Sleep homeostasis and cortical synchronization: I. Modeling the effects of synaptic strength on sleep slow waves

Abstract

Study objectives: Sleep slow-wave activity (SWA, electroencephalogram [EEG] power between 0.5 and 4.0 Hz) is homeostatically regulated, increasing with wakefulness and declining with sleep. Sleep SWA is thought to reflect sleep need, but the mechanisms of its homeostatic regulation remain unknown. Based on a recent hypothesis, we sought to determine whether a decrease in cortical synaptic strength can account for changes in sleep SWA.

Design: A large-scale computer model of the sleeping thalamocortical system was used to reproduce in detail the cortical slow oscillations underlying EEG slow waves.

Setting: N/A.

Patients or participants: N/A.

Interventions: Simulated reductions in the strength of corticocortical synapses.

Measurements and results: Decreased synaptic strength led to (1) decreased single cell membrane potential oscillations and reduced network synchronization, (2) decreased rate of neural recruitment and decruitment, and (3) emergence of local clusters of synchronized activity. These changes were reflected in the local EEG as (1) decreased incidence of high-amplitude slow waves, (2) decreased wave slope, and (3) increased number of multipeak waves. Spectral analysis confirmed that these changes were associated with a decrease in SWA.

Conclusions: A decrease in cortical synaptic strength is sufficient to account for changes in sleep SWA and is accompanied by characteristic changes in slow-wave parameters. Experimental results from rat cortical depth recordings and human high-density EEG show similar changes in slow-wave parameters with decreasing SWA, suggesting that the underlying mechanism may indeed be a net decrease in synaptic strength.

Figures

Figure 1

Schematic of the thalamocortical model with, on the left, a primary thalamocortical circuit including a 3-layered primary visual cortical area (Vp), thalamic reticular nucleus (Rp), and dorsal thalamus (Tp) and, on the right, a secondary visual area, Vs, with its associated thalamic sectors Rs and Ts. Visual inputs (left), including spontaneous random optic nerve firing, excite inhibitory (black) and excitatory (white) neurons in Tp. (1) Thalamocortical loops: excitatory Tp and Ts neurons project to L4 (corresponding to cortical layer 4), to infragranular layer L5-6 cortical neurons and, via collaterals, to Rp and Rs. (2) Reticular nucleus networks: Rp and Rs neurons are part of a dense inhibitory network that sends diffuse inhibitory projections to thalamocortical neurons in Tp and Ts. (3) Cortical interlaminar (vertical) loops: columnar projections are made from L4 to supragranular L2-3, from L2-3 to L5-6, and from L5-6 back to L4 and L2-3. (4) Cortical intralaminar (horizontal) connections: each layer contains excitatory projections (shown only for L2-3 in Vp) forming connections between patches of cells with similar response selectivity (for horizontal or vertical bars). (5) Interareal corticocortical loops: forward projections from L2-3 of Vp to L4 of Vs; backward projections from L5-6 of Vs to L2-3 of Vp. (6) Excitatory projections from L5-6 to thalamocortical neurons in Ts. (7) Diffuse neuromodulatory (cholinergic, noradrenergic, serotonergic, etc) systems project throughout the entire thalamocortical network. Not drawn to scale.

Figure 2

Signals recorded from the thalamocortical model during sleep. A. Intracellular-like recording of the membrane potential from a typical L5-6 excitatory cell. B. A plot of the membrane potentials of 80 excitatory L5-6 neurons. C. Average membrane potential in L5-6. D. Local field potential-like recording produced from synaptic currents of 1600 L5 excitatory cells. E. electroencephalogram-like recording of the average synaptic current produced from all excitatory cells from primary visual cortex, Vp.

Figure 3

Fifty intrinsically oscillating neurons were simulated for 10 s under 4 conditions with different synaptic strengths (shown in order of decreasing synaptic strength from top to bottom). Left, phase angle relative to the signals average phase, calculated using the Hilbert transform (see Methods). Synchronization between neurons can be seen to decline with decreasing synaptic strength. Specifically, the phase synchronization index was 0.885 ± 0.074, 0.383 ± 0.139, 0.154 ± 0.078, and 0.113 ± 0.057 for the 4 decreasing synaptic strength conditions. A 1-way analysis of variance revealed a significant effect of synaptic strength on the phase synchronization index (F3,39996 = 147555.87, P < 0.001). Middle, population average membrane potential. Note that spikes occurred in all cases but may not be evident due to averaging. Right, power spectrum (0–10 Hz).

