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Biomedical subjects

A Goldbeter

Publications and source records attributed to A Goldbeter.

At least 55 records · Page 3Linked to original sources
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↗
PubMed1987

From simple to complex oscillatory behaviour: analysis of bursting in a multiply regulated biochemical system.

We analyze the transition from simple to complex oscillatory behaviour in a three-variable biochemical system that consists of the coupling in series of two autocatalytic enzyme reactions. Complex periodic behaviour occurs in the form of bursting in which clusters of spikes are separated by phases of relative quiescence. The generation of such temporal patterns is investigated by a series of complementary approaches. The dynamics of the system is first cast into two different time-scales, and one of the variables is taken as a slowly-varying parameter influencing the behaviour of the two remaining variables. This analysis shows how complex oscillations develop from simple periodic behaviour and accounts for the existence of various modes of bursting as well as for the dependence of the number of spikes per period on key parameters of the model. We further reduce the number of variables by analyzing bursting by means of one-dimensional return maps obtained from the time evolution of the three-dimensional system. The analysis of a related piecewise linear map allows for a detailed understanding of the complex sequence leading from a bursting pattern with p spikes to a pattern with p + 1 spikes per period. We show that this transition possesses properties of self-similarity associated with the occurrence of more and more complex patterns of bursting. In addition to bursting, period-doubling bifurcations leading to chaos are observed, as in the differential system, when the piecewise-linear map becomes nonlinear.

Catalysis↗
PubMed1986

A mechanism for exact sensory adaptation based on receptor modification.

We provide a theoretical explanation for the observation that in many sensory systems a step increase in stimulus triggers a response that goes through a maximum and then returns to the basal level. Considered here is a receptor molecule that in the absence of ligand can be found in either of two states R and D. Two more states, RL and DL, are formed upon the addition of ligand L. It is assumed that the receptor triggers activity in a sensory system, and that the activity is proportional to a weighted combination of the fractions of molecules that are in each of the four states. It is shown that judicious choice of the weights can provide both an adequate response and exact adaptation to step increases in stimuli. The interconversion between states may operate without energy expenditure or through covalent modification. In both cases, adaptation is associated with receptor modification that acts as a counterweight to changed external conditions. Application to cAMP secretion in Dictyostelium discoideum and to chemotaxis in bacteria is discussed.

Adaptation, Physiological↗
PubMed1986

A molecular mechanism for sensory adaptation based on ligand-induced receptor modification.

Physiological responses mediated by cell-surface receptors frequently adapt or "desensitize" (i.e., terminate despite persistent occupancy of receptors by ligand). Binding of ligands to the external domains of a wide variety of surface receptors induces covalent modification of their cytoplasmic domains. A mechanism is presented in which the variety of receptor states generated by ligand binding and covalent modification act together to regulate physiological responsiveness. The development of the model is guided by observations of adaptation for chemotaxis in Escherichia coli and adenylate cyclase activation in Dictyostelium. The general features of the marked response and eventual exact adaptation predicted by the model match those observed in the experimental systems.

Adaptation, Physiological↗
PubMed1985

Selection between multiple periodic regimes in a biochemical system: complex dynamic behaviour resolved by use of one-dimensional maps.

We analyse a model biochemical system in which two autocatalytic enzyme reactions are coupled in series, in conditions where multiple stable periodic regimes coexist for the same set of parameter values. We determine how the periodic regimes are reached from different initial conditions. The structure of the attraction basins is generally simple in the case of two coexisting limit cycles (birhythmicity). This structure and the associated behaviour may, however, become highly complex. In particular, the system exhibits enhanced sensitivity to initial conditions when the boundaries of the attraction basins are fractal. In the latter case, it becomes difficult to predict the evolution towards either one of two limit cycles, a phenomenon known as final state sensitivity. We show how these complex phenomena can be explained in a unified and simple manner by means of one-dimensional return maps derived from the time evolution of the model and from fifth degree polynomial equations. We suggest experimental tests of the sensitivity to initial conditions in chemical systems presenting birhythmicity. The physiological significance of the results is discussed with respect to the sensitivity of regulatory systems admitting multiple stable biological rhythms.

Allosteric Regulation↗
PubMed1985

Excitability with multiple thresholds. A new mode of dynamic behavior analyzed in a regulated biochemical system.

We analyze in a biochemical model the phenomenon of excitability in which suprathreshold perturbations of a stable steady state are amplified in a pulsatory manner. The two-variable model is that of an autocatalytic enzyme reaction with recycling of product into the substrate. This model was previously studied for the coexistence between two stable periodic regimes (birhythmicity). We show that the multiplicity of dynamic behavioral modes extends to the phenomenon of excitability. Whereas excitable behavior is generally characterized by a single threshold for excitation, two distinct thresholds may coexist in this model. Moreover, in these conditions, two different plateaux are obtained for the response amplitude when the stimulus is gradually increased. By means of phase plane analysis we explain the origin of multiple thresholds for excitability and predict the conditions for their occurrence. Implications of the phenomenon for excitable cells, in particular for neurons, are discussed.

Animals↗
PubMed1984

Ultrasensitivity in biochemical systems controlled by covalent modification. Interplay between zero-order and multistep effects.

A previous analysis of covalent modification systems (Goldbeter, A., and Koshland, D. E., Jr. (1981) Proc. Natl. Acad. Sci. U. S. A. 78, 6840-6844) showed that steep transitions in the amount of modified protein can occur when the converter enzymes are saturated by their protein substrate. This "zero-order ultrasensitivity" can further be amplified when an effector acts at more than one step in a monocyclic or multicyclic cascade of covalent modification. We analyze the limitations of the latter "multistep ultrasensitivity" and show how it can combine with the zero-order effect to enhance the sensitivity of biochemical systems controlled by covalent modification.

Allosteric Regulation↗