Circadian regulation of sinoatrial nodal cell pacemaking function: Dissecting the roles of autonomic control, body temperature, and local circadian rhythmicity

Pan Li; Jae Kyoung Kim

doi:10.1371/journal.pcbi.1011907

. 2024 Feb 26;20(2):e1011907. doi: 10.1371/journal.pcbi.1011907

Circadian regulation of sinoatrial nodal cell pacemaking function: Dissecting the roles of autonomic control, body temperature, and local circadian rhythmicity

Pan Li ^1,^*, Jae Kyoung Kim ^1,^2,^*

Editor: Christian I Hong³

PMCID: PMC10927146 PMID: 38408116

Abstract

Strong circadian (~24h) rhythms in heart rate (HR) are critical for flexible regulation of cardiac pacemaking function throughout the day. While this circadian flexibility in HR is sustained in diverse conditions, it declines with age, accompanied by reduced maximal HR performance. The intricate regulation of circadian HR involves the orchestration of the autonomic nervous system (ANS), circadian rhythms of body temperature (CRBT), and local circadian rhythmicity (LCR), which has not been fully understood. Here, we developed a mathematical model describing ANS, CRBT, and LCR in sinoatrial nodal cells (SANC) that accurately captures distinct circadian patterns in adult and aged mice. Our model underscores how the alliance among ANS, CRBT, and LCR achieves circadian flexibility to cover a wide range of firing rates in SANC, performance to achieve maximal firing rates, while preserving robustness to generate rhythmic firing patterns irrespective of external conditions. Specifically, while ANS dominates in promoting SANC flexibility and performance, CRBT and LCR act as primary and secondary boosters, respectively, to further enhance SANC flexibility and performance. Disruption of this alliance with age results in impaired SANC flexibility and performance, but not robustness. This unexpected outcome is primarily attributed to the age-related reduction in parasympathetic activities, which maintains SANC robustness while compromising flexibility. Our work sheds light on the critical alliance of ANS, CRBT, and LCR in regulating time-of-day cardiac pacemaking function and dysfunction, offering insights into novel therapeutic targets for the prevention and treatment of cardiac arrhythmias.

Author summary

The mammalian heart relies on the sinoatrial node, known as the cardiac pacemaker, to orchestrate heartbeats. These heartbeats slow down during sleep and accelerate upon waking, in anticipation of daily environmental changes. The heart’s ability to rhythmically adapt to these 24-hour changes, known as circadian rhythms, is crucial for flexible cardiac performance throughout the day, accommodating various physiological states. However, with aging, the heart’s circadian flexibility gradually weakens, accompanied by a decline in maximal heart rate. Previous studies have implicated the involvement of a master circadian clock and a local circadian clock within the heart, but their time-of-day interactions and altered dynamics during aging remain unclear. In this study, we developed a mathematical model to simulate the regulation of sinoatrial nodal cell pacemaking function by the master and local circadian clocks in adult and aged mice. Our results unveiled distinct roles played by these clocks in determining circadian patterns of sinoatrial nodal cells, shedding light on their critical alliance in regulating time-of-day cardiac pacemaking function and dysfunction.

Introduction

The mammalian heart exhibits robust circadian rhythms in various cardiac function indices, such as heart rate (HR) and electrocardiogram waveforms [1]. During sleep, HR slows down, accompanied by prolongation of QRS duration and QT interval, while it accelerates upon waking, indicating circadian variations in the electrical properties of cardiac function [2]. In addition, cardiac arrhythmic phenotypes also show distinct circadian patterns. For instance, while bradyarrhythmias and Brugada syndrome are more prevalent at night, ventricular fibrillation and sudden cardiac death are more common in the morning [2,3].

These circadian rhythms (~24hr) in cardiac physiology and pathology are regulated by the master circadian clock located in the suprachiasmatic nucleus (SCN) [3]. The master clock in the SCN modulates time-of-day heartbeats by influencing the firing rate (FR) of the sinoatrial node, known as the cardiac pacemaker, through the autonomic nervous system (ANS) [4]. At cellular level, each heartbeat (~ hundreds of milliseconds) is initiated by an action potential (AP) generated in a sinoatrial nodal cell (SANC). The FR of SANC AP is intricately regulated through the delicate interplay between a membrane oscillator (MO) and a Ca²⁺ oscillator (CO) (Fig 1). The MO is associated with sarcolemmal ionic channels, exchangers and pumps, while the CO involves intracellular Ca²⁺ release from the sarco/endoplasmic reticulum (SR) into the cytosol, and Ca²⁺ removal through SR Ca²⁺ ATPase (SERCA) (Fig 1). Both MO and CO of SANC are tightly regulated by the ANS, influencing the circadian variation in SANC FR (Fig 1). Specifically, sympathetic nervous activities (SNA) increase SANC FR by enhancing both MO and CO through the activation of cyclic adenosine monophosphate (cAMP)—protein kinase A (PKA) signaling pathway. This cAMP-PKA signaling pathway leads to the phosphorylation of various MO targets, such as the L-type Ca²⁺ channel (I_CaL), T-type Ca²⁺ channel (I_CaT), and CO targets, including Ryanodine receptor, and phospholamban that regulates the activity of SERCA (Fig 1; yellow dot) [5]. In contrast, parasympathetic nervous activities (PNA) reduce SANC FR by weakening MO through the activation of the muscarinic K⁺ current (I_KACh), and by inhibiting the cAMP-PKA signaling pathway (Fig 1; blue dot) [6]. Both SNA and PNA display circadian variations in regulating SANC FR. Specifically, SNA peaks after awakening to increase SANC FR, whereas PNA reaches its peak during sleep to reduce SAN FR. As a result, the properties of MO and CO in SANC are delicately adjusted to generate circadian variations in SANC FR, anticipating daily environmental changes.

Besides the ANS, circadian rhythms in HR are tuned by the ups and downs of core body temperature (BT), which is regulated by the master clock in the SCN as well (Fig 1) [7,8]. BT modulates HR by inducing temperature-dependent changes in autonomic balance, intracellular ionic diffusion processes, and the properties of ion channels, exchangers, and pumps [9–14]. For instance, experimental studies demonstrated that as BT increases, PNA declines with an increase in SNA [14]. Furthermore, an elevation in BT can enhance SANC excitability by regulating the conductance and gating kinetics of ionic channels [12,13], as well as the dynamics of intracellular Ca cycling [11]. Consequently, as BT rises, HR accelerates with a temperature coefficient (Q₁₀) of ~2 in rodents [14,15]. In adult mice, circadian rhythms of BT (CRBT), ranging from 36°C to 38°C, is characterized by a decline in BT during the day, followed by an increase in BT after waking up at night [16–18].

In addition to the ANS and CRBT, circadian rhythms in HR are also influenced by local circadian rhythmicity (LCR) (Fig 1; green dot) [19]. Prior experimental studies showed that circadian HR rhythms are lost in SCN-lesioned mice, while they are preserved in mice with local circadian disruption, suggesting a primary role of the ANS and a secondary role of LCR in regulating HR circadian rhythms [20–22]. However, under ANS blockade conditions, further studies demonstrate the significant contribution of LCR in promoting diurnal variations in the intrinsic HR (HR with no autonomic control) [22,23]. Notably, circadian rhythms in intrinsic HR can be eliminated with the blockade of hyperpolarization-activated cyclic nucleotide–gated channel (I_HCN) [19], confirming the essential role of I_HCN in mediating LCR within the sinoatrial node (Fig 1; green dot).

Regulated jointly by the ANS, CRBT, and LCR (Fig 1), circadian rhythms in HR display intriguing properties of robustness, performance, and flexibility (Table 1). Despite changes in external conditions, they remain robust, ensuring the generation of rhythmic HR patterns throughout the day. They are capable of generating maximum HR (performance) in response to heightened demand or stress, often occurring after waking up. Moreover, they demonstrate flexibility, accommodating a broad range of pacing frequencies throughout a day, so that time-of-day cardiac outputs can be optimized under diverse physiological conditions, such as sleep/awake or inactive/active states. However, how ANS, CRBT, and LCR interact to facilitate circadian flexibility and performance in cardiac pacemaking function with robustness remains unclear. Furthermore, their vulnerability to adaptation under severe perturbations, such as aging (Fig 1; red dot), remains enigmatic [24–26].

Table 1. Glossary of circadian rhythms in HR.

