What this is
- This research investigates the role of vasopressin signaling in circadian rhythm regulation, focusing on the V1a receptor antagonist, balovaptan.
- The study demonstrates that administering balovaptan significantly accelerates the resynchronization of locomotor activity rhythms in mice after a 6-hour phase advance of the light-dark cycle.
- Additionally, a mathematical model is developed to simulate the effects of on circadian biomarkers, providing insights into potential therapeutic applications.
Essence
- Balovaptan administration accelerates circadian resynchronization in mice following a 6-hour phase shift, indicating its potential as a therapeutic strategy for circadian disorders.
Key takeaways
- A single dose of balovaptan (30 mg/kg) reduced the time to full behavioral re-entrainment to a new light-dark cycle from approximately 5.5 days to 3.3 days. This significant acceleration suggests that may effectively facilitate circadian rhythm adjustments.
- The developed mathematical model captures the dynamics of the and demonstrates that weakening vasopressin signaling enhances the 's resistance to internal desynchronization. This model may guide future clinical trials targeting for circadian rhythm disorders.
- The model predicts that individuals with longer endogenous periods may experience more significant therapeutic benefits from V1aR antagonism, suggesting a tailored approach to treatment based on individual circadian characteristics.
Caveats
- The mathematical model simplifies biology by focusing on two neuronal populations, potentially overlooking other relevant cell types and mechanisms involved in circadian regulation.
- The study's findings are based on mouse models, which may not fully translate to human circadian biology, necessitating caution in extrapolating results to clinical settings.
Definitions
- V1a receptor antagonism: Blocking the V1a vasopressin receptor to inhibit its signaling, which may affect circadian rhythms.
- suprachiasmatic nucleus (SCN): A brain region that serves as the primary circadian pacemaker, regulating daily physiological and behavioral rhythms.
AI simplified
Introduction
Circadian rhythms are essential for regulating many physiological processes, including sleep-wake cycles, hormone secretion, and metabolism1. Disruptions in circadian rhythms are associated with numerous health issues, such as sleep disruption, metabolic syndrome, and mood disorders2. Understanding the mechanisms underlying circadian regulation is crucial for developing therapeutic strategies to address these conditions.
The suprachiasmatic nucleus (SCN) is located within the anterior hypothalamus and serves as the primary circadian pacemaker in mammals, coordinating daily physiological and behavioral rhythms. This critical structure displays spatial heterogeneity, characterized by distinct neuronal populations in its ventrolateral (core) and dorsomedial (shell) regions. The core region is predominantly populated by vasoactive intestinal peptide (VIP) neurons, which receive direct photic input from intrinsically photoreceptive retinal ganglion cells (ipRGC) via the retinohypothalamic tract, enabling synchronization to environmental light cues. These VIP neurons play a pivotal role in intercellular communication, synchronizing other SCN neurons3,4. In contrast, the shell region is enriched with arginine vasopressin (AVP) neurons, which contribute significantly to the rhythmic output of the SCN. The differential distribution of VIP and AVP neurons, coupled with their specific functions, underlies the SCN’s complex ability to regulate circadian rhythms5. Moreover, recent single-cell RNA sequencing studies show that SCN heterogeneity is more complex than this core and shell subdivision6,7.
The vulnerability of the SCN to internal desynchronization is clearly demonstrated by experiments employing non-24-hour light cycles, such as continuous light8 or 28-hour light-dark cycles9. Notably, studies in rodents using 22-hour light-dark cycles reveal a functional dissociation between the ventrolateral (vlSCN) VIP neurons and the dorsomedial (dmSCN) AVP neurons10. While VIP neurons readily entrain to the rapid 22-hour cycle due to their higher sensitivity to light cues, AVP neurons maintain a near-24-hour rhythm, resisting the external forcing10. This diverging entrainment suggests that although VIP neurons influence the dorsal shell, significant deviations can lead to desynchronization between these two populations, distinctly affecting downstream outputs. For instance, core body temperature, which is primarily influenced by dmSCN AVP output, tends to follow the endogenous circadian period9,11,12. Conversely, melatonin secretion exhibits a complex pattern regulated by both the vlSCN (VIP) and dmSCN (AVP), reflecting the combined interplay of these neuronal populations13.
