Modeling the electrophysiology of suprachiasmatic nucleus neurons

Daily electrical activity in the master circadian clock of a diurnal mammal

Circadian rhythms in mammals are orchestrated by a central clock within the suprachiasmatic nuclei (SCN). Our understanding of the electrophysiological basis of SCN activity comes overwhelmingly from a small number of nocturnal rodent species, and the extent to which these are retained in day-active animals remains unclear. Here, we recorded the spontaneous and evoked electrical activity of single SCN neurons in the diurnal rodent Rhabdomys pumilio, and developed cutting-edge data assimilation and mathematical modeling approaches to uncover the underlying ionic mechanisms. As in nocturnal rodents, R. pumilio SCN neurons were more excited during daytime hours. By contrast, the evoked activity of R. pumilio neurons included a prominent suppressive response that is not present in the SCN of nocturnal rodents. Our modeling revealed and subsequent experiments confirmed transient subthreshold A-type potassium channels as the primary determinant of this response, and suggest a key role for this ionic mechanism in optimizing SCN function to accommodate R. pumilio's diurnal niche.

The E3 ubiquitin ligase adaptor Tango10 links the core circadian clock to neuropeptide and behavioral rhythms

Circadian transcriptional timekeepers in pacemaker neurons drive profound daily rhythms in sleep and wake. Here we reveal a molecular pathway that links core transcriptional oscillators to neuronal and behavioral rhythms. Using two independent genetic screens, we identified mutants of Transport and Golgi organization 10 (Tango10) with poor behavioral rhythmicity. Tango10 expression in pacemaker neurons expressing the neuropeptide PIGMENT-DISPERSING FACTOR (PDF) is required for robust rhythms. Loss of Tango10 results in elevated PDF accumulation in nerve terminals even in mutants lacking a functional core clock. TANGO10 protein itself is rhythmically expressed in PDF terminals. Mass spectrometry of TANGO10 complexes reveals interactions with the E3 ubiquitin ligase CULLIN 3 (CUL3). CUL3 depletion phenocopies Tango10 mutant effects on PDF even in the absence of the core clock gene timeless Patch clamp electrophysiology in Tango10 mutant neurons demonstrates elevated spontaneous firing potentially due to reduced voltage-gated Shaker-like potassium currents. We propose that Tango10/Cul3 transduces molecular oscillations from the core clock to neuropeptide release important for behavioral rhythms.

M1-Type, but Not M4-Type, Melanopsin Ganglion Cells Are Physiologically Tuned to the Central Circadian Clock

Proper circadian photoentrainment is crucial for the survival of many organisms. In mammals, intrinsically photosensitive retinal ganglion cells (ipRGCs) can use the photopigment melanopsin to sense light independently from rod and cone photoreceptors and send this information to many brain nuclei such as the suprachiasmatic nucleus (SCN), the site of the central circadian pacemaker. Here, we measure ionic currents and develop mathematical models of the electrical activity of two types of ipRGCs: M1, which projects to the SCN, and M4, which does not. We illustrate how their ionic properties differ, mainly how ionic currents generate lower spike rates and depolarization block in M1 ipRGCs. Both M1 and M4 cells have large geometries and project to higher visual centers of the brain via the optic nerve. Using a partial differential equation model, we show how axons of M1 and M4 cells faithfully convey information from the soma to the synapse even when the signal at the soma is attenuated due to depolarization block. Finally, we consider an ionic model of circadian photoentrainment from ipRGCs synapsing on SCN neurons and show how the properties of M1 ipRGCs are tuned to create accurate transmission of visual signals from the retina to the central pacemaker, whereas M4 ipRGCs would not evoke nearly as efficient a postsynaptic response. This work shows how ipRGCs and SCN neurons' electrical activities are tuned to allow for accurate circadian photoentrainment.

