A Mathematical Model of the Liver Circadian Clock Linking Feeding and Fasting Cycles to Clock Function

The seasons within: a theoretical perspective on photoperiodic entrainment and encoding

Circadian clocks are internal timing devices that have evolved as an adaption to the omnipresent natural 24 h rhythmicity of daylight intensity. Properties of the circadian system are photoperiod dependent. The phase of entrainment varies systematically with season. Plastic photoperiod-dependent re-arrangements in the mammalian circadian core pacemaker yield an internal representation of season. Output pathways of the circadian clock regulate photoperiodic responses such as flowering time in plants or hibernation in mammals. Here, we review the concepts of seasonal entrainment and photoperiodic encoding. We introduce conceptual phase oscillator models as their high level of abstraction, but, yet, intuitive interpretation of underlying parameters allows for a straightforward analysis of principles that determine entrainment characteristics. Results from this class of models are related and discussed in the context of more complex conceptual amplitude-phase oscillators as well as contextual molecular models that take into account organism, tissue, and cell-type-specific details.

An integrative mathematical model for timing treatment toxicity and Zeitgeber impact in colorectal cancer cells

Increasing evidence points to a role of the circadian clock in the regulation of cancer hallmarks with a strong impact on the understanding and treatment of this disease. Anti-cancer treatment can be personalized considering treatment timing. Here we present a new mathematical model based on data from three colorectal cancer cell lines and core-clock knock-outs, which couples the circadian and drug metabolism network, and that allows to determine toxicity profiles for a given drug and cell type. Moreover, this model integrates external Zeitgebers and thus may be used to fine-tune toxicity by using external factors, such as light, and therefore, to a certain extent, help fitting the endogenous rhythms of the patients to a defined clinic routine facilitating the implementation of time-dependent treatment in clinical practice.

The role of peroxisome proliferator-activated receptors in the tumor microenvironment, tumor cell metabolism, and anticancer therapy

Peroxisome proliferator-activated receptors (PPARs) have been extensively studied for over 3 decades and consist of three isotypes, including PPARα, γ, and β/δ, that were originally considered key metabolic regulators controlling energy homeostasis in the body. Cancer has become a leading cause of human mortality worldwide, and the role of peroxisome proliferator-activated receptors in cancer is increasingly being investigated, especially the deep molecular mechanisms and effective cancer therapies. Peroxisome proliferator-activated receptors are an important class of lipid sensors and are involved in the regulation of multiple metabolic pathways and cell fate. They can regulate cancer progression in different tissues by activating endogenous or synthetic compounds. This review emphasizes the significance and knowledge of peroxisome proliferator-activated receptors in the tumor microenvironment, tumor cell metabolism, and anti-cancer treatment by summarizing recent research on peroxisome proliferator-activated receptors. In general, peroxisome proliferator-activated receptors either promote or suppress cancer in different types of tumor microenvironments. The emergence of this difference depends on various factors, including peroxisome proliferator-activated receptor type, cancer type, and tumor stage. Simultaneously, the effect of anti-cancer therapy based on drug-targeted PPARs differs or even opposes among the three peroxisome proliferator-activated receptor homotypes and different cancer types. Therefore, the current status and challenges of the use of peroxisome proliferator-activated receptors agonists and antagonists in cancer treatment are further explored in this review.

The Influence of the Differentiation of Genes Encoding Peroxisome Proliferator-Activated Receptors and Their Coactivators on Nutrient and Energy Metabolism

Genetic components may play an important role in the regulation of nutrient and energy metabolism. In the presence of specific genetic variants, metabolic dysregulation may occur, especially in relation to the processes of digestion, assimilation, and the physiological utilization of nutrients supplied to the body, as well as the regulation of various metabolic pathways and the balance of metabolic changes, which may consequently affect the effectiveness of applied reduction diets and weight loss after training. There are many well-documented studies showing that the presence of certain polymorphic variants in some genes can be associated with specific changes in nutrient and energy metabolism, and consequently, with more or less desirable effects of applied caloric reduction and/or exercise intervention. This systematic review focused on the role of genes encoding peroxisome proliferator-activated receptors (PPARs) and their coactivators in nutrient and energy metabolism. The literature review prepared showed that there is a link between the presence of specific alleles described at different polymorphic points in PPAR genes and various human body characteristics that are crucial for the efficacy of nutritional and/or exercise interventions. Genetic analysis can be a valuable element that complements the work of a dietitian or trainer, allowing for the planning of a personalized diet or training that makes the best use of the innate metabolic characteristics of the person who is the subject of their interventions.

An Overview of the Circadian Clock in the Frame of Chronotherapy: From Bench to Bedside

Most living organisms in both the plant and animal kingdoms have evolved processes to stay in tune with the alternation of day and night, and to optimize their physiology as a function of light supply. In mammals, a circadian clock relying on feedback loops between key transcription factors will thus control the temporally regulated pattern of expression of most genes. Modern ways of life have highly altered the synchronization of human activities with their circadian clocks. This review discusses the links between an altered circadian clock and the rise of pathologies. We then sum up the proofs of concept advocating for the integration of circadian clock considerations in chronotherapy for health care, medicine, and pharmacotherapy. Finally, we discuss the current challenges that circadian biology must face and the tools to address them.

Time-keeping and decision-making in living cells: Part I

To survive and reproduce, a cell must process information from its environment and its own internal state and respond accordingly, in terms of metabolic activity, gene expression, movement, growth, division and differentiation. These signal–response decisions are made by complex networks of interacting genes and proteins, which function as biochemical switches and clocks, and other recognizable information-processing circuitry. This theme issue of Interface Focus (in two parts) brings together articles on time-keeping and decision-making in living cells—work that uses precise mathematical modelling of underlying molecular regulatory networks to understand important features of cell physiology. Part I focuses on time-keeping: mechanisms and dynamics of biological oscillators and modes of synchronization and entrainment of oscillators, with special attention to circadian clocks.

