Mathematical modeling of light-mediated HPA axis activity and downstream implications on the entrainment of peripheral clock genes

Computational modeling of the synergistic role of GCN2 and the HPA axis in regulating the integrated stress response in the central circadian timing system

The circadian timing system and integrated stress response (ISR) systems are fundamental regulatory mechanisms that maintain body homeostasis. The central circadian pacemaker in the suprachiasmatic nucleus (SCN) governs daily rhythms through interactions with peripheral oscillators via the hypothalamus-pituitary-adrenal (HPA) axis. On the other hand, ISR signaling is pivotal for preserving cellular homeostasis in response to physiological changes. Notably, disrupted circadian rhythms are observed in cases of impaired ISR signaling. In this work, we examine the potential interplay between the central circadian system and the ISR, mainly through the SCN and HPA axis. We introduce a semimechanistic mathematical model to delineate SCN's capacity for indirectly perceiving physiological stress through glucocorticoid-mediated feedback from the HPA axis and orchestrating a cellular response via the ISR mechanism. Key components of our investigation include evaluating general control nonderepressible 2 (GCN2) expression in the SCN, the effect of physiological stress stimuli on the HPA axis, and the interconnected feedback between the HPA and SCN. Simulation revealed a critical role for GCN2 in linking ISR with circadian rhythms. Experimental findings have demonstrated that a Gcn2 deletion in mice leads to rapid re-entrainment of the circadian clock following jetlag as well as to an elongation of the circadian period. These phenomena are well replicated by our model, which suggests that both the swift re-entrainment and prolonged period can be ascribed to a reduced robustness in neuronal oscillators. Our model also offers insights into phase shifts induced by acute physiological stress and the alignment/misalignment of physiological stress with external light-dark cues. Such understanding aids in strategizing responses to stressful events, such as nutritional status changes and jetlag.NEW & NOTEWORTHY This study is the first theoretical work to investigate the complex interaction between integrated stress response (ISR) sensing and central circadian rhythm regulation, encompassing the suprachiasmatic nucleus (SCN) and hypothalamus-pituitary-adrenal (HPA) axis. The findings carry implications for the development of dietary or pharmacological interventions aimed at facilitating recovery from stressful events, such as jetlag. Moreover, they provide promising prospects for potential therapeutic interventions that target circadian rhythm disruption and various stress-related disorders.

The Physiological and Pharmacological Significance of the Circadian Timing of the HPA Axis: A Mathematical Modeling Approach

As a potent endogenous regulator of homeostasis, the circadian time-keeping system synchronizes internal physiology to periodic changes in the external environment to enhance survival. Adapting endogenous rhythms to the external time is accomplished hierarchically with the central pacemaker located in the suprachiasmatic nucleus (SCN) signaling the hypothalamus-pituitary-adrenal (HPA) axis to release hormones, notably cortisol, which help maintain the body's circadian rhythm. Given the essential role of HPA-releasing hormones in regulating physiological functions, including immune response, cell cycle, and energy metabolism, their daily variation is critical for the proper function of the circadian timing system. In this review, we focus on cortisol and key fundamental properties of the HPA axis and highlight their importance in controlling circadian dynamics. We demonstrate how systems-driven, mathematical modeling of the HPA axis complements experimental findings, enhances our understanding of complex physiological systems, helps predict potential mechanisms of action, and elucidates the consequences of circadian disruption. Finally, we outline the implications of circadian regulation in the context of personalized chronotherapy. Focusing on the chrono-pharmacology of synthetic glucocorticoids, we review the challenges and opportunities associated with moving toward personalized therapies that capitalize on circadian rhythms.