Unified mechanism of inverse stochastic resonance for monostability and bistability in Hindmarsh-Rose neuron

Noise is ubiquitous and has been verified to play constructive roles in various systems, among which the inverse stochastic resonance (ISR) has aroused much attention in contrast to positive effects such as stochastic resonance. The ISR has been observed in both bistable and monostable systems for which the mechanisms are revealed as noise-induced biased switching and noise-enhanced stability, respectively. In this paper, we investigate the ISR phenomenon in the monostable and bistable Hindmarsh-Rose neurons within a unified framework of large deviation theory. The critical noise strengths for both cases can be obtained by matching the timescales between noise-induced boundary crossing and the limit cycle. Furthermore, different stages of ISR are revealed by the bursting frequency distribution, where the gradual increase of the peak bursting frequency can also be explained within the same framework. The perspective and results in this paper may shed some light on the understanding of the noise-induced complex phenomena in stochastic dynamical systems.

Shaw and Shal voltage-gated potassium channels mediate circadian changes in Drosophila clock neuron excitability

As in mammals, Drosophila circadian clock neurons display rhythms of activity with higher action potential firing rates and more positive resting membrane potentials during the day. This rhythmic excitability has been widely observed but, critically, its regulation remains unresolved. We have characterized and modelled the changes underlying these electrical activity rhythms in the lateral ventral clock neurons (LNvs). We show that currents mediated by the voltage-gated potassium channels Shaw (Kv3) and Shal (Kv4) oscillate in a circadian manner. Disruption of these channels, by expression of dominant negative (DN) subunits, leads to changes in circadian locomotor activity and shortens lifespan. LNv whole-cell recordings then show that changes in Shaw and Shal currents drive changes in action potential firing rate and that these rhythms are abolished when the circadian molecular clock is stopped. A whole-cell biophysical model using Hodgkin-Huxley equations can recapitulate these changes in electrical activity. Based on this model and by using dynamic clamp to manipulate clock neurons directly, we can rescue the pharmacological block of Shaw and Shal, restore the firing rhythm, and thus demonstrate the critical importance of Shaw and Shal. Together, these findings point to a key role for Shaw and Shal in controlling circadian firing of clock neurons and show that changes in clock neuron currents can account for this. Moreover, with dynamic clamp we can switch the LNvs between morning-like and evening-like states of electrical activity. We conclude that changes in Shaw and Shal underlie the daily oscillation in LNv firing rate.

Multi-scale modeling of the circadian modulation of learning and memory

We propose a multi-scale model to explain the time-of-day effects on learning and memory. We specifically model the circadian variation of hippocampus (HC) dependent long-term potentiation (LTP), depression (LTD), and the fear conditioning paradigm in amygdala. The model we built has both Goodwin type circadian gene regulatory network (GRN) and the conductance model of Morris-Lecar (ML) type to explain the spontaneous firing patterns (SFR) in suprachiasmatic nucleus (SCN). In the conductance model, we also include N-Methyl-D-aspartic acid receptor (NMDAR) to study the circadian dependent changes in LTP/LTD in hippocampus and include both NMDAR and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR) dynamics to explain the circadian modulation of fear conditioning paradigm in memory acquisition, recall, and extinction as seen in amygdala. Our multi-scale model captures the essential dynamics seen in the experiments and strongly supports the circadian time-of-the-day effects on learning and memory.

Neuronal oscillations on an ultra-slow timescale: daily rhythms in electrical activity and gene expression in the mammalian master circadian clockwork

Neuronal oscillations of the brain, such as those observed in the cortices and hippocampi of behaving animals and humans, span across wide frequency bands, from slow delta waves (0.1 Hz) to ultra-fast ripples (600 Hz). Here, we focus on ultra-slow neuronal oscillators in the hypothalamic suprachiasmatic nuclei (SCN), the master daily clock that operates on interlocking transcription-translation feedback loops to produce circadian rhythms in clock gene expression with a period of near 24 h (< 0.001 Hz). This intracellular molecular clock interacts with the cell's membrane through poorly understood mechanisms to drive the daily pattern in the electrical excitability of SCN neurons, exhibiting an up-state during the day and a down-state at night. In turn, the membrane activity feeds back to regulate the oscillatory activity of clock gene programs. In this review, we emphasise the circadian processes that drive daily electrical oscillations in SCN neurons, and highlight how mathematical modelling contributes to our increasing understanding of circadian rhythm generation, synchronisation and communication within this hypothalamic region and across other brain circuits.

