Quantal release, incremental detection, and long-period Ca2+ oscillations in a model based on regulatory Ca2+-binding sites along the permeation pathway

Quantal release, incremental detection, and oscillations are three types of Ca2+ responses that can be obtained in different conditions, after stimulation of the intracellular Ca2+ stores by submaximum concentrations of inositol 1,4,5-triphosphate (InsP3). All three phenomena are thought to occur through the regulatory properties of the InsP3 receptor/Ca2+ channel. In the present study, we perform further analysis of the model (Swillens et al., 1994, Proc. Natl. Acad. Sci. USA. 91:10074-10078) previously proposed for transient InsP3-induced Ca2+ release, based on the bell-shaped dependence of the InsP3 receptor activity on the Ca2+ level and on the existence of an intermediate Ca2+ domain located around the mouth of the channel. We show that Ca2+ oscillations also arise in the latter model. Conditions for the occurrence of the various behaviors are investigated. Numerical simulations also show that the existence of an intermediate Ca2+ domain can markedly increase the period of oscillations. Periods on the order of 1 min can indeed be accounted for by the model when one assigns realistic values to the kinetic constants of the InsP3 receptor, which, in the absence of a domain, lead to oscillations with periods of a few seconds. Finally, theoretical support in favor of a positive cooperativity in the regulation of the InsP3 receptor by Ca2+ is presented.

Modeling spiral Ca2+ waves in single cardiac cells: role of the spatial heterogeneity created by the nucleus

Excitation-contraction coupling in cardiomyocytes is known to rely on the Ca(2+)-induced Ca2+ release mechanism. This autoamplification process is also very apparent when voltage-clamped or Ca(2+)-overloaded myocytes exhibit fast-propagating Ca2+ waves. Although most of the fronts are planar, some adopt a spiral shape, revealing additional characteristics about the excitability and structure of the cardiac cell (P. Lipp and E. Niggli, Biophys. J. 65: 2272-2276, 1993: J. Engel, M. Fechner, A. Sowerby, S. Finch, and A. Stier, Biophys. J. 66: 1756-1762, 1994). Using a previously developed model for Ca2+ oscillations and waves (A. Goldbeter, G. Dupont, and M.J. Berridge, Proc. Natl. Acad. Sci. USA 87: 1461-1465, 1990; G. Dupont and A. Goldbeter, Biophys. J. 67: 2191-2204, 1994), we study by numerical simulations different conditions in which spiral Ca2+ waves can occur as a result of the spatial heterogeneity created by the nucleus in a system with geometry resembling that of a myocyte. A region of the cell lacking Ca2+ pools, acting as an obstacle able to break the propagation of planar waves, suffices to initiate a spiral wave; however, this region must be properly placed with respect to the pacemaker. An obstacle behaving as a barrier to diffusion is also able to create the initial bending that can lead to the spiral wave. We study how the occurrence of spiral Ca2+ waves in single cardiomyocytes is influenced by factors such as the stimulus location and the position, shape, and dimensions of the obstacle to planar wave propagation.

Phospholipase C in mouse oocytes: characterization of beta and gamma isoforms and their possible involvement in sperm-induced Ca2+ spiking

This study involved an investigation of the role of phospholipase C (PLC) in generating repetitive Ca2+ spikes at fertilization. Using a PCR-based strategy we have demonstrated that mouse oocytes have mRNA coding for PLC beta 1, PLC beta 3 and PLC gamma isoenzymes. Furthermore, immunodetection of PLC gamma 1 using monoclonal antibodies reveals that PLC gamma 1 protein is present in mature mouse oocytes, ruling out the possibility that mRNA was being transcribed but not expressed. We were unsuccessful at detecting the presence of PLC beta protein, but the presence of this isoform can be inferred from functional studies. The PLC inhibitor, U73122, exerted an inhibitory effect on oocytes activated by spermatozoa or acetylcholine at concentrations of 10 and 30 microM respectively, while its inactive analogue had no effect. The soluble tyrosine kinase inhibitors, genistein (100 microM), herbimycin (10 microM) and geldanamycin (0.6 microM) which could affect signalling through PLC gamma hindered but never completely inhibited Ca2+ spiking in response to fertilization. We conclude that the activation of PLC to generate InsP3 may play a critical role in fertilization.

