Segmentation of the axial skeleton in amniotes depends on the segmentation clock, which patterns ... more Segmentation of the axial skeleton in amniotes depends on the segmentation clock, which patterns the paraxial mesoderm and the sclerotome. While the segmentation clock clearly operates in teleosts, the role of the sclerotome in establishing the axial skeleton is unclear. We severely disrupt zebrafish paraxial segmentation, yet observe a largely normal segmentation process of the chordacentra. We demonstrate that axial entpd5+ notochord sheath cells are responsible for chordacentrum mineralization, and serve as a marker for axial segmentation. While autonomous within the notochord sheath, entpd5 expression and centrum formation show some plasticity and can respond to myotome pattern. These observations reveal for the first time the dynamics of notochord segmentation in a teleost, and are consistent with an autonomous patterning mechanism that is influenced, but not determined by adjacent paraxial mesoderm. This behavior is not consistent with a clock-type mechanism in the notochord.
We study general aspects of active motion with fluctuations in the speed and the direction of mot... more We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion, and assume that both processes can be described by independent characteristic timescales. We show the occurrence of a complex transient that can exhibit a series of alternating regimes of motion, for two different angular dynamics which correspond to persistent and directed random walks. We also show additive corrections to the diffusion coefficient. The characteristic timescales are also exposed in the velocity autocorrelation, which is a sum of exponential forms.
We analyze the synchronization transition for a pair of coupled identical Kauffman networks in th... more We analyze the synchronization transition for a pair of coupled identical Kauffman networks in the chaotic phase. The annealed model for Kauffman networks shows that synchronization appears through a transcritical bifurcation, and provides an approximate description for the whole dynamics of the coupled networks. We show that these analytical predictions are in good agreement with numerical results for sufficiently large networks, and study finite-size effects in detail. Preliminary analytical and numerical results for partially disordered networks are also presented.
We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events... more We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.
We develop a stochastic description of feedback oscillators in which functional molecules are pro... more We develop a stochastic description of feedback oscillators in which functional molecules are produced by an assembly line consisting of many identical steps. The initiation rate of this assembly is regulated by its products via a negative feedback. This model is motivated by genetic oscillators such as circadian clocks. We show that precise oscillations of high quality are possible even when the number of product molecules is low and the fluctuations of amplitude are large. We discuss parameter values which can account for high quality oscillations as observed in single cells. Furthermore, we discuss effects of stochastic amplification steps on precision to account for translational bursting.
We study synchronization of locally coupled noisy phase oscillators that move diffusively in a on... more We study synchronization of locally coupled noisy phase oscillators that move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits wave-like states displaying local order. We use a statistical description valid for a large number of oscillators to show that for any finite system there is a critical mobility above which all wave-like solutions become unstable. Through Langevin simulations, we show that the transition to global synchronization is mediated by a shift in the relative size of attractor basins associated to wave-like states. Mobility disrupts these states and paves the way for the system to attain global synchronization.
ABSTRACT Signal transduction networks generate characteristic dynamic activities to process extra... more ABSTRACT Signal transduction networks generate characteristic dynamic activities to process extracellular signals and guide cell fate decisions such as to divide or differentiate. The differentiation of pluripotent cells is controlled by FGF/ERK signaling. However, only a few studies have addressed the dynamic activity of the FGF/ERK signaling network in pluripotent cells at high time resolution. Here, we use live cell sensors in wild-type and Fgf4-mutant mouse embryonic stem cells to measure dynamic ERK activity in single cells, for defined ligand concentrations and differentiation states. These sensors reveal pulses of ERK activity. Pulsing patterns are heterogeneous between individual cells. Consecutive pulse sequences occur more frequently than expected from simple stochastic models. Sequences become more prevalent with higher ligand concentration, but are rarer in more differentiated cells. Our results suggest that FGF/ERK signaling operates in the vicinity of a transition point between oscillatory and non-oscillatory dynamics in embryonic stem cells. The resulting heterogeneous dynamic signaling activities add a new dimension to cellular heterogeneity that may be linked to divergent fate decisions in stem cell cultures.
