Biomedical subjects

A Goldbeter

Publications and source records attributed to A Goldbeter.

At least 19 recordsLinked to original sources

PubMed1992

Suppression of chaos by periodic oscillations in a model for cyclic AMP signalling in Dictyostelium cells.

We investigate how the introduction of cells oscillating periodically affects the behaviour of a suspension of Dictyostelium discoideum amoebae undergoing chaotic oscillations of cyclic AMP. The analysis of a model indicates that a tiny proportion of periodic cells suffices to transform chaos into periodic oscillations in such suspensions. A similar result is obtained by forcing the aperiodic oscillations by a small-amplitude, periodic input of cyclic AMP. The results provide an explanation for the observation of regular oscillations in suspensions of a putatively chaotic mutant of Dictyostelium discoideum. More generally, the results show how chaos in biological systems may disappear through the coupling with periodic oscillations.

Animals↗

PubMed1992

Oscillations and waves of cytosolic calcium: insights from theoretical models.

Oscillations in cytosolic Ca2+ occur in a wide variety of cells, either spontaneously or as a result of external stimulation. This process is often accompanied by intracellular Ca2+ waves. A number of theoretical models have been proposed to account for the periodic generation and spatial propagation of Ca2+ signals. These models are reviewed and their predictions compared with experimental observations. Models for Ca2+ oscillations can be distinguished according to whether or not they rely on the concomitant, periodic variation in inositol 1,4,5-trisphosphate. Such a variation, however, is not required in models based on Ca(2+)-induced Ca2+ release. When Ca2+ diffusion is incorporated into these models, propagating waves of cytosolic Ca2+ arise, with profiles and rates comparable to those seen in the experiments.

Animals↗

PubMed1992

Protein phosphorylation driven by intracellular calcium oscillations: a kinetic analysis.

Given the ubiquitous nature of signal-induced Ca2+ oscillations, the question arises as to how cellular responses are affected by repetitive Ca2+ spikes. Among these responses, we focus on those involving protein phosphorylation. We examine, by numerical simulations of a theoretical model, the situation where a protein is phosphorylated by a Ca(2+)-activated kinase and dephosphorylated by a phosphatase. This reversible phosphorylation system is coupled to a mechanism generating cytosolic Ca2+ oscillations; for definiteness, this oscillatory mechanism is based on the process of Ca(2+)-induced Ca2+ release. The analysis shows that the average fraction of phosphorylated protein increases with the frequency of repetitive Ca2+ spikes; the latter frequency generally rises with the extent of external stimulation. Protein phosphorylation therefore provides a mechanism for the encoding of the external stimulation in terms of the frequency of signal-induced Ca2+ oscillations. Such a frequency encoding requires precise kinetic conditions on the Michaelis-Menten constants of the kinase and phosphatase, their maximal rates, and the degree of cooperativity in kinase activation by Ca2+. In particular, the most efficient encoding of Ca2+ oscillations based on protein phosphorylation occurs in conditions of zero-order ultrasensitivity, when the kinase and phosphatase are saturated by their protein substrate. The kinetic analysis uncovers a wide variety of temporal patterns of phosphorylation that could be driven by signal-induced Ca2+ oscillations.

Calcium↗

PubMed1992

Pulsatile signaling in intercellular communication. Periodic stimuli are more efficient than random or chaotic signals in a model based on receptor desensitization.

The efficiency of various patterns of pulsatile stimulation is determined in a model in which a receptor becomes desensitized in the presence of its stimulatory ligand. The effect of stochastic or chaotic changes in the duration and/or interval between successive pulses in a series of square-wave stimuli is investigated. Before addressing the effect of random variations in the pulsatile signal, we first extend the results of a previous analysis (Li, Y.X., and A. Goldbeter. 1989. Biophys. J. 55:125-145) by demonstrating the existence of an optimal periodic signal that maximizes target cell responsiveness whatever the magnitude of stimulation. As to the effect of stochastic or chaotic variations in the pulsatile stimulus, three kinds of random distributions are used, namely, a Gaussian and a white-noise distribution, and a chaotic time series generated by the logistic map. All these random distributions are symmetrically centered around the reference value of the duration or interval that characterizes the optimal periodic stimulus yielding maximal responsiveness in target cells. Stochastically or chaotically varying pulses are less effective than the periodic signal that corresponds to the optimal pattern of pulsatile stimulation. The response of the receptor system is most sensitive to changes in the time interval that separates successive stimuli. Similar conclusions hold when stochastic or chaotic signals are compared to a reference periodic stimulus differing from the optimal one, although the effect of random variations is then reduced. The decreased efficiency of stochastic pulses accounts for the observed superiority of periodic versus stochastic pulses of cyclic AMP (cAMP) in Dictyostelium amoebae. The results are also discussed with respect to the efficiency of periodic versus stochastic or chaotic patterns of hormone secretion.

