Covert sleep-related biological processes are revealed by probabilistic analysis in Drosophila

Abstract

Sleep pressure and sleep depth are key regulators of wake and sleep. Current methods of measuring these parameters in Drosophila melanogaster have low temporal resolution and/or require disrupting sleep. Here we report analysis tools for high-resolution, noninvasive measurement of sleep pressure and depth from movement data. Probability of initiating activity, P(Wake), measures sleep depth while probability of ceasing activity, P(Doze), measures sleep pressure. In vivo and computational analyses show that P(Wake) and P(Doze) are largely independent and control the amount of total sleep. We also develop a Hidden Markov Model that allows visualization of distinct sleep/wake substates. These hidden states have a predictable relationship with P(Doze) and P(Wake), suggesting that the methods capture the same behaviors. Importantly, we demonstrate that both the Doze/Wake probabilities and the sleep/wake substates are tied to specific biological processes. These metrics provide greater mechanistic insight into behavior than measuring the amount of sleep alone.

Keywords: Hidden Markov Model; arousal threshold; behavior; homeostasis.

Fig. 1.

Conditional wake and doze probability determine Drosophila sleep. (A) Two exemplar activity patterns (Examples #1 and #2). Open squares: active; black squares: inactive. Transitions between activity states are indicated by curved arrows. Transitions from active to inactive (Doze) are above the blocks; transitions from inactive to active (Wake) are below. Calculation of P(Wake) and P(Doze) are described in Methods. (B) Double-plotted daily cycles of Activity (black), % Time Asleep (blue), P(Doze) (green), and P(Wake) (red) measured in WT female flies. Solid lines are the population means; tinted bands are the 95% confidence intervals of the means. Individual profiles are the average of 3 d of behavior. Gray area indicates lights-off period. ZT, Zeitgeber time or hours since lights on. (C) The same data presented in B plotted on a common set of axes. Color coding is the same as in B. (D and E) Heatmaps of in vivo (D) and in silico (E) sleep properties. The behavior of each in vivo fly was split into 90-min time intervals, and the P(Wake), P(Doze), and total sleep for that interval were calculated. Each 90-min behavioral sample was assigned to one of 51 bins from 0 to 1 based upon its respective P(Doze) and P(Wake). The mean value of total sleep was calculated for the samples in each bin, and the bin was assigned a color according to the legend (below). Coordinates without any biological samples are displayed as white. (E) For each P(Doze) and P(Wake) bin, 64 in silico flies were simulated. The mean total sleep in these simulations is displayed using the same color map as the in vivo data. The in silico behavior is subject to the same definition of sleep as in vivo data (5 min of inactivity), which results in the heatmap not having a linear/diagonal gradient. (F–I) Plots of the mean trajectory of flies through the P(Wake) vs. P(Doze) probability space across their daily rhythm superimposed on the in silico-predicted total sleep at each point. The direction of time is indicated by arrowheads. Important circadian times are indicated by small clock faces (see key below). Genotype and environmental conditions are indicated in the corner of each plot. PER⁰¹: period point mutation; LD: 12:12 light:dark cycle; DD: constant darkness.

Fig. 2.

Conditional wake probability is a measure of sleep depth. (A–E) Results of a mechanical arousal threshold experiment. (A) Schematic of experimental setup. Fly locomotion in a 96-well plate was monitored using a FlyBox. At 3-h intervals starting at ZT 1, an electromagnetic solenoid was used to tap the side of the plate. (B) Circadian profiles of % Time Asleep, P(Doze), and P(Wake). Solid lines are the population means; tinded bands are the 95% confidence intervals. Behavior was measured at 25 °C (green) and 29 °C (magenta). Tapping times are indicated by dashed vertical lines. Gray area indicates lights-off period. (C) Response to tapping was measured as the increase in arousal probability following a tap. The percentage (%) responding is plotted at 25 °C (green) and 29 °C (magenta). The symbol “#” indicates a response greater than chance (P < 0.05) as measured by Fisher’s exact test with the Holm’s step-down correction for multiple testing. (D) The effect of temperature on P(Wake) (cyan), P(Doze) (yellow), and response to tapping (pink) at each time (ZT). (E) The P(Wake) and P(Doze) of each time point was normalized by converting it to a z-score. The behavior of each fly following each tap was classified as a nonresponse (no activity 1 min after tap) or as a response. The mean z-score across all time points for responders and nonresponders is plotted. Error bars are SEM. *P < 0.05; ***P < 0.0005.