Cycle dynamics and synchronization in a coupled network of peripheral circadian clocks

The intercellular interactions between peripheral circadian clocks, located in tissues and organs other than the suprachiasmatic nuclei of the hypothalamus, are still very poorly understood. We propose a theoretical and computational study of the coupling between two or more clocks, using a calibrated, reduced model of the circadian clock to describe some synchronization properties between peripheral cellular clocks. Based on a piecewise linearization of the dynamics of the mutual CLOCK:BMAL1/PER:CRY inactivation term, we suggest a segmentation of the circadian cycle into six stages, to help analyse different types of synchronization between two clocks, including single stage duration, total period and maximal amplitudes. Finally, our model reproduces some recent experimental results on the effects of different regimes of time-restricted feeding in liver circadian clocks of mice.

Synergies of Multiple Zeitgebers Tune Entrainment

Circadian rhythms are biological rhythms with a period close to 24 h. They become entrained to the Earth's solar day via different periodic cues, so-called zeitgebers. The entrainment of circadian rhythms to a single zeitgeber was investigated in many mathematical clock models of different levels of complexity, ranging from the Poincaré oscillator and the Goodwin model to biologically more detailed models of multiple transcriptional translational feedback loops. However, circadian rhythms are exposed to multiple coexisting zeitgebers in nature. Therefore, we study synergistic effects of two coexisting zeitgebers on different components of the circadian clock. We investigate the induction of period genes by light together with modulations of nuclear receptor activities by drugs and metabolism. Our results show that the entrainment of a circadian rhythm to two coexisting zeitgebers depends strongly on the phase difference between the two zeitgebers. Synergistic interactions of zeitgebers can strengthen diurnal rhythms to reduce detrimental effects of shift-work and jet lag. Medical treatment strategies which aim for stable circadian rhythms should consider interactions of multiple zeitgebers.

A mathematical model of the circadian clock and drug pharmacology to optimize irinotecan administration timing in colorectal cancer

Scheduling anticancer drug administration over 24 h may critically impact treatment success in a patient-specific manner. Here, we address personalization of treatment timing using a novel mathematical model of irinotecan cellular pharmacokinetics and -dynamics linked to a representation of the core clock and predict treatment toxicity in a colorectal cancer (CRC) cellular model. The mathematical model is fitted to three different scenarios: mouse liver, where the drug metabolism mainly occurs, and two human colorectal cancer cell lines representing an in vitro experimental system for human colorectal cancer progression. Our model successfully recapitulates quantitative circadian datasets of mRNA and protein expression together with timing-dependent irinotecan cytotoxicity data. The model also discriminates time-dependent toxicity between the different cells, suggesting that treatment can be optimized according to their cellular clock. Our results show that the time-dependent degradation of the protein mediating irinotecan activation, as well as an oscillation in the death rate may play an important role in the circadian variations of drug toxicity. In the future, this model can be used to support personalized treatment scheduling by predicting optimal drug timing based on the patient's gene expression profile.

An effective model of endogenous clocks and external stimuli determining circadian rhythms

Circadian endogenous clocks of eukaryotic organisms are an established and rapidly developing research field. To investigate and simulate in an effective model the effect of external stimuli on such clocks and their components we developed a software framework for download and simulation. The application is useful to understand the different involved effects in a mathematical simple and effective model. This concerns the effects of Zeitgebers, feedback loops and further modifying components. We start from a known mathematical oscillator model, which is based on experimental molecular findings. This is extended with an effective framework that includes the impact of external stimuli on the circadian oscillations including high dose pharmacological treatment. In particular, the external stimuli framework defines a systematic procedure by input-output-interfaces to couple different oscillators. The framework is validated by providing phase response curves and ranges of entrainment. Furthermore, Aschoffs rule is computationally investigated. It is shown how the external stimuli framework can be used to study biological effects like points of singularity or oscillators integrating different signals at once. The mathematical framework and formalism is generic and allows to study in general the effect of external stimuli on oscillators and other biological processes. For an easy replication of each numerical experiment presented in this work and an easy implementation of the framework the corresponding Mathematica files are fully made available. They can be downloaded at the following link: https://www.biozentrum.uni-wuerzburg.de/bioinfo/computing/circadian/ .

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.

Model learning to identify systemic regulators of the peripheral circadian clock

MOTIVATION

Personalized medicine aims at providing patient-tailored therapeutics based on multi-type data toward improved treatment outcomes. Chronotherapy that consists in adapting drug administration to the patient's circadian rhythms may be improved by such approach. Recent clinical studies demonstrated large variability in patients' circadian coordination and optimal drug timing. Consequently, new eHealth platforms allow the monitoring of circadian biomarkers in individual patients through wearable technologies (rest-activity, body temperature), blood or salivary samples (melatonin, cortisol) and daily questionnaires (food intake, symptoms). A current clinical challenge involves designing a methodology predicting from circadian biomarkers the patient peripheral circadian clocks and associated optimal drug timing. The mammalian circadian timing system being largely conserved between mouse and humans yet with phase opposition, the study was developed using available mouse datasets.

RESULTS

We investigated at the molecular scale the influence of systemic regulators (e.g. temperature, hormones) on peripheral clocks, through a model learning approach involving systems biology models based on ordinary differential equations. Using as prior knowledge our existing circadian clock model, we derived an approximation for the action of systemic regulators on the expression of three core-clock genes: Bmal1, Per2 and Rev-Erbα. These time profiles were then fitted with a population of models, based on linear regression. Best models involved a modulation of either Bmal1 or Per2 transcription most likely by temperature or nutrient exposure cycles. This agreed with biological knowledge on temperature-dependent control of Per2 transcription. The strengths of systemic regulations were found to be significantly different according to mouse sex and genetic background.

AVAILABILITY AND IMPLEMENTATION

https://gitlab.inria.fr/julmarti/model-learning-mb21eccb.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

His and her mathematical models of physiological systems

Beyond the reproductive system and reproductive behaviors, men and women exhibit major differences in many organ systems, including the anatomy of the brain, the activities of the stress and immune systems, and the metabolic and cardiovascular functions. A comprehensive understanding of the impact of these sex differences on health and disease is crucial to the development of effective sex-based therapies. Mathematical modeling has the potential of facilitating and contributing to advancing the understanding of sex differences in health and disease. Indeed, explosion of mathematical models have been developed in recent decades for different aspects of human physiology and pathophysiology. This review contains a survey of sex-specific mathematical models of physiological systems, describe insights that have been revealed in those modeling studies, and discuss future opportunities.