We analyze the dynamics of two coupled elementary cellular automata with complex spatiotemporal d... more We analyze the dynamics of two coupled elementary cellular automata with complex spatiotemporal dynamics. The coupling mechanism, characterized by a probability p, is stochastic. From numerical simulations, we find that a sharp transition to full synchronization of the two cellular automata occurs at a critical value of p. This transition admits an approximate semianalytical description in terms of the evolution of the difference automaton, and is found both for symmetric and asymmetric coupling. It is argued that the behavior of cellular automata under coupling may inspire a classification of their individual dynamics. ͓S1063-651X͑98͒51407-9͔
International Journal of Bifurcation and Chaos, Apr 1, 2003
We briefly review the synchronization properties of cross-coupled spatially extended dynamical sy... more We briefly review the synchronization properties of cross-coupled spatially extended dynamical systems, with particular emphasis on elementary cellular automata and Kauffman networks subject to stochastic coupling. We also discuss the main results for the joint evolution of deterministically cross-coupled Ginzburg-Landau equations and neural networks. Both numerical and analytical approaches are addressed, and the main differences with the synchronization of zero-dimensional systems are highlighted. New results are presented characterizing the critical behavior at the synchronization transition of coupled Kauffman networks.
Segmentation of the axial skeleton in amniotes depends on the segmentation clock, which patterns ... more Segmentation of the axial skeleton in amniotes depends on the segmentation clock, which patterns the paraxial mesoderm and the sclerotome. While the segmentation clock clearly operates in teleosts, the role of the sclerotome in establishing the axial skeleton is unclear. We severely disrupt zebrafish paraxial segmentation, yet observe a largely normal segmentation process of the chordacentra. We demonstrate that axial entpd5+ notochord sheath cells are responsible for chordacentrum mineralization, and serve as a marker for axial segmentation. While autonomous within the notochord sheath, entpd5 expression and centrum formation show some plasticity and can respond to myotome pattern. These observations reveal for the first time the dynamics of notochord segmentation in a teleost, and are consistent with an autonomous patterning mechanism that is influenced, but not determined by adjacent paraxial mesoderm. This behavior is not consistent with a clock-type mechanism in the notochord.
Cell movement and intercellular signaling occur simultaneously to organize morphogenesis during e... more Cell movement and intercellular signaling occur simultaneously to organize morphogenesis during embryonic development. Cell movement can cause relative positional changes between neighboring cells. When intercellular signals are local such cell mixing may affect signaling, changing the flow of information in developing tissues. Little is known about the effect of cell mixing on intercellular signaling in collective cellular behaviors and methods to quantify its impact are lacking. Here we discuss how to determine the impact of cell mixing on cell signaling drawing an example from vertebrate embryogenesis: the segmentation clock, a collective rhythm of interacting genetic oscillators. We argue that comparing cell mixing and signaling timescales is key to determining the influence of mixing. A signaling timescale can be estimated by combining theoretical models with cell signaling perturbation experiments. A mixing timescale can be obtained by analysis of cell trajectories from live imaging. After comparing cell movement analyses in different experimental settings, we highlight challenges in quantifying cell mixing from embryonic timelapse experiments, especially a reference frame problem due to embryonic motions and shape changes. We propose statistical observables characterizing cell mixing that do not depend on the choice of reference frames. Finally, we consider situations in which both cell mixing and signaling involve multiple timescales, precluding a direct comparison between single characteristic timescales. In such situations, physical models based on observables of cell mixing and signaling can simulate the flow of information in tissues and reveal the impact of observed cell mixing on signaling.
clicking here. colleagues, clients, or customers by , you can order high-quality copies for your ... more clicking here. colleagues, clients, or customers by , you can order high-quality copies for your If you wish to distribute this article to others here. following the guidelines can be obtained by Permission to republish or repurpose articles or portions of articles
The segmentation clock is an oscillating genetic network thought to govern the rhythmic and seque... more The segmentation clock is an oscillating genetic network thought to govern the rhythmic and sequential subdivision of the elongating body axis of the vertebrate embryo into somites: the precursors of the segmented vertebral column. Understanding how the rhythmic signal arises, how it achieves precision and how it patterns the embryo remain challenging issues. Recent work has provided evidence of how the period of the segmentation clock is regulated and how this affects the anatomy of the embryo. The ongoing development of realtime clock reporters and mathematical models promise novel insight into the dynamic behavior of the clock.