The SCN-HPA-Periphery Circadian Timing System: Mathematical Modeling of Clock Synchronization and the Effects of Photoperiod on Jetlag Adaptation

Synchronizing the circadian timing system (CTS) to external light/dark cycles is crucial for homeostasis maintenance and environmental adaptation. The CTS is organized hierarchically, with the central pacemaker located in the suprachiasmatic nuclei (SCN) generating coherent oscillations that are entrained to light/dark cycles. These oscillations regulate the release of glucocorticoids by the hypothalamus-pituitary-adrenal (HPA) axis, which acts as a systemic entrainer of peripheral clocks throughout the body. The SCN adjusts its network plasticity in response to variations in photoperiod, leading to changes in the rhythmic release of glucocorticoids and ultimately impacting peripheral clocks. However, the effects of photoperiod-induced variations of glucocorticoids on the synchronization of peripheral clocks are not fully understood, and the interaction between jetlag adaption and photoperiod changes is unclear. This study presents a semi-mechanistic mathematical model to investigate how the CTS responds to changes in photoperiod. Specifically, the study focuses on the entrainment properties of a system composed of the SCN, HPA axis, and peripheral clocks. The results show that high-amplitude glucocorticoid rhythms lead to a more coherent phase distribution in the periphery. In addition, our study investigates the effect of photoperiod exposure on jetlag recovery time and phase shift, proposing different interventional strategies for eastward and westward jetlag. The findings suggest that decreasing photic exposure before jetlag during eastward traveling and after jetlag during westward traveling can accelerate jetlag readaptation. The study provides insights into the mechanisms of CTS organization and potential recovery strategies for transitions between time zones and lighting zones.

Light-induced synchronization of the SCN coupled oscillators and implications for entraining the HPA axis

The suprachiasmatic nucleus (SCN) synchronizes the physiological rhythms to the external light-dark cycle and tunes the dynamics of circadian rhythms to photoperiod fluctuations. Changes in the neuronal network topologies are suggested to cause adaptation of the SCN in different photoperiods, resulting in the broader phase distribution of neuron activities in long photoperiods (LP) compared to short photoperiods (SP). Regulated by the SCN output, the level of glucocorticoids is elevated in short photoperiod, which is associated with peak disease incidence. The underlying coupling mechanisms of the SCN and the interplay between the SCN and the HPA axis have yet to be fully elucidated. In this work, we propose a mathematical model including a multiple-cellular SCN compartment and the HPA axis to investigate the properties of the circadian timing system under photoperiod changes. Our model predicts that the probability-dependent network is more energy-efficient than the distance-dependent network. Coupling the SCN network by intra-subpopulation and inter-subpopulation forces, we identified the negative correlation between robustness and plasticity of the oscillatory network. The HPA rhythms were predicted to be strongly entrained to the SCN rhythms with a pro-inflammatory high-amplitude glucocorticoid profile under SP. The fast temporal topology switch of the SCN network was predicted to enhance synchronization when the synchronization is not complete. These synchronization and circadian dynamics alterations might govern the seasonal variation of disease incidence and its symptom severity.

Light entrainment of the SCN circadian clock and implications for personalized alterations of corticosterone rhythms in shift work and jet lag

The suprachiasmatic nucleus (SCN) functions as the central pacemaker aligning physiological and behavioral oscillations to day/night (activity/inactivity) transitions. The light signal entrains the molecular clock of the photo-sensitive ventrolateral (VL) core of the SCN which in turn entrains the dorsomedial (DM) shell via the neurotransmitter vasoactive intestinal polypeptide (VIP). The shell converts the VIP rhythmic signals to circadian oscillations of arginine vasopressin (AVP), which eventually act as a neurotransmitter signal entraining the hypothalamic–pituitary–adrenal (HPA) axis, leading to robust circadian secretion of glucocorticoids. In this work, we discuss a semi-mechanistic mathematical model that reflects the essential hierarchical structure of the photic signal transduction from the SCN to the HPA axis. By incorporating the interactions across the core, the shell, and the HPA axis, we investigate how these coupled systems synchronize leading to robust circadian oscillations. Our model predicts the existence of personalized synchronization strategies that enable the maintenance of homeostatic rhythms while allowing for differential responses to transient and permanent light schedule changes. We simulated different behavioral situations leading to perturbed rhythmicity, performed a detailed computational analysis of the dynamic response of the system under varying light schedules, and determined that (1) significant interindividual diversity and flexibility characterize adaptation to varying light schedules; (2) an individual’s tolerances to jet lag and alternating shift work are positively correlated, while the tolerances to jet lag and transient shift work are negatively correlated, which indicates trade-offs in an individual’s ability to maintain physiological rhythmicity; (3) weak light sensitivity leads to the reduction of circadian flexibility, implying that light therapy can be a potential approach to address shift work and jet lag related disorders. Finally, we developed a map of the impact of the synchronization within the SCN and between the SCN and the HPA axis as it relates to the emergence of circadian flexibility.