Relationship in Pacemaker Neurons Between the Long-Term Correlations of Membrane Voltage Fluctuations and the Corresponding Duration of the Inter-Spike Interval

Several studies of the behavior in the voltage and frequency fluctuations of the neural electrical activity have been performed. Here, we explored the particular association between behavior of the voltage fluctuations in the inter-spike segment (VFIS) and the inter-spike intervals (ISI) of F1 pacemaker neurons from H. aspersa, by disturbing the intracellular calcium handling with cadmium and caffeine. The scaling exponent α of the VFIS, as provided by detrended fluctuations analysis, in conjunction with the corresponding duration of ISI to estimate the determination coefficient R ² (48-50 intervals per neuron, N = 5) were all evaluated. The time-varying scaling exponent α(t) of VFIS was also studied (20 segments per neuron, N = 11). The R ² obtained in control conditions was 0.683 ([0.647 0.776] lower and upper quartiles), 0.405 [0.381 0.495] by using cadmium, and 0.151 [0.118 0.222] with caffeine (P < 0.05). A non-uniform scaling exponent α(t) showing a profile throughout the duration of the VFIS was further identified. A significant reduction of long-term correlations by cadmium was confirmed in the first part of this profile (P = 0.0001), but no significant reductions were detected by using caffeine. Our findings endorse that the behavior of the VFIS appears associated to the activation of different populations of ionic channels, which establish the neural membrane potential and are mediated by the intracellular calcium handling. Thus, we provide evidence to consider that the behavior of the VFIS, as determined by the scaling exponent α, conveys insights into mechanisms regulating the excitability of pacemaker neurons.

Regulation of persistent sodium currents by glycogen synthase kinase 3 encodes daily rhythms of neuronal excitability

How neurons encode intracellular biochemical signalling cascades into electrical signals is not fully understood. Neurons in the central circadian clock in mammals provide a model system to investigate electrical encoding of biochemical timing signals. Here, using experimental and modelling approaches, we show how the activation of glycogen synthase kinase 3 (GSK3) contributes to neuronal excitability through regulation of the persistent sodium current (I_NaP). I_NaP exhibits a day/night difference in peak magnitude and is regulated by GSK3. Using mathematical modelling, we predict and confirm that GSK3 activation of I_NaP affects the action potential afterhyperpolarization, which increases the spontaneous firing rate without affecting the resting membrane potential. Together, these results demonstrate a crucial link between the molecular circadian clock and electrical activity, providing examples of kinase regulation of electrical activity and the propagation of intracellular signals in neuronal networks.

It is not clear how circadian biochemical cascades are encoded into neural electrical signals. Here, using a combination of electrophysiology and modelling approaches in mice, the authors show activation of glycogen synthase kinase 3 modulates neural activity in the suprachiasmatic nuclei via regulation of the persistent sodium current, INaP.

A Conserved Bicycle Model for Circadian Clock Control of Membrane Excitability

Circadian clocks regulate membrane excitability in master pacemaker neurons to control daily rhythms of sleep and wake. Here, we find that two distinctly timed electrical drives collaborate to impose rhythmicity on Drosophila clock neurons. In the morning, a voltage-independent sodium conductance via the NA/NALCN ion channel depolarizes these neurons. This current is driven by the rhythmic expression of NCA localization factor-1, linking the molecular clock to ion channel function. In the evening, basal potassium currents peak to silence clock neurons. Remarkably, daily antiphase cycles of sodium and potassium currents also drive mouse clock neuron rhythms. Thus, we reveal an evolutionarily ancient strategy for the neural mechanisms that govern daily sleep and wake.

Distinct roles for GABA across multiple timescales in mammalian circadian timekeeping

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.