Term	Explanation
Circadian rhythms	Innate, roughly 24-hour biological cycles that regulate various physiological and behavioral processes in living organisms
Robustness	The heart’s capability to sustain rhythmic HR consistently throughout the diurnal cycle, irrespective of external factors or conditions
Performance	The heart’s capacity to achieve the maximum HR under conditions of increased demand or stress
Flexibility	The heart’s capacity to produce a diverse range of HR throughout the day

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To unravel these questions, the application of mathematical modeling and simulation proves invaluable in providing mechanistic insights into the non-linear behaviors of complex biological systems, e.g., mammalian circadian dynamics [27–31] and cardiac excitation patterns [32,33]. Earlier in silico studies have quantified the impact of circadian expression of potassium channel interacting protein-2 on shaping ventricular AP morphologies [34,35], and investigated the role of circadian rhythmicity of I_CaL expression and function in the occurrence of early after-depolarizations in guinea pig ventricular cardiomyocytes and tissues [36]. However, previous computational studies of SANC have mainly emphasized the ionic interactions between MO and CO in the generation of spontaneous pacemaking activities [33,37]. There remains a paucity of in silico studies regarding the central and local circadian aspects of SANC automaticity.

In this study, we present a novel mathematical model that captures the intricate regulation of SANC by ANS, CRBT, and LCR in mice (Fig 1) (Table 2). The model accurately reproduces diverse circadian patterns as shown in previous experimental studies in adult and aged mice (19, 25, 38). Utilizing the model, we elucidate the specific roles of ANS, CRBT, and LCR in attaining circadian flexibility, performance, and robustness in SANC. Additionally, we quantitatively dissect SANC dysfunction during the aging process. Our findings reveal that ANS plays a pivotal role in promoting SANC flexibility and performance, with CRBT and LCR acting as primary and secondary boosters, respectively, to further enhance SANC flexibility and performance. However, during the aging process, while SANC flexibility and performance experience significant reductions, robustness remains mostly preserved. Specifically, the aging-related decline in PNA acts to restore SANC robustness while compromising flexibility, suggesting a potential trade-off strategy in the aging process. Our model simulations highlight a critical dimension for time-of-day interactions between ANS, CRBT, and LCR in cardiac pacemaking function and dysfunction.

Table 2. Definitions of non-standard abbreviations.

Abbreviations	Definitions
ANS	Autonomic nervous system
AP	Action potential
BPM	Beats per minute
BT	Body temperature
cAMP	Cyclic adenosine monophosphate
CCh	Carbachol
CO	Ca²⁺ oscillator
CRBT	Circadian rhythm of BT
FR	Firing rates of a single sinoatrial nodal cell
HR	Heart rates
G_x	Maximal conductance of ion channel x
ISO	Isoproterenol
LCR	Local circadian rhythmicity
MO	Membrane oscillator
PNA	Parasympathetic nervous activities
P_up	Maximal rate of SERCA Ca²⁺ pump
PKA	Protein kinase A
SANC	Sinoatrial nodal cells
SCN	Suprachiasmatic nucleus
SERCA	SR Ca ²⁺ -ATPase
SNA	Sympathetic nervous activities
SR	Sarcoplasmic reticulum
ZT	Zeitgeber time

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Results

Quantitative reconstruction of diverse circadian patterns of SANC FR in adult and aged mice

It has been suggested that in anesthetized mice without CRBT (BT = 37°C), PNA is more dominant in determining circadian HR variations compared to SNA (Fig 2A; blue vs yellow dashed lines) [38]. Specifically, the amplitude of circadian HR variations showed a significant reduction of 75% with a PNA blockade, whereas an SNA blockade resulted in a smaller reduction of 16%. Moreover, even after a complete ANS blockade, circadian HR variations persisted (Fig 2A; green dashed line) with an amplitude of ~2% [22,23]. Although this amplitude is minimal, this suggests that in addition to the ANS and CRBT, there can be other factors or mechanisms involved in regulating the circadian rhythmicity of HR in anesthetized mice, e.g., the daily changes in the intrinsic properties of the sinoatrial node arising from changes in the expression of I_HCN (Fig 1; green dot) [19,38].

Fig 2 — (A) Averaged circadian HR fluctuations in anesthetized mice (BT = 37°C) with 12-h light cycles before (control; grey dashed line) and after SNA blockade (blue dashed line), PNA blockade (yellow dashed line), and ANS blockade (green dashed line) [38]. Circadian fluctuations were fitted using a sine function as described in [38] and normalized to HR at ZT6 with ANS blockade. (B) Simulated circadian FR patterns in a single mouse SANC (BT = 37°C; normalized to FR at ZT6 with ANS blockade) closely recapitulate experimental findings [38]. (C-D) Model simulations accurately reproduce minimal and maximal time-of-day FR (C), and normalized circadian amplitudes of FR (D) under control, SNA blockade, PNA blockade, and ANS blockade conditions. The normalized amplitude values are obtained by dividing circadian FR amplitudes in beats per minute (BPM) by the mean time-of-day FR. (E) Either additive or unidirectional modulation effects alone are insufficient to accurately reproduce time-of-day FRs under the control conditions. (F-G) Circadian rhythmicity of BT (36~38°C) enhances the circadian amplitude of FR under control conditions (grey dots) (F) with simulated Q₁₀ = 2 in agreement with experimental studies (G) (15). (H-I) In aged model, simulated maximal FR reduction (25%; red dots) (H) is consistent with experimental findings (I) [25].

Our model simulations accurately recapitulated these variations in circadian rhythms of FR under conditions of control, SNA blockade, PNA blockade, and ANS blockade, when CRBT is not present (Fig 2B). Specifically, with ANS blockade, LCR (see Methods for more details) introduces a minor circadian amplitude of FR (Fig 2B; green line and Fig 2C and 2D), as experimentally observed in Fig 2A (green dashed line). While this amplitude marginally increases with PNA blockade (SNA+LCR) (Fig 2B; yellow line and Fig 2C and 2D), it considerably increases with SNA blockade (PNA+LCR) (Fig 2B; blue line and Fig 2C and 2D), consistent with experimental findings in (Fig 2A; yellow and blue dashed lines). Importantly, when we implemented bidirectional modulation effects between PNA and SNA in the model, the circadian pattern in FR under the control condition was accurately simulated (Fig 2B; grey line and Fig 2C–2E) (see Methods for more details). Specifically, the PNA to SNA (P-S) modulation alone tends to increase the circadian amplitude of FR (Fig 2B; blue circle), while the SNA to PNA (S-P) modulation alone increases its baseline (Fig 2B; yellow triangle). As a result of the combined P-S and S-P effects, both the minimum and maximum time-of-day FR values are in close agreement with the experimental data (Fig 2E; grey filled vs. grey box). However, in the absence of the PNA-SNA interactions (i.e., additive PNA and SNA), the baseline of the simulated circadian rhythm of normalized FR (Fig 2B; red box) was lower by ~5% in comparison to the experimental data (Fig 2A; grey dashed line). This suggests that the non-additivity of PNA and SNA is required to properly reconstruct the circadian patterns of SANC function. This finding is in agreement with the interactions between the sympathetic and parasympathetic branches of the ANS as accentuated antagonism [42–44].

These non-additive interactions could be crucial for gaining insights into the distinct mechanisms that underlie PNA in promoting circadian regulation of SANC FR, both in the absence and presence of SNA (Fig 2B; blue vs. grey lines). Specifically, the contribution of PNA on circadian amplitude of SANC FR via the direct activation of I_KACh is paradoxically increased from 7% (Fig 2B; blue line) to 9% (Fig 2B; grey line) in the presence of SNA despite S-P inhibition. This might be primarily due to PNA’s indirect time-of-day “breaking” effects on SNA, even with a weakened direct effect on I_KACh.

Next, expanding on our model with ANS and LCR (Fig 2B; grey line), we further incorporated CRBT (Fig 1) as a circadian function to reproduce the circadian patterns of BT in adult mice, with an averaged time-of-day BT of 37°C, and a circadian amplitude of 1°C. Then, we incorporated temperature-dependent factors to adjust gating kinetics and conductance of ion channels as previously described [10,45]. For ionic pumps, exchangers and intracellular ionic diffusion parameters, their temperature-dependent behaviors were simulated by scaling their maximal capacity or original value with Q₁₀. Furthermore, we modeled the temperature-dependent activities of SNA and PNA by introducing linear adjustments based on experimental measurements [14] (see Methods for details). With CRBT, simulated circadian amplitude of SANC FR was further enhanced (Fig 2F; grey dots), yielding a Q₁₀ value of 2 as previously reported in experimental studies (Fig 2G) [14,15]. We refer this model with CRBT, ANS, and LCR as adult model throughout this work.