Segmentation of the axial skeleton in amniotes depends on the segmentation clock, which patterns ... more Segmentation of the axial skeleton in amniotes depends on the segmentation clock, which patterns the paraxial mesoderm and the sclerotome. While the segmentation clock clearly operates in teleosts, the role of the sclerotome in establishing the axial skeleton is unclear. We severely disrupt zebrafish paraxial segmentation, yet observe a largely normal segmentation process of the chordacentra. We demonstrate that axial entpd5+ notochord sheath cells are responsible for chordacentrum mineralization, and serve as a marker for axial segmentation. While autonomous within the notochord sheath, entpd5 expression and centrum formation show some plasticity and can respond to myotome pattern. These observations reveal for the first time the dynamics of notochord segmentation in a teleost, and are consistent with an autonomous patterning mechanism that is influenced, but not determined by adjacent paraxial mesoderm. This behavior is not consistent with a clock-type mechanism in the notochord.
We study general aspects of active motion with fluctuations in the speed and the direction of mot... more We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion, and assume that both processes can be described by independent characteristic timescales. We show the occurrence of a complex transient that can exhibit a series of alternating regimes of motion, for two different angular dynamics which correspond to persistent and directed random walks. We also show additive corrections to the diffusion coefficient. The characteristic timescales are also exposed in the velocity autocorrelation, which is a sum of exponential forms.
We analyze the synchronization transition for a pair of coupled identical Kauffman networks in th... more We analyze the synchronization transition for a pair of coupled identical Kauffman networks in the chaotic phase. The annealed model for Kauffman networks shows that synchronization appears through a transcritical bifurcation, and provides an approximate description for the whole dynamics of the coupled networks. We show that these analytical predictions are in good agreement with numerical results for sufficiently large networks, and study finite-size effects in detail. Preliminary analytical and numerical results for partially disordered networks are also presented.
We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events... more We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.
We develop a stochastic description of feedback oscillators in which functional molecules are pro... more We develop a stochastic description of feedback oscillators in which functional molecules are produced by an assembly line consisting of many identical steps. The initiation rate of this assembly is regulated by its products via a negative feedback. This model is motivated by genetic oscillators such as circadian clocks. We show that precise oscillations of high quality are possible even when the number of product molecules is low and the fluctuations of amplitude are large. We discuss parameter values which can account for high quality oscillations as observed in single cells. Furthermore, we discuss effects of stochastic amplification steps on precision to account for translational bursting.
We study synchronization of locally coupled noisy phase oscillators that move diffusively in a on... more We study synchronization of locally coupled noisy phase oscillators that move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits wave-like states displaying local order. We use a statistical description valid for a large number of oscillators to show that for any finite system there is a critical mobility above which all wave-like solutions become unstable. Through Langevin simulations, we show that the transition to global synchronization is mediated by a shift in the relative size of attractor basins associated to wave-like states. Mobility disrupts these states and paves the way for the system to attain global synchronization.
ABSTRACT Signal transduction networks generate characteristic dynamic activities to process extra... more ABSTRACT Signal transduction networks generate characteristic dynamic activities to process extracellular signals and guide cell fate decisions such as to divide or differentiate. The differentiation of pluripotent cells is controlled by FGF/ERK signaling. However, only a few studies have addressed the dynamic activity of the FGF/ERK signaling network in pluripotent cells at high time resolution. Here, we use live cell sensors in wild-type and Fgf4-mutant mouse embryonic stem cells to measure dynamic ERK activity in single cells, for defined ligand concentrations and differentiation states. These sensors reveal pulses of ERK activity. Pulsing patterns are heterogeneous between individual cells. Consecutive pulse sequences occur more frequently than expected from simple stochastic models. Sequences become more prevalent with higher ligand concentration, but are rarer in more differentiated cells. Our results suggest that FGF/ERK signaling operates in the vicinity of a transition point between oscillatory and non-oscillatory dynamics in embryonic stem cells. The resulting heterogeneous dynamic signaling activities add a new dimension to cellular heterogeneity that may be linked to divergent fate decisions in stem cell cultures.