Novel description of ionic currents recorded with the action potential clamp technique: application to excitatory currents in suprachiasmatic nucleus neurons

The traditional method of recording ionic currents in neurons has been with voltage-clamp steps. Other waveforms such as action potentials (APs) can be used. The AP clamp method reveals contributions of ionic currents that underlie excitability during an AP (Bean BP. Nat Rev Neurosci 8: 451-465, 2007). A novel usage of the method is described in this report. An experimental recording of an AP from the literature is digitized and applied computationally to models of ionic currents. These results are compared with experimental AP-clamp recordings for model verification or, if need be, alterations to the model. The method is applied to the tetrodotoxin-sensitive sodium ion current, INa, and the calcium ion current, ICa, from suprachiasmatic nucleus (SCN) neurons (Jackson AC, Yao GL, Bean BP. J Neurosci 24: 7985-7998, 2004). The latter group reported voltage-step and AP-clamp results for both components. A model of INa is constructed from their voltage-step results. The AP clamp computational methodology applied to that model compares favorably with experiment, other than a modest discrepancy close to the peak of the AP that has not yet been resolved. A model of ICa was constructed from both voltage-step and AP-clamp results of this component. The model employs the Goldman-Hodgkin-Katz equation for the current-voltage relation rather than the traditional linear dependence of this aspect of the model on the Ca(2+) driving force. The long-term goal of this work is a mathematical model of the SCN AP. The method is general. It can be applied to any excitable cell.

Characterizing spiking in noisy type II neurons

Understanding the dynamics of noisy neurons remains an important challenge in neuroscience. Here, we describe a simple probabilistic model that accurately describes the firing behavior in a large class (type II) of neurons. To demonstrate the usefulness of this model, we show how it accurately predicts the interspike interval (ISI) distributions, bursting patterns and mean firing rates found by: (1) simulations of the classic Hodgkin-Huxley model with channel noise, (2) experimental data from squid giant axon with a noisy input current and (3) experimental data on noisy firing from a neuron within the suprachiasmatic nucleus (SCN). This simple model has 6 parameters, however, in some cases, two of these parameters are coupled and only 5 parameters account for much of the known behavior. From these parameters, many properties of spiking can be found through simple calculation. Thus, we show how the complex effects of noise can be understood through a simple and general probabilistic model.

A novel analysis of excitatory currents during an action potential from suprachiasmatic nucleus neurons

A new application of the action potential (AP) voltage-clamp technique is described based on computational analysis. An experimentally recorded AP is digitized. The resulting Vi vs. ti data set is applied to mathematical models of the ionic conductances underlying excitability for the cell from which the AP was recorded to test model validity. The method is illustrated for APs from suprachiasmatic nucleus (SCN) neurons and the underlying tetrodotoxin-sensitive Na(+) current, INa, and the Ca(2+) current, ICa. Voltage-step recordings have been made for both components from SCN neurons (Jackson et al. 2004). The combination of voltage-step and AP clamp results provides richer constraints for mathematical models of voltage-gated ionic conductances than either set of results alone, in particular the voltage-step results. For SCN neurons the long-term goal of this work is a realistic mathematical model of the SCN AP in which the equations for I(Na) and I(Ca) obtained from this analysis will be a part. Moreover, the method described in this report is general. It can be applied to any excitable cell.

Causes and consequences of hyperexcitation in central clock neurons

Hyperexcited states, including depolarization block and depolarized low amplitude membrane oscillations (DLAMOs), have been observed in neurons of the suprachiasmatic nuclei (SCN), the site of the central mammalian circadian (~24-hour) clock. The causes and consequences of this hyperexcitation have not yet been determined. Here, we explore how individual ionic currents contribute to these hyperexcited states, and how hyperexcitation can then influence molecular circadian timekeeping within SCN neurons. We developed a mathematical model of the electrical activity of SCN neurons, and experimentally verified its prediction that DLAMOs depend on post-synaptic L-type calcium current. The model predicts that hyperexcited states cause high intracellular calcium concentrations, which could trigger transcription of clock genes. The model also predicts that circadian control of certain ionic currents can induce hyperexcited states. Putting it all together into an integrative model, we show how membrane potential and calcium concentration provide a fast feedback that can enhance rhythmicity of the intracellular circadian clock. This work puts forward a novel role for electrical activity in circadian timekeeping, and suggests that hyperexcited states provide a general mechanism for linking membrane electrical dynamics to transcription activation in the nucleus.

