Abstracts 1999

Abstract : In the presence of an insulinotropic glucose concentration, beta-cells, in intact pancreatic islets, exhibit periodic bursting electrical activity consisting of an alternation of active and silent phases. The fraction of time spent in the active phase over a period is called the plateau fraction and is correlated with the rate of insulin release. However, the mechanisms that regulate the plateau fraction remain unclear. In this paper we investigate the possible role of the plasma membrane Na+/Ca2+ exchange of the beta-cell in controlling the plateau fraction. We have extended different single-cell models to incorporate this Ca2+ -activated electrogenic Ca2+ transporter. We find that the Na+/Ca2+ exchange can provide a physiological mechanism to increase the plateau fraction as the glucose concentration is raised. In addition, we show theoretically that the Na+/Ca2+ exchanger is a key regulator of the cytoplasmic calcium concentration in clusters of heterogeneous cells with gap-junctional electrical coupling.

Abstract : We have combined the patch-clamp technique with microfluorimetry of the cytoplasmic Ca2+ concentration ([Ca2+]i) to characterize Na/Ca exchange in mouse beta-cells and to determine its importance for [Ca2+]i buffering and shaping of glucose-induced electrical activity. The exchanger contributes to Ca2+ removal at [Ca2+]i above 1 microM, where it accounts for > 35% of the total removal rate. At lower [Ca2+]i, thapsigargin-sensitive Ca2+ -ATPases constitute a major (70% at 0.8 microM [Ca2+]i) mechanism for Ca2+ removal. The beta-cell Na/Ca exchanger is electrogenic and has a stoichiometry of three Na+ for one Ca2+. The current arising from its operation reverses at approximately -20 mV (current inward at more negative voltages), has a conductance of 53 pS/pF (14 microM [Ca2+]i), and is abolished by removal of external Na+ or by intracellularly applied XIP (exchange inhibitory peptide). Inhibition of the exchanger results in shortening (50%) of the bursts of action potentials of glucose-stimulated beta-cells in intact islets and a slight (5 mV) hyperpolarization. Mathematical simulations suggest that the stimulatory action of glucose on beta-cell electrical activity may be accounted for in part by glucose-induced reduction of the cytoplasmic Na+ concentration with resultant activation of the exchanger.

Abstract : We investigate the various types of complex Ca²⁺ oscillations which can arise in a model based on the mechanism of Ca2+ -induced Ca2+ release (CICR), that takes into account the Ca2+ -stimulated degradation of inositol 1,4,5-trisphosphate (InsP3) by a 3-kinase. This model was previously proposed in the course of an investigation of plausible mechanisms capable of generating complex Ca2+ oscillations (Borghans et al., 1997). Besides simple periodic behavior, this model for cytosolic Ca2+ oscillations in non-excitable cells shows complex oscillatory phenomena like bursting or chaos. We show that the model also admits a coexistence between two stable regimes of sustained oscillations (birhythmicity). The occurrence of these various modes of oscillatory behavior is analyzed by means of bifurcation diagrams. Complex oscillations are characterized by means of Poincaré sections, power spectra and Lyapounov exponents. The results point to the role of self-modulation of the InsP₃ signal by 3-kinase as a possible source for complex temporal patterns in Ca2+ signaling.

Abstract : We examine theoretical models for circadian oscillations based on transcriptional regulation in Drosophila and Neurospora. For Drosophila, the molecular model is based on the negative feedback exerted on the expression of the per and tim genes by the complex formed between the PER and TIM proteins. For Neurospora, similarly, the model relies on the feedback exerted on the expression of the frq gene by its protein product, FRQ. In both models sustained rhythmic variations in protein and mRNA levels occur in continuous darkness, in the form of limit cycle oscillations. The effect of light on circadian rhythms is taken into account in the models by considering that it triggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the molecular level, we show that the models can account for the entrainment of circadian rhythms by light-dark cycles and for the damping of the oscillations in constant light, though such damping occurs more readily in the Drosophila model. The models account for the phase shifts induced by light pulses and allow the construction of phase response curves. These compare well with experimental results obtained in Drosophila. The model for Drosophila shows that when applied at the appropriate phase, light pulses of appropriate duration and magnitude can permanently or transiently suppress circadian rhythmicity. We investigate the effects of the magnitude of light-induced changes on oscillatory behavior. Finally, we discuss the common and distinctive features of circadian oscillations in the two organisms.

Abstract : In Drosophila, circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes which code for these two proteins. On the basis of these experimental observations, we have recently proposed a theoretical model for circadian oscillations of the PER and TIM proteins in Drosophila (Leloup & Goldbeter, 1998). Here we show that for constant environmental conditions this model is capable of generating autonomous chaotic oscillations. For other parameter values, the model can also display birhythmicity, i.e. the coexistence between two stable regimes of limit cycle oscillations. We analyze the occurrence of chaos and birhythmicity by means of bifurcation diagrams and locate the different domains of complex oscillatory behavior in parameter space. The relative smallness of these domains raises doubts as to the possible physiological significance of chaos and birhythmicity in regard to circadian rhythm generation. Beyond the particular context of circadian rhythms we discuss the results in the light of other mechanisms underlying chaos and birhythmicity in regulated biological systems.

Abstract : The animal cell cycle is controlled by the periodic variation of two cyclin-dependant protein kinases, cdk1 and cdk2, which govern the entry into the M (mitosis) ans S (DNA replication) phases, respectively. The ordered progression between these phases is achieved thanks to the existence of checkpoint mechanisms based on mutual inhibition of these processes. Here we study a simple theoretical model for oscillations in cdk1 and cdk2 activity, involving mutual inhibition of the two oscillators. Each minimal oscillator is described by a three-variable cascade involving a cdk, together with the associated cyclin and cyclin-degrading enzyme. The dynamics of this skeleton model of coupled oscillators is determined as a function of the strength of their mutual inhibition. The most common mode of dynamic behavior, obtained under conditions of strong mutual inhibition, is that of alternating oscillations in cdk1 and cdk2, which correspond to the physiological situation of the ordered recurrence of the M and S phases. In addition, for weaker inhibition we obtain evidence for a variety of dynamic phenomena such as complex periodic oscillations, chaos, and the coexistence between multiple periodic or chaotic attractors. We discuss the conditions of occurrence of these various modes of oscillatory behavior, as well as their possible physiological significance.

Abstract : In the cytoplasm of cells of different types, discrete clusters of inositol 1,4,5-trisphosphate-sensitive Ca2+ channels generate Ca2+ signals of graded size, ranging from blips, which involve the opening of only one channel, to moderately larger puffs, which result from the concerted opening of a few channels in the same cluster. These channel clusters are of unknown size or geometrical characteristics. The aim of this study was to estimate the number of channels and the interchannel distance within such a cluster. Because these characteristics are not attainable experimentally, we performed computer stochastic simulations of Ca2+ release events. We conclude that, to ensure efficient interchannel communication, as experimentally observed, a typical cluster should contain two or three tens of inositol 1,4,5-trisphosphate-sensitive Ca2+ channels in close contact.