Aging affects circadian clock and metabolism and modulates timing of medication

Aging is associated with impairments in the circadian rhythms, and with energy deregulation that affects multiple metabolic pathways. The goal of this study is to unravel the complex interactions among aging, metabolism, and the circadian clock. We seek to identify key factors that inform the liver circadian clock of cellular energy status and to reveal the mechanisms by which variations in food intake may disrupt the clock. To address these questions, we develop a comprehensive mathematical model that represents the circadian pathway in the mouse liver, together with the insulin/IGF-1 pathway, mTORC1, AMPK, NAD+, and the NAD+ -consuming factor SIRT1. The model is age-specific and can simulate the liver of a young mouse or an aged mouse. Simulation results suggest that the reduced NAD+ and SIRT1 bioavailability may explain the shortened circadian period in aged rodents. Importantly, the model identifies the dosing schedules for maximizing the efficacy of anti-aging medications.

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 Misalignment and Metabolic Disorders: A Story of Twisted Clocks

Simple Summary

In mammals, many physiological processes follow a 24 h rhythmic pattern. These rhythms are governed by a complex network of circadian clocks, which perceives external time cues (notably light and nutrients) and adjusts the timing of metabolic and physiological functions to allow a proper adaptation of the organism to the daily changes in the environmental conditions. Circadian rhythms originate at the cellular level through a transcriptional–translational regulatory network involving a handful of clock genes. In this review, we show how adverse effects caused by ill-timed feeding or jet lag can lead to a dysregulation of this genetic clockwork, which in turn results in altered metabolic regulation and possibly in diseases. We also show how computational modeling can complement experimental observations to understand the design of the clockwork and the onset of metabolic disorders.

Abstract

Biological clocks are cell-autonomous oscillators that can be entrained by periodic environmental cues. This allows organisms to anticipate predictable daily environmental changes and, thereby, to partition physiological processes into appropriate phases with respect to these changing external conditions. Nowadays our 24/7 society challenges this delicate equilibrium. Indeed, many studies suggest that perturbations such as chronic jet lag, ill-timed eating patterns, or shift work increase the susceptibility to cardiometabolic disorders, diabetes, and cancers. However the underlying mechanisms are still poorly understood. A deeper understanding of this complex, dynamic system requires a global holistic approach for which mathematical modeling can be highly beneficial. In this review, we summarize several experimental works pertaining to the effect of adverse conditions on clock gene expression and on physiology, and we show how computational models can bring interesting insights into the links between circadian misalignment and metabolic diseases.

An Optimal Time for Treatment-Predicting Circadian Time by Machine Learning and Mathematical Modelling

Tailoring medical interventions to a particular patient and pathology has been termed personalized medicine. The outcome of cancer treatments is improved when the intervention is timed in accordance with the patient's internal time. Yet, one challenge of personalized medicine is how to consider the biological time of the patient. Prerequisite for this so-called chronotherapy is an accurate characterization of the internal circadian time of the patient. As an alternative to time-consuming measurements in a sleep-laboratory, recent studies in chronobiology predict circadian time by applying machine learning approaches and mathematical modelling to easier accessible observables such as gene expression. Embedding these results into the mathematical dynamics between clock and cancer in mammals, we review the precision of predictions and the potential usage with respect to cancer treatment and discuss whether the patient's internal time and circadian observables, may provide an additional indication for individualized treatment timing. Besides the health improvement, timing treatment may imply financial advantages, by ameliorating side effects of treatments, thus reducing costs. Summarizing the advances of recent years, this review brings together the current clinical standard for measuring biological time, the general assessment of circadian rhythmicity, the usage of rhythmic variables to predict biological time and models of circadian rhythmicity.

ADP is the dominant controller of AMP-activated protein kinase activity dynamics in skeletal muscle during exercise

Exercise training elicits profound metabolic adaptations in skeletal muscle cells. A key molecule in coordinating these adaptations is AMP-activated protein kinase (AMPK), whose activity increases in response to cellular energy demand. AMPK activity dynamics are primarily controlled by the adenine nucleotides ADP and AMP, but how each contributes to its control in skeletal muscle during exercise is unclear. We developed and validated a mathematical model of AMPK signaling dynamics, and then applied global parameter sensitivity analyses with data-informed constraints to predict that AMPK activity dynamics are determined principally by ADP and not AMP. We then used the model to predict the effects of two additional direct-binding activators of AMPK, ZMP and Compound 991, further validating the model and demonstrating its applicability to understanding AMPK pharmacology. The relative effects of direct-binding activators can be understood in terms of four properties, namely their concentrations, binding affinities for AMPK, abilities to enhance AMPK phosphorylation, and the magnitudes of their allosteric activation of AMPK. Despite AMP's favorable values in three of these four properties, ADP is the dominant controller of AMPK activity dynamics in skeletal muscle during exercise by virtue of its higher concentration compared to that of AMP.

Conceptual Models of Entrainment, Jet Lag, and Seasonality

Understanding entrainment of circadian rhythms is a central goal of chronobiology. Many factors, such as period, amplitude, Zeitgeber strength, and daylength, govern entrainment ranges and phases of entrainment. We have tested whether simple amplitude-phase models can provide insight into the control of entrainment phases. Using global optimization, we derived conceptual models with just three free parameters (period, amplitude, and relaxation rate) that reproduce known phenotypic features of vertebrate clocks: phase response curves (PRCs) with relatively small phase shifts, fast re-entrainment after jet lag, and seasonal variability to track light onset or offset. Since optimization found multiple sets of model parameters, we could study this model ensemble to gain insight into the underlying design principles. We found complex associations between model parameters and entrainment features. Arnold onions of representative models visualize strong dependencies of entrainment on periods, relative Zeitgeber strength, and photoperiods. Our results support the use of oscillator theory as a framework for understanding the entrainment of circadian clocks.

