Figure 1

Astability induction in a Purkinje neuron. [(a), (c)] Signal output recordings of cells transitioning to an astable oscillatory mode after applying a kainate receptor agonist (PSKRA, 100 μM) in conjunction with an AMPA receptor blocker (GYKI, 10 μM) and Na${}^{+}$ channel blocker (TTX, 1 μM). Clear oscillations are at the far right (gray line in dashed box), after a short transition period (green line in dotted box). Inset: analogy between the astable firing/quiescence pattern with a digital oscillator switching between two states [(b), (d)] Fourier transforms (power spectra) of the recordings before (black), during (green inset), and after (gray) the induction of oscillations (logarithmic $x$ axis). A clear peak at 0.075 Hz can be seen in (b), whereas a split peak centered at 0.07 Hz is seen in (d), signifying a transition between two frequencies for this wave form. The transition period of the cell in (a) contained some low-frequency signatures, whereas the transition period in (c) contained nearly no low-frequency signature (other than zero-frequency noise).Reuse & Permissions

Figure 2

Measuring the induced oscillations. (a) 9 minute recordings of a cell induced to oscillate via application of glutamate (MSG, 100 μM) and an AMPA receptor blocker (GYKI, 10 μM). (b) The period of oscillation of bursts can be tracked over time to provide the average period (solid red line) and standard deviation (dashed gray line). (c) The smoothed power spectrum provides all frequency information of the recording, including calcium and sodium frequency modes [blue (dark gray) and green (light gray) arrows, respectively]. (d) Close-up of the low-frequency peak, with no smoothing to the spectrum, displaying multiple peaks, which account for the drift and shift in frequency. The central peak is fitted with a single Gaussian [green (light gray) line] with 95$\%$ confidence levels (dashed gray line), providing the standard deviation. (e) 5.5 minute recording after the application of PSKRA, GYKI, and TTX (100, 10, and 1 μM, respectively), which blocks the Na${}^{+}$ spikes, as is seen in the lack of high-frequency activity in the power spectrum (g). The standard deviation in (h) matches that of (f) since the single Gaussian fit is more accurate for this signal.Reuse & Permissions

Figure 3

Photoswitchable compound modulates the oscillation. (a) Comparison of the GluK1 selective compound LY339434 and the PSKRA, which has an added azobenzene moiety, rendering it photoswitchable at 500 and 380 nm. (b) The ultraviolet [UV, 380 nm, as shown in violet (light gray) area] and cyan [500 nm, as shown in cyan (dark gray) area] light turn the bursting on and off, respectively, as a function of the modulation period, here shown for two modulation patterns with differing periods. The stimulation pattern is noted to the right of each recording, with stimulations at 15 s cyan, 15 s UV; 10 s cyan, 10 s UV (DC $=$ 50$\%$); and 7 s cyan, 5 s UV (DC $=$ 42$\%$). (c) Photomodulation followed by induction of oscillation in a cell not displaying astability prior to the modulation. The cell continued to oscillate after the photoswitching was completed. (d) Adding synaptic blockers to the solution (such as GABAzine, 10 μm, which blocks GABA receptors) did not affect any of the photoswitching, resulting in identical traces before and after introducing the drugs, verifying the kainate mediated effect.Reuse & Permissions

Figure 4

Recovery from the photomodulation follows a forced-oscillator model. (a) Exemplary recording of a Purkinje neuron showing a natural oscillation [green (light gray) curve] that is then photomodulated at 5 s on [violet (light gray) area] /5 s off [cyan (dark gray) area] with a 10 s period for 2 min [blue (dark gray) curve], and then allowed to recover from the modulation (black curve). [(b), (c)] Period and duty-cycle tracking of the cell in (a), displaying the forced-modulation (dashed blue line) and exponential recovery. Dots are color coded as in (a). Red dotted lines are fitted exponential curves for the recovery segment, with a time constant of τ $=$ 124 s and τ $=$ 67 s for the period and duty cycle, respectively. [(d), (e)] Representative plotted periods of the natural, modulated, and recovering oscillators for two different modulations: (d) 10/10 and (e) 15/15 on/off, in seconds (τ $=$ 97, 40 s, respectively). Actual recordings appear below each plot.Reuse & Permissions

Figure 5

Period, duty-cycle, and precision of oscillation. [(a), (b)] Histograms of the average period and duty cycle ($n$ $=$ 43 cells total) showing the central frequency of 20 s/0.05 Hz, and 46$\%$ duty cycle in total (black). The cells could be broken down to PSKRA activated cells (horizontal blue, $n$ $=$ 29) and SYM-2081/MSG activated cells (diagonal green, $n$ $=$ 14), with periods of 24 ± 7 and 19 ± 8, respectively. (c) Quality factor or SNR data for the PSKRA [blue (dark gray) circles] and SYM-2081/MSG [green (light gray) triangles] activated cells, as a measure of the precision of oscillation. Each cell is plotted individually, with the PSKRA activated cells having higher precision values. (d) Histogram of the time averaged value of the slow gating variable for each cell. The average value of $〈g_S〉$ was 0.12 ± 0.1 μS/cm${}^2$.Reuse & Permissions