Modeling the seasonal adaptation of circadian clocks by changes in the network structure of the suprachiasmatic nucleus

The dynamics of circadian rhythms needs to be adapted to day length changes between summer and winter. It has been observed experimentally, however, that the dynamics of individual neurons of the suprachiasmatic nucleus (SCN) does not change as the seasons change. Rather, the seasonal adaptation of the circadian clock is hypothesized to be a consequence of changes in the intercellular dynamics, which leads to a phase distribution of electrical activity of SCN neurons that is narrower in winter and broader during summer. Yet to understand this complex intercellular dynamics, a more thorough understanding of the impact of the network structure formed by the SCN neurons is needed. To that effect, we propose a mathematical model for the dynamics of the SCN neuronal architecture in which the structure of the network plays a pivotal role. Using our model we show that the fraction of long-range cell-to-cell connections and the seasonal changes in the daily rhythms may be tightly related. In particular, simulations of the proposed mathematical model indicate that the fraction of long-range connections between the cells adjusts the phase distribution and consequently the length of the behavioral activity as follows: dense long-range connections during winter lead to a narrow activity phase, while rare long-range connections during summer lead to a broad activity phase. Our model is also able to account for the experimental observations indicating a larger light-induced phase-shift of the circadian clock during winter, which we show to be a consequence of higher synchronization between neurons. Our model thus provides evidence that the variations in the seasonal dynamics of circadian clocks can in part also be understood and regulated by the plasticity of the SCN network structure.

Circadian clocks drive the temporal coordination of internal biological processes, which in turn determine daily rhythms in physiology and behavior in the most diverse organisms. In mammals, the 24-hour timing clock resides in the suprachiasmatic nucleus (SCN) of the hypothalamus. The SCN is a network of interconnected neurons that serves as a robust self-sustained circadian pacemaker. The electrical activity of these neurons and their synchronization with the 24-hour cycle is established via the environmental day and night cycles. Apart from daily luminance changes, mammals are exposed to seasonal day length changes as well. Remarkably, it has been shown experimentally that the seasonal adaptations to different photoperiods are related to the modifications of the neuronal activity of the SCN due to the plasticity of the network. In our paper, by developing a mathematical model of the SCN architecture, we explore in depth the role of the structure of this important neuronal network. We show that the redistribution of the neuronal activity during winter and summer can in part be explained by structural changes of the network. Interestingly, the alterations of the electrical activity patterns can be related with small-world properties of our proposed SCN network.

RNA editing of the IQ domain in Ca(v)1.3 channels modulates their Ca²⁺-dependent inactivation

Adenosine-to-inosine RNA editing is crucial for generating molecular diversity, and serves to regulate protein function through recoding of genomic information. Here, we discover editing within Ca(v)1.3 Ca²⁺ channels, renown for low-voltage Ca²⁺-influx and neuronal pacemaking. Significantly, editing occurs within the channel's IQ domain, a calmodulin-binding site mediating inhibitory Ca²⁺-feedback (CDI) on channels. The editing turns out to require RNA adenosine deaminase ADAR2, whose variable activity could underlie a spatially diverse pattern of Ca(v)1.3 editing seen across the brain. Edited Ca(v)1.3 protein is detected both in brain tissue and within the surface membrane of primary neurons. Functionally, edited Ca(v)1.3 channels exhibit strong reduction of CDI; in particular, neurons within the suprachiasmatic nucleus show diminished CDI, with higher frequencies of repetitive action-potential and calcium-spike activity, in wild-type versus ADAR2 knockout mice. Our study reveals a mechanism for fine-tuning Ca(v)1.3 channel properties in CNS, which likely impacts a broad spectrum of neurobiological functions.

Circadian regulation of sleep-wake behaviour in nocturnal rats requires multiple signals from suprachiasmatic nucleus

The dynamics of sleep and wake are strongly linked to the circadian clock. Many models have accurately predicted behaviour resulting from dynamic interactions between these two systems without specifying physiological substrates for these interactions. By contrast, recent experimental work has identified much of the relevant physiology for circadian and sleep-wake regulation, but interaction dynamics are difficult to study experimentally. To bridge these approaches, we developed a neuronal population model for the dynamic, bidirectional, neurotransmitter-mediated interactions of the sleep-wake and circadian regulatory systems in nocturnal rats. This model proposes that the central circadian pacemaker, located within the suprachiasmatic nucleus (SCN) of the hypothalamus, promotes sleep through single neurotransmitter-mediated signalling to sleep-wake regulatory populations. Feedback projections from these populations to the SCN alter SCN firing patterns and fine-tune this modulation. Although this model reproduced circadian variation in sleep-wake dynamics in nocturnal rats, it failed to describe the sleep-wake dynamics observed in SCN-lesioned rats. We thus propose two alternative, physiologically based models in which neurotransmitter- and neuropeptide-mediated signalling from the SCN to sleep-wake populations introduces mechanisms to account for the behaviour of both the intact and SCN-lesioned rat. These models generate testable predictions and offer a new framework for modelling sleep-wake and circadian interactions.