Vasopressin has a critical role in maintaining SCN coherence. While it is not required for rhythm generation per se, foundational studies indicate it is critical for the coupling and high-amplitude output of the SCN network. Early work utilizing the AVP-deficient Brattleboro rat demonstrated that while these animals are rhythmic, they exhibit alterations in clock precision and robustness14,15. Crucially, these AVP-deficient animals display accelerated re-entrainment to phase shifts and reduced stability when challenged with conflicting Zeitgebers, suggesting that AVP serves to stabilize the pacemaker and maintain the coupling between photic and non-photic oscillators16,17. More recent investigations using genetic mouse models have corroborated these findings, demonstrating that loss of AVP signaling decreases rhythm precision and increases waveform plasticity, while also revealing that AVP regulates the circadian period in a sex-dependent manner18. Furthermore, AVP signaling via the V1a receptor is essential for maintaining pacemaker amplitude19,20 and sharpening the distinction between rest and activity phases, as central administration of AVP acutely suppresses voluntary locomotor behavior21. The regulation of behavioral timing is further refined by GABAergic transmission specifically from AVP neurons, which couples molecular clocks to neuronal firing to restrict activity to the appropriate circadian window22. Beyond stability, the contribution of AVP extends to the differential regulation of specific outputs: Brattleboro rats retain locomotor rhythms but show markedly reduced sleep23 and body temperature amplitudes24, supporting the existence of separate, though coupled, oscillators for temperature and activity.
Given that AVP acts as the primary stabilizer of the SCN network, modulating its signaling offers a potential mechanism to facilitate re-entrainment. The strength of AVP signaling, mediated by V1a and V1b receptors, plays a critical role in entraining circadian rhythms. Notably, co-treatment with V1b and V1a receptor antagonists, or dual genetic knockout of these receptors, has been shown to significantly accelerate entrainment in mice, particularly in experimental jet lag scenarios25. This effect has since been characterized as being mediated by two independent and additive pathways: an intra-SCN V1a pathway and an extra-SCN V1b pathway26. This suggests that strategically manipulating AVP signaling - specifically by temporarily loosening the network coupling - could offer a novel therapeutic approach to mitigating circadian rhythm disruptions.
In this study, we show that acute inhibition of only the V1a vasopressin receptor is sufficient to accelerate circadian resynchronization after a 6 hours phase advance of the light-dark (LD) cycle. Subsequently, we utilized an in silico model of the SCN to simulate the impact of V1aR antagonism on key circadian biomarkers, such as melatonin and core body temperature. By integrating experimental data with theoretical modeling, we aim to elucidate the SCN’s response to pharmacological interventions and explore the therapeutic potential of V1aR antagonism for circadian rhythm disorders.
Results
Behavioural re-synchronization to a 6 h phase-advance of the LD cycle after balovaptan administration
The re-synchronization experiment was performed twice in two independent batches of mice. Since the results were similar in both cases, we pooled the results from the two experiments. Animals from the control sham group (i.e. only handling for oral administration) needed (mean ± SEM) 5.5 ± 0.4 days to entrain to the new LD cycle. Animals receiving vehicle administration took 5.6 ± 0.4 days to re-entrain to the new LD cycle. In contrast, mice that were treated with 30 mg/kg balovaptan took only 3.3 ± 0.2 days to show a total behavioural re-entrainment after the 6 h phase shift. This effect was statistically significant (ANOVA F2,21 = 16.26, p < 0.0001) (Fig. 1B). The onset of activity showed a much more rapid daily adjustment to the new LD cycle in the first 5 days after the shift in the balovaptan treated group (ANOVA F2,21 = 35.62, p < 0.0001) (Fig. 1C). Locomotor activity induced by manipulations was not significantly different between groups (ANOVA F2,21 = 0.56, p = 0.57. Fig S1 supplementary material).
