Development and validation of computational models for mammalian circadian oscillators

Circadian rhythms are endogenous rhythms with a cycle length of approximately 24 h. Rhythmic production of specific proteins within pacemaker structures is the basis for these physiological and behavioral rhythms. Prior work on mathematical modeling of molecular circadian oscillators has focused on the fruit fly, Drosophila melanogaster. Recently, great advances have been made in our understanding of the molecular basis of circadian rhythms in mammals. Mathematical models of the mammalian circadian oscillator are needed to piece together diverse data, predict experimental results, and help us understand the clock as a whole. Our objectives are to develop mathematical models of the mammalian circadian oscillator, generate and test predictions from these models, gather information on the parameters needed for model development, integrate the molecular model with an existing model of the influence of light and rhythmicity on human performance, and make models available in BioSpice so that they can be easily used by the general community. Two new mammalian models have been developed, and experimental data are summarized. These studies have the potential to lead to new strategies for resetting the circadian clock. Manipulations of the circadian clock can be used to optimize performance by promoting alertness and physiological synchronization.     

Models of cardiac excitation-contraction coupling in ventricular myocytes

Mathematical and computational modeling of cardiac excitation-contraction coupling has produced considerable insights into how the heart muscle contracts. With the increase in biophysical and physiological data available, the modeling has become more sophisticated with investigations spanning in scale from molecular components to whole cells. These modeling efforts have provided insight into cardiac excitation-contraction coupling that advanced and complemented experimental studies. One goal is to extend these detailed cellular models to model the whole heart. While this has been done with mechanical and electophysiological models, the complexity and fast time course of calcium dynamics have made inclusion of detailed calcium dynamics in whole heart models impractical. Novel methods such as the probability density approach and moment closure technique which increase computational efficiency might make this tractable.     

Chlamydomonas reinhardtii as a unicellular model for circadian rhythm analysis

Chlamydomonas reinhardtii has been used as an experimental model organism for circadian rhythm research for more than 30 yr. Some of the physiological rhythms of this alga are well established, and several clock mutants have been isolated. The cloning of clock genes from these mutant strains by positional cloning is under way and should give new insights into the mechanism of the circadian clock. In a spectacular space experiment, the question of the existence of an endogenous clock vs. an exogenous mechanism has been studied in this organism. With the emergence of molecular analysis of circadian rhythms in plants in 1985, a circadian gene expression pattern of several nuclear and chloroplast genes was detected. Evidence is now accumulating that shows circadian control at the translational level. In addition, the gating of the cell cycle by the circadian clock has been analyzed. This review focuses on the different aspects of circadian rhythm research in C. reinhardtii over the past 30 yr. The suitability of Chlamydomonas as a model system in chronobiology research and the adaptive significance of the observed rhythms will be discussed.     

Effects of Different PER Translational Kinetics on the Dynamics of a Core Circadian Clock Model

Living beings display self-sustained daily rhythms in multiple biological processes, which persist in the absence of external cues since they are generated by endogenous circadian clocks. The period (per) gene is a central player within the core molecular mechanism for keeping circadian time in most animals. Recently, the modulation PER translation has been reported, both in mammals and flies, suggesting that translational regulation of clock components is important for the proper clock gene expression and molecular clock performance. Because translational regulation ultimately implies changes in the kinetics of translation and, therefore, in the circadian clock dynamics, we sought to study how and to what extent the molecular clock dynamics is affected by the kinetics of PER translation. With this objective, we used a minimal mathematical model of the molecular circadian clock to qualitatively characterize the dynamical changes derived from kinetically different PER translational mechanisms. We found that the emergence of self-sustained oscillations with characteristic period, amplitude, and phase lag (time delays) between per mRNA and protein expression depends on the kinetic parameters related to PER translation. Interestingly, under certain conditions, a PER translation mechanism with saturable kinetics introduces longer time delays than a mechanism ruled by a first-order kinetics. In addition, the kinetic laws of PER translation significantly changed the sensitivity of our model to parameters related to the synthesis and degradation of per mRNA and PER degradation. Lastly, we found a set of parameters, with realistic values, for which our model reproduces some experimental results reported recently for Drosophila melanogaster and we present some predictions derived from our analysis.     

Chlamydomonas reinhardtii as a unicellular model for circadian rhythm analysis

Chlamydomonas reinhardtii has been used as an experimental model organism for circadian rhythm research for more than 30 yr. Some of the physiological rhythms of this alga are well established, and several clock mutants have been isolated. The cloning of clock genes from these mutant strains by positional cloning is under way and should give new insights into the mechanism of the circadian clock. In a spectacular space experiment, the question of the existence of an endogenous clock vs. an exogenous mechanism has been studied in this organism. With the emergence of molecular analysis of circadian rhythms in plants in 1985, a circadian gene expression pattern of several nuclear and chloroplast genes was detected. Evidence is now accumulating that shows circadian control at the translational level. In addition, the gating of the cell cycle by the circadian clock has been analyzed. This review focuses on the different aspects of circadian rhythm research in C. reinhardtii over the past 30 yr. The suitability of Chlamydomonas as a model system in chronobiology research and the adaptive significance of the observed rhythms will be discussed.     

The network of time: understanding the molecular circadian system

The circadian clock provides a temporal structure that modulates biological functions from the level of gene expression to performance and behaviour. Pioneering work on the fruitfly Drosophila has provided a basis for understanding how the temporal sequence of daily events is controlled in mammals. New insights have come from work on mammals, specifically from studying the daily activity profiles of clock mutant mice; from more detailed recordings of clock gene expression under different experimental conditions and in different tissues; and from the discovery and analysis of a growing number of additional clock genes. These new results are moving the model paradigm away from a simple negative feedback loop to a molecular network. Understanding the coupling and interactions of this network will help us to understand the evolution of the circadian system, advance medical diagnosis and treatment, improve the health of shift workers and frequent travellers, and will generally enable the treatment of clock-related pathologies.     