Analysis of Variance↗

PubMed1991

A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase.

A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [Félix, M. A., Labbé, J. C., Dorée, M., Hunt, T. & Karsenti, E. (1990) Nature (London) 346, 379-382]. This conjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclin proteolysis by cdc2 kinase. The analysis shows how miototic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for the origin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification.

CDC2 Protein Kinase↗

PubMed1991

[Frequency coding in intercellular communication based on a generalized chronopharmacology].

An important function of biological rhythms is to support the frequency encoding of intercellular communications. Two examples of this phenomenon are discussed, namely, communication by cyclic AMP pulses in the slime mold Dictyostelium, and the pulsatile secretion of gonadotropic hormones. The existence of an optimal frequency of stimulation in these two systems possesses clinical implications, as attested by the use of pulsatile hormonal therapies in endocrinology. More generally, the pulsatile administration of some drugs, at the appropriate frequency, could maximize their physiological effect. Such a generalized chronopharmacology would take into account the kinetic characteristics of desensitization and resensitization in target cells, and would not be limited to the sole consideration of circadian rhythms within the organism.

Animals↗

PubMed1990

Frequency encoding of pulsatile signals of cAMP based on receptor desensitization in Dictyostelium cells.

Dictyostelium discoideum amoebae represent a prototype for the study of periodic signaling in intercellular communication. These cells synthesize cAMP in response to cAMP pulses. Cell responsiveness in Dictyostelium can be characterized by the capability to generate a large number of significant responses to cAMP signals in a given amount of time. The existence of a frequency of pulsatile cAMP signals yielding maximum responsiveness is demonstrated by analysis of a realistic model for cAMP synthesis, based on receptor desensitization. The optimal frequency of stimulation closely depends on the kinetics of receptor desensitization and resensitization in target cells. Synthesis of cAMP is determined both in conditions where cells are not excitable and in conditions where they relay suprathreshold pulses of cAMP. Moreover, the effect of the stimulus waveform is investigated, and several measures of cell responsiveness are compared. The results provide an explanation for the effectiveness of cAMP pulses delivered at 5 min intervals, and for the failure of pulses delivered at 2 min intervals, in inducing slime mold development. Besides applying to intercellular communication in Dictyostelium, the present analysis bears on patterns of pulsatile signaling observed for hormones and growth factors. In all these cases, it appears that pulsatile signals can be encoded in terms of their frequency on the basis of desensitization in target cells.

Cell Communication↗

PubMed1990

Allosteric regulation, cooperativity, and biochemical oscillations.

Allosteric regulation is associated with a number of periodic phenomena in biochemical systems. The cooperative nature of such regulatory interactions provides a source of nonlinearity that favors oscillatory behavior. We assess the role of cooperativity in the onset of biochemical oscillations by analyzing two specific examples. First, we consider a model for a product-activated allosteric enzyme which has previously been proposed to account for glycolytic oscillations. While enzyme cooperativity plays an important role in the occurrence of oscillations, we show that these may nevertheless occur in the absence of cooperativity when the reaction product is removed in a Michaelian rather than linear manner. The second model considered was recently proposed to account for signal-induced oscillations of intracellular calcium. This phenomenon originates from a nonlinear process of calcium-induced calcium release. Here also, the cooperative nature of that positive feedback favors the occurrence of oscillations but is not absolutely required for periodic behavior. Besides underlining the importance of cooperativity, the results highlight the role of diffuse nonlinearities distributed over several steps within a regulated system: even in the absence of cooperativity, such mild nonlinearities (e.g., of the Michaelian type) may combine to raise the overall degree of nonlinearity up to the level required for oscillations.

Allosteric Regulation↗

PubMed1990

Covalent modification of proteins as a threshold mechanism in development.

Thresholds are a central but somewhat neglected aspect of cellular processes in development. An analysis has been made of the conditions in which different thresholds can be generated in the covalent modification of a number of target proteins when the concentration of an effector is continuously increased. It is assumed that the effector, which could represent a morphogen, activates, for example, kinases that phosphorylate the proteins. Thresholds are found when the modifying enzymes are saturated by their protein substrates, i.e. in conditions of zero-order ultrasensitivity (Goldbeter, A. & Koshland, D. E. 1981. An amplified sensitivity arising from covalent modification in biological systems. Proc. natn. Acad. Sci. U.S.A. 78, 6840-6844). Sequential thresholds can be generated when the kinase/phosphatase pairs differ either in the ratio of maximum modification rates or in the affinity of the effector for each kinase.