Properties of intracellular Ca2+ waves generated by a model based on Ca(2+)-induced Ca2+ release

Cytosolic Ca2+ waves occur in a number of cell types either spontaneously or after stimulation by hormones, neurotransmitters, or treatments promoting Ca2+ influx into the cells. These waves can be broadly classified into two types. Waves of type 1, observed in cardiac myocytes or Xenopus oocytes, correspond to the propagation of sharp bands of Ca2+ throughout the cell at a rate that is high enough to permit the simultaneous propagation of several fronts in a given cells. Waves of type 2, observed in hepatocytes, endothelial cells, or various kinds of eggs, correspond to the progressive elevation of cytosolic Ca2+ throughout the cell, followed by its quasi-homogeneous return down to basal levels. Here we analyze the propagation of these different types of intracellular Ca2+ waves in a model based on Ca(2+)-induced Ca2+ release (CICR). The model accounts for transient or sustained waves of type 1 or 2, depending on the size of the cell and on the values of the kinetic parameters that measure Ca2+ exchange between the cytosol, the extracellular medium, and intracellular stores. Two versions of the model based on CICR are considered. The first version involves two distinct Ca2+ pools sensitive to inositol 1,4,5-trisphosphate (IP3) and Ca2+, respectively, whereas the second version involves a single pool sensitive both to Ca2+ and IP3 behaving as co-agonists for Ca2+ release. Intracellular Ca2+ waves occur in the two versions of the model based on CICR, but fail to propagate in the one-pool model at subthreshold levels of IP3. For waves of type 1, we investigate the effect of the spatial distribution of Ca(2+)-sensitive Ca2+ stores within the cytosol, and show that the wave fails to propagate when the distance between the stores exceeds a critical value on the order of a few microns. We also determine how the period and velocity of the waves are affected by changes in parameters measuring stimulation, Ca2+ influx into the cell, or Ca2+ pumping into the stores. For waves of type 2, the numerical analysis indicates that the best qualitative agreement with experimental observations is obtained for phase waves. Finally, conditions are obtained for the occurrence of "echo" waves that are sometimes observed in the experiments.

The initiation of a calcium signal in Xenopus oocytes

Application of acetylcholine to Xenopus oocytes evoked increases in the cytosolic free calcium ion concentration ([Ca2+]i) after latencies of up to several seconds depending on the agonist dose. Higher acetylcholine concentrations evoked responses with larger amplitudes and shorter latencies. The latencies of responses to acetylcholine could be increased by application of caffeine, injection of calcium buffers or depletion of intracellular calcium stores. Acute inhibition of endoplasmic reticulum calcium pumps without substantial reduction of the calcium store content (by application of thapsigargin shortly before agonist stimulation) reduced the latencies of responses to acetylcholine. A schematic and mathematical model are presented to show a possible mechanism by which a calcium signal is initiated following a latent period after the elevation of the inositol trisphosphate concentration. During the latent period, calcium is slowly released from the intracellular stores. The released calcium is rapidly buffered by cytosolic calcium-binding proteins and some is resequestered into the stores by calcium pumps. The [Ca2+]i changes very little until the buffering is locally saturated. The [Ca2+]i then rises above a threshold concentration which evokes an explosive release of calcium due to positive feedback by calcium on the inositol trisphosphate receptor.

Spatial and temporal signalling by calcium

Recent research has shown the importance of the spatial and temporal aspects of calcium signals, which depend upon regenerative properties of the inositol trisphosphate and ryanodine receptors that regulate the release of calcium from internal stores. Initiation sites have been found to spontaneously release calcium, recognized as 'hot spots' or 'sparks', and can trigger a wave that spreads through a process of calcium-induced calcium release.