Multicellular model for intercellular synchronization in circadian neural networks

We developed a multicellular model characterized by a high degree of heterogeneity to investigate possible mechanisms that underlie circadian network synchronization and rhythmicity in the suprachiasmatic nucleus (SCN). We populated a two-dimensional grid with 400 model neurons coupled via γ-aminobutyric acid (GABA) and vasoactive intestinal polypeptide (VIP) neurotransmitters through a putative Ca(2+) mediated signaling cascade to investigate their roles in gene expression and electrical firing activity of cell populations. As observed experimentally, our model predicted that GABA would affect the amplitude of circadian oscillations but not synchrony among individual oscillators. Our model recapitulated experimental findings of decreased synchrony and average periods, loss of rhythmicity, and reduced circadian amplitudes as VIP signaling was eliminated. In addition, simulated increases of VIP reduced periodicity and synchrony. We therefore postulated a physiological range of VIP within which the system is able to produce sustained and synchronized oscillations. Our model recapitulated experimental findings of diminished amplitudes and periodicity with decreasing intracellular Ca(2+) concentrations, suggesting that such behavior could be due to simultaneous decrease of individual oscillation amplitudes and population synchrony. Simulated increases in Cl(-) levels resulted in increased Cl(-) influx into the cytosol, a decrease of inhibitory postsynaptic currents, and ultimately a shift of GABA-elicited responses from inhibitory to excitatory. The simultaneous reduction of IPSCs and increase in membrane resting potential produced GABA dose-dependent increases in firing rates across the population, as has been observed experimentally. By integrating circadian gene regulation and electrophysiology with intracellular and intercellular signaling, we were able to develop the first (to our knowledge) multicellular model that allows the effects of clock genes, electrical firing, Ca(2+), GABA, and VIP on circadian system behavior to be predicted.

Multiscale complexity in the mammalian circadian clock

The field of systems biology studies how the interactions among individual components (e.g. genes and proteins) yield interesting and complex behavior. The circadian (daily) timekeeping system in mammals is an ideal system to study complexity because of its many biological scales (from genes to animal behavior). A wealth of data at each of these scales has recently been discovered. Within each scale, modeling can advance our understanding of challenging problems that arise in studying mammalian timekeeping. However, future work must focus on bridging the multiple spatial and temporal scales in the modeling of SCN network. Here we review recent advances, and then delve into a few areas that are promising research directions. We also discuss the flavor of modeling needed (simple or detailed) as well as new techniques that are needed to meet the challenges in modeling data across scales.

Emergence of noise-induced oscillations in the central circadian pacemaker

Bmal1 is an essential transcriptional activator within the mammalian circadian clock. We report here that the suprachiasmatic nucleus (SCN) of Bmal1-null mutant mice, unexpectedly, generates stochastic oscillations with periods that overlap the circadian range. Dissociated SCN neurons expressed fluctuating levels of PER2 detected by bioluminescence imaging but could not generate circadian oscillations intrinsically. Inhibition of intercellular communication or cyclic-AMP signaling in SCN slices, which provide a positive feed-forward signal to drive the intracellular negative feedback loop, abolished the stochastic oscillations. Propagation of this feed-forward signal between SCN neurons then promotes quasi-circadian oscillations that arise as an emergent property of the SCN network. Experimental analysis and mathematical modeling argue that both intercellular coupling and molecular noise are required for the stochastic rhythms, providing a novel biological example of noise-induced oscillations. The emergence of stochastic circadian oscillations from the SCN network in the absence of cell-autonomous circadian oscillatory function highlights a previously unrecognized level of circadian organization.

