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Albert Goldbeter

Publications and source records attributed to Albert Goldbeter.

12 recordsLinked to original sources
PubMed2004

Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms.

We extend the study of a computational model recently proposed for the mammalian circadian clock (Proc. Natl Acad. Sci. USA 100 (2003) 7051). The model, based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, and Clock genes, can give rise to sustained circadian oscillations in conditions of continuous darkness. These limit cycle oscillations correspond to circadian rhythms autonomously generated by suprachiasmatic nuclei and by some peripheral tissues. By using different sets of parameter values producing circadian oscillations, we compare the effect of the various parameters and show that both the occurrence and the period of the oscillations are generally most sensitive to parameters related to synthesis or degradation of Bmal1 mRNA and BMAL1 protein. The mechanism of circadian oscillations relies on the formation of an inactive complex between PER and CRY and the activators CLOCK and BMAL1 that enhance Per and Cry expression. Bifurcation diagrams and computer simulations nevertheless indicate the possible existence of a second source of oscillatory behavior. Thus, sustained oscillations might arise from the sole negative autoregulation of Bmal1 expression. This second oscillatory mechanism may not be functional in physiological conditions, and its period need not necessarily be circadian. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark (LD) cycles. Long-term suppression of circadian oscillations by a single light pulse can occur in the model when a stable steady state coexists with a stable limit cycle. The phase of the oscillations upon entrainment in LD critically depends on the parameters that govern the level of CRY protein. Small changes in the parameters governing CRY levels can shift the peak in Per mRNA from the L to the D phase, or can prevent entrainment. The results are discussed in relation to physiological disorders of the sleep-wake cycle linked to perturbations of the human circadian clock, such as the familial advanced sleep phase syndrome or the non-24h sleep-wake syndrome.

ARNTL Transcription Factors↗
PubMed2003

Toward a detailed computational model for the mammalian circadian clock.

We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression.

ARNTL Transcription Factors↗
PubMed2003

Oscillatory nucleocytoplasmic shuttling of the general stress response transcriptional activators Msn2 and Msn4 in Saccharomyces cerevisiae.

Msn2 and Msn4 are two related transcriptional activators that mediate a general response to stress in yeast Saccharomyces cerevisiae by eliciting the expression of specific sets of genes. In response to stress or nutritional limitation, Msn2 and Msn4 migrate from the cytoplasm to the nucleus. Using GFP-tagged constructs and high-resolution time-lapse video microscopy on single cells, we show that light emitted by the microscope also triggers this migration. Unexpectedly, the population of Msn2 or Msn4 molecules shuttles repetitively into and out of the nucleus with a periodicity of a few minutes. A large heterogeneity in the oscillatory response to stress is observed between individual cells. This periodic behavior, which can be induced by various types of stress, at intermediate stress levels, is not dependent upon protein synthesis and persists when the DNA-binding domain of Msn2 is removed. The cAMP-PKA pathway controls the sensitivity of the oscillatory nucleocytoplasmic shuttling. In the absence of PKA, Msn4 continues to oscillate while Msn2 is maintained in the nucleus. We show that a computational model based on the possibility that Msn2 and Msn4 participate in autoregulatory loops controlling their subcellular localization can account for the oscillatory behavior of the two transcription factors.

Binding Sites↗
PubMed2003

Stochastic models for circadian rhythms: effect of molecular noise on periodic and chaotic behaviour.

Circadian rhythms are endogenous oscillations that occur with a period close to 24 h in nearly all living organisms. These rhythms originate from the negative autoregulation of gene expression. Deterministic models based on such genetic regulatory processes account for the occurrence of circadian rhythms in constant environmental conditions (e.g., constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. When the numbers of protein and mRNA molecules involved in the oscillations are small, as may occur in cellular conditions, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering the stochastic version of a deterministic model previously proposed for circadian oscillations of the PER and TIM proteins and their mRNAs in Drosophila. The model is based on repression of the per and tim genes by a complex between the PER and TIM proteins. Numerical simulations of the stochastic version of the model are performed by means of the Gillespie method. The predictions of the stochastic approach compare well with those of the deterministic model with respect both to sustained oscillations of the limit cycle type and to the influence of the proximity from a bifurcation point beyond which the system evolves to stable steady state. Stochastic simulations indicate that robust circadian oscillations can emerge at the cellular level even when the maximum numbers of mRNA and protein molecules involved in the oscillations are of the order of only a few tens or hundreds. The stochastic model also reproduces the evolution to a strange attractor in conditions where the deterministic PER-TIM model admits chaotic behaviour. The difference between periodic oscillations of the limit cycle type and aperiodic oscillations (i.e. chaos) persists in the presence of molecular noise, as shown by means of Poincaré sections. The progressive obliteration of periodicity observed as the number of molecules decreases can thus be distinguished from the aperiodicity originating from chaotic dynamics. As long as the numbers of molecules involved in the oscillations remain sufficiently large (of the order of a few tens or hundreds, or more), stochastic models therefore provide good agreement with the predictions of the deterministic model for circadian rhythms.

Animals↗
PubMed2003

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.

Animals↗
PubMed2002

Computational approaches to cellular rhythms.

Oscillations arise in genetic and metabolic networks as a result of various modes of cellular regulation. In view of the large number of variables involved and of the complexity of feedback processes that generate oscillations, mathematical models and numerical simulations are needed to fully grasp the molecular mechanisms and functions of biological rhythms. Models are also necessary to comprehend the transition from simple to complex oscillatory behaviour and to delineate the conditions under which they arise. Examples ranging from calcium oscillations to pulsatile intercellular communication and circadian rhythms illustrate how computational biology contributes to clarify the molecular and dynamical bases of cellular rhythms.