One-pool model for Ca2+ oscillations involving Ca2+ and inositol 1,4,5-trisphosphate as co-agonists for Ca2+ release

Experimental observations indicate that Ca(2+)-induced Ca2+ release (CICR) may underlie Ca2+ oscillations in a variety of cells. In its original version, a theoretical model for signal-induced Ca2+ oscillations based on CICR assumed the existence of two types of pools, one sensitive to inositol 1,4,5-trisphosphate (IP3) and the other one sensitive to Ca2+. Recent experiments indicate that Ca2+ channels may sometimes be sensitive to both IP3 and Ca2+. Such a regulation may be viewed as Ca(2+)-sensitized IP3-induced Ca2+ release or, alternatively, as a form of IP3-sensitized CICR. We show that sustained oscillations can still occur in a one-pool model, provided that the same Ca2+ channels are sensitive to both Ca2+ and IP3 behaving as co-agonists. This model and the two-pool model based on CICR both account for a number of experimental observations but differ in some respects. Thus, while in the two-pool model the latency and period of Ca2+ oscillations are of the same order of magnitude and correlate in a roughly linear manner, latency in the one-pool model is always brief and remains much shorter than the period of oscillations. Moreover, the first Ca2+ spike is much larger than the following ones in the one-pool model. These distinctive properties might provide an explanation for the differences in Ca2+ oscillations observed in various cell types.

General surgery in patients aged 80 years and older

This study reviews 594 surgical admissions, of patients aged 80 years and older, to departments of general surgery during 1 year. Half of the patients were admitted as emergencies and 60 per cent underwent surgery. The operative mortality rate was 8 per cent and the overall mortality rate for all admissions 9 per cent. The number of complications and the mortality rate after surgery increased in emergency cases and in patients with coexisting disease. Of all admissions, 72 per cent were uncomplicated and in 70 per cent patients could be discharged directly home; such patients do not generally take up beds and are discharged as soon as medical care is no longer indicated. The number of admissions of patients over 80 years of age will increase by about 30 per cent during this decade and, unless additional resources are provided to meet this challenge, new standards must be considered for the distribution of resources and of indications for surgery in both young and old.

[Treatment of injuries in the county of Ringkøbing. 4. Referral and transport of severe traffic accident traumas]

In Denmark, all cases of severe injuries are referred to the nearest hospital regardless of the size of the hospital and the county boundaries. In order to investigate whether this type of referral functions according to plan, the authors investigated referral of all traffic accidents in the County of Ringkøbing during the period 1 January 1983 to 31 December 1990. It was demonstrated that in only one out of 310 traffic accidents with fatal outcome, referral did not function according to plan and that the patient had been transported to a hospital which was not the nearest. It is thus concluded that referral now functions according to plan in its present form. In addition, the authors investigated whether there was any basis for establishing prehospital treatment of injuries in the country. It was found, however, that during a period of eight years (analysed on the basis of post mortem data) a maximum of 20 relevant patients would be involved annually and in whom the mortality might be reduced was concerned. Simultaneously, the average distance for transport to the nearest hospital was found to be only 12.9 km. There is thus no basis for employing massive resources for advanced prehospital service in the County of Ringkøbing. With an ambulance service staffed by doctors from the anaesthetic and intensive care units of the central hospitals it is possible to provide prehospital treatment in 70% of all severe traffic injuries in the County of Ringkøbing.

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.

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.

[Repeated episodes of massive fetomaternal hemorrhage in the same woman]

A case of recurrent fetomaternal haemorrhage is described. The Kleihauer test is recommended in the monitoring of patients at risk.

