Birhythmicity in a model for the cyclic AMP signalling system of the slime mold Dictyostelium discoideum

AbstractWe demonstrate the coexistence of two simultaneously stable periodic regimes in a model based on receptor desensitization for the cyclic AMP signalling system of the slime mold Dictyostelium discoideum. These results provide the first example of autonomous birhythmicity in a biochemical model closely related to experimental observations. Whereas the transition from one stable mode of oscillations to the other can be elicited by suprathreshold stimuli, the two periodic regimes differ in their sensitivity to perturbations. That multiple oscillations occur in a model based on a single feedback loop suggests that the conditions for birhythmicity are widely satisfied in biological systems

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

Robustness of circadian clocks to daylight fluctuations: hints from the picoeucaryote Ostreococcus tauri

The development of systemic approaches in biology has put emphasis on identifying genetic modules whose behavior can be modeled accurately so as to gain insight into their structure and function. However most gene circuits in a cell are under control of external signals and thus quantitative agreement between experimental data and a mathematical model is difficult. Circadian biology has been one notable exception: quantitative models of the internal clock that orchestrates biological processes over the 24-hour diurnal cycle have been constructed for a few organisms, from cyanobacteria to plants and mammals. In most cases, a complex architecture with interlocked feedback loops has been evidenced. Here we present first modeling results for the circadian clock of the green unicellular alga Ostreococcus tauri. Two plant-like clock genes have been shown to play a central role in Ostreococcus clock. We find that their expression time profiles can be accurately reproduced by a minimal model of a two-gene transcriptional feedback loop. Remarkably, best adjustment of data recorded under light/dark alternation is obtained when assuming that the oscillator is not coupled to the diurnal cycle. This suggests that coupling to light is confined to specific time intervals and has no dynamical effect when the oscillator is entrained by the diurnal cycle. This intringuing property may reflect a strategy to minimize the impact of fluctuations in daylight intensity on the core circadian oscillator, a type of perturbation that has been rarely considered when assessing the robustness of circadian clocks

The positive circadian regulators CLOCK and BMAL1 control G2/M cell cycle transition through Cyclin B1

We previously identified a tight bidirectional phase coupling between the circadian clock and the cell cycle. To understand the role of the CLOCK/BMAL1 complex, representing the main positive regulator of the circadian oscillator, we knocked down Bmal1 or Clock in NIH3T33C mouse fibroblasts (carrying fluorescent reporters for clock and cell cycle phase) and analyzed timing of cell division in individual cells and cell populations. Inactivation of Bmal1 resulted in a loss of circadian rhythmicity and a lengthening of the cell cycle, originating from delayed G2/M transition. Subsequent molecular analysis revealed reduced levels of Cyclin B1, an important G2/M regulator, upon suppression of Bmal1 gene expression. In complete agreement with these experimental observations, simulation of Bmal1 knockdown in a computational model for coupled mammalian circadian clock and cell cycle oscillators (now incorporating Cyclin B1 induction by BMAL1) revealed a lengthening of the cell cycle. Similar data were obtained upon knockdown of Clock gene expression. In conclusion, the CLOCK/BMAL1 complex controls cell cycle progression at the level of G2/M transition through regulation of Cyclin B1 expression

Reliability of Transcriptional Cycles and the Yeast Cell-Cycle Oscillator

A recently published transcriptional oscillator associated with the yeast cell cycle provides clues and raises questions about the mechanisms underlying autonomous cyclic processes in cells. Unlike other biological and synthetic oscillatory networks in the literature, this one does not seem to rely on a constitutive signal or positive auto-regulation, but rather to operate through stable transmission of a pulse on a slow positive feedback loop that determines its period. We construct a continuous-time Boolean model of this network, which permits the modeling of noise through small fluctuations in the timing of events, and show that it can sustain stable oscillations. Analysis of simpler network models shows how a few building blocks can be arranged to provide stability against fluctuations. Our findings suggest that the transcriptional oscillator in yeast belongs to a new class of biological oscillators

Entrainment of the Mammalian Cell Cycle by the Circadian Clock: Modeling Two Coupled Cellular Rhythms