Clocks in the Wild: Entrainment to Natural Light

Entrainment denotes a process of coordinating the internal circadian clock to external rhythmic time-cues (Zeitgeber), mainly light. It is facilitated by stronger Zeitgeber signals and smaller period differences between the internal clock and the external Zeitgeber. The phase of entrainment ψ is a result of this process on the side of the circadian clock. On Earth, the period of the day-night cycle is fixed to 24 h, while the periods of circadian clocks distribute widely due to natural variation within and between species. The strength and duration of light depend locally on season and geographic latitude. Therefore, entrainment characteristics of a circadian clock vary under a local light environment and distribute along geoecological settings. Using conceptual models of circadian clocks, we investigate how local conditions of natural light shape global patterning of entrainment through seasons. This clock-side entrainment paradigm enables us to predict systematic changes in the global distribution of chronotypes.

Systems Level Understanding of Circadian Integration with Cell Physiology

The mammalian circadian clock regulates a wide variety of physiological and behavioral processes. In turn, its disruption is associated with sleep deficiency, metabolic syndrome, neurological and psychiatric disorders, and cancer. At the turn of the century, the circadian clock was determined to be regulated by a transcriptional negative feedback mechanism composed of a dozen core clock genes. More recently, large-scale genomic studies have expanded the clock into a complex network composed of thousands of gene outputs and inputs. A major task of circadian research is to utilize systems biological approaches to uncover the governing principles underlying cellular oscillatory behavior and advance understanding of biological functions at the genomic level with spatiotemporal resolution. This review focuses on the genes and pathways that provide inputs to the circadian clock. Several emerging examples include AMP-activated protein kinase AMPK, nutrient/energy sensor mTOR, NAD⁺-dependent deacetylase SIRT1, hypoxia-inducible factor HIF1α, oxidative stress-inducible factor NRF2, and the proinflammatory factor NF-κB. Among others that continue to be revealed, these input pathways reflect the extensive interplay between the clock and cell physiology through the regulation of core clock genes and proteins. While the scope of this crosstalk is well-recognized, precise molecular links are scarce, and the underlying regulatory mechanisms are not well understood. Future research must leverage genetic and genomic tools and technologies, network analysis, and computational modeling to characterize additional modifiers and input pathways. This systems-based framework promises to advance understanding of the circadian timekeeping system and may enable the enhancement of circadian functions through related input pathways.

Amplitude Effects Allow Short Jet Lags and Large Seasonal Phase Shifts in Minimal Clock Models

Mathematical models of varying complexity have helped shed light on different aspects of circadian clock function. In this work, we question whether minimal clock models (Goodwin models) are sufficient to reproduce essential phenotypes of the clock: a small phase response curve (PRC), fast jet lag, and seasonal phase shifts. Instead of building a single best model, we take an approach where we study the properties of a set of models satisfying certain constraints; here, a 1h-pulse PRC with a range of 3h and clock periods between 22h and 26h is designed. Surprisingly, almost all these randomly parameterized models showed a 4h change in phase of entrainment between long and short days and jet lag durations of three to seven days in advance and delay. Moreover, intrinsic clock period influenced jet lag duration and entrainment amplitude and phase. Fast jet lag was realized in this model by means of an interesting amplitude effect: the association between clock amplitude and clock period termed "twist." This twist allows amplitude changes to speed up and slow down clocks enabling faster shifts. These findings were robust to the addition of positive feedback to the model. In summary, the known design principles of rhythm generation - negative feedback, long delay, and switch-like inhibition (we review these in detail) - are sufficient to reproduce the essential clock phenotypes. Furthermore, amplitudes play a role in determining clock properties and must be always considered, although they are difficult to measure.

Lifestyle and Food Habits Impact on Chronic Diseases: Roles of PPARs

Peroxisome proliferator-activated receptors (PPARs) are nuclear receptors that exert important functions in mediating the pleiotropic effects of diverse exogenous factors such as physical exercise and food components. Particularly, PPARs act as transcription factors that control the expression of genes implicated in lipid and glucose metabolism, and cellular proliferation and differentiation. In this review, we aim to summarize the recent advancements reported on the effects of lifestyle and food habits on PPAR transcriptional activity in chronic disease.

Chrononutrition and Polyphenols: Roles and Diseases

Biological rhythms can influence the activity of bioactive compounds, and at the same time, the intake of these compounds can modulate biological rhythms. In this context, chrononutrition has appeared as a research field centered on the study of the interactions among biological rhythms, nutrition, and metabolism. This review summarizes the role of phenolic compounds in the modulation of biological rhythms, focusing on their effects in the treatment or prevention of chronic diseases. Heterotrophs are able to sense chemical cues mediated by phytochemicals such as phenolic compounds, promoting their adaptation to environmental conditions. This is called xenohormesis. Hence, the consumption of fruits and vegetables rich in phenolic compounds exerts several health benefits, mainly attributed to the product of their metabolism. However, the profile of phenolic compounds present in plants differs among species and is highly variable depending on agricultural and technological factors. In this sense, the seasonal consumption of polyphenol-rich fruits could induce important changes in the regulation of physiology and metabolism due to the particular phenolic profile that the fruits contain. This fact highlights the need for studies that evaluate the impact of these specific phenolic profiles on health to establish more accurate dietary recommendations.

Correlation between inflammatory markers and impaired circadian clock gene expression in type 2 diabetes mellitus

AIM

Circadian rhythm controls a wide variety of physiological processes in the body. Disruption of the circadian clock in metabolic tissues may increase the risk of diabetes, obesity, and metabolic syndrome. The following study investigated whether the expression of clock genes of peripheral blood cells is impaired in type 2 diabetes (DT2) and whether inflammatory markers are associated with circadian clock gene expression in DT2 patients.

MATERIALS AND METHODS

Blood samples were obtained from 36 DT2 patients and 14 non-diabetic volunteers. Transcript levels of circadian clock genes were analyzed using real-time quantitative PCR; plasma inflammatory markers were measured by ELISA or clinical laboratory test.

RESULTS

The CLOCK, BMAL1, PER1, CRY1 and CRY2 mRNA levels were decreased in the diabetic patients. In addition, HbA1c levels were negatively correlated with BMAL1, PER1 and CRY1 mRNA levels. The levels of IL-6, TNF-α and CRP were higher in diabetic subjects compared to control subjects. Impaired expression of circadian clock gene was interrelated with the elevated levels of plasma IL-6 and TNF. Moreover, a multiple linear regression showed that plasma IL-6 level was correlated with impaired expression of circadian clock gene.