Animals↗

PubMed1990

Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation.

In a variety of cells, hormonal or neurotransmitter signals elicit a train of intracellular Ca2+ spikes. The analysis of a minimal model based on Ca2(+)-induced Ca2+ release from intracellular stores shows how sustained oscillations of cytosolic Ca2+ may develop as a result of a rise in inositol 1,4,5-trisphosphate (InsP3) triggered by external stimulation. This rise elicits the release of a certain amount of Ca2+ from an InsP3-sensitive intracellular store. The subsequent rise in cytosolic Ca2+ in turn triggers the release of Ca2+ from a second store insensitive to InsP3. In contrast to the model proposed by Meyer and Stryer [Meyer, T. & Stryer, L. (1988) Proc. Natl. Acad. Sci. USA 85, 5051-5055], the present model, which contains only two variables, predicts the occurrence of periodic Ca2+ spikes in the absence of InsP3 oscillations. Such results indicate that repetitive Ca2+ spikes evoked by external stimuli do not necessarily require the concomitant, periodic variation of InsP3. The model is closely related to that proposed by Kuba and Takeshita [Kuba, K. & Takeshita, S. (1981) J. Theor. Biol. 93, 1009-1031] for Ca2+ oscillations in sympathetic neurones, based on Ca2(+)-induced Ca2+ release. We extend their results by showing the minimal conditions in which the latter process gives rise to periodic behavior and take into account the role of the rise in InsP3 caused by external stimulation. The analysis further shows how signal-induced Ca2+ oscillations might be effectively encoded in terms of their frequency through the phosphorylation of a cellular substrate by a protein kinase activated by cytosolic Ca2+.

Animals↗

PubMed1990

Latency correlates with period in a model for signal-induced Ca2+ oscillations based on Ca2(+)-induced Ca2+ release.

Oscillations in cytosolic Ca2+ develop in a variety of cells after an induction phase, called latency, the duration of which depends on the magnitude of external stimulation. Experiments in hepatocytes indicate that the period and latency of Ca2+ oscillations both decrease as the level of the stimulus increases. We analyze the correlation between period and latency in a model recently proposed for signal-induced Ca2+ oscillations. We show that the linear relationship between period and latency observed in the experiments arises naturally in this model as a result of the mechanism of Ca2(+)-induced Ca2+ release on which it is based.

Animals↗

PubMed1990

Oscillatory dynamics in intercellular communication.

The role of biological rhythms in the control of intercellular communication is briefly reviewed. In particular, pulsatile cAMP signaling in the slime mold, Dictyostelium discoideum, the pulsatile release of the hormone GnRH in higher animals, and cytosolic calcium oscillations are discussed, with special reference to underlying molecular mechanisms. It is pointed out that there exists an optimal pattern of periodic stimulation by hormones and that frequency encoding has some advantages in comparison with amplitude encoding, especially concerning the accuracy of control.

Biological Clocks↗

PubMed1989

Oscillatory isozymes as the simplest model for coupled biochemical oscillators.

We analyze a simple model for two autocatalytic reactions catalyzed by two distinct isozymes transforming, with different kinetic properties, a given substrate into the same product. This two-variable system can be viewed as the simplest model of chemically coupled biochemical oscillators. Phase-plane analysis indicates how the kinetic differences between the two enzymes give rise to complex oscillatory phenomena such as the coexistence of a stable steady state and a stable limit cycle, or the co-existence of two simultaneously stable oscillatory regimes (birhythmicity). The model allows one to verify a previously proposed conjecture for the origin of birhythmicity. In other conditions, the system admits multiple oscillatory domains as a function of a control parameter whose variation gives rise to markedly different types of oscillations. The latter behavior provides an explanation for the occurrence of multiple modes of oscillations in thalamic neurons.

Algorithms↗

PubMed1989

Regular oscillations in suspensions of a putatively chaotic mutant of Dictyostelium discoideum.

We have tested the light-scattering properties of suspensions of the Dictyostelium discoideum mutant HH201 derived from the mutant Fr17. Previous studies indicated that HH201 and Fr17 possess highly irregular rhythmic properties which might represent aperiodic oscillations, i.e. chaos. We report that the former mutant can display regular oscillatory behavior. Possible explanations for this result are discussed, including that of a transition from chaotic to periodic behavior resulting from some parameter change or from strong intercellular coupling in cell suspensions.