Furthermore, based on our adult model, we developed and validated an aged model that incorporates aging-dependent alterations [25,39–41]. Specifically, aging-dependent ion channel remodeling in I_CaT, I_CaL, I_HCN, I_NaK, I_NCX, I_Kr, I_Ks were modeled by scaling their maximal conductance and gating kinetics based on experimental findings [25,39,40,46]. Aging-associated reduction in the expression level of Ca²⁺ cycling proteins, e.g., SERCA (J_up) and Ryanodine receptor (J_Rel), was modeled by adjusting their maximal activities and kinetics in alignment with experimental measurements [40]. Age-related PNA impairment was simulated by a major reduction in PNA based on earlier experimental studies [41]. Additionally, CRBT disruption was modeled by reducing the baseline and amplitude of CRBT, consistent with experimental findings in aged mice [17,26,41,47] (see Methods for details). As a result, the simulated circadian amplitude of SANC FR was largely dampened in aged model (Fig 2H; red dots), with a major reduction (25%) of maximal time-of-day FR as experimentally measured (Fig 2I) [25].

The alliance of ANS, CRBT, and LCR is essential in optimizing the time-of-day SANC function in adult mice

Our model successfully recapitulated diverse circadian patterns in SANC pacemaking function (Fig 2). Subsequently, we utilized the model to investigate how CRBT, ANS and LCR interact to regulate robustness, performance, and flexibility in SANC pacemaking function. To achieve this, we simulated CO-MO parameter space maps at ZT6 and ZT18 under control conditions in adult model (Fig 3A). Specifically, each CO-MO parameter space map was generated by reducing the maximal rate of SERCA (P_up) (a CO parameter; along the vertical axis) and the maximal conductance of I_CaL and I_CaT (MO parameters; along the horizontal axis) from their original values to zero using a step size of 1%, resulting in a total of 100 × 100 simulations. The original values for these CO and MO parameters were defined with P_up = 0.04 mM/ms, G_CaL = 0.018 nS/pF and G_CaT = 0.013956 nS/pF as previously described [48]. The steady-state FR in BPM was computed for each simulation and color-coded to create the map.

Fig 3 — (A) CO-MO parameter space maps color-coded by FR in BPM at ZT6 and ZT18 under control conditions in adult model. (B) Steady-state SANC membrane potential oscillations using parameter settings sampled from panel (A; labeled 1 to 6). (C-G) CO-MO parameter space maps at ZT6 and ZT18 under (CRBT-/-) (C), (CRBT-/-; LCR-/-) (D), (CRBT-/-; ANS-/-) (E), (CRBT-/-; SNA-/-) (F), and (CRBT-/-; PNA-/-) (G) conditions. (H-J) Quantification of SANC flexibility (H), performance (I), and robustness (J) under various conditions. (K) Normalized changes in SANC flexibility, performance, and robustness compared to the control conditions in adult model.

In the CO-MO parameter space maps, borders between no firing, irregular firing, and rhythmic firing regions were denoted by yellow and blue lines, respectively (Fig 3A). Representative steady-state SANC membrane potential oscillation traces (Fig 3B) were sampled from Fig 3A (labeled 1 to 6) to illustrate distinct membrane excitation patterns under various parameter settings of CO and MO, ranging from fast (Fig 3A; 1) to slow ((Fig 3A; 5) rhythmic firing, from irregular (Fig 3A; 3,6) to no firing (Fig 3A; 4).

Because rhythmic firing regions represent the parameter space where SANC maintains rhythmic pacemaking, we quantified SANC robustness (Table 1) as the percentage area of rhythmic firing regions (Fig 3A). Under control conditions, averaged time-of-day SANC robustness is 55% (58% and 52% at ZT6 and ZT18, respectively). Such time-of-day differences in SANC robustness may be attributable to the diminished region of irregular firing (2%) at ZT6, compared to 12% at ZT18. SANC performance was quantified as the maximal time-of-day SANC FR, representing the peak FR reached during the circadian cycle, which is 531 BPM in the control. In addition, SANC flexibility was quantified as the difference between maximal (ZT18) and minimal (ZT6) time-of-day SANC FR with control CO and MO parameter values, reflecting the ability of SANC to adjust its FR over the circadian cycle. SANC flexibility under control conditions is 143 BPM, which is the difference between 531 BPM (ZT18) and 388 BPM (ZT6) (Fig 3A).

To quantitatively dissect the specific roles of CRBT, ANS and LCR in promoting SANC pacemaking function, we simulated CO-MO parameter space maps under various conditions: (CRBT-/-), (CRBT-/-; LCR-/-), (CRBT-/-; ANS-/-), (CRBT-/-; SNA-/-), and (CRBT-/-; PNA-/-) (Fig 3C–3G). Then we quantified the flexibility (Fig 3H), performance (Fig 3I) and robustness (Fig 3J) under these conditions and how much they are changed (Fig 3K). Without CRBT, both SANC flexibility (77BPM) and performance (496BPM) are significantly decreased; yet, averaged time-of-day robustness is slightly enhanced (57%). When LCR is additionally blocked, SANC flexibility (48BPM) and performance (483BPM) are further reduced, with averaged SANC robustness of 57.5%. Similarly, without CRBT and ANS, SANC flexibility (19BPM) and performance (416BPM) are substantially impaired, with a minor reduction in averaged SANC robustness (52%). Additionally, without CRBT and SNA, SANC performance (382BPM) and robustness (averaged at 33%) are preferentially impaired over flexibility (50BPM). On the other hand, without CRBT and PNA, both performance (515BPM) and robustness (averaged at 63.5%) are markedly enhanced, while SANC flexibility (30BPM) is further reduced. These findings suggest that SNA preferentially enhances performance and robustness, while PNA inclines to amplify flexibility at the expense of both performance and robustness (Fig 3K). As a result, ANS promotes both SANC flexibility and performance, without compromising robustness. In addition, CRBT and LCR may act as primary and secondary boosters for SANC flexibility and performance (Fig 3K).

Quantitative dissection of SANC pacemaking dysfunction in aged mice

Using aged model (Fig 2H; red dots), we simulated CO-MO parameter space maps at ZT6 and ZT18 under control conditions (aged; Fig 4A). According to the map, both SANC flexibility (34BPM) and performance (400BPM) were significantly impaired; yet, surprisingly, SANC robustness was well preserved (averaged at 55.5%) (Fig 4F–4H) compared to the adult model (Fig 3A).

To understand how each aging-dependent alteration collectively contributes to the deterioration in SANC pacemaking function during aging, we conducted additional simulations of CO-MO parameter space maps at ZT6 and ZT18 by incorporating aging-dependent MO remodeling (aged MO; Fig 4B), PNA impairment (aged PNA; Fig 4C) and CO alteration (aged CO; Fig 4D) individually, and their combination (aged MO+PNA+CO; Fig 4E). With aged MO (Fig 4B), SANC flexibility (88BPM), performance (417BPM), and robustness (averaged at 38.5%) were all substantially impaired compared to the adult model (Fig 4F–4H). On the other hand, with aged PNA (Fig 4C), SANC performance (545BPM) and robustness (averaged at 60.5%) were largely enhanced instead, with a reduction in SANC flexibility (98BPM) (Fig 4F–4H). Furthermore, with aged CO (Fig 4D), SANC performance (522BPM) and flexibility (159BPM) were moderately reduced and enhanced, respectively, while robustness (averaged at 55%) was mostly unchanged (Fig 4F–4H). With combined aging effects associated with MO, PNA, and CO (aged MO+PNA+CO; Fig 4E), SANC flexibility (54BPM) and performance (411BPM) were further reduced; yet, there was a full restoration of SANC robustness (averaged at 55.5%) compared to the adult model (Fig 4F–4H). When aged CRBT is added to the aged MO+PNA+CO (aged; Fig 4A), SANC flexibility (34BPM) and performance (400BPM) are further reduced, while robustness is unchanged (averaged at 55.5%) (Fig 4F–4H). These model simulations suggest that while aging-dependent MO remodeling in aging impairs all aspects of SANC pacemaking function, aging-dependent changes in PNA and CO may counteract MO remodeling in aging to buffer its damaging effects in SANC (Fig 4I). In addition, CRBT disruption further promotes aging-dependent reduction in both flexibility and performance of SANC (Fig 4I).

Distinct mechanisms underlying circadian patterns in SANC FR in adult and aged mice

To dissect key mechanisms underlying circadian patterns in SANC, we assessed the relative contributions of each module in the model to circadian flexibility and performance of SANC. Specifically, we quantified how much the flexibility or performance of SANC was perturbed after fully inhibiting ANS, CRBT, or LCR in the adult model (Fig 5A) and aged model (Fig 5B). Furthermore, as the role of intracellular Na⁺ ([Na]_i⁺) accumulation in regulating cardiac excitation patterns has been previously reported [49–51], we also clamped the time-of-day [Na]_i⁺ content at its steady-state concentration at ZT6 to evaluate its potential role in regulating the flexibility and performance of SANC.

