Papers by Albert Goldbeter
Stochastic modelling of nucleocytoplasmic oscillations of the transcription factor Msn2 in yeast
Journal of The Royal Society Interface, 2008
Stress induces oscillatory nucleocytoplasmic shuttling of the transcription factor Msn2 in yeast.... more Stress induces oscillatory nucleocytoplasmic shuttling of the transcription factor Msn2 in yeast. The subcellular localization of Msn2 is controlled by the cAMP-dependent protein kinase, PKA. Recent experimental observations corroborated by a deterministic computational model for the cAMP-PKA pathway in yeast suggest that the oscillatory dynamics of Msn2 results from the periodic activation of PKA associated with stress-induced oscillations in the level of cAMP. The model accounts for the occurrence of oscillations of Msn2 in a window bounded by two critical values of the stress intensity. In contrast to the rather irregular oscillatory behaviour observed within single yeast cells by means of fluorescence measurements, the deterministic model can only produce a regular pattern of oscillations. To investigate whether the experimentally observed variability could be explained by molecular noise due to the small number of molecules involved in the oscillatory mechanism, we examine a stochastic version of the model for periodic nucleocytoplasmic shuttling of Msn2 coupled to oscillations in the cAMP-PKA pathway. The results of stochastic simulations compare well to the irregular oscillations observed experimentally in the nucleocytoplasmic shuttling of Msn2 in individual yeast cells. The stochastic model retains the property of oscillations within a range bounded by two critical values of stress intensity. We determine the dynamic behaviour as a function of this control parameter and show that the effect of noise markedly depends on the distance from the bifurcation points in the domain of oscillatory behaviour. Finally, we assess the role played by thresholds due to zero-order ultrasensitivity in phosphorylation-dephosphorylation cycles, both in the cAMP-PKA pathway and in the reactions controlling nucleocytoplasmic shuttling of Msn2. In regard to these thresholds, stochastic simulations show that large-amplitude variations of Msn2 associated with large-amplitude oscillations in cAMP can occur outside the domain of sustained oscillations predicted by the deterministic approach.
Biophysical Chemistry, Jan 1, 1985
European Biophysics Journal, Jan 1, 1988
NATO ASI series. Series …, Jan 1, 1987
Biophysical Chemistry, 1984
Journal of The Royal Society Interface, 2008
To introduce this special issue on biological switches and clocks, we review the historical devel... more To introduce this special issue on biological switches and clocks, we review the historical development of mathematical models of bistability and oscillations in chemical reaction networks. In the 1960s and 1970s, these models were limited to well-studied biochemical examples, such as glycolytic oscillations and cyclic AMP signalling. After the molecular genetics revolution of the 1980s, the field of molecular cell biology was thrown wide open to mathematical modellers. We review recent advances in modelling the gene-protein interaction networks that control circadian rhythms, cell cycle progression, signal processing and the design of synthetic gene networks.
To introduce this special issue on biological switches and clocks, we review the historical devel... more To introduce this special issue on biological switches and clocks, we review the historical development of mathematical models of bistability and oscillations in chemical reaction networks. In the 1960s and 1970s, these models were limited to well-studied biochemical examples, such as glycolytic oscillations and cyclic AMP signalling. After the molecular genetics revolution of the 1980s, the field of molecular cell biology was thrown wide open to mathematical modellers. We review recent advances in modelling the gene-protein interaction networks that control circadian rhythms, cell cycle progression, signal processing and the design of synthetic gene networks.
Journal of Theoretical Biology, 1987
We analyze the transition from simple to complex oscillatory behaviour in a threevariable biochem... more We analyze the transition from simple to complex oscillatory behaviour in a threevariable biochemical system that consists of the coupling in series of two autocatalytic enzyme reactions. Complex periodic behaviour occurs in the form of bursting in which clusters of spikes are separated by phases of relative quiescence. The generation of such temporal patterns is investigated by a series of complementary approaches. The dynamics of the system is first cast into two different time-scales, and one of the variables is taken as a slowly-varying parameter influencing the behaviour of the two remaining variables. This analysis shows how complex oscillations develop from simple periodic behaviour and accounts for the existence of various modes of bursting as well as for the dependence of the number of spikes per period on key parameters of the model. We further reduce the number of variables by analyzing bursting by means of one-dimensional return maps obtained from the time evolution of the three-dimensional system. The analysis of a related piecewise linear map allows for a detailed understanding of the complex sequence leading from a bursting pattern with p spikes to a pattern with p+ 1 spikes per period. We show that this transition possesses properties of self-similarity associated with the occurrence of more and more complex patterns of bursting. In addition to bursting, period-doubling bifurcations leading to chaos are observed, as in the differential system, when the piecewise-linear map becomes nonlinear. 219
Amplification and adaptation in regulatory and sensory systems
Science, 1982
Development (Cambridge, England), 2014
During blastocyst formation, inner cell mass (ICM) cells differentiate into either epiblast (Epi)... more During blastocyst formation, inner cell mass (ICM) cells differentiate into either epiblast (Epi) or primitive endoderm (PrE) cells, labeled by Nanog and Gata6, respectively, and organized in a salt-and-pepper pattern. Previous work in the mouse has shown that, in absence of Nanog, all ICM cells adopt a PrE identity. Moreover, the activation or the blockade of the Fgf/RTK pathway biases cell fate specification towards either PrE or Epi, respectively. We show that, in absence of Gata6, all ICM cells adopt an Epi identity. Furthermore, the analysis of Gata6(+/-) embryos reveals a dose-sensitive phenotype, with fewer PrE-specified cells. These results and previous findings have enabled the development of a mathematical model for the dynamics of the regulatory network that controls ICM differentiation into Epi or PrE cells. The model describes the temporal dynamics of Erk signaling and of the concentrations of Nanog, Gata6, secreted Fgf4 and Fgf receptor 2. The model is able to recapitu...