Modeling the Influence of Chronic Sleep Restriction on Cortisol Circadian Rhythms, with Implications for Metabolic Disorders

Chronic sleep deficiency is prevalent in modern society and is associated with increased risk of metabolic and other diseases. While the mechanisms by which chronic sleep deficiency induces pathophysiological changes are yet to be elucidated, the hypothalamic–pituitary–adrenal (HPA) axis may be an important mediator of these effects. Cortisol, the primary hormone of the HPA axis, exhibits robust circadian rhythmicity and is moderately influenced by sleep and wake states and other physiology. Several studies have explored the effects of acute or chronic sleep deficiency (i.e., usually from self-selected chronic sleep restriction, CSR) on the HPA axis. Quantifying long-term changes in the circadian rhythm of cortisol under CSR in controlled conditions is inadequately studied due to practical limitations. We use a semi-mechanistic mathematical model of the HPA axis and the sleep/wake cycle to explore the influence of CSR on cortisol circadian rhythmicity. In qualitative agreement with experimental findings, model simulations predict that CSR results in physiologically relevant disruptions in the phase and amplitude of the cortisol rhythm. The mathematical model presented in this work provides a mechanistic framework to further explore how CSR might lead to HPA axis disruption and subsequent development of chronic metabolic complications.

Mathematical modeling of mammalian circadian clocks affecting drug and disease responses

To align with daily environmental changes, most physiological processes in mammals exhibit a time-of-day rhythmicity. This circadian control of physiology is intrinsically driven by a cell-autonomous clock gene network present in almost all cells of the body that drives rhythmic expression of genes that regulate numerous molecular and cellular processes. Accordingly, many aspects of pharmacology and toxicology also oscillate in a time-of-day manner giving rise to diverse effects on pharmacokinetics and pharmacodynamics. Genome-wide studies and mathematical modeling are available tools that have significantly improved our understanding of these nonlinear aspects of physiology and therapeutics. In this manuscript current literature and our prior work on the model-based approaches that have been used to explore circadian genomic systems of mammals are reviewed. Such basic understanding and having an integrative approach may provide new strategies for chronotherapeutic drug treatments and yield new insights for the restoration of the circadian system when altered by diseases.

Circadian rhythms and the HPA axis: A systems view

The circadian timing system comprises a network of time-keeping clocks distributed across a living host whose responsibility is to allocate resources and distribute functions temporally to optimize fitness. The molecular structures generating these rhythms have evolved to accommodate the rotation of the earth in an attempt to primarily match the light/dark periods during the 24-hr day. To maintain synchrony of timing across and within tissues, information from the central clock, located in the suprachiasmatic nucleus, is conveyed using systemic signals. Leading among those signals are endocrine hormones, and while the hypothalamic-pituitary-adrenal axis through the release of glucocorticoids is a major pacesetter. Interestingly, the fundamental units at the molecular and physiological scales that generate local and systemic signals share critical structural properties. These properties enable time-keeping systems to generate rhythmic signals and allow them to adopt specific properties as they interact with each other and the external environment. The purpose of this review is to provide a broad overview of these structures, discuss their functional characteristics, and describe some of their fundamental properties as these related to health and disease. This article is categorized under: Immune System Diseases > Computational Models Immune System Diseases > Biomedical Engineering.

Transitioning from Basic toward Systems Pharmacodynamic Models: Lessons from Corticosteroids

