Brain clock driven by neuropeptides and second messengers

The master circadian pacemaker in mammals is localized in a small portion of the brain called the suprachiasmatic nucleus (SCN). It is unclear how the SCN produces circadian rhythms. A common interpretation is that the SCN produces oscillations through the coupling of genetic oscillators in the neurons. The coupling is effected by a network of neuropeptides and second messengers. This network is crucial for the correct function of the SCN. However, models that study a possible oscillatory behavior of the network itself have received little attention. Here we propose and analyze a model to examine this oscillatory potential. We show that an intercellular oscillator emerges in the SCN as a result of the neuropeptide and second messenger dynamics. We find that this intercellular clock can produce circadian rhythms by itself with and without genetic clocks. We also found that the model is robust to perturbation of parameters and can be entrained by light-dark cycles.

Figure 1

Intercellular clock model of the SCN. (a) A local network. Each neuron is connected to its four neighbors in a 2D square lattice with periodic boundary conditions. The connection from neuron A to neuron B is denoted by 1 and the connection from B to A is denoted by 2. (b) A detailed model of the two connections between neurons A and B. Activated receptors in neuron A stimulate the synthesis and accumulation of second messengers (cAMP and ${\mathrm{Ca}}^{2+}$) (I). The second messengers modulate the release of neuropeptides $V_1$ (II) in connection 1. The peptidases $P_1$ degrade the neuropeptides $V_1$ by an enzymatic reaction (III). The receptors of neuron B are activated by $V_1$ (IV). In neuron B this activation triggers the same signaling as in neuron A. The signaling ends in the release of neuropeptides $V_2$ and peptidases $P_2$ in connection 2.

Figure 2

Simulations of the intercellular clock model. (a) Time evolution of the biomolecules involved in the 400 connections: neuropeptides ($V$, blue), peptidases ($P$, red), neuropeptide-peptidase complexes (V:P, cyan), and the strength of the ${\mathrm{cAMP}\mathrm{and}\mathrm{Ca}}^{2+}$ signaling ($m$, magenta, dimensionless, scaled by 250). Black lines represent the average. (b) Power spectrum and $O_p$ (inset) for square lattices of 16, 25, 36, 49, 64, 81, and 100 neurons (64, 100, 144, 196, 256, 324, and 400 connections, respectively). Computed time for each lattice: 1000 hours. (c) $O_p$ as a function of the number of connections for 100 neurons in a square lattice. Except if otherwise stated, we calculated the mean and standard deviation of the $O_p$ for ten simulations (one simulation for 360 and 400 connections). Computed time for each simulation: 400 hours (see Table SV for parameter values [39]).

Figure 3

Model robustness to perturbation of parameters. The value was increased and decreased by 15% for each parameter [10, 40] (in total: 16 simulations). (a) Robustness of the order parameter. (b) Robustness of the period. The 16 simulations are denoted in the $x$ axis. Simulations 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16 correspond to $r_1^p=1.15r_1,r_1^p=0.85r_1,r_2^p=1.15r_2,r_2^p=0.85r_2,r_{-2}^p=1.15r_{-2},r_{-2}^p=0.85r_{-2},r_3^p=1.15r_3,r_3^p=0.85r_3,r_4^p=1.15r_4,r_4^p=0.85r_4,r_5^p=1.15r_5,r_5^p=0.85r_5,m_0^p=1.15m_0,m_0^p=0.85m_0,K^p=1.15K$, and $K^p=0.85K$, respectively. The red lines denote the value of the order parameter and the period without perturbations. The superscript $p$ denotes parameter perturbed. (Computed time for each simulation: 1000 hours.)

Figure 4

Entrainment of the intercellular clock by light-dark cycles (12 hours of light and 12 hours of darkness). (a) Time evolution of the neuropeptides without entrainment. (b) Time evolution of the neuropeptides with entrainment. Black and green (light gray) lines represent the neuropeptides and average, respectively. Blue lines (square wave form) represent the light-dark cycles. Light increases the amount of second messengers in SCN neurons [2, 41]. Therefore, we assume that the strength of the second messenger signaling in the SCN is maximum with light, i.e., $m_j=1$. And during darkness, $m_j$ follows Eq. (4). The rates are the same as in Table SV [39], but now $r_1=90$ molecules $\mathrm{hour}{}^{-1}$ in order to produce oscillations with a period shorter than 24 hours [32]. (c) Power spectrum of average neuropeptides for (a) (blue line) and (b) (dashed red line). (Computed time for each simulation: 1000 hours.)

Figure 5

Intercellular clock coupled with genetic clocks. (a) Wild-type neuron model. Each neuron contains a genetic clock in which a gene, called Per, represses the activation of its promoter, called E-box. The transcription rate of Per is stimulated by cAMP and ${\mathrm{Ca}}^{2+}$ through the activation of a promoter called CRE [21] (V). The genetic clock stimulates neuropeptide release [30, 32] (VI). (b) Mutant neuron model. The promoter CRE is inoperative, then the transcription of the gene is not stimulated by second messengers. This means that the genetic oscillators are uncoupled. (c) and (d) Time evolution of ${\mathrm{Ca}}^{2+}$ (top) and raster plot of time evolution of Per mRNA (bottom) in wild-type and mutant SCN, respectively. We scale $m$ to calculate [${\mathrm{Ca}}^{2+}$] (see calculation of [${\mathrm{Ca}}^{2+}$] in Appendix pp2). (e) $O_p$ as a function of the number of connections in wild-type (blue circle, calculated for Per mRNA) and mutant SCN (red square, calculated for neuropeptides). To simulate (c), (d), and (e) we used $r_1=80$ molecules $\mathrm{hour}{}^{-1}$ and $r_6=0.04 \mathrm{hour}{}^{-1}$ (see Fig. S3 and Table SVI [39]).

Figure 6

The abolition of second messenger activity, neuropeptide release, or nascent gene expression by drugs stop the oscillations in the SCN. (a) Abolition of second messenger activity. We have changed the rate in reaction (1) by $\gamma m_j{r}_1$ and now $v_l=v_0+\gamma c{m}_l$. (b) Abolition of neuropeptide release. We have changed the rates in reactions (1) and (6) by $\gamma m_j{r}_1$ and $\gamma {\text{mRNA}}_j{r}_6$. (c) Abolition of nascent gene expression. We have changed the rate in reaction (1) by $\gamma m_j{r}_1$ and now $v_l=\gamma (v_0+c{m}_l)$. In (a), (b), and (c) the parameter $\gamma$ takes into account the strength of the drugs in the SCN (as in [32]). $\gamma =1$ means no presence of drugs and $\gamma =0$ means presence of drugs. In (a), (b), and (c) time evolution of ${\mathrm{Ca}}^{2+}$ (top) and raster plot of time evolution of Per mRNA (bottom).