Balovaptan accelerates behavioral resynchronization following a 6-hour phase advance in mice. Representative actograms of the locomotor activity of mice from each group treated at ZT6 (mid rest period) and exposed to a 6 h phase shift of the LD cycle. Color dots in actograms represent time of manipulation, and yellow and black bars in top and bottom indicate the light and dark period, respectively.Rate of re-entrainment (number of days) to show full synchronization to the new LD cycle (Dunnett’s post-hoc test vs vehicle.**** p < 0.0001).The speed of entrainment was evaluated daily and on the first 5 days the 30 mg/kg group showed a significantly faster re-entrainment than the vehicle group (Dunnett’s post-hoc test vs vehicle. *< 0.05, **< 0.01, ****< 0.0001) (sham= 6, vehicle= 8, 30 mg/kg= 10). A B C p p p n n n
In silico model of V1aR antagonism effect on the SCN
In order to mechanistically understand the impact of V1aR antagonism, we developed a mathematical model to simulate the suprachiasmatic nucleus (SCN), its regulation of key circadian biomarkers (melatonin and core body temperature), and the effect of V1aR antagonism.
The model framework is based on the Kuramoto model28 describing the temporal evolution of individual cell phases, and many previous models have been a source of inspiration29–33. For more details and mathematical representation of the model please refer to the Methods section.
Graphical representation of the suprachiasmatic nucleus (SCN) model, its modulation of circadian biomarkers, and effect of V1aR antagonism. The model represents the SCN as two interacting neuronal populations: ventrolateral (vlSCN - core) VIP and dorsomedial (dmSCN - shell) AVP neurons. These populations communicate via VIP and AVP neurotransmission, respectively, and independently modulate circadian biomarker expression. Core body temperature is exclusively regulated by AVP output, while melatonin is influenced by light input and both VIP and AVP outputs. V1aR antagonism is modeled as a reduction in AVP signaling efficacy. Key parameters: κ(light input strength); κ(strength of VIP self-modulation); κ(strength of VIP modulation of AVP neurons); κ(strength of AVP self-modulation); κ(strength of AVP modulation of VIP neurons). Z VV VA AA AV
Entrainment to light input (Zeitgeber)
As a first step to validate our mathematical model and translate preclinical findings to humans, we simulated the behavior of SCN under various light conditions to replicate experimental observations and assess the model’s ability to capture the fundamental properties of circadian rhythm regulation.
SCN entrainment to varying light conditions . Absence of light input (DD). VIP and AVP neurons exhibit a free-running period of approximately 24.2 hours, consistent with their intrinsic molecular clocks, and maintain synchrony.Light-dark (LD) cycle. Both VIP and AVP neurons entrain to the 24-hour LD cycle, with VIP neurons slightly phase-advanced relative to AVP neurons.Constant light (LL). VIP neurons exhibit a longer period due to direct light input, while AVP neurons maintain a free-running period, leading to desynchronization. Melatonin expression is suppressed by both VIP-AVP desynchrony and light, whereas core body temperature oscillates with a period close to the AVP output and the endogenous period. A B C
Light pulse and phase response curve
Our model also replicates the experimental observation that a light pulse administered before the rise in melatonin levels suppresses melatonin onset and results in a shorter subsequent melatonin peak (Ref. 34, Fig. S2). This compression of the melatonin profile arises from the desynchronization of VIP and AVP neuronal outputs, both of which regulate melatonin expression. This phenomenon has also been observed in rodents subjected to forced desynchronization experiments13.