Technology in bioanalysis, -omics, and computation have evolved over the past half century to allow for comprehensive assessments of the molecular to whole body pharmacology of diverse corticosteroids. Such studies have advanced pharmacokinetic and pharmacodynamic (PK/PD) concepts and models that often generalize across various classes of drugs. These models encompass the "pillars" of pharmacology, namely PK and target drug exposure, the mass-law interactions of drugs with receptors/targets, and the consequent turnover and homeostatic control of genes, biomarkers, physiologic responses, and disease symptoms. Pharmacokinetic methodology utilizes noncompartmental, compartmental, reversible, physiologic [full physiologically based pharmacokinetic (PBPK) and minimal PBPK], and target-mediated drug disposition models using a growing array of pharmacometric considerations and software. Basic PK/PD models have emerged (simple direct, biophase, slow receptor binding, indirect response, irreversible, turnover with inactivation, and transduction models) that place emphasis on parsimony, are mechanistic in nature, and serve as highly useful "top-down" methods of quantitating the actions of diverse drugs. These are often components of more complex quantitative systems pharmacology (QSP) models that explain the array of responses to various drugs, including corticosteroids. Progressively deeper mechanistic appreciation of PBPK, drug-target interactions, and systems physiology from the molecular (genomic, proteomic, metabolomic) to cellular to whole body levels provides the foundation for enhanced PK/PD to comprehensive QSP models. Our research based on cell, animal, clinical, and theoretical studies with corticosteroids have provided ideas and quantitative methods that have broadly advanced the fields of PK/PD and QSP modeling and illustrates the transition toward a global, systems understanding of actions of diverse drugs. SIGNIFICANCE STATEMENT: Over the past half century, pharmacokinetics (PK) and pharmacokinetics/pharmacodynamics (PK/PD) have evolved to provide an array of mechanism-based models that help quantitate the disposition and actions of most drugs. We describe how many basic PK and PK/PD model components were identified and often applied to the diverse properties of corticosteroids (CS). The CS have complications in disposition and a wide array of simple receptor-to complex gene-mediated actions in multiple organs. Continued assessments of such complexities have offered opportunities to develop models ranging from simple PK to enhanced PK/PD to quantitative systems pharmacology (QSP) that help explain therapeutic and adverse CS effects. Concurrent development of state-of-the-art PK, PK/PD, and QSP models are described alongside experimental studies that revealed diverse CS actions.

Chronopharmacology of glucocorticoids

Glucocorticoids influence a wide array of metabolic, anti-inflammatory, immunosuppressive, and cognitive signaling processes, playing an important role in homeostasis and preservation of normal organ function. Synthesis is regulated by the hypothalamic-pituitary-adrenal (HPA) axis of which cortisol is the primary glucocorticoid in humans. Synthetic glucocorticoids are important pharmacological agents that augment the anti-inflammatory and immunosuppressive properties of endogenous cortisol and are widely used for the treatment of asthma, Crohn's disease, and rheumatoid arthritis, amongst other chronic conditions. The homeostatic activity of cortisol is disrupted by the administration of synthetic glucocorticoids and so there is interest in developing treatment options that minimize HPA axis disturbance while maintaining the pharmacological effects. Studies suggest that optimizing drug administration time can achieve this goal. The present review provides an overview of endogenous glucocorticoid activity and recent advances in treatment options that have further improved patient safety and efficacy with an emphasis on chronopharmacology.

At the Interface of Lifestyle, Behavior, and Circadian Rhythms: Metabolic Implications

Nutrient metabolism is under circadian regulation. Disruption of circadian rhythms by lifestyle and behavioral choices such as work schedules, eating patterns, and social jetlag, seriously impacts metabolic homeostasis. Metabolic dysfunction due to chronic misalignment of an organism's endogenous rhythms is detrimental to health, increasing the risk of obesity, metabolic and cardiovascular disease, diabetes, and cancer. In this paper, we review literature on recent findings on the mechanisms that communicate metabolic signals to circadian clocks and vice versa, and how human behavioral changes imposed by societal and occupational demands affect the physiological networks integrating peripheral clocks and metabolism. Finally, we discuss factors possibly contributing to inter-individual variability in response to circadian changes in the context of metabolic (dys)function.

Allostatic adaptation and personalized physiological trade-offs in the circadian regulation of the HPA axis: A mathematical modeling approach

