Distinct roles for GABA across multiple timescales in mammalian circadian timekeeping

Abstract

The suprachiasmatic nuclei (SCN), the central circadian pacemakers in mammals, comprise a multiscale neuronal system that times daily events. We use recent advances in graphics processing unit computing to generate a multiscale model for the SCN that resolves cellular electrical activity down to the timescale of individual action potentials and the intracellular molecular events that generate circadian rhythms. We use the model to study the role of the neurotransmitter GABA in synchronizing circadian rhythms among individual SCN neurons, a topic of much debate in the circadian community. The model predicts that GABA signaling has two components: phasic (fast) and tonic (slow). Phasic GABA postsynaptic currents are released after action potentials, and can both increase or decrease firing rate, depending on their timing in the interspike interval, a modeling hypothesis we experimentally validate; this allows flexibility in the timing of circadian output signals. Phasic GABA, however, does not significantly affect molecular timekeeping. The tonic GABA signal is released when cells become very excited and depolarized; it changes the excitability of neurons in the network, can shift molecular rhythms, and affects SCN synchrony. We measure which neurons are excited or inhibited by GABA across the day and find GABA-excited neurons are synchronized by-and GABA-inhibited neurons repelled from-this tonic GABA signal, which modulates the synchrony in the SCN provided by other signaling molecules. Our mathematical model also provides an important tool for circadian research, and a model computational system for the many multiscale projects currently studying brain function.

Keywords: GABA; circadian; mathematical modeling; network; synchronization.

Fig. 1.

Interactions between components of the SCN model. The full SCN model contains both a detailed molecular-clock model as well as a conductance-based electrophysiology model of the dynamics of each cell in the network. The connections between these components are highlighted here. The molecular-clock state, determined by E-box activity, influences the permeability of KCa and K−leak channels. These drive changes in membrane voltage, which affect intracellular calcium concentrations. Both calcium and VIP can lead to activation of CREB, causing transcription of Per1 and Per2. Calcium also causes release of VIP in VIP-producing cells. The activity of the VPAC2 receptor is inhibited by CRY. GABA can lead to excitation or inhibition of membrane voltage depending on E_GABA.

Fig. 2.

Effects of inhibitory pulses on SCN neuron firing activity. (A) Sample firing activity of an SCN neuron before and after the administration of a hyperpolarizing pulse (time of pulse denoted by red dashed line). (B) The model predicted phase response curve (dark blue line) is plotted along with the mean and SE of responses to inhibitory pulses given experimentally to SCN neurons (red), binned by phase of pulse initiation (for the electrophysiology model, parameter R = 2). Both the model-predicted and experimentally determined responses show that the response to the pulse depends on when in the ISI it is given, with pulses given shortly after the firing of an action potential shortening the ISI (as in A), whereas pulses given late in the ISI lengthen it.

Fig. 3.

Experimentally measured intracellular chloride is used to determine E_GABA for simulations, leading to predictions of strong effects of GABA signaling on cellular electrical activity rhythms. (A) Confocal microscopy of MQAE fluorescence in a unilateral SCN from an acute slice. (Scale bar, 100 μm.) MQAE is quenched by chloride, so areas with high fluorescence represent low intracellular chloride. Magnified images of cell bodies in dorsal, D, cells show lower fluorescence than those in ventral, V, cells. (B) Fluorescence values from the whole SCN slice are averaged over cell-sized regions, and (C) used to estimate the relative distribution of E_GABA. Cells with high E_GABA are excited by GABA, and with low E_GABA are inhibited by it. Note that cells are plotted on a grid for visualization purposes only and that connectivity is determined independently of distance between cells, as described in the methods. (D) Estimated E_GABA levels across the SCN are found to be roughly normally distributed but with a clear spatial bias between the dorsal and ventral SCN. (E) A raster plot of simulated PER2 rhythms over 20 d for an SCN with the experimentally estimated E_GABA values from C (cells are sorted by E_GABA). (F–H) Circadian variation in electrical activity for sample cells with E_GABA values of −80 mV (F), −60 mV (G), and −32 mV (H), plotted as the range of voltages attained by the cells throughout the day. Circadian time is determined relative to the peak in whole SCN PER2 protein levels, which is defined to be CT12.