Model-generated phase response curves (PRCs) for SCN neurons and circadian biomarkers. The PRCs illustrate the phase shifts after 3 days induced by a light pulse administered at different circadian phases. The color gradient from light to dark represents the predicted PRC for varying light intensities. PRC forVIP neurons,AVP neurons,melatonin, andcore body temperature. A B C D
Targeting V1aR leads to fast entrainment under jet lag paradigm
Effects of V1aR antagonism on VIP and AVP neuronal synchronization following simulated jet lag . This figure illustrates the phase differences of VIP and AVP neurons relative to their original schedule after a 6-hour phase advance or delay simulating a jet lag paradigm.Phase difference of VIP neurons.Phase difference of AVP neurons. The model predicts that without V1aR blockade, VIP neurons recover faster than AVP neurons. However, complete V1aR antagonism eliminates this difference, resulting in a coordinated and rapid resynchronization of both neuronal populations. A B
Impact of AVP signaling strength on SCN synchronization
Importantly, the model predicts that the strength of AVP signaling modulates the range of zeitgeber periods over which VIP and AVP neurons remain synchronized. Strengthening AVP signaling narrows the synchronization range (Fig. 6B), increasing the susceptibility to desynchronization. Conversely, weakening AVP signaling, such as through V1aR antagonism, broadens this synchronization range (Fig. 6C). Similar behavior is observed when simulating the SCN output for different values of endogenous period (tau). For values of tau close to 24 hours, the SCN output (VIP and AVP) is synchronized (Fig. 6D). However, increasing the strength of AVP signaling leads to a shorter window of synchronization (Fig. 6E), while weakening it leads to a broader range of synchronization (Fig. 6F). These findings highlight the crucial role of AVP signaling in regulating SCN synchrony and suggest that modulating AVP signaling strength, such as through V1aR antagonism, could be a strategy to restore SCN synchrony.
AVP signaling strength modulates SCN synchronization in response to changes in the zeitgeber period or endogenous period. This figure illustrates the relationship between the period of the zeitgeber (external time cue), the endogenous period (tau), and the synchronization of VIP and AVP neuronal outputs, highlighting the role of AVP signaling strength.VIP and AVP neurons typically synchronize to zeitgeber periods close to 24 hours.Stronger AVP signaling (double the standard value of κand κ) narrows the range of synchronizing zeitgeber periods,while weaker AVP signaling (half the standard value of κand κ) broadens this range.Similar effects are observed when varying tau.Stronger AVP signaling leads to a shorter window of synchronization, () compared to weaker AVP signaling. A B C D E F AA Av AA Av
Relationship between endogenous period, circadian phase and V1aR antagonism
Relationship between the endogenous period (tau) and the timing of the minimum of core body temperature (CBT) and the effect of V1aR antagonism . –An increase in tau in 30 min leads to a phase advance of approximately 2 h of circadian rhythm.,V1aR antagonism induces phase shifts in the CBT rhythm, with the direction (advance or delay) and magnitude determined by the deviation of tau from 24 hours. tau > 24 hours leads to phase advances, with larger deviations resulting in greater advances. Conversely, tau < 24 hours leads to phase delays, with larger deviations resulting in greater delays. A D E F
Discussion
This study shows that a single dose of the V1aR antagonist balovaptan is sufficient to significantly accelerate the resynchronization of behavioral rhythms following an experimental 6-hour jet lag in rodents. While simultaneous inhibition of V1a and V1b vasopressin receptors has been shown to speed up recovery from an experimental jet lag condition25, our finding that a single dose of balovaptan is sufficient to induce faster circadian resynchronization is in line with more recent mechanistic studies. Specifically, Yamaguchi et al.26 showed that the robustness of the circadian clock is mediated by two independent AVP pathways: one intra-SCN (V1a) and the other extra-SCN (V1b). These pathways were shown to contribute independently and additively to the speed of re-entrainment after a jet lag paradigm. SCN-specific V1a knockout mice showed significantly faster re-entrainment compared to wild-type mice, confirming the direct role of the intra-SCN V1a pathway25. This demonstration that both intra-SCN (V1a) and extra-SCN (V1b) pathways contribute additively to this effect further supports the therapeutic potential of targeting the V1a pathway alone. In addition, we introduced a mechanistic mathematical model of the SCN that simulates the regulation of key circadian biomarkers and the effects of V1aR antagonism. To validate our model, we showed that the model was able to replicate many well-established behaviors of the SCN, including the disruption of synchrony between AVP and VIP neurons under forced synchronization experiments, constant light exposure, and jet lag conditions. Once we were confident that our model was able to capture essential features of the SCN and V1aR antagonism effect on resynchronization after jet lag, we used the model to make predictions regarding the effect of V1aR antagonism in humans.