Signal-induced Ca2+ oscillations: properties of a model based on Ca(2+)-induced Ca2+ release

We consider a simple, minimal model for signal-induced Ca2+ oscillations based on Ca(2+)-induced Ca2+ release. The model takes into account the existence of two pools of intracellular Ca2+, namely, one sensitive to inositol 1,4,5 trisphosphate (InsP3) whose synthesis is elicited by the stimulus, and one insensitive to InsP3. The discharge of the latter pool into the cytosol is activated by cytosolic Ca2+. Oscillations in cytosolic Ca2+ arise in this model either spontaneously or in an appropriate range of external stimulation; these oscillations do not require the concomitant, periodic variation of InsP3. The following properties of the model are reviewed and compared with experimental observations: (a) Control of the frequency of Ca2+ oscillations by the external stimulus or extracellular Ca2+; (b) correlation of latency with period of Ca2+ oscillations obtained at different levels of stimulation; (c) effect of a transient increase in InsP3; (d) phase shift and transient suppression of Ca2+ oscillations by Ca2+ pulses, and (e) propagation of Ca2+ waves. It is shown that on all these counts the model provides a simple, unified explanation for a number of experimental observations in a variety of cell types. The model based on Ca(2+)-induced Ca2+ release can be extended to incorporate variations in the level of InsP3 as well as desensitization of the InsP3 receptor; besides accounting for the phenomena described by the minimal model, the extended model might also account for the occurrence of complex Ca2+ oscillations.

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.

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.

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+.

Comparison of creatinine and inulin clearances in multiple trauma

Creatinine clearance (Ccr) is a good predictor of renal dysfunction. However, numerous analytical interferences have been observed with the classical measurement of creatinine by Jaffé's procedure. This prospective study was conducted to compare 4 methods for determining creatinine; and also endogenous creatinine clearance with inulin clearance (Cin) to estimate the glomerular filtration rate. The 4 different techniques for measuring creatinine were: 1) 2 techniques using Jaffé's colorimetric reaction: one with rapid and the other with slow kinetics: 2) 2 more selective methods: enzymatic procedure and high performance liquid chromatography (HPLC). Measurements were performed in 13 multiple trauma patients after stabilization and in 5 comatose patients (control group) over a 3-day period, with strict 24-h urine collection. On the second day, inulin clearance and para-aminohippuric acid clearance (Cpah) were measured. Measurement of creatinine by Jaffé's procedure yields significantly higher levels than those obtained by the other methods. Higher levels of both plasma and urinary creatinine were observed in the multiple trauma patients with all the methods used. There were no significant differences in Ccr, Cin, Cpah between the multiple trauma patients and the control patients. The best correlations between inulin clearance and creatinine clearance were observed for Jaffé's rapid kinetics (r = 0.90) in the control group and for the enzymatic procedure in the multiple trauma group (r = 0.55). Plasma creatinine is not a useful indicator in multiple trauma. The correlation between creatinine clearance and inulin clearance is not very strong in multiple trauma, indicating that the relative evolution (not the absolute values) of creatinine clearance is of interest.

Are branched chain amino-acids beneficial for nutrition of severe surgical patients with sepsis?

This study investigated in severe sepsis the metabolic effects of two amino acid diets, including the same protein (0.3 gN/kg/day) and caloric intake (2g/kg/day glucose) but with different amino acid composition, 24% branched chain amino-acids (B.C.A.A.) for diet A (8 cases), 41% B.C.A.A. for diet B (11 cases). The two groups were obtained by randomisation at the operative day (D0) and were observed six days (D1-D6). During study, total nitrogen using a Kjeldhal method was measured. At D0 and D6, albumin, total hemolytic complement, transferrin, cholesterol, ammonaemia, insulin and amino acid pattern were studied in blood and skin tests were performed. The data were analysed by Mann-Whitney test.

RESULTS

1) The cumulative nitrogen balances of the six days are not significantly different, but at day 6 in diet B, patients started to be in an anabolic state (+3.7 gN) and in diet A catabolism persisted (-12 gN) (p<0.02). 2) Plasma B.C.A.A. are significantly higher and aromatic acids significantly lower in diet B. In order, Fischer ratio is also significantly different between the two regimens. All the other measured parameters are not significantly different. In this study, the B.C.A.A. enriched diet seems to be beneficial in surgical patients with severe sepsis.