In adult model (Fig 5A), while ANS inhibition significantly reduces the circadian flexibility (-78%) and performance (-20.2%) of SANC, the effects of CRBT or LCR inhibition are secondary in reducing circadian flexibility (-46.5% and -6.7%, respectively) and performance (-19.2% and -2.8%, respectively). Furthermore, [Na]_i⁺ clamping exerts an enhancing effect on both SANC flexibility (-10.6%) and performance (-2.9%), attributed to a higher [Na]_i⁺ content at faster FR. However, in aged model, different mechanisms underlying the circadian flexibility and performance of SANC were observed (Fig 5B). While the effects of ANS inhibition remain most sensitive, leading to a reduction in SANC flexibility (-77.9%) and performance (-15.9%), the effects of CRBT and LCR inhibition are enhanced, causing a reduction in flexibility (-56.6% and -31.9%, respectively) compared to the adult model (Fig 5A and 5B). This enhanced effect may be attributable to aging-dependent PNA impairment. In addition, the effect of [Na]_i⁺ clamping becomes diminished and reversed in the aged model (Fig 5B) compared to the adult model (Fig 5A).

To further quantify mechanisms underlying aging-dependent reduction in SANC flexibility and performance in aged model, we additionally quantified the extent to which either flexibility or performance of SANC was perturbed by fully inhibiting MO remodeling, PNA impairment, CO alteration and CRBT disruption using the aged model (Fig 5C). The reduction of SANC flexibility in aging is mostly dampened by the inhibition of PNA impairment (-30.8%) and MO remodeling (-26.4%), with a secondary contribution of the inhibition of CRBT disruption (-18.3%), and a negligible effect by the inhibition of CO alteration (-1%). However, the reduction of SANC performance in aging is predominantly weakened by the inhibition of MO remodeling (-118.4%), with secondary contributions of the inhibition of CO alteration (-14.2%) and CRBT disruption (-8.4%). On the other hand, the reduction of SANC performance in aging is promoted by the inhibition of PNA impairment (9.6%).

Discussion

It is known that circadian rhythms in HR can arise from either the master circadian clock located in the SCN or the local circadian clock in the heart [2,4]. Previous experimental studies have suggested that the 24h HR rhythm is primarily governed by the SCN through the ANS [4,19,52,53]. However, instead of solely focusing on determining which one, the master or local circadian clock, dominates, our study was motivated to understand the necessity of having two circadian clocks to regulate cardiac pacemaking function and to explore their specific roles. Earlier computational studies have primarily focused on the dynamic interactions between Ca²⁺ and membrane oscillations in generating spontaneous pacemaking activities in SANC [37,54]. However, the circadian aspects of SANC pacemaking function over the course of the day have not been established [55].

Our study sheds light on a critical yet understudied dimension of time-of-day interactions between master and local clocks in cardiac pacemaking function and dysfunction, by developing a model of ANS, CRBT, and LCR in SANC to recapitulate diverse circadian patterns in both adult and aged mice. Leveraging this model, we elucidated the distinctive roles of ANS, CRBT, and LCR as a dominant amplifier, a primary booster, and a secondary booster, respectively, in achieving circadian flexibility and performance with robustness in SANC. As illustrated in Fig 6A, departing uphill from the baseline state (grey circle), the introduction of LCR (green circle) moderately enhances SANC flexibility and slightly increases performance without affecting robustness. SNA addition (yellow circle) primarily enhances SANC robustness and performance, while PNA (blue circle) promotes SANC flexibility at the expense of both performance and robustness. The combination of ANS and LCR (grey circle) significantly enhances both flexibility and performance without compromising robustness. The final incorporation of CRBT (grey dot; adult) further augments both flexibility and performance.

Fig 6 — (A) Uphill trajectories show the transition from baseline (grey circle) to adult (CRBT + ANS + LCR; grey dot) model states. (B) Downhill trajectories demonstrate the transition from adult (grey dot) to aged model states (red dot).

However, under aging conditions, the cooperative alliance of ANS, CRBT, and LCR is disrupted, resulting in a substantial reduction in the performance and flexibility of SANC. Surprisingly, SANC robustness remains well-preserved. As shown in Fig 6B, departing downhill from the adult state (grey dot), aging-dependent ion channel remodeling (blue circle) undermines all aspects of the SANC function. However, aging-dependent PNA impairment (yellow circle) enhances both SANC performance and robustness with a trade-off in flexibility, countering the effects of MO remodeling. Moreover, aging-dependent Ca²⁺ handling alterations (green circle) introduce a minor reduction and enhancement in performance and flexibility respectively, without affecting robustness. The combined effects of aging-dependent changes in MO, PNA, and CO (red circle) further reduce SANC flexibility, yet fully restore robustness compared to the adult state (grey dot). With the final addition of CRBT disruption in aging, SANC flexibility and performance are both further reduced without affecting robustness. Comparing Fig 6A and 6B, it is intriguing to observe the well-preserved robustness evident in both adult and aged states [56,57]. In adult model, SNA counters PNA, ensuring the preservation of robustness. In aged model, the impairment of PNA works against ion channel remodeling to restore SANC robustness and maintain basal cardiac function.

These mechanistic insights governing the circadian regulation of SANC pacemaking could be a critical step towards a comprehensive understanding of the circadian control of cardiac function and dysfunction [2,4]. For instance, the circadian variation in SANC automaticity alone can be an important factor in determining arrhythmogenic vulnerabilities in ventricular excitation, due to rate-dependent properties of ventricular myocytes [58]. While an elevated HR may promote the occurrence of electric and Ca²⁺ alternans in ventricular tissue [59], a slow HR could contribute to the development of ventricular repolarization abnormalities [49,60], potentially leading to life-threatening ventricular arrhythmias [61]. In addition, the role of LCR in regulating cardiac function could be tissue-specific. While LCR may act as a secondary booster for SANC function, earlier experimental studies suggest that in ventricular myocytes, LCR can serve as a buffer against QT interval prolongation and circadian changes in neurohormonal signaling [4]. Mathematical models that quantitatively describe tissue-specific circadian regulation of the heart, may serve as invaluable tools in dissecting the chronobiological mechanisms that underlie diverse circadian patterns of cardiac arrhythmic phenotypes [2].

The timing of drug administration (e.g., morning or afternoon) can significantly impact its effectiveness and side effects due to circadian rhythms [62,63]. For instance, taken in the morning, melatonin can delay sleep onset, while evening administration can promote it [64]. Similarly, simvastatin, a cholesterol-lowering medication, exhibits greater efficacy when taken at night [63]. Even the efficacy and toxicity of cancer chemotherapy strongly depend on dosing time [65,66]. Chronotherapy of cardiac and vascular disease has been recently reported [67]. Because mathematical models have played critical roles to investigate the chronotherapy [68–71], it would be interesting future work to investigate cardiac chronotherapy using the mathematical model developed in this study. For example, melatonin exhibits antiarrhythmic effects linked to its role in promoting intercellular coupling and reducing heterogeneity of ventricular repolarization. However, chronic melatonin supplementation with personalized chronotherapy remains to be established [72]. In addition, while hERG channel inhibition and the Comprehensive In Vitro Proarrhythmia Assay are widely used to assess drug-induced arrhythmic events, the circadian aspects of drug-induced arrhythmic risks have not been considered [73]. Our model may help to optimize chronotherapeutic strategies and accelerate the identification of novel therapeutic targets within circadian clocks for the prevention and treatment of cardiac arrhythmias.

We have made several assumptions for simplicity in developing our model that may impact the generalizability and interpretation of our model simulations. Our adult model was calibrated to experimental data in anesthetized mice [38] assuming limited circadian activities in SNA [26], which may potentially underestimate the role of SNA in SANC flexibility in free-moving mice living in a thermoneutral environment [74]. Our aged model was parameterized based on a cross-sectional experimental dataset in >32 months old mice, thus lacking the capacity to capture functional trajectories throughout the aging process. We modeled LCR as a diurnal variation in the expression level of I_HCN, but it might not be the only mechanism underlying LCR in SANC. For example, a day/night difference has been reported in several K⁺ channels and in Ca²⁺/calmodulin-dependent protein kinase II delta expression [38]. We modeled CRBT as a simplified sinus function that peaks at ZT18, while actual experimental recordings of CRBT could feature additional complexities with surges in BT immediately after waking up and before sleep, and potential phase advances in aged mice [17]. Inherited from the baseline model [48,51,75], specific molecular identities of several ion channels (e.g., I_st, I_Nab, I_Cab) remain unknown, and a biochemical description of beta-adrenergic and cholinergic signaling pathways and their interactions is absent. In addition, our model is limited by the lack of a detailed transcription-translation feedback loop model for LCR in SANC, owing to the scope of this study and the limited availability of experimental data. Additional model development or experimental studies would be helpful to further advance our understanding of circadian SANC function and dysfunction, e.g., non-additive interactions between SNA and PNA[6], the mechanistic coupling between the ANS and LCR [76], trajectory of functional aging [77], and entrainment dynamics between the master circadian clock and LCR during jet lag or with shift work disorder [78].

