Biomedical subjects

J Keizer

Publications and source records attributed to J Keizer.

At least 19 recordsLinked to original sources

PubMed2001

Modeling temporal behavior of postnatal cat retinal ganglion cells.

During development, mammalian retinal ganglion cells (RGCs) go through marked ontogenetic changes with respect to their excitable membrane properties. Voltage-clamp studies conducted in our laboratory have shown that the amplitude, voltage-dependence and kinetics of activation and inactivation (where present) of Na(+), K(+) and Ca(2+) conductances all exhibit developmental changes during a time when the firing patterns of mammalian ganglion cells shift from being transient to being predominantly sustained in nature. In order to better understand the contribution of each conductance to the generation of spikes and spiking patterns, we have developed a model based on our experimental data. For simplicity, we have initially used experimental data obtained from postnatal ganglion cells. At this age the ontogenetic changes observed in the characteristics of the various ionic currents are complete. Utilizing the methods adopted by Hodgkin and Huxley for the giant squid axon, we have determined rate equations for the activation and inactivation properties of the I(A), I(K dr), I(Na), I(Ca L), I(Ca N), and I(leak) currents in postnatal cat RGCs. Combining these with a simplified model of the calcium-activated potassium current (I(KCa)), we have solved and analysed the resulting differential equations. While spikes and spiking patterns resembling experimental data could be obtained from a model in which [Ca(2+)i] was averaged across the whole cell, more accurate simulations were obtained when the diffusion of intracellular Ca(2+) was modeled spatially. The resulting spatial calcium gradients were more effective in gating I(KCa), and our simulations more accurately matched the recorded amplitude and shape of individual spikes as well as the frequency of maintained discharges observed in mammalian postnatal RGCs.

Action Potentials↗

PubMed1999

Fire-diffuse-fire model of dynamics of intracellular calcium waves.

When Ca2+ is released from internal stores in living cells, the resulting wave of increased concentration can travel without deformation (continuous propagation) or with burst-like behavior (saltatory propagation). We analyze the "fire-diffuse-fire" model in order to illuminate the differences between these two modes of propagation. We show that the Ca2+ release wave in immature Xenopus oocytes and cardiac myocytes is saltatory, whereas the fertilization wave in the mature oocyte is continuous.

Animals↗

PubMed1998

Spark-to-wave transition: saltatory transmission of calcium waves in cardiac myocytes.

Using a modular approach, in which kinetic models of various mechanisms of calcium handling in cells are fine-tuned to in vivo and in vitro measurements before combining them into whole-cell models, three distinct modes of transmission of calcium waves in mature and immature frog eggs have been defined. Two modes of transmission are found in immature eggs, where the inositol 1,4,5-trisphosphate receptor (IP3R) controls release of calcium from the endoplasmic reticulum (ER). The first mode corresponds to an excitable physiological state of the cytoplasm and results in solitary waves that can appear as circular or spiral waves in two dimensions with the wave speed proportional to the square root of the diffusion constant of calcium. A second mode occurs when the state of the cytoplasm is oscillatory and because of the small size of the buffered diffusion constant for calcium, the wave speed can appear to be weakly dependent on diffusion. In the mature frog egg, where the sperm-induced Ca2+ fertilization wave is a propagating front, the cytoplasm appears to be bistable and in this mode the wave speed is also proportional to the square root of the diffusion constant. Here we investigate a fourth mode of propagation for cardiac myocytes, in which calcium release from the sarcoplasmic reticulum (SR) is dominated by clusters of ryanodine receptors spaced at regular intervals. In myocytes a stochastically excitable myoplasm leads to the spontaneous production of calcium 'sparks' that under certain conditions can merge into saltatory waves with a speed proportional to the diffusion constant.

Animals↗

PubMed1998

Saltatory propagation of Ca2+ waves by Ca2+ sparks.

Punctate releases of Ca2+, called Ca2+ sparks, originate at the regular array of t-tubules in cardiac myocytes and skeletal muscle. During Ca2+ overload sparks serve as sites for the initiation and propagation of Ca2+ waves in myocytes. Computer simulations of spark-mediated waves are performed with model release sites that reproduce the adaptive Ca2+ release observed for the ryanodine receptor. The speed of these waves is proportional to the diffusion constant of Ca2+, D, rather than D, as is true for reaction-diffusion equations in a continuous excitable medium. A simplified "fire-diffuse-fire" model that mimics the properties of Ca2+-induced Ca2+ release (CICR) from isolated sites is used to explain this saltatory mode of wave propagation. Saltatory and continuous wave propagation can be differentiated by the temperature and Ca2+ buffer dependence of wave speed.