Fig. 3.

Conditional doze probability is a measure of sleep pressure. Results of a daytime sleep deprivation experiment. (A) The percentage (%) of Time Asleep of shaken (cyan) and unshaken control (gray) flies over 3 d, including 1 d of sleep deprivation. (B) Sleep debt accumulated during daytime sleep deprivation and recovered following release from deprivation. (C) Change in P(Doze) (green) and P(Wake) (red) during sleep deprivation and following release from deprivation. (D and E) Comparison of P(Doze) (D) and P(Wake) (E) between shaken (cyan) and control (gray) flies following release from sleep deprivation. Error bars are SEM. n.s., no significant difference; *P < 0.05; ***P < 0.0005.

Fig. 4.

Dopaminergic tone regulates sleep depth. (A) Sleep, P(Doze), and P(Wake) during the thermogenetic activation of dopamine neurons. The experimental flies (red) were compared with control flies carrying only the driver (TH-Gal4 alone, blue) or only the actuator (UAS-dTrpA, black). (B–D) Comparison of the heat-induced change in total sleep (B), P(Doze) (C), and P(Wake) (D) between experimental flies and control flies. (E) The population mean of the TH-Gal4/UAS-dTrpA experimental group during the thermogenetic activation experiment is overlaid on the in silico-predicted sleep heatmap. Arrows indicate the direction of time; gray circles: 21 °C; red circles: 29 °C. Circles with white borders are daytime values, circles with black borders are nighttime values. Error bars are SEM. n.s., no significant difference; *P < 0.05; **P < 0.005, ***P < 0.0005.

Fig. 5.

High-sucrose diet promotes sleep consolidation by decreasing sleep pressure. (A) Daily cycle of percentage (%) Time Asleep, P(Doze), and P(Wake) for wild-type (CS) flies fed either a low-sucrose (2.5% sucrose in agar, blue) or a high-sucrose (30% sucrose in agar, green) diet. (B–E) Comparison of low- and high-sucrose diet time asleep (B), number (#) of sleep episodes (C), P(Wake) (D), and P(Doze) (E) during daytime and nighttime. n.s., no significant difference; *P < 0.05, **P < 0.005, ***P < 0.0005.

Fig. 6.

Changes in sleep due to age are due to both sleep pressure and depth. (A) Daily cycle of percentage (%) of Time Asleep, P(Doze), and P(Wake) for wild-type (CS) flies at 1, 3, 5, or 7+ wk post eclosion. (B–D) Comparison of time asleep (B), number (#) of sleep episodes (C), P(Doze) (D), and P(Wake) (E) across aging during daytime (open circles) and nighttime (filled circles). Error bars are SEM. (F) The population means of the aging fly cohorts are overlaid on the in silico-predicted sleep heatmap. Daytime values: white outline; nighttime values: black outline. n.s., no significant difference; *P < 0.05; ***P < 0.0005.

Fig. 7.

A four-state Hidden Markov Model. (A) The states and state-transition probabilities (per minute) of the HMM. Thickness of the arrows roughly indicates the probability of each state transition; numbers indicate exact probability inferred from per⁰¹ flies in constant darkness. Transitions between states with no line connecting them (e.g., deep sleep and full wake) are not permitted by the model. (B) Example of decoded state history of a single WT fly around the time of the light-to-dark transition at ZT 12. Gray area indicates lights-off time. (C and D) Daily cycle of state probability for the sleep states (C) and wake states (D) in WT flies (same fly cohort as presented in Fig. 1). (E) Daily cycle of total sleep in WT flies measured by HMM decoding and by the 5-min inactivity threshold. (F) Percentage (%) of flies in each of the four hidden states that respond to a gentle tap (Left) or a brief light flash (Right). Means with the different letters are significantly different from one another (P < 0.0001; same fly cohorts as presented in Fig. 2 and SI Appendix, Fig. S4). (G) Percentage (%) of Total Sleep spent in Light Sleep (Left) and % Total Wake spent in Light Wake (Right) in control (w¹¹¹⁸), fumin (dat^fmn), and insomniac (inc²) flies (same fly cohort as presented in SI Appendix, Fig. S7). ***P < 0.0005.