Abstract : Spiral waves of intracellular Ca2+ have often been observed in Xenopus oocytes. Such waves can be accounted for by most realistic models for Ca2+ oscillations taking diffusion of cytosolic Ca2+ into account, but their initiation requires rather demanding and unphysiological initial conditions. Here, it is shown by means of numerical simulations that these spiral Ca2+ waves naturally arise if the cytoplasm is assumed to be heterogeneous both at the level of the synthesis and metabolism of D-myo-inositol 1,4,5-trisphosphate [Ins(1,4,5)P3] and at the level of the distribution of the Ins(1,4,5)P3 receptors. In such conditions, a spiral can be initiated in the simulations after an increase in Ins(1,4,5)P3 concentration, with the direction of rotation being determined by the position of the region of high receptor density with respect to the locus of Ins(1,4,5)P3 production.
Abstract : Mammalian eggs are ovulated in metaphase II of meiosis, in a state characterized by high levels of cyclin B and of active maturation promoting factor (MPF). This arrest is mediated by an activity referred to as cytostatic factor (CSF) which prevents the degradation of cyclin. Fertilization triggers a train of Ca2+ spikes which is responsible for the decrease in activity of both MPF and CSF. The decline in MPF however much precedes that in CSF. Experimental observations on mammalian eggs indicate that the kinetics of cell cycle resumption much depends on the temporal pattern of the repetitive Ca2+ spikes. Here, we propose a theoretical model which accounts for Ca2+ -induced relief from metaphase II arrest in mammalian eggs. The model is based on the fact that Ca2+/calmodulin kinase II (CaMKII) activation is the primary event leading to inactivation of both CSF and MPF. To account for experimental observations, it has to be assumed that CaMKII activation affects the level of the active form of the anaphase promoting complex (APC), which initiates the degradation of cyclin, through two pathways characterized by different time scales. Thus, we hypothesize that CaMKII activation by Ca2+ leads to the transformation of a mediator protein from a form which stimulates the inactivation of the APC into a form which gradually and indirectly induces the deactivation of CSF. In consequence, a sufficient number of Ca2+ spikes first triggers the decrease of MPF, thus allowing the egg to enter in interphase, and later that of CSF. Finally, when CSF is low and when Ca2+ oscillations have stopped, the level of MPF can increase again, a phenomenon that would correspond to the first mitosis. This model also accounts for the observed dependence of the time of entry in interphase (marked by the appearance of the pronuclei) on the frequency of Ca2+ spikes, as well as for the possible entry in metaphase III arrest, a pathological state of the egg which results from an insufficient activation by Ca2+. This study provides some theoretical prediction as to the time of the first mitosis as a function of the temporal pattern of Ca2+ oscillations.
Abstract : In many cell types, Ca2+ signals are organized in the form of repetitive spikes. The frequency of these intracellular Ca2+ oscillations increases with the level of stimulation, suggesting the existence of a frequency encoding phenomenon. The question arises as to how the frequency of Ca2+ oscillations can be decoded inside the cell. Ca2+/calmodulin kinase II has long been proposed as an attractive candidate, as it is a key target of Ca2+ signals. By immobilizing the Ca2+/calmodulin kinase II and subjecting it to pulses of Ca2+ of variable amplitude, duration, and frequency, De Koninck and Schulman have shown for the first time that the autonomous activity of Ca2+/calmodulin kinase II is highly sensitive to the temporal pattern of Ca2+ oscillations.
Abstract : We examine the theoretical aspects of temporal and spatiotemporal organization in the cAMP signaling system of Dictyostelium discoideum amoebae which aggregate in a wavelike manner after starvation, in response to pulses of cAMP emitted with a periodicity of several minutes by cells behaving as aggregation centers. We first extend the model based on receptor desensitization, previously proposed by Martiel and Goldbeter, by incorporating the role of G proteins in signal transduction. The extended model accounts for observations on the response of the signaling system to successive step increases in extracellular cAMP. In the presence of the positive feedback loop in cAMP synthesis, this model generates sustained oscillations in cAMP and in the fraction of active cAMP receptor, similar to those obtained in the simpler model where the role of the G proteins is not taken into account explicitly. We use the latter model to address the formation of concentric and spiral waves of cAMP in the course of D. discoideum aggregation. Previous analyses of the model showed that a progressive increase in the activity of adenylate cyclase and phosphodiesterase can account for the transitions no relay-relay-oscillations-relay observed in the experiments. We show that the degree of cellular synchronization on such a developmental path in parameter space markedly affects the nature of the spatial patterns generated by the model. These patterns range from concentric waves to a small number of large spirals, and finally to a large number of smaller spirals, as the degree of developmental desynchronization between cells increases.