The cell division cycle and the circadian clock represent two major cellular rhythms. These two periodic processes are coupled in multiple ways, given that several molecular components of the cell cycle network are controlled in a circadian manner. For example, in the network of cyclin-dependent kinases (Cdks) that governs progression along the successive phases of the cell cycle, the synthesis of the kinase Wee1, which inhibits the G2/M transition, is enhanced by the complex CLOCK-BMAL1 that plays a central role in the circadian clock network. Another component of the latter network, REV-ERBα, inhibits the synthesis of the Cdk inhibitor p21. Moreover, the synthesis of the oncogene c-Myc, which promotes G1 cyclin synthesis, is repressed by CLOCK-BMAL1. Using detailed computational models for the two networks we investigate the conditions in which the mammalian cell cycle can be entrained by the circadian clock. We show that the cell cycle can be brought to oscillate at a period of 24 h or 48 h when its autonomous period prior to coupling is in an appropriate range. The model indicates that the combination of multiple modes of coupling does not necessarily facilitate entrainment of the cell cycle by the circadian clock. Entrainment can also occur as a result of circadian variations in the level of a growth factor controlling entry into G1. Outside the range of entrainment, the coupling to the circadian clock may lead to disconnected oscillations in the cell cycle and the circadian system, or to complex oscillatory dynamics of the cell cycle in the form of endoreplication, complex periodic oscillations or chaos. The model predicts that the transition from entrainment to 24 h or 48 h might occur when the strength of coupling to the circadian clock or the level of growth factor decrease below critical values

Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area

Global Self-Organization of the Cellular Metabolic Structure

Background: Over many years, it has been assumed that enzymes work either in an isolated way, or organized in small catalytic groups. Several studies performed using "metabolic networks models'' are helping to understand the degree of functional complexity that characterizes enzymatic dynamic systems. In a previous work, we used "dissipative metabolic networks'' (DMNs) to show that enzymes can present a self-organized global functional structure, in which several sets of enzymes are always in an active state, whereas the rest of molecular catalytic sets exhibit dynamics of on-off changing states. We suggested that this kind of global metabolic dynamics might be a genuine and universal functional configuration of the cellular metabolic structure, common to all living cells. Later, a different group has shown experimentally that this kind of functional structure does, indeed, exist in several microorganisms. Methodology/Principal Findings: Here we have analyzed around 2.500.000 different DMNs in order to investigate the underlying mechanism of this dynamic global configuration. The numerical analyses that we have performed show that this global configuration is an emergent property inherent to the cellular metabolic dynamics. Concretely, we have found that the existence of a high number of enzymatic subsystems belonging to the DMNs is the fundamental element for the spontaneous emergence of a functional reactive structure characterized by a metabolic core formed by several sets of enzymes always in an active state. Conclusions/Significance: This self-organized dynamic structure seems to be an intrinsic characteristic of metabolism, common to all living cellular organisms. To better understand cellular functionality, it will be crucial to structurally characterize these enzymatic self-organized global structures.Supported by the Spanish Ministry of Science and Education Grants MTM2005-01504, MTM2004-04665, partly with FEDER funds, and by the Basque Government, Grant IT252-07

Threshold-dominated regulation hides genetic variation in gene expression networks

<p>Abstract</p> <p>Background</p> <p>In dynamical models with feedback and sigmoidal response functions, some or all variables have thresholds around which they regulate themselves or other variables. A mathematical analysis has shown that when the dose-response functions approach binary or on/off responses, any variable with an equilibrium value close to one of its thresholds is very robust to parameter perturbations of a homeostatic state. We denote this threshold robustness. To check the empirical relevance of this phenomenon with response function steepnesses ranging from a near on/off response down to Michaelis-Menten conditions, we have performed a simulation study to investigate the degree of threshold robustness in models for a three-gene system with one downstream gene, using several logical input gates, but excluding models with positive feedback to avoid multistationarity. Varying parameter values representing functional genetic variation, we have analysed the coefficient of variation (<it>CV</it>) of the gene product concentrations in the stable state for the regulating genes in absolute terms and compared to the <it>CV </it>for the unregulating downstream gene. The sigmoidal or binary dose-response functions in these models can be considered as phenomenological models of the aggregated effects on protein or mRNA expression rates of all cellular reactions involved in gene expression.</p> <p>Results</p> <p>For all the models, threshold robustness increases with increasing response steepness. The <it>CV</it>s of the regulating genes are significantly smaller than for the unregulating gene, in particular for steep responses. The effect becomes less prominent as steepnesses approach Michaelis-Menten conditions. If the parameter perturbation shifts the equilibrium value too far away from threshold, the gene product is no longer an effective regulator and robustness is lost. Threshold robustness arises when a variable is an active regulator around its threshold, and this function is maintained by the feedback loop that the regulator necessarily takes part in and also is regulated by. In the present study all feedback loops are negative, and our results suggest that threshold robustness is maintained by negative feedback which necessarily exists in the homeostatic state.</p> <p>Conclusion</p> <p>Threshold robustness of a variable can be seen as its ability to maintain an active regulation around its threshold in a homeostatic state despite external perturbations. The feedback loop that the system necessarily possesses in this state, ensures that the robust variable is itself regulated and kept close to its threshold. Our results suggest that threshold regulation is a generic phenomenon in feedback-regulated networks with sigmoidal response functions, at least when there is no positive feedback. Threshold robustness in gene regulatory networks illustrates that hidden genetic variation can be explained by systemic properties of the genotype-phenotype map.</p