Figure 4

The local field potential (LFP) of activity recorded from a large scale model of the thalamocortical system under conditions of high (A,C) and low (B,D) synaptic strength. C and D depict individual slow-wave detections (thicker line segments) on the band-pass-filtered signal (0.5–2 Hz) for the high- and low-synaptic-strength conditions, respectively. It is clear that detected slow waves constitute most of the signal. The autocorrelations (E) of the LFPs show the reduction in slow oscillatory activity with the decrease in synaptic strength. F depicts a representative slow wave. The first and second segment of the slow wave are indicated between the negative peaks below the zero crossing (*) and the positive peak (**).

Figure 5

The power spectrum (0–10 Hz) under conditions of high and low synaptic strength. Error bars indicate standard error.

Figure 6

Changes in slow-wave parameters as synaptic strength decreases. A. Distribution of slow-wave amplitude, shown with bin width increasing in a logarithmic fashion. B. Absolute value of the slope of the first and second segment of the slow waves (error bars depict standard error). C. Absolute value of the maximum instantaneous slope of the first and second segment of the slow waves (error bars depict standard error). In both slope figures, the absolute value of the slope is shown for ease of comparison. D. Number of multipeak waves.

Figure 7

Activity in the model during typical waves from the high- and low-synaptic-strength conditions. A. Topographic depiction of intracellular membrane potentials from a 40×40 array of neurons in each layer of primary visual cortical area. Membrane potentials are depicted for the beginning of the wave and the wave peak. Note how activity is similar in corresponding topographic locations in all layers (i.e. throughout the cortical column). B. The local field potential of the wave being measured. C. A typical intracellular recording from a neuron in L5-6. The decreased amplitude of single-cell membrane-potential oscillations that occurs during the low-synaptic-strength condition can be seen in this example. D. Traces depicting the membrane potential from 80 L5-6 neurons. Note the decreased synchrony of the membrane potential oscillations in the low-synaptic-strength condition. E. For 1600 L5-6 neurons in each condition, the distribution of membrane potential phase relative to the phase of the average membrane potential across the 45-s simulation is depicted. Phases are sorted into 50 equal-sized bins.

Figure 8

Rates of recruitment and decruitment at 10 time points prior to, and following, the peak of each wave and at the time of the peak (vertical dashed line). Plots show mean ± standard error. A. Rate of decruitment (percentage of L5-6 excitatory cells decruited at that time point). Under conditions of high synaptic strength, cells are decruited more quickly than under conditions of low synaptic strength, particularly in the first segment of the wave. B. Rate of recruitment (percentage of L5-6 excitatory cells recruited at that time point). Under conditions of high synaptic strength, cells are recruited more quickly than under conditions of low-synaptic-strength during the second segment of the wave.

Figure 9

The spatiotemporal distribution of activity and number of peaks in the local field potential (LFP). Right top, multipeak wave from the low-synaptic-strength condition. The grey bars (p1 and p2) mark 100 ms on either side of the first and second peak, respectively. Right middle, average membrane potential for all cells in L5-6 computed from activity during p1 and p2. Right bottom, LFP traces recorded from cells that either become decruited (average membrane potential < −70 mV) during a given peak (red) or do not become decruited during a given peak (black). Note that it is possible to distinguish 2 populations that are primarily active during 1 or the other of the 2 peaks (only 13.7% of cells that were decruited during the first peak were also decruited during the second peak). For comparison, a single-peak wave from the high-synaptic-strength condition is shown on the left.

Figure 10

A. The filtered (0.5–2 Hz) local field potential (LFP) of activity recorded under conditions of decreased synaptic strength (synaptic strength 85%, neuromodulation 0%). B. The filtered (0.5–2 Hz) LFP of activity recorded under conditions of increased arousal promoting neuromodulation (synaptic strength 100%, neuromodulation 15%). One hundred thirty-three wave pairs equated for amplitude from the decreased synaptic strength and increased neuromodulation conditions were compared for amplitude (C) and first- and second-wave segment slope (D).

Figure 11

Wave parameters with all connections at 100% strength or with specific sets of connections at 85% strength. A. Distribution of slow-wave amplitude, with bin widths increasing in a logarithmic fashion. B. Absolute value of the slope of the first segment of the slow waves. C. Absolute value of the slope of the second segment of the slow waves. For both B and C, t-tests were performed testing the difference between slopes from the baseline condition and slopes from each of the other conditions. Significance is indicated by asterisks (*P < 0.05; **P < 0.01; ***P < 0.001). To facilitate comparisons, absolute slope values are shown. D. Number of multipeak waves. Exc refers to excitatory; Inh, inhibitory.