CONCLUSIONS

Circadian clock genes are reduced in peripheral leucocytes of DT2 patients. Furthermore, impaired expression of circadian clock gene are interrelated with the elevated levels of plasma inflammatory markers.

Transcription-based circadian mechanism controls the duration of molecular clock states in response to signaling inputs

The molecular oscillator of the mammalian circadian clock consists in a dynamical network of genes and proteins whose main regulatory mechanisms occur at the transcriptional level. From a dynamical point of view, the mechanisms leading to an oscillatory solution with an orderly protein peak expression and a clear day/night phase distinction remain unclear. Our goal is to identify the essential interactions needed to generate phase opposition between the activating CLOCK:BMAL1 and the repressing PER:CRY complexes and to better distinguish these two main clock molecular phases relating to rest/activity and fast/feeding cycles. To do this, we develop a transcription-based mathematical model centered on linear combinations of the clock controlled elements (CCEs): E-box, R-box and D-box. Each CCE is responsive to activators and repressors. After model calibration with single-cell data, we explore entrainment and period tuning via interplay with metabolism. Variation of the PER degradation rate γ_p, relating to the tau mutation, results in asymmetric changes in the duration of the different clock molecular phases. Time spent at the state of high PER/PER:CRY decreases with γ_p, while time spent at the state of high BMAL1 and CRY1, both proteins with activity in promoting insulin sensitivity, remains constant. This result suggests a possible mechanism behind the altered metabolism of tau mutation animals. Furthermore, we expose the clock system to two regulatory inputs, one relating to the fast/feeding cycle and the other to the light-dependent synchronization signaling. We observe the phase difference between these signals to also affect the relative duration of molecular clock states. Simulated circadian misalignment, known to correlate with insulin resistance, leads to decreased duration of BMAL1 expression. Our results reveal a possible mechanism for clock-controlled metabolic homeostasis, whereby the circadian clock controls the relative duration of different molecular (and metabolic) states in response to signaling inputs.

Weak coupling between intracellular feedback loops explains dissociation of clock gene dynamics

Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described in recent experimental studies that applied various perturbations such as slice preparations, light pulses, jet-lag, and culture medium exchange. In this paper, we provide evidence that this "presumably transient" dissociation of circadian gene expression oscillations may occur at the single-cell level. Conceptual and detailed mechanistic mathematical modeling suggests that such dissociation is due to a weak interaction between multiple feedback loops present within a single cell. The dissociable loops provide insights into underlying mechanisms and general design principles of the molecular circadian clock.

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.

PPARs as Nuclear Receptors for Nutrient and Energy Metabolism

It has been more than 36 years since peroxisome proliferator-activated receptors (PPARs) were first recognized as enhancers of peroxisome proliferation. Consequently, many studies in different fields have illustrated that PPARs are nuclear receptors that participate in nutrient and energy metabolism and regulate cellular and whole-body energy homeostasis during lipid and carbohydrate metabolism, cell growth, cancer development, and so on. With increasing challenges to human health, PPARs have attracted much attention for their ability to ameliorate metabolic syndromes. In our previous studies, we found that the complex functions of PPARs may be used as future targets in obesity and atherosclerosis treatments. Here, we review three types of PPARs that play overlapping but distinct roles in nutrient and energy metabolism during different metabolic states and in different organs. Furthermore, research has emerged showing that PPARs also play many other roles in inflammation, central nervous system-related diseases, and cancer. Increasingly, drug development has been based on the use of several selective PPARs as modulators to diminish the adverse effects of the PPAR agonists previously used in clinical practice. In conclusion, the complex roles of PPARs in metabolic networks keep these factors in the forefront of research because it is hoped that they will have potential therapeutic effects in future applications.

The circadian clock and liver function in health and disease

Each day, all organisms are subjected to changes in light intensity because of the Earth's rotation around its own axis. To anticipate this geo-physical variability, and to appropriately respond biochemically, most species, including mammals, have evolved an approximate 24-hour endogenous timing mechanism known as the circadian clock (CC). The 'clock' is self-sustained, cell autonomous and present in every cell type. At the core of the clock resides the CC-oscillator, an exquisitely crafted transcriptional-translational feedback system. Remarkably, components of the CC-oscillator not only maintain daily rhythmicity of their own synthesis, but also generate temporal variability in the expression levels of numerous target genes through transcriptional, post-transcriptional and post-translational mechanisms, thus, ensuring proper chronological coordination in the functioning of cells, tissues and organs, including the liver. Indeed, a variety of physiologically critical hepatic functions and cellular processes are CC-controlled. Thus, it is not surprising that modern lifestyle factors (e.g. travel and jet lag, night and rotating shift work), which force 'circadian misalignment', have emerged as major contributors to global health problems including obesity, non-alcoholic fatty liver disease and steatohepatitis. Herein, we provide an overview of the CC-dependent pathways which play critical roles in mediating several hepatic functions under physiological conditions, and whose deregulation is implicated in chronic liver diseases including non-alcoholic steatohepatitis and alcohol-related liver disease.

Mathematical modeling of circadian rhythms

Circadian rhythms are endogenous ~24-hr oscillations usually entrained to daily environmental cycles of light/dark. Many biological processes and physiological functions including mammalian body temperature, the cell cycle, sleep/wake cycles, neurobehavioral performance, and a wide range of diseases including metabolic, cardiovascular, and psychiatric disorders are impacted by these rhythms. Circadian clocks are present within individual cells and at tissue and organismal levels as emergent properties from the interaction of cellular oscillators. Mathematical models of circadian rhythms have been proposed to provide a better understanding of and to predict aspects of this complex physiological system. These models can be used to: (a) manipulate the system in silico with specificity that cannot be easily achieved using in vivo and in vitro experimental methods and at lower cost, (b) resolve apparently contradictory empirical results, (c) generate hypotheses, (d) design new experiments, and (e) to design interventions for altering circadian rhythms. Mathematical models differ in structure, the underlying assumptions, the number of parameters and variables, and constraints on variables. Models representing circadian rhythms at different physiologic scales and in different species are reviewed to promote understanding of these models and facilitate their use. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Computational modeling and analysis of the impacts of sleep deprivation on glucose stimulated insulin secretion

Circadian clock is an exquisite internal biological clock functioning in all living organisms. Lifestyle changes such as shift work or frequent travelling might result in malfunctioning of the central and consequently the peripheral clocks leading to different metabolic disorders. Disruptions in β cell clock have been found to be a potential reason behind β cell failure that makes a person prone towards developing type 2 diabetes (T2DM). In this study, a Petri net model for β cell circadian clock has been developed, followed by analysis of the negative impacts of sleep deprivation conditions on the process of glucose stimulated insulin secretion (GSIS) through misalignment of circadian clock. The analysis of structural properties of the Petri net model reveals robustness of the circadian system. The simulation results predict that sleep loss negatively affects the expression of circadian genes which eventually leads to impaired GSIS and β cell failure. These results suggest that sleep/wake cycle is a vital contributor for the entrainment of the circadian clock and normal functioning of β cell.

