Neuronal synchronization in Dr oso phila

Abstract

Collective rhythms are intrinsic to biological processes across temporal and spatial scales. In the brain, synchronized neuronal oscillations underlie collective rhythms essential for complex functions. Neuronal oscillations were reported in individual Drosophila neurons that underlie circadian and sleep behaviors. However, it is still unclear whether and how these participate in a collective rhythm. We perform whole-cell patch clamp recordings and demonstrate that membrane potential oscillations disappear after blocking nicotinic acetylcholine receptors. Perturbations to membrane potential do not change the phase of oscillation, further suggesting they depend on external inputs. We propose a theoretical description that accounts for experimental observations and predicts phase-locked neuronal synchronization. Simultaneous electrophysiological recordings of neuronal pairs confirm this prediction and show that this is a widespread phenomenon in accessory medulla neurons. Our findings suggest the possibility that brain waves may arise from collective neuronal activity within this region of the fly brain.

Keywords: Neuroscience; Sensory neuroscience.

Graphical abstract

Figure 1

lLNvs display membrane potential oscillations (A) Left: Scheme of the Drosophila head. Middle: Scheme of brain explant (only right side is shown) displaying lLNvs and recording electrode. Right: zoom into the box from B. (B) Representative recording from a lLNv, beginning 22 min after dissection. (C) Top: fraction of detrended recording from B (gray line) and denoised trace (black line). Three threshold values (dashed lines) and corresponding threshold crossings (black dots) are indicated. Bottom: corresponding valid (blue dots) and non valid (red dot) CD measurements. (D) Duration of $n=112$ individual recordings represented by horizontal bars. (E) Top: detrended and denoised recording from B. Shaded region indicates the threshold range. Bottom: corresponding CD measurements (color dots) and linear fit (line). Box marks the zoom in C, and the bracket indicates the span for the initial CD calculation. (F) Initial CD vs. time since dissection (dots) are positively correlated (Pearson $r=0.67$). Error bars are the standard deviation (SD). (G) Left: CD slope vs. time since dissection (dots) shows no correlation (Pearson $r=0.22$). Error bars are slope fitting errors. Right: histogram of CD slopes, mean is 0.09 s/min. Slope is significantly different from zero ($p<{10}^{-8}$, Wilcoxon signed-rank test). (H) 2D histogram of pooled CD values (24949 cycles) from all lLNvs recorded, aligned in time since dissection. (I) Initial CD vs. ZT shows no correlation (Pearson $r<{10}^{-1}$). Error bars are SD.

Figure 2

sLNvs display membrane potential oscillations (A) Left: scheme of brain explant displaying sLNvs and recording electrode. Right: representative recording from a sLNv, beginning 35 min after dissection. Inset: zoom into the box. (B) Duration of $n=44$ individual recordings represented by horizontal bars. (C) Top: detrended and denoised recording from A. Shaded region indicates the threshold range. Bottom: corresponding valid (pink dots) and non valid (red dots) CD measurements, and linear fit (line). Bracket indicates the span for the initial CD calculation. (D) Initial CD vs. time since dissection (dots) are positively correlated (Pearson $r=0.62$). Error bars are SD. (E) Left: CD slope vs. time since dissection (dots) show no correlation (Pearson $r=-5\times {10}^{-3}$). Error bars are slope fitting errors. Right: histogram of CD slopes, mean is 0.021 s/min. Slope is significantly different from zero ($p<0.5\times {10}^{-1}$, Wilcoxon signed-rank test). (F) 2D histogram of pooled CD values (5001 cycles) from all sLNvs recorded, aligned in time since dissection. (G) Initial CD vs. ZT show no correlation (Pearson $r<{10}^{-1}$). Error bars are SD.

Figure 3

Phase response curve and current step injection experiment are consistent with non-autonomous oscillations (A) Left: scheme of brain explant displaying lLNvs, electrode, and current injection. Right: recording fragment from current injection experiment (gray line), denoised trace (black line), and injected current (green line). Representative threshold (horizontal dashed line) used to define the perturbed and the two previous cycles as indicated, and the mapping of $T_1$ onto the $\left[0,2\pi \right]$ interval is shown. (B) Phase shift $P_1$ as a function of stimulus phase (STAR Methods). Blue dots correspond to a single perturbed cycle, from $n=10$ different neurons, totaling 274 cycles. Black dots are the average of 11 consecutive blue dots, and error bars are SD. Shaded area is the SD of the reference cycles. (C) Representative recording of current injection experiment on a lLNv (gray line), with $-6$ pA current step of 30 s duration (green line). (D) Fold change of CD during and after the current injection, relative to CD before current injection, is not significantly different from one ($n=11$, $\alpha =0.9$, one-sample Wilcoxon test).