Fig. 4.

Tonic but not phasic GABA causes shifts in PER2 rhythms, with different phasing depending on the cell’s GABA equilibrium potential. Cells with E_GABA ranging from −80 (red) to −32 (blue) are stimulated with 5 h of phasic GABA at 10 Hz (A) or low-level tonic GABA (B); GABA equilibrium potentials denoted by colors as in Fig. 3C. PER2 rhythms for cells in A overlap, showing that 5 h of phasic GABA does not shift the molecular rhythms of any of the cells, and they do not entrain to it regardless of when in the cycle it is given. Cells do shift to entrain to the tonic GABA stimulus with the phase relationships shown in B. The timing and relative amplitude of the GABA stimulus are denoted by the black curve. (C) A PRC of strongly inhibited (E_GABA = −80) and excited (E_GABA = −32) cells in response to the 5-h tonic GABA stimulus. Initial phase is defined as the time of the beginning of the stimulus and for each cell, circadian time is determined relative to the peak in the cell’s PER2 protein levels, which is defined to be CT12.

Fig. 5.

Cells excited by GABA retain synchrony over time. (A) Snapshots of PER2 rhythms in a simulated SCN every 2 h over the 10th day of simulated time (CT0 to CT22 from left to right, top to bottom, all values normalized by the maximum value in the simulation). A movie of the full simulation can be found in Movie S1. The cells excited by GABA, located in the dorsal shell region, form a clear cluster. Circadian time is determined relative to the peak in whole SCN PER2 protein levels, which is defined to be CT12. (B) A raster plot of PER2 rhythms for the full 11-d simulation. Cells excited by GABA are sorted to the top, and can be seen to retain synchrony better over time whereas those inhibited by GABA desynchronize. Color bars for each scale are shown on the right.

Fig. 6.

Random networks with large fractions of cells excited by GABA form excited and inhibited clusters in antiphase, driven by calcium. (A) A raster plot of normalized PER2 rhythms in a network with 60% cells excited by GABA shows the formation of two clusters, one with the excited cells and one with the inhibited. These clusters increase in coherence as the percentage of excited cells is increased (SI Appendix, Fig. S5). (B) The formation of these clusters can be seen in Rayleigh plots of the mean PER2 (solid line), calcium (dashed line), and firing rate (dotted line) rhythms for the excited (blue) and inhibited (red) populations. At day 5, each of the three rhythms has the same phasing in both populations. By day 10, however, tonic GABA signaling pushes the inhibited calcium rhythm to antiphase of the excited calcium rhythm, and by day 20, the PER2 rhythm has followed as well. All phases are relative to the total SCN PER2 protein rhythm (black), and are determined as the difference in hours between the trough of the rhythm and the trough of the global PER2 rhythm (positive numbers are advanced and negative delayed).

Fig. 7.

SD of the PER2 peak time distribution as a function of the proportion of GABA-excited to GABA-inhibited cells (E:I) in the network. Mean values and SEs for three networks with different randomized parameters are shown for each network type. Cells are best synchronized and most in phase in the network where either 100% of cells are excited by GABA or when GABA is knocked out. Networks with E:I proportions between 20:80 and 80:20 are less in phase, with increasing numbers of excited cells leading to increased variance in the distribution of phases in the network. Entirely inhibitory networks (0:100) rank in between the 40:60 and 60:40 networks.

Fig. 8.

Rhythms in firing rate differ in amplitude and phasing depending on the proportion of excited to inhibited cells in the network. (A) Networks with large fractions of GABA-inhibited neurons are unimodal and those with large fractions of excited neurons can show bimodal, crepuscular firing patterns. The excited (B) and inhibited (C) subsets can each show either of these patterns depending on the balance of excited to inhibited neurons in the network. Circadian time is determined relative to the peak in whole SCN PER2 protein levels, which is defined to be CT12.