The hypothalamic-pituitary-adrenal (HPA) axis orchestrates the physiological response to unpredictable acute stressors. Moreover, the HPA axis exhibits prominent circadian activity and synchronizes peripheral circadian clocks to daily environmental cycles, thereby promoting homeostasis. Persistent disruption of homeostatic glucocorticoid circadian rhythmicity due to chronic stress exposure is correlated with the incidence of various pathological conditions including depression, diabetes and cancer. Allostatic habituation of the HPA axis, such that glucocorticoid levels retain homeostatic levels upon chronic exposure to stress, can therefore confer fitness advantages by preventing the sustained dysregulation of glucocorticoid-responsive signaling pathways. However, such allostatic adaptation results in a physiological cost (allostatic load) that might impair the homeostatic stress-responsive and synchronizing functions of the HPA axis. We use mathematical modeling to characterize specific chronic stress-induced allostatic adaptations in the HPA network. We predict the existence of multiple individualized regulatory strategies enabling the maintenance of homeostatic glucocorticoid rhythms, while allowing for flexible HPA response characteristics. We show that this regulatory variability produces a trade-off between the stress-responsive and time-keeping properties of the HPA axis. Finally, allostatic regulatory adaptations are predicted to cause a time-of-day dependent sensitization of the acute stress response and impair the entrainability of the HPA axis.

Mathematical modeling informs the impact of changes in circadian rhythms and meal patterns on insulin secretion

Disruption of circadian rhythms has been associated with metabolic syndromes, including obesity and diabetes. A variety of metabolic activities are under circadian modulation, as local and global clock gene knockouts result in glucose imbalance and increased risk of metabolic diseases. Insulin release from the pancreatic β cells exhibits daily variation, and recent studies have found that insulin secretion, not production, is under circadian modulation. As consideration of daily variation in insulin secretion is necessary to accurately describe glucose-stimulated insulin secretion, we describe a mathematical model that incorporates the circadian modulation via insulin granule trafficking. We use this model to understand the effect of oscillatory characteristics on insulin secretion at different times of the day. Furthermore, we integrate the dynamics of clock genes under the influence of competing environmental signals (light/dark cycle and feeding/fasting cycle) and demonstrate how circadian disruption and meal size distribution change the insulin secretion pattern over a 24-h day.

Modeling the influence of chronopharmacological administration of synthetic glucocorticoids on the hypothalamic-pituitary-adrenal axis

Natural glucocorticoids, a class of cholesterol-derived hormones, modulate an array of metabolic, anti-inflammatory, immunosuppressive and cognitive signaling. The synthesis of natural glucocorticoids, largely cortisol in humans, is regulated by the hypothalamic-pituitary-adrenal (HPA) axis and exhibits pronounced circadian variation. Considering the central regulatory function of endogenous glucocorticoids, maintenance of the circadian activity of the HPA axis is essential to host survival and chronic disruption of such activity leads to systemic complications. There is a great deal of interest in synthetic glucocorticoids due to the immunosuppressive and anti-inflammatory properties and the development of novel dosing regimens that can minimize the disruption of endogenous activity, while still maintaining the pharmacological benefits of long-term synthetic glucocorticoid therapy. Synthetic glucocorticoids are associated with an increased risk of developing the pathological disorders related to chronic suppression of cortisol rhythmicity as a result of the potent negative feedback by synthetic glucocorticoids on the HPA axis precursors. In this study, a mathematical model was developed to explore the influence of chronopharmacological dosing of exogenous glucocorticoids on the endogenous cortisol rhythm considering intra-venous and oral dosing. Chronic daily dosing resulted in modification of the circadian rhythmicity of endogenous cortisol with the amplitude and acrophase of the altered rhythm dependent on the administration time. Simulations revealed that the circadian features of the endogenous cortisol rhythm can be preserved by proper timing of administration. The response following a single dose was not indicative of the response following long-term, repeated chronopharmacological dosing of synthetic glucocorticoids. Furthermore, simulations revealed the inductive influence of long-term treatment was only associated with low to moderate doses, while high doses generally led to suppression of endogenous activity regardless of the chronopharmacological dose. Finally, chronic daily dosing was found to alter the responsiveness of the HPA axis, such that a decrease in the amplitude of the cortisol rhythm resulted in a partial loss in the time-of-day dependent response to CRH stimulation, while an increase in the amplitude was associated with a more pronounced time-of-day dependence of the response.

