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

Photosynthetic Entrainment of the Circadian Clock Facilitates Plant Growth under Environmental Fluctuations: Perspectives from an Integrated Model of Phase Oscillator and Phloem Transportation

Plants need to avoid carbon starvation and resultant growth inhibition under fluctuating light environments to ensure optimal growth and reproduction. As diel patterns of carbon metabolism are influenced by the circadian clock, appropriate regulation of the clock is essential for plants to properly manage their carbon resources. For proper adjustment of the circadian phase, higher plants utilize environmental signals such as light or temperature and metabolic signals such as photosynthetic products; the importance of the latter as phase regulators has been recently elucidated. A mutant of Arabidopsis thaliana that is deficient in phase response to sugar has been shown, under fluctuating light conditions, to be unable to adjust starch turnover and to realize carbon homeostasis. Whereas, the effects of light entrainment on growth and survival of higher plants are well studied, the impact of phase regulation by sugar remains unknown. Here we show that endogenous sugar entrainment facilitates plant growth. We integrated two mathematical models, one describing the dynamics of carbon metabolism in A. thaliana source leaves and the other growth of sink tissues dependent on sucrose translocation from the source. The integrated model predicted that sugar-sensitive plants grow faster than sugar-insensitive plants under constant as well as changing photoperiod conditions. We found that sugar entrainment enables efficient carbon investment for growth by stabilizing sucrose supply to sink tissues. Our results highlight the importance of clock entrainment by both exogenous and endogenous signals for optimizing growth and increasing fitness.

Adjustment of the Arabidopsis circadian oscillator by sugar signalling dictates the regulation of starch metabolism

Arabidopsis plants store part of the carbon fixed by photosynthesis as starch to sustain growth at night. Two competing hypotheses have been proposed to explain this diel starch turnover based on either the measurement of starch abundance with respect to circadian time, or the sensing of sugars to feedback to the circadian oscillator to dynamically adjust the timing of starch turnover. We report a phase oscillator model that permitted derivation of the ideal responses of the circadian regulation of starch breakdown to maintain sucrose homeostasis. Testing the model predictions using a sugar-unresponsive mutant of Arabidopsis demonstrated that the dynamics of starch turnover arise from the circadian clock measuring and responding to the rate of change of cellular sucrose. Our theory and experiments suggest that starch turnover is controlled by the circadian clock acting as a dynamic homeostat responding to sucrose signals to maintain carbon homeostasis.

Circadian and Feeding Rhythms Orchestrate the Diurnal Liver Acetylome

Lysine acetylation is involved in various biological processes and is considered a key reversible post-translational modification in the regulation of gene expression, enzyme activity, and subcellular localization. This post-translational modification is therefore highly relevant in the context of circadian biology, but its characterization on the proteome-wide scale and its circadian clock dependence are still poorly described. Here, we provide a comprehensive and rhythmic acetylome map of the mouse liver. Rhythmic acetylated proteins showed subcellular localization-specific phases that correlated with the related metabolites in the regulated pathways. Mitochondrial proteins were over-represented among the rhythmically acetylated proteins and were highly correlated with SIRT3-dependent deacetylation. SIRT3 activity being nicotinamide adenine dinucleotide (NAD)+ level-dependent, we show that NAD+ is orchestrated by both feeding rhythms and the circadian clock through the NAD+ salvage pathway but also via the nicotinamide riboside pathway. Hence, the diurnal acetylome relies on a functional circadian clock and affects important diurnal metabolic pathways in the mouse liver.

Period Robustness and Entrainability of the Kai System to Changing Nucleotide Concentrations

Circadian clocks must be able to entrain to time-varying signals to keep their oscillations in phase with the day-night rhythm. On the other hand, they must also exhibit input compensation: their period must remain approximately one day in different constant environments. The posttranslational oscillator of the Kai system can be entrained by transient or oscillatory changes in the ATP fraction, yet is insensitive to constant changes in this fraction. We study in three different models of this system how these two seemingly conflicting criteria are met. We find that one of these (our recently published Paijmans model) exhibits the best tradeoff between input compensation and entrainability: on the footing of equal phase-response curves, it exhibits the strongest input compensation. Performing stochastic simulations at the level of individual hexamers allows us to identify a new, to our knowledge, mechanism, which is employed by the Paijmans model to achieve input compensation: at lower ATP fraction, the individual hexamers make a shorter cycle in the phosphorylation state space, which compensates for the slower pace at which they traverse the cycle.

Systems Chronotherapeutics

Chronotherapeutics aim at treating illnesses according to the endogenous biologic rhythms, which moderate xenobiotic metabolism and cellular drug response. The molecular clocks present in individual cells involve approximately fifteen clock genes interconnected in regulatory feedback loops. They are coordinated by the suprachiasmatic nuclei, a hypothalamic pacemaker, which also adjusts the circadian rhythms to environmental cycles. As a result, many mechanisms of diseases and drug effects are controlled by the circadian timing system. Thus, the tolerability of nearly 500 medications varies by up to fivefold according to circadian scheduling, both in experimental models and/or patients. Moreover, treatment itself disrupted, maintained, or improved the circadian timing system as a function of drug timing. Improved patient outcomes on circadian-based treatments (chronotherapy) have been demonstrated in randomized clinical trials, especially for cancer and inflammatory diseases. However, recent technological advances have highlighted large interpatient differences in circadian functions resulting in significant variability in chronotherapy response. Such findings advocate for the advancement of personalized chronotherapeutics through interdisciplinary systems approaches. Thus, the combination of mathematical, statistical, technological, experimental, and clinical expertise is now shaping the development of dedicated devices and diagnostic and delivery algorithms enabling treatment individualization. In particular, multiscale systems chronopharmacology approaches currently combine mathematical modeling based on cellular and whole-body physiology to preclinical and clinical investigations toward the design of patient-tailored chronotherapies. We review recent systems research works aiming to the individualization of disease treatment, with emphasis on both cancer management and circadian timing system–resetting strategies for improving chronic disease control and patient outcomes.

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.

Distinct but complementary contributions of PPAR isotypes to energy homeostasis

Peroxisome proliferator-activated receptors (PPARs) regulate energy metabolism and hence are therapeutic targets in metabolic diseases such as type 2 diabetes and non-alcoholic fatty liver disease. While they share anti-inflammatory activities, the PPAR isotypes distinguish themselves by differential actions on lipid and glucose homeostasis. In this Review we discuss the complementary and distinct metabolic effects of the PPAR isotypes together with the underlying cellular and molecular mechanisms, as well as the synthetic PPAR ligands that are used in the clinic or under development. We highlight the potential of new PPAR ligands with improved efficacy and safety profiles in the treatment of complex metabolic disorders.

Computational modeling of the cell-autonomous mammalian circadian oscillator

This review summarizes various mathematical models of cell-autonomous mammalian circadian clock. We present the basics necessary for understanding of the cell-autonomous mammalian circadian oscillator, modern experimental data essential for its reconstruction and some special problems related to the validation of mathematical circadian oscillator models. This work compares existing mathematical models of circadian oscillator and the results of the computational studies of the oscillating systems. Finally, we discuss applications of the mathematical models of mammalian circadian oscillator for solving specific problems in circadian rhythm biology.