Methods

Model development

Autonomic, electrophysiologic, and circadian properties of cardiac function are species-dependent [26,79]. Given the availability of experimental data in mice, our model is constructed to be mouse-specific.

We used the mathematical model of mouse SANC AP developed by Ding et al. [48,51], based on the original work of Kharche et al. [75], as our baseline model. All baseline model definitions, equations, and parameter settings were unchanged from those previously described and implemented by Ding et al. [48]. Due to the absence of circadian regulation in the baseline model, we extended it to quantitatively describe circadian variations in ANS, CRBT, and LCR for both adult and aged mice. Detailed descriptions of model equations are provided in the following section, along with all parameter values and settings listed in S1 Table.

Incorporation of LCR into the baseline model

First, without considering CRBT, LCR was introduced and calibrated into the baseline model as a circadian variation in the I_HCN (Fig 1; green dot) to generate a weak circadian amplitude (~2%) in SANC FR as observed in adult mice under full ANS blockade with BT = 37°C (Fig 2A; green dashed line) [19,38]. Specifically, to introduce circadian variations in I_HCN into the baseline model with ANS blockade, I_HCN was modified from its original form $I_{H C N} = I_{H C N, N a} + I_{H C N, K}$ as follows:

I_{H C N} = (1 + A_{LCR} \times \cos (\frac{2 π T}{T_{L C R}})) \times (I_{H C N, N a} + I_{H C N, K}),

where A_LCR is the amplitude of LCR, T_LCR is the period of LCR, T is the current ZT in hours, $I_{H C N, N a} and I_{H C N, K}$ are the Na⁺ and K⁺ specific HCN channel currents, respectively [48]. It should be noted that, while experimental recordings of HR with ANS blockade [38] show troughs at ZT12, experimental measurements of I_HCN currents [19] show troughs at ZT6. We speculated that this might be attributable to a phase shift in LCR due to a lack of external cues from the ANS. For this, when the ANS is present, I_HCN was modeled as follows:

I_{H C N} = (1 + A_{LCR} \times \cos (\frac{2 π \times (T + 6)}{T_{L C R}})) \times (I_{H C N, N a} + I_{H C N, K}) .

Incorporation of the circadian regulation of ANS into the baseline model

Then, circadian PNA (Fig 1; blue dot) was added and calibrated as a circadian function of carbachol (CCh) concentrations, to reproduce the circadian amplitude (~7%) effects based on experimental data under SNA blockade conditions with BT = 37°C (Fig 2A; blue dashed line) [38]. For this, CCh was modified from its original form $C C h = {C C h}_{b a s a l}$ [48] as follows:

C C h = {C C h}_{b a s a l} + A_{C C h} \times \cos (\frac{2 π \times (T - 6)}{T_{C C h}}),

where CCh_basal is the basal concentration of CCh, A_CCh is the circadian amplitude of CCh, T_CCh is the period of CCh variations, and T is the current time in ZT hours. This circadian variation in CCh leads to the circadian variation in the muscarinic K⁺ current (I_KACh) because I_KACh is regulated by CCh in the original baseline model as follows (Fig 1; blue dot) [48]:

I_{K A C h} = G_{K A c h} \times w (V, C C h, t) \times (V - E_{K}),

where G_KACh is the maximal conductance of I_KACh, V is the membrane potential in mV, t is current time in ms, w(V,CCh,t) is the voltage- and CCh-dependent channel activation function, and E_K is the K⁺ equilibrium potential in mV.

Furthermore, SNA (Fig 1; yellow dot) was implemented to mimic isoproterenol (ISO) effects by modifying the kinetics and/or conductance of I_st, I_Na1.1, I_CaT, I_CaL, I_K1, I_Ks, I_Kr, I_to, and the activities of J_Rel and J_up, using parameter settings as previously described (see S1 Table for more details) [48]. The administration of ISO was scaled to align with experimental measurements of HR acceleration under PNA blockade conditions (BT = 37°C) (Fig 2A; yellow dots) [38]. A combination of LCR and ISO administration is enough to generate a circadian amplitude (~3%) in SANC FR as measured in the experiments [38], allowing little room for additional in-phase circadian variations in SNA. Therefore, SNA in this study was modeled with no circadian variations when CRBT is not present (BT = 37°C). This modeling choice aligns with earlier experimental findings indicating a high sympathetic drive in mice, potentially limiting additional time-of-day variations to maintain a normal core temperature (37°C) under standard laboratory conditions (20°C) [26,74].

When SNA and PNA were both present, bidirectional modulation effects between PNA and SNA (P-S and S-P) (Fig 2B) were formulated and calibrated to account for the non-additivity effects [6,42,80,81] and to be consistent with experimental measurements (Fig 2A; grey dots) [38]. The non-additivity effects with ISO and CCh were implicitly modeled (e.g., via cAMP-PKA dependent pathways or crosstalk between sympathetic and parasympathetic nervous systems) by introducing the ISO effects at a given concentration of CCh as follows:

E_{I S O} = e_{i s o} \times \frac{k_{p_s}^{h}}{k_{p_s}^{h} + {C C h}^{h}},

where e_iso is the stand-alone ISO effects as previously described [48], k_{p_s} is the P-S modulation constant, and h is the Hill coefficient. Furthermore, CCh effects with ISO were introduced as

E_{C C h} = e_{c c h} \times k_{s_p},

where e_cch is the CCh effects alone as previously described [48], and k_{s_p} is the S-P modulation scaling factor (e.g., to account for the cross-talk between SNA and PNA [6,42,80,81]).

Incorporation of CRBT into the baseline model

CRBT (Fig 1) was added and calibrated as a circadian function of BT to reproduce the circadian patterns of BT in adult mice (with averaged time-of-day BT of 37°C and a circadian amplitude of 1°C) [38] (Fig 2F; grey dots). For this, BT was modified from its original form BT = BT_α [48] as follows:

B T = {B T}_{a} + A_{B T} \times \cos (\frac{2 π \times (T + 6)}{T_{B T}}),

where BT_a is the reference BT, A_BT is the circadian amplitude of BT, T_BT is the period of BT variations, and T is the current time in ZT hours.

To account for the effects of CRBT for all ion channels (excluding ionic pumps and exchangers) in our model, we introduced two temperature-dependent factors φ(BT) and η(BT), to scale gating kinetics and conductance of ion channels respectively, as previously described in [10,45] as follows:

φ (B T) = Q_{10}^{\frac{B T - {B T}_{a}}{10}},

η (B T) = 1 + B (B T - {B T}_{a}),

where BT is the current body temperature, BT_a is the reference body temperature, B is a scaling coefficient. For example, the temperature dependence of ion channel x was modeled as follows:

τ_{x, B T} = \frac{τ_{x}}{φ (B T)}

G_{x, B T} = η (B T) G_{x},

where G_x and τ_x are the original conductance and gating time constant of ion channel x as in the baseline model, G_x,BT and τ_x,BT are the conductance and gating time constant of ion channel x at a given BT.

For ionic pumps, exchangers, and intracellular ionic diffusion parameters, their temperature-dependent behaviors were modeled by scaling their maximal activity or original value (if a constant) with φ(BT) For SNA and PNA, it has been reported in earlier experiments [14] that around normal BT (e.g., 37°C), as BT increases, there is a linear increase and decrease in SNA and PNA, respectively, to promote HR acceleration. Thus, the temperature-dependent behaviors of SNA and PNA were modeled by scaling their activities with η(BT) based on experimental findings [14].

Modeling aging-dependent alternations

Aging-dependent ion channel remodeling (Fig 1; red dot) was calibrated to be consistent with electrophysiological measurements by Larson et al. [25], Tellez et al. [39] and Liu et al. [40] as follows:

I_{C a T, a g i n g} = a_{c a t} \times I_{C a T,}

I_{C a L, a g i n g} = a_{c a l} \times I_{C a L},

I_{H C N, a g i n g} = a_{h c n} \times I_{H C N},

I_{N a K, a g i n g} = a_{n a k} \times I_{N a K},

I_{N C X, a g i n g} = a_{n c x} \times I_{N C X},

I_{K r, a g i n g} = a_{h c n} \times I_{K r},

I_{K s, a g i n g} = a_{h c n} \times I_{K s}

where a_cat, a_cal, a_hcn, a_nak, a_ncx, a_kr, a_ks are the scaling factors for I_CaT, I_CaL, I_HCN, I_NaK, I_NCX, I_Kr, and I_Ks under aging conditions, respectively. Moreover, the aging-dependent shift of the activation midpoint of I_HCN was modeled as the following:

V_{H C N, a g i n g} = V_{H C N} + v_{h c n},

where V_HCN is the activation midpoint of I_HCN in adult model, and v_hcn is the activation shift of I_HCN in aged model.