Multimodal transition and stochastic antiresonance in squid giant axons

The experimental data of Takahashi [Physica D 43, 318 (1990)], on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude I0 in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity, which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs I0 above the transition is also confirmed.

Modeling the spontaneous activity in suprachiasmatic nucleus neurons: role of cation single channels

A population of interconnected neurons of the mammalian suprachiasmatic nuclei (SCN) controls circadian rhythms in physiological functions. In turn, a circadian rhythm of individual neurons is driven by intracellular processes, which via activation of specific membrane channels, produce circadian modulation of electrical firing rate. Yet the membrane target(s) of the cellular clock have remained enigmatic. Previously, subthreshold voltage-dependent cation (SVC) channels have been proposed as the membrane target of the cellular clock responsible for circadian modulation of the firing rate in SCN neurons. We tested this hypothesis with computational modeling based on experimental results from on-cell recording of SVC channel openings in acutely isolated SCN neurons and long-term continuous recording of activity from dispersed SCN neurons in a multielectrode array dish (MED). The model reproduced the circadian behavior if the number of SVC channels or their kinetics were modulated in accordance with protein concentration in a model of the intracellular clock (Scheper et al., 1999. J. Neurosci. 19, 40-47). Such modulation changed the average firing rate of the model neuron from zero ("subjective-night" silence) up to 18 Hz ("subjective-day" peak). Furthermore, the variability of interspike intervals (ISI) and the circadian pattern of firing rate (i.e. silence-to-activity ratio and shape of circadian peaks) are in reasonable agreement with experimental data obtained in dispersed SCN neurons in MED. These results suggest that the variability of ISI in intact SCN neurons is mostly due to stochastic single-channel openings, and that the circadian pattern of the firing rate is specified by threshold properties of dependence of the spontaneous firing rate on the number of single channels (R-N relationship). This plausible mathematical modeling supports the hypothesis that SVC channels could be a critical element in circadian modulation of firing rate in SCN neurons.

A multiscale model to investigate circadian rhythmicity of pacemaker neurons in the suprachiasmatic nucleus

The suprachiasmatic nucleus (SCN) 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 (nimodipine, IP3- and ryanodine-blockers) 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.

Circadian rhythms are ∼24 hour cycles in biochemical, physiological and behavioral processes observed in a diverse range of organisms including Cyanobacteria, Neurospora, Drosophila, mice and humans. In mammals, the dominant circadian pacemaker that drives daily rhythms is located in the suprachiasmatic nucleus (SCN) of the hypothalamus. The SCN is composed of a highly connected network of ∼20,000 neurons. Within each individual SCN neuron core clock genes and proteins interact through intertwined regulatory loops to generate circadian oscillations on the molecular level. These neurons express daily rhythmicity in their firing frequency and other electrophysiological properties. The mechanisms by which the core clock produces synchronized rhythms in neural firing and gene expression are postulated to involve intracellular calcium, a second messenger that regulates many cellular processes. The interaction between the various clock components however remains unknown. In this paper, we present a single cell model that incorporates the circadian gene regulatory pathway, cellular electrophysiological properties, and cytosolic calcium dynamics. Our results suggest a possible system architecture that accounts for the robustness of the circadian clock at the single cell level. Our simulations predict a dual role for intracellular pathways instigated by intracellular calcium and VIP: maintaining the periodicity and amplitude of the core clock genes as well as the firing frequency oscillations.

Determining k channel activation curves from k channel currents often requires the goldman-hodgkin-katz equation

Potassium ion current in nerve membrane, I(K), has traditionally been described by I(K) = g(K)(V - E(K)), where g(K) is the K ion conductance, V is membrane potential and E(K) is the K(+) Nernst potential. This description has been unchallenged by most investigators in neuroscience since its introduction almost 60 years ago. The problem with the I(K) approximately (V - E(K)) proportionality is that it is inconsistent with the unequal distribution of K ions in the intra- and extracellular bathing media. Under physiological conditions the intracellular K(+) concentration is significantly higher than the extracellular concentration. Consequently, the slope conductance at potentials positive to E(K) cannot be the same as that for potentials negative to E(K), as the linear proportionality between I(K) and (V - E(K)) requires. Instead I(K) has a non-linear dependence on (V - E(K)) which is well described by the Goldman-Hodgkin-Katz equation. The implications of this result for K(+) channel gating and membrane excitability are reviewed in this report.

