12 for all n = 135 stimulus sets in n = 3 cells).
(B1) Stimulus discrimination plotted as mean rank as a function of stimulus number in simulation in an InF neuron. Inset: Mean rank scores for low numbers of stimuli. For all panels, filled red circles indicate where the discrimination for the oscillation case is significantly better than the respective control discrimination ( p < 0.05, Mann-Whitney). Dotted lines indicate perfect and chance levels of stimulus discrimination.
(B2) Discrimination in an InF neuron is plotted against injected noise levels (Gaussian noise, low pass filtered at 830 Hz, value given is SD of membrane potential) for ten (circles), 100 (triangles), and 1,000 (diamonds) stimuli with (red) and without oscillatory current injection (black open circles, black/gray-filled triangles and diamonds). Solid lines are sigmoidal least square fits. The inset trace (top right) is an example of the in vivo membrane potential (recorded in the presence of TTX) used to estimate realistic noise levels (arrow). This level of noise is used in all simulations unless otherwise stated. Scale bar is 200 ms and 200 μV. Dotted lines indicate optimal and chance levels of stimulus discrimination.
(C) Increased discrimination in InF neurons is due to enhanced AP precision. (C1) AP precision was measured for control and oscillation cases. The difference in AP precision was subtracted (jitter was added to the output spikes as described in Materials and Methods) from the oscillation case so that overall AP precision was identical to control conditions and the simulation was re-run. The sigmoidal fit to both oscillation data (red) and control data (open circles) is plotted. Sigmoidal fits from B2 are provided for comparison.
(C2) In this simulation, the oscillatory drive was replaced by brief, large amplitude current injections every 250 ms to evoke precise APs. Discrimination is plotted as a function of membrane noise and is indistinguishable from the oscillation case [F(1,120) = 1.32, p > 0.25]. Lines indicate best fits of the discrimination data for oscillation and nonoscillation conditions shown in B2.
Figure 7.
Improved Stimulus Encoding Is Largely Independent of Oscillation and Stimulus Properties
(A) Stimulus discrimination in an InF neuron for ten different stimulus situations is shown as mean ± SEM for ten repetitions as a function of oscillation frequency. Horizontal black line indicates the mean discrimination level for the control case without oscillatory current injection. Filled red symbols indicate where discrimination for the oscillation case is significantly better than for the control case ( p < 0.05, Mann-Whitney). The terms theta, beta, and gamma indicate the respective physiologically relevant oscillation frequency ranges with respect to the levels of discrimination observed in the oscillation condition.
(B) Same as (A) but with varying oscillation amplitude.
(C) The dependence of stimulus discrimination on input strength in an InF neuron is shown by varying stimulus EPSP amplitude. For large inputs, discrimination is similar in the presence or absence of oscillatory activity, whereas the subthreshold drive significantly increases discrimination for lower EPSP amplitudes.
(D) Influence of imperfect phase-locking of stimuli. Stimulus repetitions were presented after introducing a temporal shift (“jitter”) obtained from a Gaussian distribution with a width indicated as jitter (range: 0.1 to 600 ms). All other parameters, including noise, input and output firing rate, membrane time constant, EPSP kinetics, and amplitude, were kept constant (see Materials and Methods). Oscillation-enhanced discrimination begins to decline only when jitter values exceed 10 ms.
Figure 8.
Oscillation Phase Is Critical for Optimal Discrimination
(A) Two examples of input waveforms, each containing seven stimulus input trains (overlaid) that differed only during the indicated 100° windows (centered around −20° for the peak/falling phase situation (1) and 160° for the rising phase situation (2); the phase was measured relative to the downward midline crossing of the oscillatory drive).
(B1) Rasters from an in vitro recording from a CA1 pyramidal neuron. The two stimuli only differ in the phase window indicated in (A). (Middle panels) PSTHs for both stimuli; the gray shading indicates the SD of the PSTH for stimulus 2. Note that while for the falling phase (1) both PSTHs overlap, they are easily separable for stimuli differing in the rising phase (2). (Bottom panels) Difference between the two PSTHs normalized to the combined SD. Red bars indicate where this normalized difference is larger than 1, that is, regions where the two stimuli are discernible based on the PSTHs.
(B2) Summary of the in vitro recordings for the PSTH difference (the fraction of time where the normalized difference between the two PSTHs is larger than 1) for 22 stimulus pairs. The PSTH difference for rising phase stimuli is significantly larger than for falling phase stimuli ( p < 0.05).
(C1) Stimulus discrimination is plotted under control and oscillation conditions as a function of the phase of the window for simulations in an InF neuron. A sinusoidal fit to the membrane potential is shown as a thin red line for reference. Stimulus windows similar to those shown in (A) are indicated by (1) and (2). To allow for higher temporal resolution the phase window was reduced to 60° and varied in steps of 12° across the cycle. Phase is measured relative to the downward midline crossing of the MPO. Solid bar indicates a period of best discrimination, while the open bar shows the period for the oscillatory case where discrimination is relatively poor.
(C2) A sinusoid is fitted to the discrimination–phase plot. “Phase dominance” is defined as the peak-to-trough amplitude of the fitted sinusoid and plotted as a function of the oscillation frequency. As a control, the black line indicates the average phase dominance in the absence of a MPO. The red line is a Gaussian fit on a lin-log scale.