Modeling circadian variability of core-clock and clock-controlled genes in four tissues of the rat

Circadian clocks, present in almost all cells of the body, are entrained to rhythmic changes in the environment (e.g. light/dark cycles). Genes responsible for this timekeeping are named core-clock genes, which through transcriptional feedback interactions mediated by transcription factor binding to Ebox/RRE/Dbox elements can generate oscillatory activity of their expression. By regulating the transcription of other clock-controlled genes (CCGs) circadian information is transmitted to tissue and organ levels. Recent studies have indicated that there is a considerable variability of clock-controlled gene expression between tissues both with respect to the circadian genes that are regulated and to their phase lags. In this work, a mathematical model was adapted to explore the dynamics of core-clock and clock-controlled genes measured in four tissues of the rat namely liver, muscle, adipose, and lung. The model efficiently described the synchronous rhythmicity of core-clock genes and further predicted that their phases are mainly regulated by Per2 and Cry1 transcriptional delays and Rev-Erba and Cry1 degradation rates. Similarly, after mining databases for potential Ebox/RRE/Dbox elements in the promoter region of clock-controlled genes, the phase variabilities of the same genes between different tissues were described. The analysis suggests that inter-tissue circadian variability of the same clock-controlled genes is an inherent component of homeostatic function and may arise due to different transcription factor activities on Ebox/RRE/Dbox elements.

Mathematical analysis of circadian disruption and metabolic re-entrainment of hepatic gluconeogenesis: the intertwining entraining roles of light and feeding

The circadian rhythms influence the metabolic activity from molecular level to tissue, organ, and host level. Disruption of the circadian rhythms manifests to the host's health as metabolic syndromes, including obesity, diabetes, and elevated plasma glucose, eventually leading to cardiovascular diseases. Therefore, it is imperative to understand the mechanism behind the relationship between circadian rhythms and metabolism. To start answering this question, we propose a semimechanistic mathematical model to study the effect of circadian disruption on hepatic gluconeogenesis in humans. Our model takes the light-dark cycle and feeding-fasting cycle as two environmental inputs that entrain the metabolic activity in the liver. The model was validated by comparison with data from mice and rat experimental studies. Formal sensitivity and uncertainty analyses were conducted to elaborate on the driving forces for hepatic gluconeogenesis. Furthermore, simulating the impact of Clock gene knockout suggests that modification to the local pathways tied most closely to the feeding-fasting rhythms may be the most efficient way to restore the disrupted glucose metabolism in liver.

Daily variation of gene expression in diverse rat tissues

Circadian information is maintained in mammalian tissues by a cell-autonomous network of transcriptional feedback loops that have evolved to optimally regulate tissue-specific functions. An analysis of daily gene expression in different tissues, as well as an evaluation of inter-tissue circadian variability, is crucial for a systems-level understanding of this transcriptional circuitry. Affymetrix gene chip measurements of liver, muscle, adipose, and lung tissues were obtained from a rich time series light/dark experiment, involving 54 normal rats sacrificed at 18 time points within the 24-hr cycle. Our analysis revealed a high degree of circadian regulation with a variable distribution of phases among the four tissues. Interestingly, only a small number of common genes maintain circadian activity in all tissues, with many of them consisting of "core-clock" components with synchronous rhythms. Our results suggest that inter-tissue circadian variability is a critical component of homeostatic body function and is mediated by diverse signaling pathways that ultimately lead to highly tissue-specific transcription regulation.

Modeling the Influence of Seasonal Differences in the HPA Axis on Synchronization of the Circadian Clock and Cell Cycle

Synchronization of biological functions to environmental signals enables organisms to anticipate and appropriately respond to daily external fluctuations and is critical to the maintenance of homeostasis. Misalignment of circadian rhythms with environmental cues is associated with adverse health outcomes. Cortisol, the downstream effector of hypothalamic-pituitary-adrenal (HPA) activity, facilitates synchronization of peripheral biological processes to the environment. Cortisol levels exhibit substantial seasonal rhythmicity, with peak levels occurring during the short-photoperiod winter months and reduced levels occurring in the long-photoperiod summer season. Seasonal changes in cortisol secretion could therefore alter its entraining capabilities, resulting in a season-dependent modification in the alignment of biological activities with the environment. We develop a mathematical model to investigate the influence of photoperiod-induced seasonal differences in the circadian rhythmicity of the HPA axis on the synchronization of the peripheral circadian clock and cell cycle in a heterogeneous cell population. Model simulations predict that the high-amplitude cortisol rhythms in winter result in the greatest entrainment of peripheral oscillators. Furthermore, simulations predict a circadian gating of the cell cycle with respect to the expression of peripheral clock genes. Seasonal differences in cortisol rhythmicity are also predicted to influence mitotic synchrony, with a high-amplitude winter rhythm resulting in the greatest synchrony and a shift in timing of the cell cycle phases, relative to summer. Our results highlight the primary interactions among the HPA axis, the peripheral circadian clock, and the cell cycle and thereby provide an improved understanding of the implications of circadian misalignment on the synchronization of peripheral regulatory processes.