Aging-dependent Ca²⁺ cycling dysfunction (Fig 1; red dot) in SERCA (J_up) and Ryanodine receptor Ca release (J_Rel) were calibrated according to previous experimental measurements by Liu et al. [40] as follows:

J_{u p, a g i n g} = a_{u p} \times J_{u p}

J_{R e l, a g i n g} = a_{r e l} \times J_{R e l}

where a_up, a_rel are the scaling factors for J_up, J_Rel under aging conditions, respectively. Moreover, the aging-dependent increase in the ratio between phospholamban and SERCA [40] was modeled by an increase to the original value of cytoplasmic Ca²⁺ sensitivity coefficient (K_mf) in the baseline model [48] as follows:

K_{m f, a g i n g} = a_{k m f} \times K_{m f}

where a_kmf is the scaling factor for K_mf under aging conditions.

In addition, aging-related PNA impairment (Fig 1; red dot) was introduced by a major reduction in PNA to be consistent with previous experimental studies [41] as follows:

{C C h}_{a g i n g} = a_{c c h} \times C C h

where a_cch is the scaling factor of CCh under aging conditions. SNA was assumed to be unchanged in aged mice as reported by Larson et al. [25].

Moreover, aging-dependent CRBT disruption was modeled by a reduction in both averaged time-of-day BT and circadian amplitude of BT in aged mice as previously reported [17]. Specifically:

{B T}_{a g i n g} = {B T}_{a, a g i n g} + A_{B T, a g i n g} \times \cos (\frac{2 π \times (T + 6)}{T_{B T}}),

where BT_a,aging is the reference BT in aged model, and A_BT,aging is the circadian amplitude of BT in aged model.

Simulation protocols

A 12h:12h light/dark lighting regime was implemented as in the experimental studies [19,38]. FR (Figs 2–5) was calculated as the averaged FR of the last 10 seconds of simulation after reaching steady-state, with model implementation and initial conditions previously described by Ding et al. [48]. Each CO-MO parameter space map (Figs 3 and 4) [37] was reproduced by reducing P_up (CO) and the maximal conductance of I_CaL and I_CaT (MO) from their original values [48] to zero, using a step size of 1%, resulting in a total of 100 × 100 simulations. Regarding the choice of parameters to represent CO and MO, respectively, we chose P_up to represent CO as often used in previous modeling studies [37,54,82]. Both I_CaL and I_NCX have been used to represent MO in earlier studies [37,54,82]. Given the importance of I_CaT in mouse SANC [51,83], we chose to use I_CaL and I_CaT to represent MO to ensure that our simulation results are less dependent on the properties and mathematical formalism of a given single ion channel. Each simulation was color-coded by steady-state FR in BPM. For each CO-MO map, the border between no-firing and irregular firing regions (Figs 3 and 4; yellow lines) was identified by segregating zero and non-zero values of FR. Additionally, the border between irregular and rhythmic firing regions (Figs 3 and 4; blue lines) was established by pinpointing the location of the first local trough along the direction of CO and MO reduction.

To access SANC robustness, we quantify robustness as the percentage area of rhythmic firing regions in CO-MO parameter space maps (Figs 3 and 4). To evaluate SANC performance and flexibility, we quantify performance as the maximal time-of-day SANC FR in BPM, flexibility as the difference between the maximal and minimal time-of-day SANC FR in BPM with the control CO and MO. Sensitivity analysis was conducted with a full inhibition of each module of interest (Fig 5). Additionally, sensitivity analysis for [Na]_i⁺ accumulation was performed by clamping time-of-day [Na]_i⁺ content at its steady-state concentration at ZT6.

All model simulations were performed with parallel computing on a ThinkStation P620 tower workstation with an AMD Threadripper processor. Model codes were implemented and solved in MATLAB (Version: 9.13.0 (R2022b)) using ode15s, and will be provided for public download from https://github.com/Mathbiomed/CircSANC.

Supporting information

S1 Table. Model parameters and settings.

(DOCX)

pcbi.1011907.s001.docx^{(52.7KB, docx)}

Acknowledgments

The authors thank all members of the Biomedical Mathematics Group at the Institute for Basic Science for their most helpful discussions.

Data Availability

Model codes are provided for public download from https://github.com/Mathbiomed/CircSANC.

Funding Statement

This work was supported by Institute for Basic Science IBS-R029-C3 (to J.K.K.). The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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PLoS Comput Biol. doi: 10.1371/journal.pcbi.1011907.r001

Decision Letter 0

Daniel A Beard, Christian I Hong

20 Oct 2023

Dear %TITLE% Kim,

Thank you very much for submitting your manuscript "Central and peripheral clocks synergistically enhance circadian robustness, flexibility and performance of cardiac pacemaking" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

The submitted manuscript utilized mathematical modeling to simulate cardiac pacemaking controlled by central and peripheral clocks uncovering potential impacts of aging in circadian regulation of heart rate. The reviewers acknowledge that synergistic interactions between PNA, SNA, and LCR regulating cardiac pacemaking are interesting. However, reviewers raised some major concerns including lack of technical details, potential effects of temperature, and impact of calcium signaling over aging. Importantly, it will be critical to clearly define the terms used in the manuscript improving clarity of conclusions and overall readability of the manuscript.

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.

Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Christian I. Hong, Ph.D.

Academic Editor

PLOS Computational Biology

Daniel Beard

Section Editor

PLOS Computational Biology

***********************

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: Summary: This report features a mathematical model describing autonomic control and LCR in sinoatrial nodal cells that attempts to capture distinct circadian patterns in adult and aged mice. Although the paper is interesting, a number of technical concerns require clarification, and additional modeling of how calcium oscillations change with aging is required.

Major Comments

1) The entire paper is about how “PNA, SNA, and LCR, … synergistically work together”. By definition, “synergistically” means that together they achieve more than in isolation. Please be specific and refer to your results for separate or concerted actions and clearly formulate (and prove) conclusions as claimed in your title. How much synergy (in quantitative terms) is achieved in your model? Please add this data in the abstract and provide clear conclusions after or within the discussion section.

2) In fig3C, I see only a synergistic effect for flexibility, while the title claims synergistic effects also for robustness and performance. Please explain.

3) In Methods you refer to three papers (27, 31, 40) for your model. You also say that “In this study, we present a novel mathematical model”. In any case, please be more specific and cite the closest oldest model published previously that was used as a basis for your novel model. Also, describe in full detail what is novel compared to previous models and, very importantly, please provide full computer code for your new model for all of your simulations. Your working code should be in the paper supplement or in GitHub or any other public database. This will allow anyone (incl. reviewers, editors, and readers) to reproduce your results and to use in further studies by running your actual (tested and working) code.

4) You wrote: “This modeling choice aligns with earlier experimental findings on the effects of a thermoneutral environment on heart rate variability, where mice exhibit a high sympathetic drive to maintain a normal core temperature (37°C) under standard laboratory conditions (20°C) (15, 36).” Please provide more details about how your model implemented the factor of temperature, and why and how specifically “This modeling choice aligns with earlier experimental findings”

5) “We modeled LCR as a diurnal variation in the expression level of IHCN, but it might not be the only mechanism underlying LCR in SANC.”

Yes, sure but this is a major study limitation of the study and should be discussed in more detail. You perform parametric sensitivity analysis for both CO and MO (i.e. Ca and membrane oscillators), but model LCRs only as one component in MO.

6) How were CO-MO parameter space maps created in Figs 3 and 4? You showed MO changes from 0 to 1 and CO also from 0 to 1. Which specific model parameters were varied, in what specific range, and why were these parameters and ranges chosen?

7) Explain pattern disruption (black band in the middle) in Fig.3 for ZT18 in SNAB and ANSB. There are also clear disruptions of BPM within rhythmic firing areas between the black area and blue line. This may indicate the way you changed model parameters in the sensitivity analysis for the MO and CO between 0 and 1, or possibly may indicate problems with your model integration or automatic analysis of the data. Please check and explain.

8) What algorithm was used to analyze the simulation data in Figs 3 and 4? In other terms, how did you get BPM in each simulation trace? This may make a big difference in the results, depending how you define AP, i.e. how you separate AP from a Vm oscillation near 0 mV.

9) In Figs 3 and 4 the black area indicates: “Chaotic or no firing”. There is a big difference between chaotic vs. no firing. Please separate “Chaotic” and “no firing”. Also, in many panels (e.g., Fig 3 ZT18-control) there is a mosaic pattern of BPM between the blue line and black area. Is this a mosaic pattern chaotic firing? If so, why then it is not within the black area that includes chaotic firing as per your description? It’s important to provide clear definitions for chaotic and rhythmic firing in your analysis.

10) What was your rational to perform sensitivity analysis with the key model parameter reduced exactly by 25% in Fig. 5B?

