Figure 1.
The SCN is divided in two identical hemispheres (left and right), each composed of two groups of neurons (core and shell, shown on the right hemisphere), distinguished by the type of neurotransmitters they release. In the ventro-lateral part (VL), the neurons mainly express VIP (shown on the left hemisphere), whereas in the dorso-medial part (DM), AVP is expressed. The two parts also differ by their coupling properties. Moreover, only a subset of VL neurons are light-sensitive and are entrained by light cues originating from the optical chiasm (OC).
Figure 2.
Scheme of the single-cell circadian oscillator.
The intracellular oscillator consists of interlocked positive and negative transcriptional/translational feedback loops. In the negative feedback loop, Per and Cry genes (treated as a single variable) inhibit their own transcription by preventing BMAL1 activity. In the positive feedback loop, the PER/CRY complex activates the transcription of their common transcriptional activator, Bmal1 [24]. The release of the neurotransmitter is activated by PER/CRY. In turn, the neurotransmitter activates, in the downstream cell, a signaling cascade (involving PKA and CREB) that increases Per/Cry mRNA expression [23]. In this model, light enhances Per/Cry mRNA expression. In this schematic representation, solid arrows denote transport, translation steps, or phosphorylation/dephosphorylation reactions, while dashed arrows denote transcriptional or post-translational regulations. The stars indicate the active (phosphorylated or complexed) forms of the proteins.
Figure 3.
(A) Concentration of and
in different cells. The cell is isolated and entrained by light until
, then the number of oscillations (pseudo-cycles) is measured until the relative amplitude is lower than 0.1. (B) Distribution of oscillating and damped cells depending on the parameter variability
. ‘Not Osc.’ stands for ‘Not Oscillating’ (see Models). (C) Mean and standard deviation of the pseudo-period of individual cells for different values of
. (D) Distribution of the cell dynamics for
: more than one third of the cells show sustained oscillations and the others display from 5 to 20 pseudo-cycles. (E) Distribution of the pseudo-periods for
for the oscillating and damped cells (see Models).
Figure 4.
The different topologies tested.
Three types of networks are used in this work: random architecture (first row, ), scale-free architecture (second row,
) and local connections (last row,
). Note that the spatial distribution plays a role only in the ‘local’ networks. In the first column the corresponding adjacency matrix
is shown (a black square at position
represents a connection from the
-th to the
-th cell). In the second column, a representative network is drawn showing outgoing edges (blue lines) from certain cells (larger black circles) and a random distribution of light-sensitive cells (small yellow dots in the black circles). These networks are named
,
and
respectively. In the third column, the network has a biased distribution of light-sensitive cells, either on the cells with a higher outgoing degree (for random and scale-free networks, first two row, named respectively
and
), or spatially localized (for local networks, last row, named
).
Figure 5.
Effect of CHX and TTX treatments.
(A) Resynchronization in constant dark for a scale-free network with and
after addition of CHX (no protein production) for 32 hours and its removal. (B) Same network exposed to TTX (no cell-cell communication) for 72 hours. Gray lines represent PER/CRY concentration in individual cells and the thick black line is the population average
. (C–D) Comparison of the phases of the individual oscillators before (x-axis) and after (left y-axis) CHX (C) or TTX (D) exposure (black dots). In blue, the distribution of the phase prior to the perturbation is plotted on the right y-axis. A positive phase difference corresponds to a phase advance of the individual cell compared to the average
concentration.
Figure 6.
Properties of the synchronized network.