Abstract : We present a model for circadian oscillations of the PERIOD (PER) and TIMELESS (TIM) proteins in Drosophila. The model for the circadian clock is based on multiple phosphorylation of PER and TIM and on the negative feedback exerted by a nuclear PER-TIM complex on the transcription of the per and tim genes. Periodic behavior occurs in a large domain of parameter space in the form of limit cycle oscillations. These sustained oscillations occur in conditions corresponding to continuous darkness or to entrainment by light-dark cycles, and are in good agreement with experimental observations on the temporal variations of PER and TIM and of per and tim mRNAs. Birhythmicity (coexistence of two periodic regimes) and aperiodic oscillations (chaos) occur in a restricted range of parameter values. The results are compared with the predictions of a model based on the sole regulation by PER. Both the formation of a complex between PER and TIM and protein phosphorylation are found to favor oscillatory behavior. Determining how the period depends on several key parameters allows us to test possible molecular explanations proposed for the altered period in the perl and pers mutants. The extended model further allows the construction of phase response curves based on the light-induced triggering of TIM degradation. These curves, established as a function of both the duration and magnitude of the effect of a light pulse, match the phase response curves obtained experimentally in the wild type and perS mutant of Drosophila.
Abstract : The mechanism of circadian oscillations in the period (PER) and the timeless (TIM) proteins in Drosophila is investigated by means of a theoretical model. A first version of this model takes into account only the PER protein, while the second, extended version incorporates the formation of a PER-TIM complex. The model for the Drosophila circadian clock is based on multiple phosphorylation of PER (and TIM) and on the negative feedback exerted by the nuclear form of PER (or PER-TIM complex) on the transcription of the per (and tim) genes. Periodic behavior in the model occurs in the form of limit cycle oscillations. The size of the oscillatory domain in parameter space becomes larger as the degree of cooperativity of the negative feedback process increases, although sustained oscillations can occur in the absence of such cooperativity. The extended model accounts for the phase-shifts induced by light pulses, when incorporating the observation that light triggers TIM degradation.
Abstract : Confocal microscope studies with fluorescent dyes of inositol 1,4,5-trisphosphate (InsP3)-induced intracellular Ca2+ mobilization recently established the existence of 'elementary' events, dependent on the activity of individual InsP3-sensitive Ca2+ channels. In the present work, we try by theoretical stochastic simulation to explain the smallest signals observed in those studies, which were referred to as Ca2+ 'blips' [Parker I., Yao Y. Ca2+ transients associated with openings of inositol trisphosphate-gated channels in Xenopus oocytes. J Physiol Lond 1996; 491: 663-668]. For this purpose, we assumed a simple molecular model for the InsP3-sensitive Ca2+ channel and defined a set of parameter values accounting for the results obtained in electrophysiological bilayer experiments [Bezprozvanny I., Watras J., Ehrlich B.E. Bell-shaped calcium-response curves of Ins(1,4,5)P3- and calcium-gated channels from endoplasmic reticulum of cerebellum. Nature 1991; 351: 751-754; Bezprozvanny I., Ehrlich B.E. Inositol (1,4,5)-trisphosphate (InsP3)-gated Ca channels from cerebellum: conduction properties for divalent cations and regulation by intraluminal calcium. J. Gen. Physiol. 1994; 104: 821-856]. With a stochastic procedure which considered cytosolic Ca2+ diffusion explicitly, we then simulated the behaviour of a single channel, placed in a realistic physiological environment. An attractive result was that the simulated channel exhibited bursts of activity, arising from repetitive channel openings, which were responsible for transient rises in Ca2+ concentration and were reminiscent of the relatively long-duration experimental Ca2+ blips. The influence of the values chosen for the various parameters (affinity and diffusion coefficient of the buffers, luminal Ca2+ concentration) on the kinetic characteristics of these theoretical blips is analyzed.