11) How did you define the specific model parameter changes in aging in Fig.5A? Was your choice based on experimental studies? If so, please cite the respective literature in the figure legend. If not, then explain your reasoning for the parameters you use in the simulations.

12) I found it very difficult to read the paper. It seems like cryptography with numerous abbreviations: FR, MO, CO, SNA, ANS, LCR, SANC, AP, NUC, PNA, PNA, SNAB, ANSB, HR, iHR, DCN, GPCR, PKA, AC, SR, HCN, SERCA. P-S, S-P, BPM. Further, many abbreviations are not explicitly given like ZT6 and ZT18. Please reduce abbreviations to a minimum to make the text readable. For example, why not write simply firing rate instead of FR or Ca oscillator instead of CO, etc.? Also please include a table defining all terms.

13) Ist has a strong contribution to your model, whereas molecular identity of this current remains unknown. The same is about INab, and Cab. Please explain.

14) In Fig.1 only 3 currents are affected by aging (ICaL, ICaT, I HCN), all other 13 current remain unchanged, including currents of major functional importance, such as NCX, NaK, KACh, Ito, Na currents. Please explain why only three currents change with aging in your model. What is known about how the other 13 currents change with aging. If some or all these currents do change with aging, your results would likely be different?

15) In Fig.1 Jup and Jrel (and the entire Ca oscillator module - CO) are not affected by aging. This is not correct. There is evidence that Ca signaling (SERCA, RyR, NCX) deteriorates with age, see e.g. Liu et al. Am J Physiol Heart Circ Physiol. 2014;306(10):H1385-97. Thus, your model does not reproduce a major change in the Ca oscillator. Please explain or make respective additional simulations.

///////////////////////////////////////////////////////////

Minor Comments

1) Please clearly define Robustness, Flexibility, and Performance, and explain why those definitions are reasonable.

2) You wrote: “This AC cAMP-PKA signaling cascade leads to the phosphorylation of various targets, such as the L-type Ca2+channel (ICaL), Ryanodine receptor, and sarco/endoplasmic reticulum (SR) Ca2+ ATPase (SERCA)”

In fact, PKA activates SERCA by phosphorylation of phospholamban, is there any evidence that SERCA, itself becomes phosphorylated?

Reviewer #2: The authors develop a mathematical model designed to predict the impact and importance of various factors (parasympathetic and sympathetic nervous system and intrinsic gene changes) in circadian regulation of heart rate (HR). The authors conclude that “our work shed light on their critical synergistic interactions in regulating time-of-day cardiac pacemaking function and dysfunction, which may help to identify potential therapeutic targets within the circadian clock for the prevention and treatment of cardiac arrhythmias.”

Reviewer #3: “Central and peripheral clocks synergistically enhance circadian robustness, flexibility

and performance of cardiac pacemaking” by Li and Kim is an ambitious attempt to understand how 24-hour oscillations in receptor-mediated signaling and ion channel expression impact sinoatrial nodal cells' firing rate and functionality. They extend the modelization to include a model of sinoatrial node cells in aged mice. The authors are commended for their approach to model a complex interaction at a new level of detail. My high enthusiasm for the work is somewhat diminished by the lack of data showing the temperature's impact on the system. Temperature addition may be complex, but a fundamental component of intrinsic circadian signaling is the daily rhythm in core body temperature. The addition is expected to impact the results of the work and perhaps its conclusions. This limitation should be addressed. Another challenge is that the article contains a lot of jargon and abbreviations. The jargon and the numerous non-standard abbreviations lower the understandability and readability of the article. The authors are encouraged to define terms clearly. The authors are encouraged not to use many non-standard abbreviations to improve readability. Lastly, some aspects of the premise appear misrepresented or overstated.

Concerns:

Please provide a clear, succinct definition for the following terms in a table: circadian rhythms (this has many different meanings based on the field), circadian flexibility, reliance and adaptability of circadian rhythms, and circadian robustness. The authors are encouraged to use terms/definitions widely accepted by chronobiologists. This should broaden research interest in this important work.

Please reduce the number of non-standard abbreviations to improve readability.

Please discuss or include temperature rhythms. A hallmark feature of biological rhythms is that the 24-hour rhythm in core body temperature serves as an intrinsic Zeitgeber for local circadian clocks in the peripheral tissues. Please discuss how a daily rhythm in core body temperature may play a role in the modelization. Can the authors include this concept in the simulations?

Figure 2A data is based on data from Barazi. The authors show hourly data with error bars, but the original article shows around five-time points. How was the data in Figure 2A generated? The authors are encouraged to show only the actual data or alter the description of Figure 2A. It is misleading as presented.

The Barazi article also suggests no significant fluctuation in the 24-hour rhythm in the heart rate with ANS block or PNS block (Figure 1 in Barazi). Why do the authors discuss these data sets as being circadian? What was the data that the authors used to make this conclusion?

ANS block data in Figures 2A and 2B are qualitatively different when the amplitude peaks (ZT 24 vs ZT 18). Why?

Reviewer #4: This paper is focused on circadian regulation of cardiac excitability, an important aspect of physiology that has not been thoroughly addressed in previous computational modeling studies. The authors extend a published model of action potential generation in mouse sinoatrial node cells (SANC) to incorporate the regulation of cardiac pacemaking by both the central circadian clock—through the autonomic nervous system--and local circadian rhythmicity (LCR) within the heart. The authors perform simulations and sensitivity analysis to assess the role of parasympathetic nervous activity (PNA), sympathetic nervous activity (SNA), and LCR on circadian rhythms in heart rate (HR). They also use their model to study mechanisms underlying the age-related decline of circadian rhythms in HR.

Overall, the study is well-motivated, and the manuscript is well-written. The findings on the importance of non-additive interactions between PNA and SNA for reproducing circadian patterns in SANC firing rate are potentially interesting. My main concern is that the evidence supporting this finding is not yet adequately explained in the manuscript, as I describe in my comments below.

Major comments

1) It is stated on lines 175-178 that when additive PNA and SNA (no PNA-SNA interactions) is assumed, the baseline of the simulated circadian rhythms is approximately 5% lower than the experimental data. I don’t understand how this 5% is calculated… for example, it looks like the trough of the simulated curve is 400 BPM at ZT6 (Fig 2B, grey boxes) compared to a trough of 500 BPM in the experimental data at ZT6 (Fig 2A, grey dots), which would correspond to a 20% difference. A similar calculation using the peak of the simulated and experimental curves at ZT18 (475 and 575 BPM, respectively) gives a 21% difference. How was the 5% result obtained?

2) The authors go on to say that when they implemented bidirectional modulation effects, the circadian pattern in FR under the control condition was accurately simulated (Fig 2B, grey line). The trough and peak of this simulated curve appear to be at 425 and 500 BPM at ZT6 and ZT18, which are still 17% and 15% lower than the corresponding experimental values, respectively. Thus, more explanation is needed to justify the claim of accurate simulation as well as the statement on line 199-200 that the incorporation of bidirectional effects “aligns the simulated FR with experimental data (A; grey dots)”.

3) Based on the above calculations, the simulated non-additive curve (grey line) does indeed agree better with the experimental curve (grey dots) than the simulated additive curve (grey boxes) by a few percent, but given the large error bars associated with the grey dots in the experimental data (Fig 2A) it is not clear to me that there is enough evidence to support the strong claim on lines 186-187 that the “results unequivocally indicate that the non-additivity of PNA and SNA is required to properly construct the circadian patterns of SANC function”.

Is it not possible that with other parameter choices, the experimental data could be equally well-recapitulated with purely additive effects?

4) The authors write on lines 183-184 that both minimal and maximal time-of-day FR are in quantitative agreement with the experimental data (Fig 2C). The caption of Fig 2C explains that the FR values were normalized to FR at ZT12 under the ANSB condition. I’m afraid I don’t quite understand how this normalization was applied. The curve of green dots in Fig 2A appears to reach a minimum at ZT12, thus I would expect the Normalized HR Min value under the ANSB condition to be exactly 1 for the experimental data. However, in Fig 2C the Normalized HR Min value under the ANSB condition shown for the experimental data is less than 1.

5) Why does the simulated FR curve under ANSB condition (Fig 2B green line) have a trough at ZT6, whereas the experimental FR curve under ANSB condition (Fig 2A green dots) has a trough at ZT12?

Does this discrepancy affect the appropriateness of using FR at ZT12 under ANSB condition as the reference value for normalization?

6) In general, why are the simulated FR lower than the experimental HR, as evidenced by the lower range used for the y-axis in Fig 2B (300 to 550 BPM) than Fig 2A (350 to 700 BPM)?

