### abstract ###
The suprachiasmatic nucleus of the hypothalamus is a multicellular system that drives daily rhythms in mammalian behavior and physiology.
Although the gene regulatory network that produces daily oscillations within individual neurons is well characterized, less is known about the electrophysiology of the SCN cells and how firing rate correlates with circadian gene expression.
We developed a firing rate code model to incorporate known electrophysiological properties of SCN pacemaker cells, including circadian dependent changes in membrane voltage and ion conductances.
Calcium dynamics were included in the model as the putative link between electrical firing and gene expression.
Individual ion currents exhibited oscillatory patterns matching experimental data both in current levels and phase relationships.
VIP and GABA neurotransmitters, which encode synaptic signals across the SCN, were found to play critical roles in daily oscillations of membrane excitability and gene expression.
Blocking various mechanisms of intracellular calcium accumulation by simulated pharmacological agents reproduced experimentally observed trends in firing rate dynamics and core-clock gene transcription.
The intracellular calcium concentration was shown to regulate diverse circadian processes such as firing frequency, gene expression and system periodicity.
The model predicted a direct relationship between firing frequency and gene expression amplitudes, demonstrated the importance of intracellular pathways for single cell behavior and provided a novel multiscale framework which captured characteristics of the SCN at both the electrophysiological and gene regulatory levels.
### introduction ###
In mammals many physiological and behavioral responses are subject to internal time-keeping mechanisms or biological clocks.
Daily rhythms are generated by an internal, self-sustained oscillator located in the suprachiasmatic nucleus of the hypothalamus.
The SCN produces autonomous 24h cycles in gene expression and firing frequency from the synchronization of multiple individual oscillatory signals across the network CITATION.
The single cell gene regulatory mechanism involves a number of interlocking positive and negative feedback loops in which the Period gene occupies the central position CITATION.
The circadian modulation of neural firing affects a number of electrophysiological properties of the cell membrane which also fluctuate over the course of the day CITATION .
In vitro studies of SCN slices and cultures have demonstrated diurnal modulation of neural firing CITATION, resting potential CITATION and membrane resistance CITATION, as well as daily oscillations in a number of ionic currents that include the fast delayed rectifier potassium CITATION, L-type calcium CITATION and the large-conductance Ca 2 -activated potassium CITATION, CITATION channels.
Although individual SCN neurons contain molecular feedback loops that drive such rhythms, membrane excitability and synaptic transmission also play significant roles in generating daily oscillations.
Experimental studies in Drosophila have demonstrated the dependence of core clock oscillations on electrical activity, as electrical silencing resulted in abolishment of circadian oscillations of the free-running molecular clock CITATION.
In mammalian organisms a direct association between membrane excitability and core-clock rhythms has also been reported in multiple studies, providing evidence for a positive correlation between Per gene transcription and neural spike frequency output CITATION CITATION.
For example, activation of GABA A receptors via muscimol enhanced inhibitory postsynaptic currents leads to lower firing rates CITATION, CITATION and suppression of Per1 mRNA CITATION.
Another example involves mice deficient in vasoactive intenstinal peptide receptors known to display lower amplitude oscillations of both core clock genes CITATION and neural firing CITATION .
The mechanisms by which the single cells produce synchronized rhythms in neural firing, gene expression and neuropeptide secretion are postulated to involve intracellular second messengers CITATION.
A candidate second messenger that regulates diverse cellular processes is intracellular calcium.
Cytosolic calcium is known to oscillate over the course of the day preceding rhythms in multiple-unit-activity recordings by a mean phase of 4.5 hr CITATION.
Variations in intracellular calcium concentrations have been demonstrated to induce Per1 gene expression by activating the Ca 2 /calmodulin dependent kinase, which in turn phosphorylates the cAMP-response-element binding protein CITATION.
Reduced Ca 2 concentrations have been shown to abolish daily Per1 mRNA oscillations in SCN slices CITATION.
Cytosolic Ca 2 rhythms also affect neural firing frequency, as dampening of Ca 2 oscillations via blockade of calcium release from ryanodine-sensitive pools results in decreased firing activity CITATION, CITATION .
To our knowledge, detailed cell models with molecular descriptions of gene expression and neural firing coupled by intracellular signaling pathways are not currently available for any circadian system.
In a recent study, a Hodgkin-Huxley type model of SCN neurons was developed and shown to reproduce a significant amount of experimentally observed electrophysiological behavior on a millisecond timescale.
While this study facilitated the formulation of our electrophysiology model by providing guidelines for the mathematical representation of a number of relevant ionic currents, our modeling study was distinct due to its focus on the circadian timescale.
In addition to incorporating single-cell electrophysiological properties, our model has accounted for circadian rhythmicity by coupling electrophysiology to daily oscillations in core-clock gene expression and calcium dynamics.
The objective of the present study was to model couplings between the circadian gene-regulatory pathway, cellular electrophysiology and cytosolic calcium dynamics to evaluate the role of extracellular synaptic stimuli on firing rate behavior over a circadian timescale.
The role of distinct intracellular pathways as well as the directionality of information flow along the network nodes was evaluated by analyzing single cell model behavior following the introduction of various external stimuli.
Calcium dynamics, adapted from a published model CITATION, included the contributions of IP3- and ryanodine stores as well as the flux of Ca 2 in and out of the cell membrane.
Our model has demonstrated the dependence of membrane excitability on synaptic input conveyed by VIP and GABA, and predicted reduced neural firing and Per mRNA oscillation amplitudes as well as shorter circadian periods with reduced cytosolic Ca 2 concentrations.
These results suggest a dual effect of signaling pathways instigated by VIP and calcium that potentially operate as coupling agents between the gene regulatory network and the electrophysiology of SCN neurons.