We analyze the dynamics of two coupled elementary cellular automata with complex spatiotemporal d... more We analyze the dynamics of two coupled elementary cellular automata with complex spatiotemporal dynamics. The coupling mechanism, characterized by a probability p, is stochastic. From numerical simulations, we find that a sharp transition to full synchronization of the two cellular automata occurs at a critical value of p. This transition admits an approximate semianalytical description in terms of the evolution of the difference automaton, and is found both for symmetric and asymmetric coupling. It is argued that the behavior of cellular automata under coupling may inspire a classification of their individual dynamics. ͓S1063-651X͑98͒51407-9͔
International Journal of Bifurcation and Chaos, Apr 1, 2003
We briefly review the synchronization properties of cross-coupled spatially extended dynamical sy... more We briefly review the synchronization properties of cross-coupled spatially extended dynamical systems, with particular emphasis on elementary cellular automata and Kauffman networks subject to stochastic coupling. We also discuss the main results for the joint evolution of deterministically cross-coupled Ginzburg-Landau equations and neural networks. Both numerical and analytical approaches are addressed, and the main differences with the synchronization of zero-dimensional systems are highlighted. New results are presented characterizing the critical behavior at the synchronization transition of coupled Kauffman networks.
Segmentation of the axial skeleton in amniotes depends on the segmentation clock, which patterns ... more Segmentation of the axial skeleton in amniotes depends on the segmentation clock, which patterns the paraxial mesoderm and the sclerotome. While the segmentation clock clearly operates in teleosts, the role of the sclerotome in establishing the axial skeleton is unclear. We severely disrupt zebrafish paraxial segmentation, yet observe a largely normal segmentation process of the chordacentra. We demonstrate that axial entpd5+ notochord sheath cells are responsible for chordacentrum mineralization, and serve as a marker for axial segmentation. While autonomous within the notochord sheath, entpd5 expression and centrum formation show some plasticity and can respond to myotome pattern. These observations reveal for the first time the dynamics of notochord segmentation in a teleost, and are consistent with an autonomous patterning mechanism that is influenced, but not determined by adjacent paraxial mesoderm. This behavior is not consistent with a clock-type mechanism in the notochord.
Cell movement and intercellular signaling occur simultaneously to organize morphogenesis during e... more Cell movement and intercellular signaling occur simultaneously to organize morphogenesis during embryonic development. Cell movement can cause relative positional changes between neighboring cells. When intercellular signals are local such cell mixing may affect signaling, changing the flow of information in developing tissues. Little is known about the effect of cell mixing on intercellular signaling in collective cellular behaviors and methods to quantify its impact are lacking. Here we discuss how to determine the impact of cell mixing on cell signaling drawing an example from vertebrate embryogenesis: the segmentation clock, a collective rhythm of interacting genetic oscillators. We argue that comparing cell mixing and signaling timescales is key to determining the influence of mixing. A signaling timescale can be estimated by combining theoretical models with cell signaling perturbation experiments. A mixing timescale can be obtained by analysis of cell trajectories from live imaging. After comparing cell movement analyses in different experimental settings, we highlight challenges in quantifying cell mixing from embryonic timelapse experiments, especially a reference frame problem due to embryonic motions and shape changes. We propose statistical observables characterizing cell mixing that do not depend on the choice of reference frames. Finally, we consider situations in which both cell mixing and signaling involve multiple timescales, precluding a direct comparison between single characteristic timescales. In such situations, physical models based on observables of cell mixing and signaling can simulate the flow of information in tissues and reveal the impact of observed cell mixing on signaling.
clicking here. colleagues, clients, or customers by , you can order high-quality copies for your ... more clicking here. colleagues, clients, or customers by , you can order high-quality copies for your If you wish to distribute this article to others here. following the guidelines can be obtained by Permission to republish or repurpose articles or portions of articles
The segmentation clock is an oscillating genetic network thought to govern the rhythmic and seque... more The segmentation clock is an oscillating genetic network thought to govern the rhythmic and sequential subdivision of the elongating body axis of the vertebrate embryo into somites: the precursors of the segmented vertebral column. Understanding how the rhythmic signal arises, how it achieves precision and how it patterns the embryo remain challenging issues. Recent work has provided evidence of how the period of the segmentation clock is regulated and how this affects the anatomy of the embryo. The ongoing development of realtime clock reporters and mathematical models promise novel insight into the dynamic behavior of the clock.
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Papers by Luis G Morelli