The first insight from our model is that variations in the strength of AVP signaling can influence the SCN’s ability to maintain synchronization. Our model predicts that stronger AVP signaling increases the susceptibility of the SCN to desynchronization (Fig. 6). This suggests that AVP signaling strength could be a factor leading to SCN desynchronization, contributing to circadian dysfunctions related to circadian disruption, and could be the subject of further investigation. Additionally, the model indicates that weakening AVP signaling, achievable through V1aR antagonism, could enhance the SCN’s robustness against internal desynchrony and serve as a therapeutic target for disorders linked with SCN desynchrony. Many disorders, such as non-24-hour sleep-wake rhythm disorder (N24SWRD), have been associated with circadian disruption. N24SWRD has been linked to a longer endogenous period39, which could be one potential cause of SCN desynchronization. Our model suggests that an endogenous period far from 24 hours could lead to SCN internal desynchrony and that weakening vasopressin signaling could restore this synchrony (Fig. 6). Bipolar disorder (BD) has also been associated with SCN desynchrony, where individuals with BD often exhibit irregular sleep patterns and mood fluctuations corresponding with circadian rhythm disruptions40,41. Genetic studies implicate circadian genes, such as CLOCK and ARNTL, in BD pathophysiology, reinforcing the link between circadian disruption and mood disorders42. Despite being speculative, our model suggests that V1aR antagonism could be beneficial for these disorders.
The second insight from our model concerns the relationship between the endogenous period, phase of circadian rhythm, and V1aR antagonism. Our model predicts that an increase in the endogenous period results in a phase delay in circadian rhythms, where a 30-minute increase in tau leads to an approximate 2-hour phase delay. This observation is consistent with findings in individuals with Delayed Sleep-Wake Phase Disorder (DSWPD)39,43. Furthermore, the model predicts that V1aR antagonism can induce a phase advance in individuals with longer endogenous periods, with the phase advance’s magnitude proportional to the length of the endogenous period. Experimental observations have suggested a longer tau as one potential cause of circadian delay in DSWPD39,43. Although there is debate over whether tau is the cause of DSWPD or if it causes phase advances in only a subset of DSWPD individuals, our model suggests that targeting the V1aR pathway could present a novel therapeutic strategy for treating DSWPD by phase advancing their circadian rhythm.
Our model has several limitations. While we attempted to represent the key features of SCN biology, it is based on a simplified view of the SCN. Specifically, we assumed it consists of two regions: the vlSCN (core), primarily containing VIP neurons, and the dmSCN (shell), primarily containing AVP neurons. This approach overlooks the presence of various other cell types and entrainment agents within the SCN22. Additionally, our model integrates experimental data from both humans and rodents, presuming a shared underlying biology, which may not always hold true. In this context, it is important to distinguish between the experimental animal model and the computational outputs. While our in vivo experiments utilized C57BL/6 mice - a strain well-documented to be deficient in pineal melatonin synthesis44 - we incorporated a specific melatonin output into the computational model. This component was included to enhance the translational relevance of the framework to humans, where the dim-light melatonin onset (DLMO) serves as the gold-standard biomarker for circadian phase. However, we do not think this difference in melatonin being present or not poses a problem, since the current model focuses on output regulation and does not account for the reciprocal feedback of melatonin on SCN rhythmicity or downstream sleep homeostatic mechanisms. Despite these limitations, our study provides a theoretical framework for evaluating the potential effects of targeting the SCN with pharmacological interventions. This framework can be readily adapted to include the pharmacodynamics of V1aR antagonism, assess its impact on SCN and circadian biomarkers, and support the design of future trials. The translation of these findings to humans could be tested by using a brain penetrant and selective V1a antagonist small molecule like balovaptan27, which has been shown to be safe and well tolerated in clinical studies45,46.
Methods
Mouse resynchronization studies
We used male young-adult (4 weeks old at the beginning of experiments) C57BL/6 J mice. Animals were exposed to a light-dark cycle (LD) 12:12 (lights on from 8 h to 20 h geographical time; light intensity at 200lux; during dark period dim red light of 5lux) in individual cages with food (UAR, Epinay sur Orge, France) and water ad libitum and temperature (22 ± 1°C) and humidity (55% ± 5%) controlled. LD cycle was represented as zeitgeber times (ZT) where ZT0 represents the lights on and ZT12 lights off. Experiments were performed in accordance with the Principles of Laboratory Animal Care (National Institutes of Health publication 86-23, revised 1985) and the French national laws.