Circadian clocks and insulin resistance

Insulin resistance is a main determinant in the development of type 2 diabetes mellitus and a major cause of morbidity and mortality. The circadian timing system consists of a central brain clock in the hypothalamic suprachiasmatic nucleus and various peripheral tissue clocks. The circadian timing system is responsible for the coordination of many daily processes, including the daily rhythm in human glucose metabolism. The central clock regulates food intake, energy expenditure and whole-body insulin sensitivity, and these actions are further fine-tuned by local peripheral clocks. For instance, the peripheral clock in the gut regulates glucose absorption, peripheral clocks in muscle, adipose tissue and liver regulate local insulin sensitivity, and the peripheral clock in the pancreas regulates insulin secretion. Misalignment between different components of the circadian timing system and daily rhythms of sleep-wake behaviour or food intake as a result of genetic, environmental or behavioural factors might be an important contributor to the development of insulin resistance. Specifically, clock gene mutations, exposure to artificial light-dark cycles, disturbed sleep, shift work and social jet lag are factors that might contribute to circadian disruption. Here, we review the physiological links between circadian clocks, glucose metabolism and insulin sensitivity, and present current evidence for a relationship between circadian disruption and insulin resistance. We conclude by proposing several strategies that aim to use chronobiological knowledge to improve human metabolic health.

On chaotic dynamics in transcription factors and the associated effects in differential gene regulation

The control of proteins by a transcription factor with periodically varying concentration exhibits intriguing dynamical behaviour. Even though it is accepted that transcription factors vary their dynamics in response to different situations, insight into how this affects downstream genes is lacking. Here, we investigate how oscillations and chaotic dynamics in the transcription factor NF-κB can affect downstream protein production. We describe how it is possible to control the effective dynamics of the transcription factor by stimulating it with an oscillating ligand. We find that chaotic dynamics modulates gene expression and up-regulates certain families of low-affinity genes, even in the presence of extrinsic and intrinsic noise. Furthermore, this leads to an increase in the production of protein complexes and the efficiency of their assembly. Finally, we show how chaotic dynamics creates a heterogeneous population of cell states, and describe how this can be beneficial in multi-toxic environments.

It is becoming clear that the dynamics of transcription factors may be important for gene regulation. Here, the authors study the implications of oscillatory and chaotic dynamics of NF-κB and demonstrate that it allows a degree of control of gene expression and can generate phenotypic heterogeneity.

Dietary Genistein Could Modulate Hypothalamic Circadian Entrainment, Reduce Body Weight, and Improve Glucose and Lipid Metabolism in Female Mice

Genistein has beneficial effects on metabolic disorders. However, the specific mechanism is not clearly understood. In light of the significant role of the hypothalamus in energy and metabolic homeostasis, this study was designed to explore whether dietary genistein intake could mitigate the harmful effects of a high-fat diet on glucose and lipid metabolism and whether any alterations caused by dietary genistein were associated with hypothalamic gene expression profiles. C57BL/6 female mice were fed a high-fat diet without genistein (HF), a high-fat diet with genistein (HFG), or a normal control diet (CON) for 8 weeks. Body weight and energy intake were assessed. At the end of the study, glucose tolerance and serum levels of insulin and lipids were analyzed. Hypothalamic tissue was collected for whole transcriptome sequencing and reverse transcription quantitative PCR (RT-qPCR) validation. Energy intake and body weight were significantly reduced in the mice of the HFG group compared with those of the HF group. Mice fed the HFG diet had improved glucose tolerance and decreased serum triacylglycerol, free fatty acids, and low-density lipoprotein cholesterol compared with those fed the HF diet. The HFG diet also modulated gene expression in the hypothalamus; the most abundant genes were enriched in the circadian entrainment pathway. Dietary genistein intake could reduce body weight, improve glucose and lipid metabolism, and regulate hypothalamic circadian entrainment. The ability of genistein intake to influence regulation of the hypothalamic circadian rhythm is important since this could provide a novel target for the treatment of obesity and diabetes.

Coherency of circadian rhythms in the SCN is governed by the interplay of two coupling factors

Circadian clocks are autonomous oscillators driving daily rhythms in physiology and behavior. In mammals, a network of coupled neurons in the suprachiasmatic nucleus (SCN) is entrained to environmental light-dark cycles and orchestrates the timing of peripheral organs. In each neuron, transcriptional feedbacks generate noisy oscillations. Coupling mediated by neuropeptides such as VIP and AVP lends precision and robustness to circadian rhythms. The detailed coupling mechanisms between SCN neurons are debated. We analyze organotypic SCN slices from neonatal and adult mice in wild-type and multiple knockout conditions. Different degrees of rhythmicity are quantified by pixel-level analysis of bioluminescence data. We use empirical orthogonal functions (EOFs) to characterize spatio-temporal patterns. Simulations of coupled stochastic single cell oscillators can reproduce the diversity of observed patterns. Our combination of data analysis and modeling provides deeper insight into the enormous complexity of the data: (1) Neonatal slices are typically stronger oscillators than adult slices pointing to developmental changes of coupling. (2) Wild-type slices are completely synchronized and exhibit specific spatio-temporal patterns of phases. (3) Some slices of Cry double knockouts obey impaired synchrony that can lead to co–existing rhythms (“splitting”). (4) The loss of VIP-coupling leads to desynchronized rhythms with few residual local clusters. Additional information was extracted from co–culturing slices with rhythmic neonatal wild-type SCNs. These co–culturing experiments were simulated using external forcing terms representing VIP and AVP signaling. The rescue of rhythmicity via co–culturing lead to surprising results, since a cocktail of AVP-antagonists improved synchrony. Our modeling suggests that these counter-intuitive observations are pointing to an antagonistic action of VIP and AVP coupling. Our systematic theoretical and experimental study shows that dual coupling mechanisms can explain the astonishing complexity of spatio-temporal patterns in SCN slices.