Animals↗

PubMed1998

Simulation of the fertilization Ca2+ wave in Xenopus laevis eggs.

In the preceding paper Fontanilla and Nuccitelli (Biophysical Journal 75:2079-2087 (1998)) present detailed measurements of the shape and speed of the fertilization Ca2+ wave in Xenopus laevis eggs. In order to help interpret their results, we develop here a computational technique based on the finite element method that allows us to carry out realistic simulations of the fertilization wave. Our simulations support the hypothesis that the physiological state of the mature egg is bistable, i.e., that its cytoplasm can accommodate two alternative physiological Ca2+ concentrations: a low concentration characteristic of the prefertilization state and a greatly elevated concentration characteristic of the state following the passage of the wave. We explore this hypothesis by assuming that the bistability is due to the release and re-uptake properties of the endoplasmic reticulum (ER) as determined by inositol trisphosphate (IP3) receptor/Ca2+ channels and sarcoendoplasmic reticulum calcium ATPase (SERCA) pumps. When combined with buffered diffusion of Ca2+ in the cytoplasm, our simulations show that inhomogeneities in the Ca2+ release properties near the plasma membrane are required to explain the temporal and spatial dependences of the shape and speed of these waves. Our results are consistent with an elevated IP3 concentration near the plasma membrane in the unfertilized egg that is augmented significantly near the site of fertilization. These gradients are essential in determining the concave shape of the Ca2+ fertilization wave front.

Animals↗

PubMed1998

A fluorometric method for estimating the calcium content of internal stores.

The concentration of Ca2+ in intracellular stores is an important factor in many aspects of Ca2+ signaling, including the generation of Ca2+ spikes, oscillations and waves, control of mitochondrial respiration, and activation of store-operated Ca2+ channels. Here we describe a consistent method for estimating the content of stores, based on the release of stored Ca2+ by thapsigargin (TG) or ionomycin (IO). Once released from stores, Ca2+ elevates [Ca2+]i transiently before it is pumped across the plasma membrane. If the dependence of the pump rate on [Ca2+]i is known, then the kinetics and amplitude of the Ca2+ transient allows the total amount of releasable Ca2+ to be estimated. We develop this quantitative approach and validate its use in human T cells, in which the Ca2+ clearance rate is an approximately linear function of [Ca2+]i. Our results support the assumption that the ER Ca2+ leak in resting T cells is unregulated, i.e. its rate is proportional to luminal [Ca2+]. The characteristic time constant for basal Ca2+ release is 110-140 s, comparable to that for activation of Ca2+ release-activated Ca2+ (CRAC) channels by TG and consistent with the dependence of ICRAC on store depletion. This method for estimating store content may be useful for quantifying the overlap between functionally distinct stores and for defining the relation between store content and cellular responses.

Calcium↗

PubMed1998

Initial high anti-emetic efficacy of granisetron with dexamethasone is not maintained over repeated cycles.

We have reported previously that the anti-emetic efficacy of single agent 5HT3 antagonists is not maintained when analysed with the measurement of cumulative probabilities. Presently, the most effective anti-emetic regimen is a combination of a 5HT3 antagonist plus dexamethasone. We, therefore, assessed the sustainment of efficacy of such a combination in 125 patients, scheduled to receive cisplatin > or = 70 mg m(-2) either alone or in combination with other cytotoxic drugs. Anti-emetic therapy was initiated with 10 mg of dexamethasone and 3 mg of granisetron intravenously, before cisplatin. On days 1-6, patients received 8 mg of dexamethasone and 1 mg of granisetron twice daily by oral administration. Protection was assessed during all cycles and calculated based on cumulative probability analyses using the method of Kaplan-Meier and a model for transitional probabilities. Irrespective of the type of analysis used, the anti-emetic efficacy of granisetron/dexamethasone decreased over cycles. The initial complete acute emesis protection rate of 66% decreased to 30% according to the method of Kaplan-Meier and to 39% using the model for transitional probabilities. For delayed emesis, the initial complete protection rate of 52% decreased to 21% (Kaplan-Meier) and to 43% (transitional probabilities). In addition, we observed that protection failure in the delayed emesis period adversely influenced the acute emesis protection in the next cycle. We conclude that the anti-emetic efficacy of a 5HT3 antagonist plus dexamethasone is not maintained over multiple cycles of highly emetogenic chemotherapy, and that the acute emesis protection is adversely influenced by protection failure in the delayed emesis phase.

Adolescent↗

PubMed1998

Model of beta-cell mitochondrial calcium handling and electrical activity. I. Cytoplasmic variables.