Behavioural recording and analysis
The locomotor activity rhythms were measured using infra-red detectors on the top of the cages and/or running wheels. Data were acquired with Circadian Activity Monitoring System (CAMS, INSERM Lyon). Activity data were displayed as actograms and analyzed using the program ClockLab (Actimetrics, Evanston, IL, USA).
Re-entrainment (jet lag tests)
For 6 hours phase-shift (jet lag protocol) we quantified the number of days after the shift for total re-entrainment, considering both the onset and offset of activity. The onsets and offsets of activity were identified automatically using ClockLab software. Thus, full resynchronization to a new LD cycle, after 6-hour phase shifts of the time of lights off, was considered when activity onset took place at the new time of lights off ±30 minutes. We calculated the number of days (transitory cycles) required to re-synchronize each mouse. The speed of re-entrainment was evaluated by calculating the onset of activity and the advance of it, in hours, daily. To evaluate the effects of manipulation on locomotion, we quantified the locomotor activity changes from 0 to 6 h after each treatment in 30 min intervals.
Statistical analysis
Values in all experiments are means ± SEM. Statistical comparisons were performed using two-way analysis of variance (ANOVA) followed by post hoc Dunnett’s test for multiple comparison for the phase advance experiment. One way analysis of variance (ANOVA) was used for the numbers of days needed to reentrain. The critical value for statistical significance was p < 0.05 for all experiments. We used GraphPad prism for the calculations (version 10.5).
Mathematical model
Mathematical models have been instrumental in deciphering the complex mechanisms governing SCN function and circadian timing. Early work established the role of negative feedback loops in gene regulation for generating sustained oscillations47. Subsequent models expanded upon this foundation by incorporating light input and emphasizing the importance of intercellular coupling for achieving SCN neuron synchronization28,48.
This study utilizes a coupled oscillator model, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}_{V}$$\end{document}NV and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}_{A}$$\end{document}NA represent the respective populations of VIP and AVP neurons. The model, based on the Kuramoto framework28, describes the temporal evolution of individual cell phases. Many previous studies have used Kuramoto based models to simulate synchronization in the SCN, which have been a source of inspiration of the model implemented here29–33. This specific model architecture, which posits a critical role for AVP in maintaining SCN synchronization and network coherence, aligns with the conceptual framework proposed by Bittman49, wherein vasopressin acts not merely as an output signal but as an essential intra-SCN coupling agent that stabilizes the SCN against desynchronization. For a more in-depth theoretical analysis of Kuramoto based model that simulates the SCN divided into core and shell see Taylor et al.50 and Goltsev et al.38.
The phase \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta }_{k}$$\end{document}θk of each cell is translated into expression levels using the relationship \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{k}=\frac{\sin \,\left({\theta }_{k}\right)\,+1}{2}$$\end{document}Ek=sinθk+12, which varies from 0 to 1. The temporal dynamics of the phase are described by the equation:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{d{\theta }_{k}}{dt}=\frac{2\pi }{{\tau }_{k}}+\frac{\alpha }{{\kappa }_{V}+{\kappa }_{A}+{\kappa }_{Z}}\,\left[{\kappa }_{V}\sum sin({\theta }_{j}-{\theta }_{k})+{\kappa }_{A}\sum sin({\theta }_{j}-{\theta }_{k})+{\kappa }_{Z}{I}_{Z}cos\left(\frac{\pi }{2}-{\theta }_{k}\right)\right]$$\end{document}dθkdt=2πτk+ακV+κA+κZκV∑sin(θj−θk)+κA∑sin(θj−θk)+κZIZcosπ2−θkwhere \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tau }_{k}$$\end{document}τk is the endogenous period of oscillator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}k, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}α is the coupling constant, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{V}$$\end{document}κV, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{A}$$\end{document}κA and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{Z}$$\end{document}κZ represent the coupling strengths of VIP, AVP, and light input, respectively. For AVP cells, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{ZA}}=0$$\end{document}κZA=0 and representing the absence of light effect on the phase of AVPs. Physiologically, the coupling constants \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}k represent the efficacy of intercellular communication. We assigned a higher coupling strength to VIP neurons (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{VV}}$$\end{document}κVV, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{VA}}$$\end{document}κVA) compared to the influence of AVP on VIP neurons (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{AV}}$$\end{document}κAV), reflecting physiological evidence that VIP is the primary synchronizer of SCN neurons4. Conversely, AVP signaling is modeled as a critical stabilizer of the dorsal shell. The reduction of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{AA}}$$\end{document}κAA, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{AV}}$$\end{document}κAV, during simulated V1a antagonism corresponds to the pharmacological blockade of V1a receptors, which diminishes the ability of AVP neurons to synchronize their neighbors, a mechanism supported by observations that V1a/V1b deficient mice are more susceptible to phase shifts25.