The mammalian circadian clock is orchestrated by a network of coupled neurons. Brain slice preparations allow the analysis of coupling mechanisms mediated by neuropeptides. From bioluminescence recordings, we extract single cell characteristics such as period, amplitude and damping rate. Our data-based stochastic network model involves local coupling between cells and additional external forcing. Available experimental data guide our simulations with two distinct coupling and forcing mechanisms representing the neuropeptides VIP and AVP. We compare our simulations with experiments from neonatal and adult wild-type brain slices and multiple knockouts. Furthermore, we study co–culturing of slices with synchronized neonatal wild-type slices. The extreme complexity of the spatio-temporal patterns is quantified using empirical orthogonal functions (EOFs). The experimental reduction of AVP coupling leads to surprising observations. In double knockouts, inhibition of AVP signaling can improve synchrony, whereas, in triple knockouts, coherency is reduced. Our network modeling shows that these counter-intuitive observations can be explained by an antagonistic action of VIP and AVP signaling. The agreement of experiments and simulations suggests that quite complex spatio-temporal patterns can appear as emergent properties of oscillator networks with dual coupling mechanisms.

NAD metabolism and the SLC34 family: evidence for a liver-kidney axis regulating inorganic phosphate

The solute carrier 34 (SLC34) family of membrane transporters is a major contributor to Pi homeostasis. Many factors are involved in regulating the SLC34 family. The roles of the bone mineral metabolism factors parathyroid hormone (PTH) and fibroblast growth factor 23 (FGF23) in Pi homeostasis are well studied. Intracellular Pi is thought to be involved in energy metabolism, such as ATP production. Under certain conditions of altered energy metabolism, plasma Pi concentrations are affected by the regulation of a Pi shift into cells or release from the tissues. We recently investigated the mechanism of hepatectomy-related hypophosphatemia, which is thought to involve an unknown phosphaturic factor. Hepatectomy-related hypophosphatemia is due to impaired nicotinamide adenine dinucleotide (NAD) metabolism through its effects on the SLC34 family in the liver-kidney axis. The oxidized form of NAD, NAD⁺, is an essential cofactor in various cellular biochemical reactions. Levels of NAD⁺ and its reduced form NADH vary with the availability of dietary energy and nutrients. Nicotinamide phosphoribosyltransferase (Nampt) generates a key NAD⁺ intermediate, nicotinamide mononucleotide, from nicotinamide and 5-phosphoribosyl 1-pyrophosphate. The liver, an important organ of NAD metabolism, is thought to release metabolic products such as nicotinamide and may control NAD metabolism in other organs. Moreover, NAD is an important regulator of the circadian rhythm. Liver-specific Nampt-deficient mice and heterozygous Nampt mice have abnormal daily plasma Pi concentration oscillations. These data indicate that NAD metabolism in the intestine, liver, and kidney is closely related to Pi metabolism through the SLC34 family. Here, we review the relationship between the SLC34 family and NAD metabolism based on our recent studies.

Modeling clock-related metabolic syndrome due to conflicting light and food cues

Most organisms possess a light- and food- entrainable circadian clock system enabling their adaptation to daily environmental changes in sunlight and food availability. The mammalian circadian system is composed of multiple clocks throughout the body. These local clocks are entrained by nutrient, neural, endocrine and temperature cues and drive diverse physiological functions including metabolism. In particular, the clock of the pancreatic β cell rhythmically regulates the transcription of genes involved in glucose-stimulated insulin secretion. Perturbations of this fine-tuned oscillatory network increase the susceptibility to diseases. Besides chronic jet lag and shift work, common perturbations are ill-timed eating patterns which can lead to metabolic troubles (such as hypoinsulinemia). We have built a mathematical model describing the clock-dependent pancreatic regulation of glucose homeostasis in rodents. After calibrating the model using experimental data, we have investigated the effect of restricting food access to the normal rest phase. Our simulations show that the conflict between the light-dark cycle and the feeding-fasting cycle creates a differential phase shift in the expression of core clock genes (consistent with experimental observations). Our model further predicts that this induces a non-concomitance between nutrient cues and clock-controlled cues driving metabolic outputs which results in hypoinsulinemia, hyperglycemia as well as in a loss of food anticipation.

Co-existing feedback loops generate tissue-specific circadian rhythms

The analysis of tissue-specific data-based models of the gene regulatory network of the mammalian circadian clock reveals organ-specific synergies of feedback loops.

Gene regulatory feedback loops generate autonomous circadian rhythms in mammalian tissues. The well-studied core clock network contains many negative and positive regulations. Multiple feedback loops have been discussed as primary rhythm generators but the design principles of the core clock and differences between tissues are still under debate. Here we use global optimization techniques to fit mathematical models to circadian gene expression profiles for different mammalian tissues. It turns out that for every investigated tissue multiple model parameter sets reproduce the experimental data. We extract for all model versions the most essential feedback loops and find auto-inhibitions of period and cryptochrome genes, Bmal1–Rev-erb-α loops, and repressilator motifs as possible rhythm generators. Interestingly, the essential feedback loops differ between tissues, pointing to specific design principles within the hierarchy of mammalian tissue clocks. Self-inhibitions of Per and Cry genes are characteristic for models of suprachiasmatic nucleus clocks, whereas in liver models many loops act in synergy and are connected by a repressilator motif. Tissue-specific use of a network of co-existing synergistic feedback loops could account for functional differences between organs.

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.