It is not necessary for a model to exactly reproduce the same range of values as seen in experiments to be useful, but since the simulated FRs are systematically and significantly lower than the experimental HRs it would be helpful for the authors to explain or at least comment on this discrepancy. Furthermore, this difference between the simulated FR and the experimental HR suggests that it might be more appropriate to describe the results as “qualitative” rather than “quantitative” reconstructions of diverse circadian patterns in SANC FR the section heading on line 164 and the Fig 2 caption. Similarly, is it accurate to say on line 173 that the model simulations “meticulously recapitulated” the experimental findings given that there is about a 100 BPM difference between the two?

7) More details on how the model was calibrated to experimental data should be provided. For example, on lines 55-57 the authors say the bidirectional modulation effects P-S and S-P were formulated and calibrated to account for the non-additivity effects (8-11) but it is not explained what these effects are.

Similarly, it is mentioned that the model was calibrated for time-of-day PNA (line 420), time-of-day SNA (line 423), age-dependent MO reduction (line 436), aging-dependent PNA impairment (line 439), but it is not described how exactly the model was calibrated. Were the data sufficient to constrain the parameters, or are there multiple parameter sets that can reproduce the data well?

Some discussion of parameter identifiability and how the authors modeling approach and parameter fitting does or does not account for the variability/heterogeneity of cardiac electrophysiology in general (and more specifically, the variability/heterogeneity depicted by the error bars in Fig 2A) seems warranted.

8) Is there a way to experimentally test the model prediction that non-additive interactions between PNA and SNA are important for the circadian patterns, or to experimentally validate that these interactions were modeled appropriately? If so, it would be helpful to discuss these possibilities in the Discussion section.

Minor Comments

1) The authors conclude on lines 156-158 that SNA serves as a SANC robustness and performance enhancer, PNA acts as a flexibility amplifier, and LCR functions as a flexibility and performance booster.

Do the words “enhancer, amplifier, and booster” as used here all mean the same thing, or were the 3 different words employed to indicate some differences in the roles that SNA, PNA, and LCR play when it comes to interpreting their simulation results? For example, would it be just as accurate to say that PNA acts as a flexibility booster or enhancer instead of as a flexibility amplifier? If so, then the authors should just pick one of these 3 words to use throughout this sentence (as well as in lines 346-349) so that different meanings aren’t implied.

2) The phrase “SNA in this study was modeled as a high ISO tone” on lines 52-52 struck me as strange as I do not usually see the word tone associated with a drug. Also, a brief explanation of why using isoproterenol to model SNA would be helpful even if it was previously described in (3).

3) In line 144 of the Abstract, replace “Our work shed light” with “Our work sheds light”

4) An easier-to-follow explanation of what simulations were performed to obtain the curves in Fig 2B would be helpful for readers to be able to reproduce the results. All of the information may already be provided in the Materials and Methods or Supporting Information, but it is not explicitly spelled out. For example, to go from the Control curve to the P-S curve, does one simply set the parameter k_{s_p} to 1? Similarly, what parameters would one change to go from the Control curve to the S-P curve, the Additive curve, or the 3 blockade curves? If the authors would prefer not to include that type of description in the manuscript itself, it could go in the readme file associated with the model code instead.

**********

Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No: See comments to authors

Reviewer #2: No:

Reviewer #3: No: They will after acceptance

Reviewer #4: Yes

**********

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Reviewer #1: Yes: Edward G. Lakatta, MD

Reviewer #2: No

Reviewer #3: No

Reviewer #4: No

Figure Files:

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PLoS Comput Biol. 2024 Feb 26;20(2):e1011907. doi: 10.1371/journal.pcbi.1011907.r002

Author response to Decision Letter 0

5 Jan 2024

Attachment

Submitted filename: PLoSCB-Point-by-Point-Response.docx

pcbi.1011907.s002.docx^{(4.7MB, docx)}

PLoS Comput Biol. doi: 10.1371/journal.pcbi.1011907.r003

Decision Letter 1

Daniel A Beard, Christian I Hong

12 Feb 2024

Dear Prof Kim,

We are pleased to inform you that your manuscript 'Circadian regulation of sinoatrial nodal cell pacemaking function: dissecting the roles of autonomic control, body temperature, and local circadian rhythmicity' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology.

Best regards,

Christian I. Hong, Ph.D.

Academic Editor

PLOS Computational Biology

Daniel Beard

Section Editor

PLOS Computational Biology

***********************************************************

The revised manuscript addressed all of the previous concerns raised by the reviewers. One of the reviewers insists that the authors upload their model code to a public repository. Please make sure to deposit your model into an open software archive following the PLoS Computational Biology guidelines.

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The author’s have adequately responded to my comments and have satisfactorily modified the revised manuscript. The response to my comment #3 is not satisfactory.

My comment #3 …Your working code should be in the paper supplement or in GitHub or any other public database. This will allow anyone (incl. reviewers, editors, and readers) to reproduce your results and to use in further studies by running your actual (tested and working) code.

Your response was ‘..will upload model codes underlying our study to our group’s website on GitHub for public download once the manuscript is accepted’

Reviewer #2: My comments have adequately addressed.

Reviewer #3: The authors have addressed my concerns. The inclusion of temperature has elevated the impact of the paper.

Reviewer #4: The authors have thoroughly revised the manuscript and addressed my concerns.

**********

Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

Reviewer #1: No: See Comments to Editor

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

**********

PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: Yes: Edward G. Lakatta, MD

Reviewer #2: No

Reviewer #3: No

Reviewer #4: No

PLoS Comput Biol. doi: 10.1371/journal.pcbi.1011907.r004

Acceptance letter

Daniel A Beard, Christian I Hong

21 Feb 2024

PCOMPBIOL-D-23-01268R1

Circadian regulation of sinoatrial nodal cell pacemaking function: dissecting the roles of autonomic control, body temperature, and local circadian rhythmicity

Dear Dr Kim,

I am pleased to inform you that your manuscript has been formally accepted for publication in PLOS Computational Biology. Your manuscript is now with our production department and you will be notified of the publication date in due course.

The corresponding author will soon be receiving a typeset proof for review, to ensure errors have not been introduced during production. Please review the PDF proof of your manuscript carefully, as this is the last chance to correct any errors. Please note that major changes, or those which affect the scientific understanding of the work, will likely cause delays to the publication date of your manuscript.

Soon after your final files are uploaded, unless you have opted out, the early version of your manuscript will be published online. The date of the early version will be your article's publication date. The final article will be published to the same URL, and all versions of the paper will be accessible to readers.

Thank you again for supporting PLOS Computational Biology and open-access publishing. We are looking forward to publishing your work!

With kind regards,

Bernadett Koltai

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

S1 Table. Model parameters and settings.

(DOCX)

pcbi.1011907.s001.docx^{(52.7KB, docx)}

Attachment

Submitted filename: PLoSCB-Point-by-Point-Response.docx

pcbi.1011907.s002.docx^{(4.7MB, docx)}

Data Availability Statement

Model codes are provided for public download from https://github.com/Mathbiomed/CircSANC.

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PERMALINK

Circadian regulation of sinoatrial nodal cell pacemaking function: Dissecting the roles of autonomic control, body temperature, and local circadian rhythmicity

Pan Li

Jae Kyoung Kim

Roles

Abstract

Author summary

Introduction

Fig 1. Model schematic for ANS, CRBT and LCR in mouse SANC.

Table 1. Glossary of circadian rhythms in HR.

Table 2. Definitions of non-standard abbreviations.

Results

Quantitative reconstruction of diverse circadian patterns of SANC FR in adult and aged mice

Fig 2. Quantitative reconstruction of diverse circadian patterns in SANC FR under various conditions.

The alliance of ANS, CRBT, and LCR is essential in optimizing the time-of-day SANC function in adult mice

Fig 3. The alliance of ANS, CRBT and LCR is essential to achieve circadian flexibility and performance while preserving robustness in SANC automaticity.

Quantitative dissection of SANC pacemaking dysfunction in aged mice

Fig 4. Quantitative dissection of SANC pacemaking dysfunction in aging.

Distinct mechanisms underlying circadian patterns in SANC FR in adult and aged mice

Fig 5. Distinct mechanisms underlying circadian patterns of SANC FR in adult and aged mice.

Discussion

Fig 6. Illustrative trajectories in the parameter space of SANC flexibility, performance and robustness.

Methods

Model development

Incorporation of LCR into the baseline model

Incorporation of the circadian regulation of ANS into the baseline model

Incorporation of CRBT into the baseline model

Modeling aging-dependent alternations

Simulation protocols

Supporting information

Acknowledgments

Data Availability

Funding Statement

References

Decision Letter 0

Daniel A Beard

Christian I Hong

Roles

Author response to Decision Letter 0

Decision Letter 1

Daniel A Beard

Christian I Hong

Roles

Acceptance letter

Daniel A Beard

Christian I Hong

Roles

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

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