Adrián E. Granada

Bio: Adrián E. Granada is an academic researcher from Charité. The author has contributed to research in topics: Entrainment (chronobiology) & Circadian clock. The author has an hindex of 10, co-authored 17 publications receiving 676 citations. Previous affiliations of Adrián E. Granada include Harvard University & Humboldt State University.

Coupling governs entrainment range of circadian clocks.

Abstract: Circadian clocks are endogenous oscillators driving daily rhythms in physiology and behavior. Synchronization of these timers to environmental light–dark cycles (‘entrainment’) is crucial for an organism’s fitness. Little is known about which oscillator qualities determine entrainment, i.e., entrainment range, phase and amplitude. In a systematic theoretical and experimental study, we uncovered these qualities for circadian oscillators in the suprachiasmatic nucleus (SCN—the master clock in mammals) and the lung (a peripheral clock): (i) the ratio between stimulus (zeitgeber) strength and oscillator amplitude and (ii) the rigidity of the oscillatory system (relaxation rate upon perturbation) determine entrainment properties. Coupling among oscillators affects both qualities resulting in increased amplitude and rigidity. These principles explain our experimental findings that lung clocks entrain to extreme zeitgeber cycles, whereas SCN clocks do not. We confirmed our theoretical predictions by showing that pharmacological inhibition of coupling in the SCN leads to larger ranges of entrainment. These differences between master and the peripheral clocks suggest that coupling-induced rigidity in the SCN filters environmental noise to create a robust circadian system.

Human chronotypes from a theoretical perspective.

Abstract: The endogenous circadian timing system has evolved to synchronize an organism to periodically recurring environmental conditions. Those external time cues are called Zeitgebers. When entrained by a Zeitgeber, the intrinsic oscillator adopts a fixed phase relation to the Zeitgeber. Here, we systematically study how the phase of entrainment depends on clock and Zeitgeber properties. We combine numerical simulations of amplitude-phase models with predictions from analytically tractable models. In this way we derive relations between the phase of entrainment to the mismatch between the endogenous and Zeitgeber period, the Zeitgeber strength, and the range of entrainment. A core result is the “180° rule” asserting that the phase varies over a range of about 180° within the entrainment range. The 180° rule implies that clocks with a narrow entrainment range (“strong oscillators”) exhibit quite flexible entrainment phases. We argue that this high sensitivity of the entrainment phase contributes to the wide range of human chronotypes.

Tuning the phase of circadian entrainment.

Abstract: The circadian clock coordinates daily physiological, metabolic and behavioural rhythms. These endogenous oscillations are synchronized with external cues (‘zeitgebers’), such as daily light and temperature cycles. When the circadian clock is entrained by a zeitgeber, the phase difference ψ between the phase of a clock-controlled rhythm and the phase of the zeitgeber is of fundamental importance for the fitness of the organism. The phase of entrainment ψ depends on the mismatch between the intrinsic period τ and the zeitgeber period T and on the ratio of the zeitgeber strength to oscillator amplitude. Motivated by the intriguing complexity of empirical data and by our own experiments on temperature entrainment of mouse suprachiasmatic nucleus (SCN) slices, we present a theory on how clock and zeitgeber properties determine the phase of entrainment. The wide applicability of the theory is demonstrated using mathematical models of different complexity as well as by experimental data. Predictions of the theory are confirmed by published data on Neurospora crassa strains for different period mismatches τ − T and varying photoperiods. We apply a novel regression technique to analyse entrainment of SCN slices by temperature cycles. We find that mathematical models can explain not only the stable asymptotic phase of entrainment, but also transient phase dynamics. Our theory provides the potential to explore seasonal variations of circadian rhythms, jet lag and shift work in forthcoming studies.

How to Achieve Fast Entrainment? The Timescale to Synchronization

Abstract: Entrainment, where oscillators synchronize to an external signal, is ubiquitous in nature. The transient time leading to entrainment plays a major role in many biological processes. Our goal is to unveil the specific dynamics that leads to fast entrainment. By studying a generic model, we characterize the transient time to entrainment and show how it is governed by two basic properties of an oscillator: the radial relaxation time and the phase velocity distribution around the limit cycle. Those two basic properties are inherent in every oscillator. This concept can be applied to many biological systems to predict the average transient time to entrainment or to infer properties of the underlying oscillator from the observed transients. We found that both a sinusoidal oscillator with fast radial relaxation and a spike-like oscillator with slow radial relaxation give rise to fast entrainment. As an example, we discuss the jet-lag experiments in the mammalian circadian pacemaker.

Phase response curves elucidating the dynamics of coupled oscillators.