(A) Synchronization in constant darkness (DD) of a scale-free architecture ) network with
and
. The measured properties are the amplitude of the
oscillations and the period of these oscillations. Each gray line represents the concentration of
in an individual cell; the thick black line is
. (B) Synchronization in 12 h∶12 h light/dark conditions (LD) for the same network as (A). (C–D) Amplitude of the
oscillations in the DD (C) and LD (D) conditions for different network types as a function of
. (E–F) Period of the
oscillations in the DD conditions (E) and in LD conditions (F) for different network types as a function of
. The amplitude and period in the LD conditions for the
and
networks (D and F) shows large variability because some networks with low connectivity are not properly entrained. This weak entrainment (due to the architecture) induces amplitude modulation and biases the results. In C–F, error bars represent the standard deviation for the results of 30 different networks of the same type. The network types are abbreviated as
for random,
for scale-free, and
for local; the subscript
stands for a random distribution of the light-sensitive cells and the subscripts
or
for a biased distribution as shown in figure 4.
Figure 7.
Effect of a jet lag on the SCN model.
(A) In the case of an network with
, the 8-hour shift due to a long night (at
) affects the phase of the peak of
(black line) for about 3 cycles. Before the jet lag, the peak occurs about 4 hours after the night. In the first 3 cycles, the peak is in the late day and regains its initial phase at the fourth cycle (top inset, a positive value implies a phase advance). Throughout this perturbation, the cells remain well synchronized: the phase order parameter (blue line) is even increased. (B) For an
network with
, the system needs about 6 cycles to recover its correct phase and suffers a strong desynchronization. (C) For an
network with
, the system needs only 4 cycles to recover the phase, but cells are strongly desynchronized and the amplitude of oscillations decreases significantly. (D–E) Decrease in the phase order parameter after the jet lag (D), and number of cycles needed for the phase to be within 1 hour of the phase prior to the jet lag (E) as a function of the network type and the average degree. In both plots, lower values correspond to a faster adaptation:
networks show better results for both properties. Note that the results for the
networks are less relevant as the oscillation amplitude is low (Fig. 4D). Results using other types of jet lags are plotted in figure S5. (F–G) Decrease in the phase order parameter (F), and number of cycles needed for phase resynchronization (G) after the jet lag as a function of the shift in hours for
and
networks with
. In all cases, except
with
, advance shifts (dots) have a stronger impact than the corresponding delay shifts (circles).
Figure 8.
Simulation of the SCN composed of two regions in DD and LD conditions.
Simulation of the SCN with different architectures for the VL and DM regions (an coupled to an
network, see Fig. S7 for a sketch of the topology), where the coupling constant
between the DM cells is 0.15 and the DM cells are oscillating faster (see Models). (A–B) Phase difference of the cells in DD (A) and LD (B) conditions. Dots represent cells of the VL (beige region), whereas DM cells are small squares (light yellow region). Phase difference is color encoded: green corresponds to a phase delay, blue to a phase advance and red to antiphase (see also Fig. S13). (C–D) Concentration of
in the individual VL (cyan lines) and DM cells (magenta lines), as well as the average over the VL cells (thick blue line), the DM cells (bold red line), and over the entire SCN (thick black line) in DD (C) and LD (D) conditions.
Figure 9.
Effects of entrainment perturbations on the SCN composed of two regions.
(A) Effect of a 4-hour interruption of the light entrainment during the day (see arrow a ) on VL (blue) and DM (red) average
concentrations in the same SCN network as in figure 8. Dashed lines represent the unperturbed trajectories. (B) Effect of an 8-hour jet lag (long night, see arrow at
) on VL (blue), DM (red) average
concentrations (same network). Dashed lines represent the unperturbed trajectory shifted from 8 hours. (C–D) Average concentration of
at the extremum (points) of oscillations after an interruption of the light entrainment of 4 hours during the day (C), corresponding to panel A, or after a jet lag of 8 hours equivalent to a long night (D), corresponding to panel B. The average of VL cells is in blue and of DM cells in red. Dashed lines show unperturbed values. (E–F) Phase shift of the peak of
for the VL (blue) and DM (red) after an interruption of the light entrainment of 4 hours during the day (E), corresponding to panel A, or after a jet lag of 8 hours equivalent to a long night (F), corresponding to panel B. A positive value corresponds to a phase advance.