Biological Clocks↗

PubMed1989

Frequency specificity in intercellular communication. Influence of patterns of periodic signaling on target cell responsiveness.

Cells often communicate by means of periodic signals, as exemplified by a large number of hormones and by the aggregation of Dictyostelium discoideum amebas in response to periodic pulses of cyclic AMP. Periodic signaling allows bypassing the phenomenon of desensitization brought about by constant stimuli. To gain further insight into the efficiency of pulsatile signaling, we analyze the effect of periodic stimulation on the dynamic behavior of a receptor system capable of desensitization toward its ligand. We first show that the receptor system adapts to square-wave stimuli, i.e., the response eventually reaches a steady, periodic pattern after a transient phase. By analyzing the dependence of the response on the characteristics of the square-wave stimulation, we show that there exist a waveform and a period of that signal that result in maximum responsiveness of the target system. Similar results are obtained when the signal takes the more realistic form of a periodically repeated stimulation followed by exponential decay of the ligand. The results are discussed with respect to the role of pulsatile secretion of gonadotropin-releasing hormone (GnRH) by the hypothalamus and of periodic signaling by cyclic AMP pulses in Dictyostelium. The analysis accounts for the existence, in both cases, of an optimal frequency and waveform of the periodic stimulus that correspond to maximum target cell responsiveness.

Animals↗

PubMed1988

Dynamics of a biochemical system with multiple oscillatory domains as a clue for multiple modes of neuronal oscillations.

We analyze the behavior of a two-variable biochemical model in conditions where it admits multiple oscillatory domains in parameter space. The model represents an autocatalytic enzyme reaction with input of substrate both from a constant source and from non-linear recycling of product into substrate. This system was previously studied for birhythmicity, i.e. the coexistence between two stable periodic regimes (Moran and Goldbeter 1984), and for multi-threshold excitability (Moran and Goldbeter 1985). When two distinct oscillatory domains obtain as a function of the substrate injection rate, the system is capable of exhibiting two markedly different modes of oscillations for slightly different values of this control parameter. Phase plane analysis shows how the multiplicity of oscillatory domains depends on the parameters that govern the underlying biochemical mechanism of product recycling. We analyze the response of the model to various kinds of transient perturbations and to periodic changes in the substrate input that bring the system through the two ranges of oscillatory behavior. The results provide a qualitative explanation for experimental observations (Jahnsen and Llinas 1984b) related to the occurrence of two different modes of oscillations in thalamic neurones.

Models, Biological↗

PubMed1988

Finding complex oscillatory phenomena in biochemical systems. An empirical approach.

Starting with a model for a product-activated enzymatic reaction proposed for glycolytic oscillations, we show how more complex oscillatory phenomena may develop when the basic model is modified by addition of product recycling into substrate or by coupling in parallel or in series two autocatalytic enzyme reactions. Among the new modes of behavior are the coexistence between two stable types of oscillations (birhythmicity), bursting, and aperiodic oscillations (chaos). On the basis of these results, we outline an empirical method for finding complex oscillatory phenomena in autonomous biochemical systems, not subjected to forcing by a periodic input. This procedure relies on finding in parameter space two domains of instability of the steady state and bringing them close to each other until they merge. Complex phenomena occur in or near the region where the two domains overlap. The method applies to the search for birhythmicity, bursting and chaos in a model for the cAMP signalling system of Dictyostelium discoideum amoebae.

Cyclic AMP↗

PubMed1987

Energy expenditure in the control of biochemical systems by covalent modification.

Regulation by reversible, covalent modification of proteins requires a continuous expenditure of energy, even in a steady-state situation. The cost of this energy drain is evaluated for the case of an effector controlling the modifying enzyme and an effector controlling the demodifying enzyme and for the case of dual control in which an effector activates one of these enzymes and inhibits the other. Energy consumption is determined when the converter enzymes are functioning in the first-order and zero-order domains. The profile of energy expenditure versus fractional protein modification at steady state varies both as a function of the mechanism of control of the converter enzymes and of the kinetic domain in which they operate. This theory allows one to predict the strategies that would minimize energy costs. Dual control appears to provide maximum sensitivity with minimal energy expenditure. The analysis is applied to two experimental systems. Comparison of ATP turnover rates with rates for individual modification enzymes in living systems shows that a significant fraction of the total energy expenditure of an organism is required for the large number of reactions which involve covalent modification of proteins. It is concluded that there will be selection pressure for energy-efficient control of covalent regulation.

Adenosine Triphosphate↗