Journal of biological physics, 2002
Circadian rhythms which occur with a period close to 24 h in nearly all living organisms originat... more Circadian rhythms which occur with a period close to 24 h in nearly all living organisms originate from the negative autoregulation of gene expression.Deterministic models based on genetic regulatory processes account for theoccurrence 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. At low numbers of protein and mRNA molecules, 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 two stochastic versions of a core model for circadian rhythms. The deterministic version of this core modelwas previously proposed for circadian oscillations of the PER protein in Drosophila and of the FRQ protein in Neurospora. In the first, non-developed version of the stochastic model, we introduce molecular noise without decomposing the deter...
Modeling spiral Ca2+ waves in single cardiac cells: role of the spatial heterogeneity created by the nucleus
The American journal of physiology, 1996
Excitation-contraction coupling in cardiomyocytes is known to rely on the Ca(2+)-induced Ca2+ rel... more Excitation-contraction coupling in cardiomyocytes is known to rely on the Ca(2+)-induced Ca2+ release mechanism. This autoamplification process is also very apparent when voltage-clamped or Ca(2+)-overloaded myocytes exhibit fast-propagating Ca2+ waves. Although most of the fronts are planar, some adopt a spiral shape, revealing additional characteristics about the excitability and structure of the cardiac cell (P. Lipp and E. Niggli, Biophys. J. 65: 2272-2276, 1993: J. Engel, M. Fechner, A. Sowerby, S. Finch, and A. Stier, Biophys. J. 66: 1756-1762, 1994). Using a previously developed model for Ca2+ oscillations and waves (A. Goldbeter, G. Dupont, and M.J. Berridge, Proc. Natl. Acad. Sci. USA 87: 1461-1465, 1990; G. Dupont and A. Goldbeter, Biophys. J. 67: 2191-2204, 1994), we study by numerical simulations different conditions in which spiral Ca2+ waves can occur as a result of the spatial heterogeneity created by the nucleus in a system with geometry resembling that of a myocyte....
Quarterly reviews of biophysics, 1982
The Scientific World JOURNAL, 2003
DOMAINS: cell biology, intracellular signaling, microscopy, computational biology, modeling, fung... more DOMAINS: cell biology, intracellular signaling, microscopy, computational biology, modeling, fungal biology, molecular biology, biochemistry Rhythmic behaviors of molecular components of the cell represent a fascinating aspect of biology because they imply complex feedback regulations . Biological oscillatory phenomena have been observed over a very large range of time periods, extending from fractions of a second to years. The involvement of oscillations in gene expression has been characterized more recently, with the finding that circadian rhythms rely upon negative autoregulatory feedback giving rise to periodic gene expression . Oscillations that involve the negative regulation of transcription have also been described for P53 NFκB[5], and somite formation during development .
From Simple to Complex Ca 2+ Oscillations: Regulatory Mechanisms and Theoretical Models
Lecture Notes in Physics, 2003
Intracellular Ca 2+ oscillations most often appear as regular spikes. However, complex Ca 2+ osci... more Intracellular Ca 2+ oscillations most often appear as regular spikes. However, complex Ca 2+ oscillations in the form of bursting or chaos have also been observed. These oscillations most probably originate from the interplay between multiple regulatory mechanisms. From an experimental point of view, the mechanism underlying these types of Ca 2+ oscillations remain poorly understood. In this review, we
Bistability without Hysteresis in Chemical Reaction Systems: The Case of Nonconnected Branches of Coexisting Steady States
The Journal of Physical Chemistry A, 1998
The coexistence between two stable steady states, referred to as bistability, is generally associ... more The coexistence between two stable steady states, referred to as bistability, is generally associated with a phenomenon of hysteresis in which a system jumps back and forth between the two branches of stable states for different, critical values of some control ...
The Journal of Cell Biology, 2003
sn2 and Msn4 are two related transcriptional activators that mediate a general response to stress... more sn2 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 M 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.
Far from equilibrium synthesis of small polymer chains and chemical evolution
Biophysik, 1972
Summary A number of simple models for the synthesis of small polymers are considered. The role of... more Summary A number of simple models for the synthesis of small polymers are considered. The role of autocatalysis and primitive template processes is examined. It is shown that far from equilibrium such systems may exhibit multiple steady state or sigmoidal transitions, favouring the enhancement of the (oligomer/monomer) ratio in the medium. A thermodynamic analysis in the non-linear range shows that
Proceedings of the National Academy of Sciences, 1975
Type and range of entrainment of glycolytic oscillations by a periodic source of substrate are de... more Type and range of entrainment of glycolytic oscillations by a periodic source of substrate are determined experimentally in yeast extracts. Subharmonic entrainment proves the nonlinear nature of the glycolytic oscillator Random variation of the substrate input yields sustained oscillations of irregular waveform and stable period. The results agree with the predictions of an allosteric model for phosphofructokinase (EC 2.7.1.11; ATP:D-fructose-6-phosphate 1-phosphotransferase), which is the enzyme responsible for periodic operation of glycolysis. A comparison between model and experiment in the case of a constant source of substrate further indicates that the oscillatory dynamics of the glycolytic system can satisfactorily be described by the phosphofructokinase model.
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Papers by Albert Goldbeter