Animals↗
PubMed2002

A model for the enhancement of fitness in cyanobacteria based on resonance of a circadian oscillator with the external light-dark cycle.

Fitness enhancement based on resonating circadian clocks has recently been demonstrated in cyanobacteria [Ouyang et al. (1998). Proc. Natl Acad. Sci. U.S.A.95, 8660-8664]. Thus, the competition between two cyanobacterial strains differing by the free-running period (FRP) of their circadian oscillations leads to the dominance of one or the other of the two strains, depending on the period of the external light-dark (LD) cycle. The successful strain is generally that which has an FRP closest to the period of the LD cycle. Of key importance for the resonance phenomenon are observations which indicate that the phase angle between the circadian oscillator and the LD cycle depends both on the latter cycle's length and on the FRP. We account for these experimental observations by means of a theoretical model which takes into account (i) cell growth, (ii) secretion of a putative cell growth inhibitor, and (iii) the existence of a cellular, light-sensitive circadian oscillator controlling growth as well as inhibitor secretion. Building on a previous analysis in which the phase angle was considered as a freely adjustable parameter [Roussel et al. (2000). J. theor. Biol.205, 321-340], we incorporate into the model a light-sensitive version of the van der Pol oscillator to represent explicitly the cellular circadian oscillator. In this way, the model automatically generates a phase angle between the circadian oscillator and the LD cycle which depends on the characteristic FRP of the strain and varies continuously with the period of the LD cycle. The model provides an explanation for the results of competition experiments between strains of different FRPs subjected to entrainment by LD cycles of different periods. The model further shows how the dominance of one strain over another in LD cycles can be reconciled with the observation that two strains characterized by different FRPs nevertheless display the same growth kinetics in continuous light or in LD cycles when present alone in the medium. Theoretical predictions are made as to how the outcome of competition depends on the initial proportions and on the FRPs of the different strains. We also determine the effect of the photoperiod and extend the analysis to the case of a competition between three cyanobacterial strains.

Circadian Rhythm↗
PubMed2002

Robustness of circadian rhythms with respect to molecular noise.

We use a core molecular model capable of generating circadian rhythms to assess the robustness of circadian oscillations with respect to molecular noise. The model is based on the negative feedback exerted by a regulatory protein on the expression of its gene. Such a negative regulatory mechanism underlies circadian oscillations of the PER protein in Drosophila and of the FRQ protein in Neurospora. The model incorporates gene transcription into mRNA, translation of mRNA into protein, reversible phosphorylation leading to degradation of the regulatory protein, transport of the latter into the nucleus, and repression of gene expression by the nuclear form of the protein. To assess the effect of molecular noise, we perform stochastic simulations after decomposing the deterministic model into elementary reaction steps. The oscillations predicted by the stochastic simulations agree with those obtained with the deterministic version of the model. We show that robust circadian oscillations can occur already with a limited number of mRNA and protein molecules, in the range of tens and hundreds, respectively. Entrainment by light/dark cycles and cooperativity in repression enhance the robustness of circadian oscillations with respect to molecular noise.

Animals↗
PubMed2001

From simple to complex oscillatory behavior in metabolic and genetic control networks.

We present an overview of mechanisms responsible for simple or complex oscillatory behavior in metabolic and genetic control networks. Besides simple periodic behavior corresponding to the evolution toward a limit cycle we consider complex modes of oscillatory behavior such as complex periodic oscillations of the bursting type and chaos. Multiple attractors are also discussed, e.g., the coexistence between a stable steady state and a stable limit cycle (hard excitation), or the coexistence between two simultaneously stable limit cycles (birhythmicity). We discuss mechanisms responsible for the transition from simple to complex oscillatory behavior by means of a number of models serving as selected examples. The models were originally proposed to account for simple periodic oscillations observed experimentally at the cellular level in a variety of biological systems. In a second stage, these models were modified to allow for complex oscillatory phenomena such as bursting, birhythmicity, or chaos. We consider successively (1) models based on enzyme regulation, proposed for glycolytic oscillations and for the control of successive phases of the cell cycle, respectively; (2) a model for intracellular Ca(2+) oscillations based on transport regulation; (3) a model for oscillations of cyclic AMP based on receptor desensitization in Dictyostelium cells; and (4) a model based on genetic regulation for circadian rhythms in Drosophila. Two main classes of mechanism leading from simple to complex oscillatory behavior are identified, namely (i) the interplay between two endogenous oscillatory mechanisms, which can take multiple forms, overt or more subtle, depending on whether the two oscillators each involve their own regulatory feedback loop or share a common feedback loop while differing by some related process, and (ii) self-modulation of the oscillator through feedback from the system's output on one of the parameters controlling oscillatory behavior. However, the latter mechanism may also be viewed as involving the interplay between two feedback processes, each of which might be capable of producing oscillations. Although our discussion primarily focuses on the case of autonomous oscillatory behavior, we also consider the case of nonautonomous complex oscillations in a model for circadian oscillations subjected to periodic forcing by a light-dark cycle and show that the occurrence of entrainment versus chaos in these conditions markedly depends on the wave form of periodic forcing. (c) 2001 American Institute of Physics.

Journal Article↗