Chlamydomonas reinhardtii as a new model system for studying the molecular basis of the circadian clock

The genome of the unicellular green alga Chlamydomonas reinhardtii has both plant-like and animal-like genes. It is of interest to know which types of clock genes this alga has. Recent forward and reverse genetic studies have revealed that its clock has both plant-like and algal clock components. In addition, since C. reinhardtii is a useful model organism also called "green yeast", the identification of clock genes will make C. reinhardtii a powerful model for studying the molecular basis of the eukaryotic circadian clock. In this review, we describe our forward genetic approach in C. reinhardtii and discuss some recent findings about its circadian clock.     

Solving the mystery of human sleep schedules one mutation at a time

Abstract

Sleep behavior remains one of the most enigmatic areas of life. The unanswered questions range from “why do we sleep?” to “how we can improve sleep in today’s society?” Identification of mutations responsible for altered circadian regulation of human sleep lead to unique opportunities for probing these territories. In this review, we summarize causative circadian mutations found from familial genetic studies to date. We also describe how these mutations mechanistically affect circadian function and lead to altered sleep behaviors, including shifted or shortening of sleep patterns. In addition, we discuss how the investigation of mutations can not only expand our understanding of the molecular mechanisms regulating the circadian clock and sleep duration, but also bridge the pathways between clock/sleep and other human physiological conditions and ailments such as metabolic regulation and migraine headaches.     

Combining Theoretical and Experimental Approaches to Understand the Circadian Clock

This review is intended as a summary of our work carried out as part of the German Research Association (DFG) Center Program on Circadian Rhythms. Over the last six years, our approach to understanding circadian systems combined theoretical and experimental tools, and Gonyaulax and Neurospora have proven ideal for these efforts. Both of these model organisms demonstrate that even simple circadian systems can have multiple light input pathways and more than one rhythm generator. They have both been used to elaborate basic circadian features in conjunction with formal models. The models introduce the “zeitnehmer,” i.e., a clock‐regulated input pathway, to the conceptual framework of circadian systems, and proposes networks of individual feedbacks as the basis for circadian rhythmicity.     

Interactions of circadian clock genes with the hallmarks of cancer

The molecular machinery of the circadian clock regulates the expression of many genes and processes in the organism, allowing the adaptation of cellular activities to the daily light-dark cycles.Disruption of the circadian rhythm can lead to various pathologies, including cancer. Thus, disturbance of the normal circadian clock at both genetic and environmental levels has been described as an independent risk factor for cancer. In addition, researchers have proposed that circadian genes may have a tissue-dependent and/or context-dependent role in tumorigenesis and may function both as tumor suppressors and oncogenes.Finally, circadian clock core genes may trigger or at least be involved in different hallmarks of cancer. Hence, expanding the knowledge of the molecular basis of the circadian clock would be helpful to identify new prognostic markers of tumorigenesis and potential therapeutic targets.     

Potential Conservation of Circadian Clock Proteins in the phylum Nematoda as Revealed by Bioinformatic Searches

Although several circadian rhythms have been described in C. elegans, its molecular clock remains elusive. In this work we employed a novel bioinformatic approach, applying probabilistic methodologies, to search for circadian clock proteins of several of the best studied circadian model organisms of different taxa (Mus musculus, Drosophila melanogaster, Neurospora crassa, Arabidopsis thaliana and Synechoccocus elongatus) in the proteomes of C. elegans and other members of the phylum Nematoda. With this approach we found that the Nematoda contain proteins most related to the core and accessory proteins of the insect and mammalian clocks, which provide new insights into the nematode clock and the evolution of the circadian system.     

Data-Derived Modeling Characterizes Plasticity of MAPK Signaling in Melanoma

The majority of melanomas have been shown to harbor somatic mutations in the RAS-RAF-MEK-MAPK and PI3K-AKT pathways, which play a major role in regulation of proliferation and survival. The prevalence of these mutations makes these kinase signal transduction pathways an attractive target for cancer therapy. However, tumors have generally shown adaptive resistance to treatment. This adaptation is achieved in melanoma through its ability to undergo neovascularization, migration and rearrangement of signaling pathways. To understand the dynamic, nonlinear behavior of signaling pathways in cancer, several computational modeling approaches have been suggested. Most of those models require that the pathway topology remains constant over the entire observation period. However, changes in topology might underlie adaptive behavior to drug treatment. To study signaling rearrangements, here we present a new approach based on Fuzzy Logic (FL) that predicts changes in network architecture over time. This adaptive modeling approach was used to investigate pathway dynamics in a newly acquired experimental dataset describing total and phosphorylated protein signaling over four days in A375 melanoma cell line exposed to different kinase inhibitors. First, a generalized strategy was established to implement a parameter-reduced FL model encoding non-linear activity of a signaling network in response to perturbation. Next, a literature-based topology was generated and parameters of the FL model were derived from the full experimental dataset. Subsequently, the temporal evolution of model performance was evaluated by leaving time-defined data points out of training. Emerging discrepancies between model predictions and experimental data at specific time points allowed the characterization of potential network rearrangement. We demonstrate that this adaptive FL modeling approach helps to enhance our mechanistic understanding of the molecular plasticity of melanoma.