Asymmetry in Signal Oscillations Contributes to Efficiency of Periodic Systems

Oscillations are an important feature of cellular signaling that result from complex combinations of positive- and negative-feedback loops. The encoding and decoding mechanisms of oscillations based on amplitude and frequency have been extensively discussed in the literature in the context of intercellular and intracellular signaling. However, the fundamental questions of whether and how oscillatory signals offer any competitive advantages-and, if so, what-have not been fully answered. We investigated established oscillatory mechanisms and designed a study to analyze the oscillatory characteristics of signaling molecules and system output in an effort to answer these questions. Two classic oscillators, Goodwin and PER, were selected as the model systems, and corresponding no-feedback models were created for each oscillator to discover the advantage of oscillating signals. Through simulating the original oscillators and the matching no-feedback models, we show that oscillating systems have the capability to achieve better resource-to-output efficiency, and we identify oscillatory characteristics that lead to improved efficiency.

On the analysis of complex biological supply chains: From Process Systems Engineering to Quantitative Systems Pharmacology

The use of models in biology has become particularly relevant as it enables investigators to develop a mechanistic framework for understanding the operating principles of living systems as well as in quantitatively predicting their response to both pathological perturbations and pharmacological interventions. This application has resulted in a synergistic convergence of systems biology and pharmacokinetic-pharmacodynamic modeling techniques that has led to the emergence of quantitative systems pharmacology (QSP). In this review, we discuss how the foundational principles of chemical process systems engineering inform the progressive development of more physiologically-based systems biology models.

The Synergistic Role of Light-Feeding Phase Relations on Entraining Robust Circadian Rhythms in the Periphery

The feeding and fasting cycles are strong behavioral signals that entrain biological rhythms of the periphery. The feeding rhythms synchronize the activities of the metabolic organs, such as liver, synergistically with the light/dark cycle primarily entraining the suprachiasmatic nucleus. The likely phase misalignment between the feeding rhythms and the light/dark cycles appears to induce circadian disruptions leading to multiple physiological abnormalities motivating the need to investigate the mechanisms behind joint light-feeding circadian entrainment of peripheral tissues. To address this question, we propose a semimechanistic mathematical model describing the circadian dynamics of peripheral clock genes in human hepatocyte under the control of metabolic and light rhythmic signals. The model takes the synergistically acting light/dark cycles and feeding rhythms as inputs and incorporates the activity of sirtuin 1, a cellular energy sensor and a metabolic enzyme activated by nicotinamide adenine dinucleotide. The clock gene dynamics was simulated under various light-feeding phase relations and intensities, to explore the feeding entrainment mechanism as well as the convolution of light and feeding signals in the periphery. Our model predicts that the peripheral clock genes in hepatocyte can be completely entrained to the feeding rhythms, independent of the light/dark cycle. Furthermore, it predicts that light-feeding phase relationship is a critical factor in robust circadian oscillations.

Understanding Physiology in the Continuum: Integration of Information from Multiple -Omics Levels

In this paper, we discuss approaches for integrating biological information reflecting diverse physiologic levels. In particular, we explore statistical and model-based methods for integrating transcriptomic, proteomic and metabolomics data. Our case studies reflect responses to a systemic inflammatory stimulus and in response to an anti-inflammatory treatment. Our paper serves partly as a review of existing methods and partly as a means to demonstrate, using case studies related to human endotoxemia and response to methylprednisolone (MPL) treatment, how specific questions may require specific methods, thus emphasizing the non-uniqueness of the approaches. Finally, we explore novel ways for integrating -omics information with PKPD models, toward the development of more integrated pharmacology models.