Abstract: Phase response curves (PRCs) are widely used in circadian clocks, neuroscience, and heart physiology. They quantify the response of an oscillator to pulse-like perturbations. Phase response curves provide valuable information on the properties of oscillators and their synchronization. This chapter discusses biological self-sustained oscillators (circadian clock, physiological rhythms, etc.) in the context of nonlinear dynamics theory. Coupled oscillators can synchronize with different frequency ratios, can generate toroidal dynamics (superposition of independent frequencies), and may lead to deterministic chaos. These nonlinear phenomena can be analyzed with the aid of a phase transition curve, which is intimately related to the phase response curve. For illustration purposes, this chapter discusses a model of circadian oscillations based on a delayed negative feedback. In a second part, the chapter provides a step-by-step recipe to measure phase response curves. It discusses specifications of this recipe for circadian rhythms, heart rhythms, neuronal spikes, central pattern generators, and insect communication. Finally, it stresses the predictive power of measured phase response curves. PRCs can be used to quantify the coupling strength of oscillations, to classify oscillator types, and to predict the complex dynamics of periodically driven oscillations.

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

Central and Peripheral Circadian Clocks in Mammals

Abstract: The circadian system of mammals is composed of a hierarchy of oscillators that function at the cellular, tissue, and systems levels. A common molecular mechanism underlies the cell-autonomous circadian oscillator throughout the body, yet this clock system is adapted to different functional contexts. In the central suprachiasmatic nucleus (SCN) of the hypothalamus, a coupled population of neuronal circadian oscillators acts as a master pacemaker for the organism to drive rhythms in activity and rest, feeding, body temperature, and hormones. Coupling within the SCN network confers robustness to the SCN pacemaker, which in turn provides stability to the overall temporal architecture of the organism. Throughout the majority of the cells in the body, cell-autonomous circadian clocks are intimately enmeshed within metabolic pathways. Thus, an emerging view for the adaptive significance of circadian clocks is their fundamental role in orchestrating metabolism.

Molecular components of the Mammalian circadian clock

Abstract: Mammals synchronize their circadian activity primarily to the cycles of light and darkness in the environment This is achieved by ocular photoreception relaying signals to the suprachiasmatic nucleus (SCN) in the hypothalamus Signals from the SCN cause the synchronization of independent circadian clocks throughout the body to appropriate phases Signals that can entrain these peripheral clocks include humoral signals, metabolic factors, and body temperature At the level of individual tissues, thousands of genes are brought to unique phases through the actions of a local transcription/translation-based feedback oscillator and systemic cues In this molecular clock, the proteins CLOCK and BMAL1 cause the transcription of genes which ultimately feedback and inhibit CLOCK and BMAL1 transcriptional activity Finally, there are also other molecular circadian oscillators which can act independently of the transcription-based clock in all species which have been tested

The Mathematical Model

Abstract: Let X(t) be the number of tumor cells at time t, and Pr{X(t) = n} = pn(t) is the density of X. A “birth”, i.e., an increase of one of the total population of cancer cells, can occur either by mutation of a normal cell caused by the action of the carcinogen, consisting of randomly (Poisson) distributed hits, or by reproduction of existing cancer cells. A death of a tumor cell occurs as an additive combination of non-immunological and immunological elements. Once a tumor is initiated by carcinogenic action, it undergoes a birth and death process with infinitesimal birth rate linear and infinitesimal death rate composed of a linear and a nonlinear term, the former due to non-immunological deaths, the latter to immunological feedback. The death rate per tumor cell due to immunological response is proportional to the total number of antigen-producing (tumor) cells; thus, the total death rate is quadratic. Although this assumes a very simple mechanism for the action of immunological feedback, it is nevertheless a first step.

Genetics of circadian rhythms in Mammalian model organisms.

Abstract: The mammalian circadian system is a complex hierarchical temporal network which is organized around an ensemble of uniquely coupled cells comprising the principal circadian pacemaker in the suprachiasmatic nucleus of the hypothalamus. This central pacemaker is entrained each day by the environmental light/dark cycle and transmits synchronizing cues to cell-autonomous oscillators in tissues throughout the body. Within cells of the central pacemaker and the peripheral tissues, the underlying molecular mechanism by which oscillations in gene expression occur involves interconnected feedback loops of transcription and translation. Over the past 10 years, we have learned much regarding the genetics of this system, including how it is particularly resilient when challenged by single-gene mutations, how accessory transcriptional loops enhance the robustness of oscillations, how epigenetic mechanisms contribute to the control of circadian gene expression, and how, from coupled neuronal networks, emergent clock properties arise. Here, we will explore the genetics of the mammalian circadian system from cell-autonomous molecular oscillations, to interactions among central and peripheral oscillators and ultimately, to the daily rhythms of behavior observed in the animal.