Light input is the primary zeitgeber in the model, affecting the phase of the molecular clock in VIP cells. Light input is represented by the term \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{Z}{I}_{Z}$$\end{document}κZIZ where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{Z}$$\end{document}κZ is the strength of light input, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I}_{Z}={ZI}(t)$$\end{document}IZ=ZI(t), where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z$$\end{document}Z is the strength of light input and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I(t)$$\end{document}I(t) is the temporal regulation of the light input and assume values from 0 (dark/night) and 1 (light/day). Note that the light input is dependent on the term \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cos$$\end{document}cos\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left(\frac{\pi }{2}-{\theta }_{k}\right)$$\end{document}π2−θk Mechanistically, this means that light input tends to drive the phase of the clock to\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,{\theta }_{k}\to \,\frac{\pi }{2}$$\end{document}θk→π2 which represents the maximum expression of clock genes. Therefore, light input upregulates the expression of clock genes, and consequently VIP expression in VIP cells. Put another way, if the expression of VIP is increasing, a light input further accelerates its increase (therefore phase advancing). On the other hand, if the expression of VIP is decreasing, light delays its decrease (therefore phase delaying).
To visualize the dynamics of coupled oscillators it is convenient to define order parameters based on the following relationship:2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r{e}^{i\varphi }=\frac{1}{N}\mathop{\sum }\limits_{j=1}^{N}{e}^{i{\theta }_{j}}$$\end{document}reiφ=1N∑j=1Neiθjwhere, the radius \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r$$\end{document}r(t) measures the phase coherence, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi \left(t\right)$$\end{document}φt is the average phase. Based on that, and following the analysis in reference 51, we can rewrite the model in a more computationally efficient version:3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{d{\theta }_{k}}{dt}=\frac{2\pi }{{\tau }_{k}}+\frac{\alpha }{{\kappa }_{V}+{\kappa }_{A}+{\kappa }_{Z}}[\,{\kappa }_{V}{r}_{V}\,sin({\varphi }_{V}-{\theta }_{k})+{\kappa }_{A}{r}_{A}\,sin\,({\varphi }_{A}-{\theta }_{k})+{\kappa }_{Z}{I}_{Z}cos({\theta }_{k})]$$\end{document}dθkdt=2πτk+ακV+κA+κZ[κVrVsin(φV−θk)+κArAsin(φA−θk)+κZIZcos(θk)]
Whereandare the phase coherence and average phase of VIPs, andandare the phase coherence and average phase of AVPs. The output of VIPs and AVPs can be defined byand, respectively. We also used the following equality:. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{V}$$\end{document} r V \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{V}$$\end{document} φ V \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{A}$$\end{document} r A \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{A}$$\end{document} φ A \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,\frac{\sin \,\left({\varphi }_{V}\right)+1}{2}$$\end{document} sin φ V + 1 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{\sin \,\left({\varphi }_{A}\right)+1\,}{2}$$\end{document} sin φ A + 1 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cos \,\left({\theta }_{k}\right)=\sin \left(\frac{\pi }{2}-\,{\theta }_{k}\right)$$\end{document} cos sin θ k π 2 − θ k =
The model relies on the following key assumptions: no spatial diffusion of VIP and AVP, no spatial localization of neurons (all neurons in the same population are equally affected), heterogeneity in the period of the molecular clock as a source of variability, the key circadian biomarkers are independently affected by the output of VIPs and AVPs, and unless indicated otherwise the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I}_{Z}(t)$$\end{document}IZ(t) represents a modern human light schedule of 16 h of light and 8 h of dark (as shown in Fig. 3B).