Physiologically-based pharmacokinetic models: approaches for enabling personalized medicine

Personalized medicine strives to deliver the 'right drug at the right dose' by considering inter-person variability, one of the causes for therapeutic failure in specialized populations of patients. Physiologically-based pharmacokinetic (PBPK) modeling is a key tool in the advancement of personalized medicine to evaluate complex clinical scenarios, making use of physiological information as well as physicochemical data to simulate various physiological states to predict the distribution of pharmacokinetic responses. The increased dependency on PBPK models to address regulatory questions is aligned with the ability of PBPK models to minimize ethical and technical difficulties associated with pharmacokinetic and toxicology experiments for special patient populations. Subpopulation modeling can be achieved through an iterative and integrative approach using an adopt, adapt, develop, assess, amend, and deliver methodology. PBPK modeling has two valuable applications in personalized medicine: (1) determining the importance of certain subpopulations within a distribution of pharmacokinetic responses for a given drug formulation and (2) establishing the formulation design space needed to attain a targeted drug plasma concentration profile. This review article focuses on model development for physiological differences associated with sex (male vs. female), age (pediatric vs. young adults vs. elderly), disease state (healthy vs. unhealthy), and temporal variation (influence of biological rhythms), connecting them to drug product formulation development within the quality by design framework. Although PBPK modeling has come a long way, there is still a lengthy road before it can be fully accepted by pharmacologists, clinicians, and the broader industry.

Mathematical modeling of the circadian dynamics of the neuroendocrine-immune network in experimentally induced arthritis

The circadian dynamics of important neuroendocrine-immune mediators have been implicated in progression of rheumatoid arthritis pathophysiology, both clinically as well as in animal models. We present a mathematical model that describes the circadian interactions between mediators of the hypothalamic-pituitary-adrenal (HPA) axis and the proinflammatory cytokines. Model predictions demonstrate that chronically elevated cytokine expression results in the development of adrenal insufficiency and circadian variability in paw edema. Notably, our model also predicts that an increase in mean secretion of corticosterone (CST) after the induction of the disease is accompanied by a decrease in the amplitude of the CST oscillation. Furthermore, alterations in the phase of circadian oscillation of both cytokines and HPA axis mediators are observed. Therefore, by incorporating the circadian interactions between the neuroendocrine-immune mediators, our model is able to simulate important features of rheumatoid arthritis pathophysiology.

The role of the hypothalamic-pituitary-adrenal axis in modulating seasonal changes in immunity

Seasonal changes in environmental conditions are accompanied by significant adjustment of multiple biological processes. In temperate regions, the day fraction, or photoperiod, is a robust environmental cue that synchronizes seasonal variations in neuroendocrine and metabolic function. In this work, we propose a semimechanistic mathematical model that considers the influence of seasonal photoperiod changes as well as cellular and molecular adaptations to investigate the seasonality of immune function. Our model predicts that the circadian rhythms of cortisol, our proinflammatory mediator, and its receptor exhibit seasonal differences in amplitude and phase, oscillating at higher amplitudes in the winter season with peak times occurring later in the day. Furthermore, the reduced photoperiod of winter coupled with seasonal alterations in physiological activity induces a more exacerbated immune response to acute stress, simulated in our studies as the administration of an acute dose of endotoxin. Our findings are therefore in accordance with experimental data that reflect the predominance of a proinflammatory state during the winter months. These changes in circadian rhythm dynamics may play a significant role in the seasonality of disease incidence and regulate the diurnal and seasonal variation of disease symptom severity.

Circadian characteristics of permissive and suppressive effects of cortisol and their role in homeostasis and the acute inflammatory response

In this work we explore a semi-mechanistic model that considers cortisol's permissive and suppressive effects through the regulation of cytokine receptors and cytokines respectively. Our model reveals the proactive role of cortisol during the resting period and its reactive character during the body's activity phase. Administration of an acute LPS dose during the night, when cortisol's permissive effects are higher than suppressive, leads to increased cytokine levels compared to LPS administration at morning when cortisol's suppressive effects are higher. Interestingly, our model presents a hysteretic behavior where the relative predominance of permissive or suppressive effects results not only from cortisol levels but also from the previous states of the model. Therefore, for the same cortisol levels, administration of an inflammatory stimulus at cortisol's ascending phase, that follows a time period where cytokine receptor expression is elevated ultimately sensitizing the body for the impending stimulus, leads to higher cytokine expression compared to administration of the same stimulus at cortisol's descending phase.