Daily electrical silencing in the mammalian circadian clock

Neurons in the brain's suprachiasmatic nuclei (SCNs), which control the timing of daily rhythms, are thought to encode time of day by changing their firing frequency, with high rates during the day and lower rates at night. Some SCN neurons express a key clock gene, period 1 (per1). We found that during the day, neurons containing per1 sustain an electrically excited state and do not fire, whereas non-per1 neurons show the previously reported daily variation in firing activity. Using a combined experimental and theoretical approach, we explain how ionic currents lead to the unusual electrophysiological behaviors of per1 cells, which unlike other mammalian brain cells can survive and function at depolarized states.

Clustering predicted by an electrophysiological model of the suprachiasmatic nucleus

Despite the wealth of experimental data on the electrophysiology of individual neurons in the suprachiasmatic nuclei (SCN), the neural code of the SCN remains largely unknown. To predict the electrical activity of the SCN, the authors simulated networks of 10,000 GABAergic SCN neurons using a detailed model of the ionic currents within SCN neurons. Their goal was to understand how neuronal firing, which occurs on a time scale faster than a second, can encode a set phase of the circadian (24-h) cycle. The authors studied the effects of key network properties including: 1) the synaptic density within the SCN, 2) the magnitude of postsynaptic currents, 3) the heterogeneity of circadian phase in the neuronal population, 4) the degree of synaptic noise, and 5) the balance between excitation and inhibition. Their main result was that under a wide variety of conditions, the SCN network spontaneously organized into (typically 3) groups of synchronously firing neurons. They showed that this type of clustering can lead to the silencing of neurons whose intracellular clocks are out of circadian phase with the rest of the population. Their results provide clues to how the SCN may generate a coherent electrical output signal at the tissue level to time rhythms throughout the body.

Inhibition of rhythmic neural spiking by noise: the occurrence of a minimum in activity with increasing noise

The effects of noise on neuronal dynamical systems are of much current interest. Here, we investigate noise-induced changes in the rhythmic firing activity of single Hodgkin-Huxley neurons. With additive input current, there is, in the absence of noise, a critical mean value mu=mu(c) above which sustained periodic firing occurs. With initial conditions as resting values, for a range of values of the mean micro near the critical value, we have found that the firing rate is greatly reduced by noise, even of quite small amplitudes. Furthermore, the firing rate may undergo a pronounced minimum as the noise increases. This behavior has the opposite character to stochastic resonance and coherence resonance. We found that these phenomena occurred even when the initial conditions were chosen randomly or when the noise was switched on at a random time, indicating the robustness of the results. We also examined the effects of conductance-based noise on Hodgkin-Huxley neurons and obtained similar results, leading to the conclusion that the phenomena occur across a wide range of neuronal dynamical systems. Further, these phenomena will occur in diverse applications where a stable limit cycle coexists with a stable focus.

Design principles for phase-splitting behaviour of coupled cellular oscillators: clues from hamsters with 'split' circadian rhythms

Nonlinear interactions among coupled cellular oscillators are likely to underlie a variety of complex rhythmic behaviours. Here we consider the case of one such behaviour, a doubling of rhythm frequency caused by the spontaneous splitting of a population of synchronized oscillators into two subgroups each oscillating in anti-phase (phase-splitting). An example of biological phase-splitting is the frequency doubling of the circadian locomotor rhythm in hamsters housed in constant light, in which the pacemaker in the suprachiasmatic nucleus (SCN) is reconfigured with its left and right halves oscillating in anti-phase. We apply the theory of coupled phase oscillators to show that stable phase-splitting requires the presence of negative coupling terms, through delayed and/or inhibitory interactions. We also find that the inclusion of real biological constraints (that the SCN contains a finite number of non-identical noisy oscillators) implies the existence of an underlying non-uniform network architecture, in which the population of oscillators must interact through at least two types of connections. We propose that a key design principle for the frequency doubling of a population of biological oscillators is inhomogeneity of oscillator coupling.