Effect of V1aR antagonists
We assumed that V1aR antagonists suppress the communication via AVP by blocking its receptor. Mathematically, we defined a variable V1aRa that represents the effect of V1aR antagonists and assume values from 0 (no effect) to 1 (full receptor blockage). Under the presence of V1aR antagonists we assumed that→V1aRa and→V1aRa. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{AA}}$$\end{document} κ AA \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{AA}}$$\end{document} κ AA \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{AV}}$$\end{document} κ AV \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{AV}}$$\end{document} κ AV
Effect on circadian biomarkers
To translate neuronal synchronization into physiological output levels, we utilized Hill functions to model the nonlinear relationship between SCN activity and downstream biomarkers. The negative Hill function (H−), representing inhibition or suppression, and the positive Hill function (H+), representing activation, are defined as: H+(y, y0, n) = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{y}}}^{n}$$\end{document}yn/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${({\rm{y}}}^{n}\,{+\,{{y}}_{0}}^{n})$$\end{document}(yn+ y0n) and H−(y, y0, n) = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1$$\end{document}1/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${({\rm{y}}}^{n}\,{+\,{{y}}_{0}}^{n})$$\end{document}(yn+ y0n) where, y is the input variable (neuronal phase coherence or light intensity), y0 is the half-maximal threshold, and n is the Hill coefficient, which determines the steepness of the response.
We modeled two distinct physiological outputs based on the integrated activity of the SCN subregions:
Core body temperature (CBT)
Consistent with physiological evidence that the AVP-rich shell drives temperature rhythm amplitude24, CBT was modeled as a downstream output positively correlated with the mean phase coherence of the AVP population \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi }_{A}$$\end{document}φA:4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CBT(t)={H}^{+}({\varphi }_{A},0.4,2)$$\end{document}CBT(t)=H+(φA,0.4,2)
Melatonin
Melatonin levels (Mel) were modeled as being suppressed by three factors: environmental light, VIP neuronal activity (core), and AVP neuronal activity (shell). This multiplicative formulation ensures that melatonin levels peak only during the biological night when both light input and SCN neuronal firing are low. 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Mel(t)={H}^{-}({I}_{Z},0.4,2)\,{H}^{-}({\varphi }_{V},0.2,2){H}^{-}({\varphi }_{A},0.2,2)$$\end{document} M e l ( ) t ( ) I Z , , 0.4 2 ( ) φ V , , 0.2 2 ( ) φ A , , 0.2 2 = H − H − H −
While the experimental component of this study utilized C57BL/6 mice, which are genetically deficient in pineal melatonin synthesis44, this melatonin output was explicitly included in the computational model to serve as a translational biomarker. This allows the model’s predictions to be extrapolated to humans and other melatonin-proficient species, where Dim Light Melatonin Onset (DLMO) is the gold standard for assessing circadian phase.
Simulated light pulse
To generate the Phase Response Curve (PRC) and assess acute light effects, we implemented a simulation protocol designed to mimic the standard experimental conditions used in human circadian studies (e.g.,reference 34). In these ‘in silico’ experiments, the model was subjected to a single, distinct pulse of light - modeled as a square-wave increase in intensity -against a background of constant darkness. This light stimulus was applied for 6.7h34 at different circadian times. An example of the application of the light pulse just before the expected melatonin rise is presented in Figure S2.
Standard parameter values
| Parameter | Value | Unit |
|---|---|---|
| N, NVA | 100, 200 | — |
| \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tau }_{k}$$\end{document} τ k | 24.2 + - 0.5 | h |
| \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} α | 0.25 | 1/h |
| Z | 0.8 | — |
| , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{VV}}$$\end{document} κ VV \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{VA}}$$\end{document} κ VA | 1.0, 0.5 | — |
| , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{AV}}$$\end{document} κ AV \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{AA}}$$\end{document} κ AA | 0.5, 5.0 | — |
| , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{ZV}}$$\end{document} κ ZV \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{{ZA}}$$\end{document} κ ZA | 25.0, 0.0 | — |
Supplementary information
Supplementary Material