We continue our development of a kinetic model of bursting electrical activity in the pancreatic beta-cell (J. Keizer and G. Magnus. Biophys. J. 56: 229-242, 1989), including the influence of Ca2+ handling by the mitochondria. Our minimal model of mitochondrial Ca2+ handling [G. Magnus and J. Keizer. Am. J. Physiol. 273 (Cell Physiol. 42): C717-C733, 1997] is expanded to include the D-glucose dependence of the rate of production of mitochondrial reducing equivalents. The Ca2+ dependence of the mitochondrial dehydrogenases, which is also included in the model, plays only a small role in the simulations, since the dehydrogenases appear to be maximally activated when D-glucose concentrations are sufficient to produce bursting. A previous model of ionic currents in the plasma membrane is updated using a recent experimental characterization of the dependence of the conductance of the ATP-sensitive K+ (KATP) current on adenine nucleotides. The resulting whole cell model is complex, involving 12 dynamic variables that couple Ca2+ handling in the cytoplasm and the mitochondria with electrical activity in the plasma and inner mitochondrial membranes. Simulations with the whole cell model give rise to bursting electrical activity similar to that seen in pancreatic islets and clusters of pancreatic beta-cells. The full D-glucose dose response of electrical activity is obtained if the cytosolic rate of ATP hydrolysis is a sigmoidal function of glucose. The simulations give the correct shape, period, and phase of the associated oscillations in cytosolic Ca2+, predict that the conductance of the KATP current oscillates out of phase with electrical activity [as recently observed in ob/ob mice (O. Larsson, H. Kindmark, R. Bränstrom, B. Fredholm, and P.-O. Berggren. Proc. Natl. Acad. Sci. USA 93: 5161-5165, 1996)], and make other novel predictions. In this model, bursting results because Ca2+ uptake into mitochondria during the active phase reduces the mitochondrial inner membrane potential, reducing the rate of production of ATP, which in turn activates the KATP current and repolarizes the plasma membrane.

Animals↗

PubMed1998

Model of beta-cell mitochondrial calcium handling and electrical activity. II. Mitochondrial variables.

In the preceding article [Am. J. Physiol. 274 (Cell Physiol. 43): C1158-C1173, 1998], we describe the development of a kinetic model for the interaction of mitochondrial Ca2+ handling and electrical activity in the pancreatic beta-cell. Here we describe further results of those simulations, focusing on mitochondrial variables, the rate of respiration, and fluxes of metabolic intermediates as a function of D-glucose concentration. Our simulations predict relatively smooth increases of O2 consumption, adenine nucleotide transport, oxidative phosphorylation, and ATP production by the tricarboxylic acid cycle as D-glucose concentrations are increased from basal to 20 mM. On the other hand, we find that the active fraction of pyruvate dehydrogenase saturates, due to increases in matrix Ca2+, near the onset of bursting electrical activity and that the NADH/NAD+ ratio in the mitochondria increases by roughly an order of magnitude as glucose concentrations are increased. The mitochondrial ATP/ADP ratio increases by factor of < 2 between the D-glucose threshold for bursting and continuous spiking. According to our simulations, relatively small changes in mitochondrial membrane potential (approximately 1 mV) caused by uptake of Ca2+ are sufficient to alter the cytoplasmic ATP/ADP ratio and influence ATP-sensitive K+ channels in the plasma membrane. In the simulations, these cyclic changes in the mitochondrial membrane potential are due to synchronization of futile cycle of Ca2+ from the cytoplasm through mitochondria via Ca2+ uniporters and Na+/Ca2+ exchange. Our simulations predict steady mitochondrial Ca2+ concentrations on the order of 0.1 microM at low glucose concentrations that become oscillatory with an amplitude on the order of 0.5 microM during bursting. Abrupt increases in mitochondrial Ca2+ concentration > 5 microM may occur during continuous electrical activity.

Adenosine Triphosphate↗

PubMed1997

Agonist-induced calcium waves in oscillatory cells: a biological example of Burgers' equation.

Oscillations in cytosolic Ca2+ concentrations in living cells are often a manifestation of propagating waves of Ca2+. Numerical simulations with a realistic model of inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ wave trains lead to wave speeds that increase linearly at long times when (a) IP3 levels are in the range for Ca2+ oscillations, (b) a gradient of phase is established by either an initial ramp or pulse of IP3, and (c) IP3 concentrations asymptotically become uniform. We explore this phenomenon with analytical and numerical methods using a simple two-variable reduction of the De Young-Keizer model of the IP3 receptor that includes the influence of Ca2+ buffers. For concentrations of IP3 in the oscillatory regime, numerical solution of the resulting reaction diffusion equations produces nonlinear wave trains that shows the same asymptotic growth of wave speed. Due to buffering, diffusion of Ca2+ is quite slow and, as previously noted, these waves occur without appreciable bulk movement of Ca2+. Thus, following Neu and Murray, we explore the behavior of these waves using an asymptotic expansion based on the small size of the buffered diffusion constant for Ca2+. We find that the gradient in phase of the wave obeys Burgers' equation asymptotically in time. This result is used to explain the linear increase of the wave speed observed in the simulations.