Predicted effect of circadian clock modulation of NHE3 of a proximal tubule cell on sodium transport

Major renal functions such as renal blood flow, glomerular filtration rate, and urinary excretion are known to exhibit circadian oscillations. However, the underlying mechanisms that govern these variations have yet to be fully elucidated. To better understand the impact of the circadian clock on renal solute and water transport, we have developed a computational model of the renal circadian clock and coupled that model to an epithelial transport model of the proximal convoluted cell of the rat kidney. The activity of the Na⁺-H⁺ exchanger 3 (NHE3) is assumed to be regulated by changes in transcription of the NHE3 mRNA due to regulation by circadian clock proteins. The model predicts the rhythmic oscillations in NHE3 activity, which gives rise to significant daily fluctuations in Na⁺ and water transport of the proximal tubule cell. Additionally, the model predicts that 1) mutation in period 2 (Per2) or cryptochrome 1 (Cry1) preserves the circadian rhythm and modestly raises Na⁺ reabsorption; 2) mutation in Bmal1 or CLOCK eliminates the circadian rhythm and modestly lowers Na⁺ reabsorption; 3) mutation in Rev-Erb or ROR-related orphan receptor (Ror) has minimal impact on the circadian oscillations. The model represents the first step in building a tool set aimed at increasing our understanding of how the molecular clock affects renal ion transport and renal function, which likely has important implications for kidney disease.

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

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

The sodium phosphate cotransporter family and nicotinamide phosphoribosyltransferase contribute to the daily oscillation of plasma inorganic phosphate concentration

Circulating inorganic phosphate exhibits a remarkable daily oscillation based on food intake. In humans and rodents, the daily oscillation in response to food intake may be coordinated to control the intestinal absorption, renal excretion, cellular shifts, and extracellular concentration of inorganic phosphate. However, mechanisms regulating the resulting oscillation are unknown. Here we investigated the roles of the sodium phosphate cotransporter SLC34 (Npt2) family and nicotinamide phosphoribosyltransferase (Nampt) in the daily oscillation of plasma inorganic phosphate levels. First, it is roughly linked to urinary inorganic phosphate excretion. Second, expression of renal Npt2a and Npt2c, and intestinal Npt2b proteins also exhibit a dynamic daily oscillation. Analyses of Npt2a, Npt2b, and Npt2c knockout mice revealed the importance of renal inorganic phosphate reabsorption and cellular inorganic phosphate shifts in the daily oscillation. Third, experiments in which nicotinamide and a specific Nampt inhibitor (FK866) were administered in the active and rest phases revealed that the Nampt/NAD⁺ system is involved in renal inorganic phosphate excretion. Additionally, for cellular shifts, liver-specific Nampt deletion disturbed the daily oscillation of plasma phosphate during the rest but not the active phase. In systemic Nampt^+/- mice, NAD levels were significantly reduced in the liver, kidney, and intestine, and the daily oscillation (active and rest phases) of the plasma phosphate concentration was attenuated. Thus, the Nampt/NAD⁺ system for Npt2 regulation and cellular shifts to tissues such as the liver play an important role in generating daily oscillation of plasma inorganic phosphate levels.

The Ink4a/Arf locus operates as a regulator of the circadian clock modulating RAS activity

The mammalian circadian clock and the cell cycle are two major biological oscillators whose coupling influences cell fate decisions. In the present study, we use a model-driven experimental approach to investigate the interplay between clock and cell cycle components and the dysregulatory effects of RAS on this coupled system. In particular, we focus on the Ink4a/Arf locus as one of the bridging clock-cell cycle elements. Upon perturbations by the rat sarcoma viral oncogene (RAS), differential effects on the circadian phenotype were observed in wild-type and Ink4a/Arf knock-out mouse embryonic fibroblasts (MEFs), which could be reproduced by our modelling simulations and correlated with opposing cell cycle fate decisions. Interestingly, the observed changes can be attributed to in silico phase shifts in the expression of core-clock elements. A genome-wide analysis revealed a set of differentially expressed genes that form an intricate network with the circadian system with enriched pathways involved in opposing cell cycle phenotypes. In addition, a machine learning approach complemented by cell cycle analysis classified the observed cell cycle fate decisions as dependent on Ink4a/Arf and the oncogene RAS and highlighted a putative fine-tuning role of Bmal1 as an elicitor of such processes, ultimately resulting in increased cell proliferation in the Ink4a/Arf knock-out scenario. This indicates that the dysregulation of the core-clock might work as an enhancer of RAS-mediated regulation of the cell cycle. Our combined in silico and in vitro approach highlights the important role of the circadian clock as an Ink4a/Arf-dependent modulator of oncogene-induced cell fate decisions, reinforcing its function as a tumour-suppressor and the close interplay between the clock and the cell cycle network.

In mammals, the circadian clock controls the punctual regulation of biological processes, which, in turn, affect physiology and behaviour, allowing for the synchronisation of internal time to environmental light-dark cycles. Malfunctions of the circadian clock are associated with pathological phenotypes including cancer. Given the range of molecular time-dependent processes, including metabolism, DNA repair, and the cell cycle, the clock is hypothesised to act as a tumour suppressor. With the help of mathematical modelling and whole-genome analysis combined with machine learning, we investigated the RAS-dependent dysregulation of the circadian clock. We find that the tumour-suppressor Ink4a/Arf acts as a key mediator of RAS oncogene-induced changes in the circadian system, thereby mediating the interplay between the clock and the cell cycle.

Computational Modeling in Liver Surgery

The need for extended liver resection is increasing due to the growing incidence of liver tumors in aging societies. Individualized surgical planning is the key for identifying the optimal resection strategy and to minimize the risk of postoperative liver failure and tumor recurrence. Current computational tools provide virtual planning of liver resection by taking into account the spatial relationship between the tumor and the hepatic vascular trees, as well as the size of the future liver remnant. However, size and function of the liver are not necessarily equivalent. Hence, determining the future liver volume might misestimate the future liver function, especially in cases of hepatic comorbidities such as hepatic steatosis. A systems medicine approach could be applied, including biological, medical, and surgical aspects, by integrating all available anatomical and functional information of the individual patient. Such an approach holds promise for better prediction of postoperative liver function and hence improved risk assessment. This review provides an overview of mathematical models related to the liver and its function and explores their potential relevance for computational liver surgery. We first summarize key facts of hepatic anatomy, physiology, and pathology relevant for hepatic surgery, followed by a description of the computational tools currently used in liver surgical planning. Then we present selected state-of-the-art computational liver models potentially useful to support liver surgery. Finally, we discuss the main challenges that will need to be addressed when developing advanced computational planning tools in the context of liver surgery.