Abstracts 2008

Abstract : A basic challenge in cell biology is to understand how interconnected metabolic pathways are regulated to provide the adequate cellular outcome when changing levels of metabolites and enzyme expression. In Escherichia coli, the arginine and pyrimidine biosynthetic pathways are connected through a common metabolite provided by a single enzyme. The different elements of the arginine biosynthetic system of Escherichia coli, including the connection with pyrimidine biosynthesis, and the principal regulatory mechanisms operating at genetic and enzymatic levels were integrated in a mathematical model using a molecular kinetic approach combined with a modular description of the system. The model was then used to simulate a set of perturbed conditions: genetic derepression, feedback resistance of the first enzymatic step, low constitutive synthesis of the intermediate carbamyl phosphate. In all cases, an excellent quantitative agreement between simulations and experimental results was found. The model allowed to gain further insight into the function of the system, including the synergy between the different regulations. The outcome of combinations of perturbations on cellular arginine concentration was predicted accurately, establishing the model as a powerful tool for the design of arginine overproducing strains.

Abstract : Signal-induced Ca²⁺ oscillations have been observed in many cell types and play a primary role in cell physiology. Although it is the regular character of these oscillations that first catches the attention, a closer look at time series of Ca²⁺ increases reveals that the fluctuations on the period during individual spike trains are far from being negligible. Here, we perform a statistical analysis of the regularity of Ca²⁺ oscillations in noradrenaline-stimulated hepatocytes and find that the coefficient of variation lies between 10 and 15%. Stochastic simulations based on the Gillespie's algorithm and considering realistic numbers of Ca²⁺ ions and InsP₃ receptors account for this variability if the receptors are assumed to be grouped in clusters of a few tens of channels. Given the relatively small number of clusters (~200), the model predicts the existence of repetitive spikes induced by fluctuations (stochastic resonance). Oscillations of such type are found in hepatocytes at sub-threshold concentrations of noradrenaline. We next predict with the model that the isoforms of the InsP₃ receptor can affect the variability of the oscillations. In contrast, possible accompanying InsP₃ oscillations have no impact on the robustness of signal-induced repetitive Ca²⁺ spikes.

Abstract : The formation of somites in the course of vertebrate segmentation is governed by an oscillator known as the segmentation clock, which is characterized by a period ranging from 30 min to a few hours depending on the organism. This oscillator permits the synchronized activation of segmentation genes in successive cohorts of cells in the presomitic mesoderm in response to a periodic signal emitted by the segmentation clock, thereby defining the future segments. Recent microarray experiments (Dequeant et al, 2006) indicate that the Notch, Wnt and FGF signaling pathways are involved in the mechanism of the segmentation clock. By means of computational modeling we investigate the conditions in which sustained oscillations occur in these three signaling pathways. First we show that negative feedback mediated by the Lunatic Fringe protein on intracellular Notch activation can give rise to periodic behavior in the Notch pathway. We then show that negative feedback exerted by Axin2 on the degradation of ÉÝÅ|catenin through formation of the Axin2 destruction complex can produce oscillations in the Wnt pathway. Likewise, negative feedback on FGF signaling mediated by the phosphatase product of the gene MKP3/Dusp6 can produce oscillatory gene expression in the FGF pathway. Coupling the Wnt, Notch and FGF oscillators through common intermediates can lead to synchronized oscillations in the three signaling pathways or to complex periodic behavior, depending on the relative periods of oscillations in the three pathways. The phase relationships between cycling genes in the three pathways depend on the nature of the coupling between the pathways and on their relative autonomous periods. The model provides a framework for analyzing the dynamics of the segmentation clock in terms of a network of oscillating modules involving the Wnt, Notch and FGF signaling pathways.

Abstract : On the basis of experimental observations, it has been suggested that glycolytic oscillations underlie the pulsatile secretion of insulin by pancreatic β cells, with a periodicity of about 13 min. If β cells within an islet are synchronized through gap junctions, the question arises as to how β cells located in different islets of Langerhans synchronize to produce oscillations in plasma levels of insulin. We address this question by means of a minimal model that incorporates the secretion of insulin by cells undergoing glycolytic oscillations. Global coupling and synchronization result from the inhibition exerted by insulin on the production of glucose, which serves as the substrate for metabolic oscillations. Glycolytic oscillations are described by a simple two-variable model centered on the product-activated reaction catalyzed by the allosteric enzyme phosphofructokinase. We obtain bifurcation diagrams for the cases in which insulin secretion is controlled solely by the product or by the substrate of the metabolic oscillator. Remarkably, we find that the oscillating cells in these conditions synchronize, respectively, in phase or out of phase. Numerical simulations show that in-phase and out-of-phase synchronization can sometimes coexist when insulin release is controlled by both the substrate and the product of the metabolic oscillator. The results provide an example of a system in which the selection of in-phase or out-of-phase synchronization is governed by the nature of the coupling between the intracellular oscillations and the secretion of the biochemical signal through which the oscillating cells are globally coupled.

Abstract : 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 cAMP­PKA 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 cAMP­PKA 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 phosphorylation­dephosphorylation cycles, both in the cAMP­PKA 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.

Abstract : Based on genetic and biochemical advances on the molecular mechanism of circadian rhythms, a computational model for the mammalian circadian clock is used to examine the dynamical bases of circadian-clock-related physiological disorders in humans. Entrainment by the light­dark cycle with a phase advance or a phase delay is associated with the Familial advanced sleep phase syndrome (FASPS) or the Delayed sleep phase syndrome (DSPS), respectively. Lack of entrainment corresponding to the occurrence of quasiperiodic oscillations with or without phase jump can be associated with the non-24 h sleep­wake syndrome. In the close vicinity of the entrainment domain, the model uncovers the possibility of infradian oscillations of very long period. Perturbation in the form of chronic jet lag, as used in mice, prevents entrainment of the circadian clock and results in chaotic or quasiperiodic oscillations. It is important to clarify the conditions for entrainment and for its failure because dysfunctions of the circadian clock may lead to physiological disorders, which pertain not only to the sleep­ wake cycle but also to mood and cancer.

Abstract : The circadian timing system (CTS) controls drug metabolism and cellular proliferation over the 24 hour day through molecular clocks in each cell. These cellular clocks are coordinated by a hypothalamic pacemaker, the suprachiasmatic nuclei, that generates or controls circadian physiology. The CTS plays a role in cancer processes and their treatments through the downregulation of malignant growth and the generation of large and predictable 24 hour changes in toxicity and efficacy of anti-cancer drugs. The tight interactions between circadian clocks, cell division cycle and pharmacology pathways have supported sinusoidal circadian-based delivery of cancer treatments. Such chronotherapeutics have been mostly implemented in patients with metastatic colorectal cancer, the second most common cause of death from cancer. Stochastic and deterministic models of the interactions between circadian clock, cell cycle and pharmacology confirmed the poor therapeutic value of both constant-rate and wrongly timed chronomodulated infusions. An automaton model for the cell cycle revealed the critical roles of variability in circadian entrainment and cell cycle phase durations in healthy tissues and tumours for the success of properly timed circadian delivery schedules. The models showed that additional therapeutic strategy further sets the constraints for the identification of the most effective chronomodulated schedules.

Abstract : 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 gene­protein interaction networks that control circadian rhythms, cell cycle progression, signal processing and the design of synthetic gene networks.