Figure 4

Membrane oscillations are ACh-dependent (A and B) Left: scheme of brain explant in a bath with mec perfusion, displaying (A) lLNvs and (B) sLNvs, and recording electrode. Right: Representative recordings of mec treated neurons, with gray arrow indicating the beginning of mec (10μM) application. Insets show zoom into boxes displaying fragments of the recording (gray line) and denoised traces of (A) lLNvs (blue line) and (B) sLNvs (pink line). Recordings performed (A) 56 min and (B) 37 min after dissection.

Figure 5

A forced oscillator theory is consistent with a flat PRC (A) Left: numerical solutions to Equations 3 to 2 showing the driver (yellow line and dot) and the driven cell (dashed line and black dot). Time lag τ and amplitude $2r$ are indicated. Right: polar coordinates the representation of the oscillations (dashed line), showing polar amplitude r, driver phase ψ (yellow dot), driven cell phase θ (black dot), and phase lag δ. Driver amplitude is not drawn to scale, and parameters are chosen for illustration. (B) Numerical solution of an unperturbed oscillator (dashed line) and a perturbed oscillator (blue line). Instantaneous perturbation is indicated (green line). Left: temporal representation. Right: polar coordinates representation. (C) Numerical PRC of the model. Parameters as in Table S1, except $f=0$ and $\mu =1$ for autonomous oscillations (dashed line), and $f=104,10.4,1.04$ for driven oscillations (darker to lighter yellow lines). (D) Fragment of recording from a current injection experiment (gray line), with exponential fit of the perturbation response (black line), and current injection (green line). (E) Relaxation time $t_r$ scaled by CD at the time of perturbation $T_1$ (dots) (STAR Methods). Boxes are the interquartile range, bar is the median, and whiskers extend 1.5 times the interquartile range.

Figure 6

There is a lag between lLNvs and sLNvs membrane oscillations (A) Left: scheme of brain explant displaying lLNvs and sLNvs together with recording electrodes. Right: Fragment of representative dual recording from a lLNv (blue) and a sLNv (pink), beginning 33 min after dissection. Box marks zoom in D. (B–D) Top: scheme of recorded (B) lLNv pairs, (C) sLNv pairs, and (D) lLNv-sLNv pairs. Bottom: Representative fragments of corresponding dual recordings with threshold crossing analysis (dashed line and dots). Vertical lines guide the eye to highlight the absence (B, C) or presence (D) of a time lag. In (A-D) data is detrended (gray) and further denoised (color). (E) Quantification of average lag measurements from threshold crossing analysis for different LNv pairs. (F–H) Representative cross correlation functions for (F) lLNv pairs (G) sLNv pairs and (H) lLNv-sLNv pairs. (I) Quantification of lags from cross correlation analysis for different LNv pairs. (E and I) Boxes are the interquartile range, bar is the median, and whiskers extend to 1.5 times the interquartile range. Lag distributions are not significantly different from zero ($\alpha =0.95$) for pairs of cells of the same type, but significantly differ from zero for lLNv-sLNv pairs ($p<{10}^{-4}$), by one-sample Wilcoxon test, with $n=9$ lLNv-lLNv pairs, $n=9$ sLNv-sLNv pairs and $n=18$ lLNv-sLNv pairs.

Figure 7

Theoretical relations between parameters and observables (A) Parameter relations Equations 45, 46, and 47 for lLNvs (blue line) and sLNvs (pink line) with parameters and observables as in Table S1 (dots). Gray dashed lines indicate parameter choices that result in $\mu >0$. Parameters a and f are scaled using $r_0$ to have the same units as μ, so that their magnitudes can be compared. Phase lag δ is normalized to $2\pi$, and detuning $\Delta =\mathrm{\Omega }-\omega$ to the forcing frequency $\mathrm{\Omega }$. (B) Amplitude $2r_0$, time lag τ, and relaxation time $t_r$ scaled by CD, as a function of normalized detuning and forcing strength f normalized by amplitude $r_0$. Vertical bar in the lag plot indicates the relative lag between lLNvs and sLNvs, satisfying the experimental constraint. Schemes on the right illustrate corresponding observables.

Figure 8

Other aMe neurons also oscillate coherently with LNvs (A and B) Left: scheme of brain explant displaying aMe neurons together with (A) lLNvs and (B) sLNvs, with recording electrodes. Dark gray shade indicates the aMe region. Right: Fragment of representative dual recording from (top) LNv and (bottom) aMe-PDF(−) neuron, beginning (A) 32 min and (B) 28 min after dissection. Boxes mark zooms in C and D. (C and D) Representative fragments from boxes in A and B. (E and F) Lags obtained from (top) cross correlation and (bottom) threshold crossing analysis for individual dual recordings of aMe-PDF(−) neurons and (E) lLNvs and (F) sLNvs. Recordings in A and B correspond to pair 4 in E and 5 in F.