Abstract : Calcium is an ubiquitous second messenger that mediates vital physiological responses ranging from fertilization to secretion, gene expression or apoptosis. Given this variety of processes mediated by Ca2+, these signals are highly organized both in time and space to ensure reliability and specificity. This review deals with the spatio-temporal organization of the Ca2+ signalling pathway in electrically non excitable cells, in which InsP3 receptors are by far the most important Ca2+ channels. We focus on those aspects of this highly regulated dynamical system for which an interplay between experiments and modelling is particularly fruitful. In particular, the importance of the relative densities of the different InsP3 receptor subtypes will be discussed on the basis of a modelling approach linking the steady-state behaviours of these channels in electrophysiological experiments, with their behaviour in a cellular environment. Also, the interplay between InsP3 metabolism and Ca2+ oscillations will be considered. Finally, we discuss the possible relationships between stochastic openings of the Ca2+ releasing channels at the microscopic level and the coordinated, regular behaviour observed at the whole cell level on the basis of a combined experimental and modelling approach.
Abstract : Fertilization in mammals is accompanied by Ca2+ oscillations in the egg cytoplasm, leading to exit from meiosis and entry into the first embryonic cell cycle. The signal transduction pathway linking these Ca2+ changes to cell-cycle related kinases has not yet been fully elucidated, but involves activation of calmodulin-dependent kinase II (CaMKII). Here, we develop a computational model to investigate the mechanism by which cell cycle resumption can be sensitive to the temporal pattern of Ca2+ increases. Using a model for CaMKII activation that reproduces the frequency sensitivity of this kinase, simulations confirm that Ca2+ spikes are accompanied by in phase variations in the level of CaMKII activity and suggest that in most mammalian species, Ca2+ spikes are well suited to maximize CaMKII activation. The full model assumes that CaMKII brings about a decrease in the level of cyclinB-cdk1 by two pathways, only one of which is CSFdependent. Parameters are selected to account for the experimental observations where mouse eggs were artificially activated by different Ca2+ stimulatory protocols. The model is then used in the context of "assisted oocyte activation (AOA)" to investigate why the best rates of successful activation are obtained when eggs are submitted to two applications of Ca2+ ionophores.
Abstract : Les rythmes cellulaires représentent un domaine d'investigation de choix pour la biologie des systèmes. Les exemples des rythmes circadiens et du cycle cellulaire montrent comment l'expérience et la modélisation permettent de clarifier les conditions dans lesquelles les comportements périodiques surviennent de manière spontanée au sein des réseaux de régulation cellulaire. Les rythmes circadiens résultent de boucles de rétroactions positives et négatives contrôlant l'expression de gènes de l'horloge. Le cycle cellulaire repose sur de multiples régulations entrecroisées au sein d'un réseau de kinases dépendantes de cyclines. Dans les deux cas, comme pour d'autres rythmes cellulaires décrits au cours des années récentes, le comportement périodique représente une propriété émergente des systèmes biologiques liée à leurs régulations.
Abstract : Switches (bistability) and oscillations (limit cycle) are omnipresent in biological networks. Synthetic genetic networks producing bistability and oscillations have been designed and constructed experimentally. However, in real biological systems, regulatory circuits are usually interconnected and the dynamics of those complex networks is often richer than the dynamics of simple modules. Here we couple the genetic Toggle switch and the Repressilator, two prototypic systems exhibiting bistability and oscillations, respectively. We study two types of coupling. In the first type, the bistable switch is under the control of the oscillator. Numerical simulation of this system allows us to determine the conditions under which a periodic switch between the two stable steady states of the Toggle switch occurs. In addition we show how birhythmicity characterized by the coexistence of two stable small-amplitude limit cycles, can easily be obtained in the system. In the second type of coupling, the oscillator is placed under the control of the Toggle switch. Numerical simulation of this system shows that this construction could for example be exploited to generate a permanent transition from a stable steady state to self-sustained oscillations (and vice versa) after a transient external perturbation. Those results thus describe qualitative dynamical behaviors that can be generated through the coupling of two simple network modules. These results differ from the dynamical properties resulting from interlocked feedback loops systems in which a given variable is involved at the same time in both positive and negative feedbacks. Finally the models described here may be of interest in synthetic biology, as they give hints on how the coupling should be designed to get the required properties.