Abstract : Glycogenolytic agonists induce coordinated Ca(2+) oscillations in multicellular rat hepatocyte systems as well as in the intact liver. The coordination of intercellular Ca(2+) signals requires functional gap-junction coupling. The mechanisms ensuring this coordination are not precisely known. We investigated possible roles of Ca(2+) or inositol 1,4,5-trisphosphate (InsP(3)) as a coordinating messengers for Ca(2+) spiking among connected hepatocytes. Application of ionomycin or of supra-maximal concentrations of agonists show that Ca(2+) does not significantly diffuse between connected hepatocytes, although gap junctions ensure the passage of small signaling molecules, as demonstrated by FRAP experiments. By contrast, coordination of Ca(2+) spiking among connected hepatocytes can be favored by a rise in the level of InsP(3), via the increase of agonist concentrations, or by a shift in the affinity of InsP(3) receptor for InsP(3). In the same line, coordination cannot be achieved if the InsP(3) is rapidly metabolized by InsP(3)-phosphatase in one cell of the multiplet. These results demonstrate that even if small amounts of Ca(2+) diffuse across gap junctions, they most probably do not play a significant role in inducing a coordinated Ca(2+) signal among connected hepatocytes. By contrast, coordination of Ca(2+) oscillations is fully dependent on the diffusion of InsP(3) between neighboring cells.
Abstract : We consider a model for a network of phosphorylation-dephosphorylation cycles coupled through forward and backward regulatory interactions, such that a protein phosphorylated in a given cycle activates the phosphorylation of a protein by a kinase in the next cycle as well as the dephosphorylation of a protein by a phosphatase in a preceding cycle. The network is cyclically organized in such a way that the protein phosphorylated in the last cycle activates the kinase in the first cycle. We study the dynamics of the network in the presence of both forward and backward coupling, in conditions where a threshold exists in each cycle in the amount of protein phosphorylated as a function of the ratio of kinase to phosphatase maximum rates. We show that this system can display sustained (limit-cycle) oscillations in which each cycle in the pathway is successively turned on and off, in a sequence resembling the fall of a series of dominoes. The model thus provides an example of a biochemical system displaying the dynamics of dominoes and clocks (Murray & Kirschner, 1989). It also shows that a continuum of clock waveforms exists of which the fall of dominoes represents a limit. When the cycles in the network are linked through only forward (positive) coupling, bistability is observed, while in the presence of only backward (negative) coupling, the system can display multistability or oscillations, depending on the number of cycles in the network. Inhibition or activation of any kinase or phosphatase in the network immediately stops the oscillations by bringing the system into a stable steady state; oscillations resume when the initial value of the kinase or phosphatase rate is restored. The progression of the system on the limit cycle can thus be temporarily halted as long as an inhibitor is present, much as when a domino is held in place. These results suggest that the eukaryotic cell cycle, governed by a network of phosphorylation-dephosphorylation reactions in which the negative control of cyclin-dependent kinases plays a prominent role, behaves as a limit-cycle oscillator impeded in the presence of inhibitors. We contrast the case where the sequence of domino-like transitions constitutes the clock with the case where the sequence of transitions is passively coupled to a biochemical oscillator operating as an independent clock.
Abstract : Using a molecular model for circadian rhythms in Drosophila based on transcriptional regulation, we show how a single, critical pulse of light can permanently suppress circadian rhythmicity, while a second light pulse can restore the abolished rhythm. The phenomena occur via the pulsatile induction of either protein degradation or gene expression, in conditions where a stable steady state coexists with stable circadian oscillations of the limit cycle type. The model indicates that suppression by a light pulse can only be accounted for by assuming that the biochemical effects of such a pulse much outlast its actual duration. We determine the characteristics of critical pulses suppressing the oscillations, as a function of the phase at which the rhythm is perturbed. The model predicts how the amplitude and duration of the biochemical changes induced by critical pulses vary with this phase. The results provide a molecular, dynamical explanation for the long-term suppression of circadian rhythms observed in a variety of organisms in response to a single light pulse, and for the subsequent restoration of the rhythms by a second light pulse.
Abstract : We present an overview of mechanisms responsible for simple or complex oscillatory behavior in metabolic and genetic control networks. Besides simple periodic behavior corresponding to the evolution toward a limit cycle we consider complex modes of oscillatory behavior such as complex periodic oscillations of the bursting type and chaos. Multiple attractors are also discussed, e.g. the coexistence between a stable steady state and a stable limit cycle (hard excitation), or the coexistence between two simultaneously stable limit cycles (birhythmicity). We discuss mechanisms responsible for the transition from simple to complex oscillatory behavior by means of a number of models serving as selected examples. The models were originally proposed to account for simple periodic oscillations observed experimentally at the cellular level in a variety of biological systems. In a second stage, these models were modified to allow for complex oscillatory phenomena such as bursting, birhythmicity, or chaos. We consider successively (1) models based on enzyme regulation, proposed for glycolytic oscillations and for the control of successive phases of the cell cycle, respectively; (2) a model for intracellular Ca(2+) oscillations based on transport regulation; (3) a model for oscillations of cAMP based on receptor desensitization in Dictyostelium cells; and (4) a model based on genetic regulation for circadian rhythms in Drosophila. Two main classes of mechanism leading from simple to complex oscillatory behavior are identified, namely (i) the interplay between two endogenous oscillatory mechanisms, which can take multiple forms, overt or more subtle, depending on whether the two oscillators each involve their own regulatory feedback loop or share a common feedback loop while differing by some related process, and (ii) self-modulation of the oscillator through feedback from the system's output on one of the parameters controlling oscillatory behavior. However, the latter mechanism may also be viewed as involving the interplay between two feedback processes, each of which might be capable of producing oscillations. Although our discussion primarily focuses on the case of autonomous oscillatory behavior, we also consider the case of nonautonomous complex oscillations in a model for circadian oscillations subjected to periodic forcing by a light-dark cycle and show that the occurrence of entrainment versus chaos in these conditions markedly depends on the waveform of periodic forcing.