Animals↗

PubMed1997

Sensing and refilling calcium stores in an excitable cell.

Inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ mobilization leads to depletion of the endoplasmic reticulum (ER) and an increase in Ca2+ entry. We show here for the gonadotroph, an excitable endocrine cell, that sensing of ER Ca2+ content can occur without the Ca2+ release-activated Ca2+ current (Icrac), but rather through the coupling of IP3-induced Ca2+ oscillations to plasma membrane voltage spikes that gate Ca2+ entry. Thus we demonstrate that capacitative Ca2+ entry is accomplished through Ca(2+)-controlled Ca2+ entry. We develop a comprehensive model, with parameter values constrained by available experimental data, to simulate the spatiotemporal behavior of agonist-induced Ca2+ signals in both the cytosol and ER lumen of gonadotrophs. The model combines two previously developed models, one for ER-mediated Ca2+ oscillations and another for plasma membrane potential-driven Ca2+ oscillations. Simulations show agreement with existing experimental records of store content, cytosolic Ca2+ concentration ([Ca2+]i), and electrical activity, and make a variety of new, experimentally testable predictions. In particular, computations with the model suggest that [Ca2+]i in the vicinity of the plasma membrane acts as a messenger for ER content via Ca(2+)-activated K+ channels and Ca2+ pumps in the plasma membrane. We conclude that, in excitable cells that do not express Icrac, [Ca2+]i profiles provide a sensitive mechanism for regulating net calcium flux through the plasma membrane during both store depletion and refilling.

Animals↗

PubMed1997

Minimal model of beta-cell mitochondrial Ca2+ handling.

We develop a simplified, but useful, mathematical model to describe Ca2+ handling by mitochondria in the pancreatic beta-cell. The model includes the following six transport mechanisms in the inner mitochondrial membrane: proton pumping via respiration and proton uptake by way of the F1Fzero-ATPase (adapted from D. Pietrobon and S. Caplan. Biochemistry 24: 5764-5778, 1985), a proton leak, adenine nucleotide exchange, the Ca2+ uniporter, and Na+/Ca2+ exchange. Each mechanism is developed separately into a kinetic model for the rate of transport, with parameters taken from experiments on isolated mitochondrial preparations. These mechanisms are combined in a modular fashion first to describe state 4 (nonphosphorylating) and state 3 (phosphorylating) mitochondria with mitochondrial NADH and Ca2+ concentrations as fixed parameters and then to describe Ca2+ handling with variable mitochondrial Ca2+ concentration. Simulations are compared to experimental measurements and agree well with the threshold for Ca2+ uptake, measured mitochondrial Ca2+ levels, and the influence of Ca2+ on oxygen uptake. In the absence of Ca2+ activation of mitochondrial dehydrogenases, the simulations predict a significant reduction in the rate of production of ATP that involves a "short circuit" via Ca2+ uptake through the uniporter. This effect suggests a potential role for mitochondrial Ca2+ handling in determining the ATP-ADP ratio in the pancreatic beta-cell.

Animals↗

PubMed1996

Ryanodine receptor adaptation and Ca2+(-)induced Ca2+ release-dependent Ca2+ oscillations.

A simplified mechanism that mimics "adaptation" of the ryanodine receptor (RyR) has been developed and its significance for Ca2+(-)induced Ca2+ release and Ca2+ oscillations investigated. For parameters that reproduce experimental data for the RyR from cardiac cells, adaptation of the RyR in combination with sarco/endoplasmic reticulum Ca2+ ATPase Ca2+ pumps in the internal stores can give rise to either low [Cai2+] steady states or Ca2+ oscillations coexisting with unphysiologically high [Cai2+] steady states. In this closed-cell-type model rapid, adaptation-dependent Ca2+ oscillations occur only in limited ranges of parameters. In the presence of Ca2+ influx and efflux from outside the cell (open-cell model) Ca2+ oscillations occur for a wide range of physiological parameter values and have a period that is determined by the rate of Ca2+ refilling of the stores. Although the rate of adaptation of the RyR has a role in determining the shape and the period of the Ca2+ spike, it is not essential for their existence. This is in marked contrast with what is observed for the inositol 1,4,5-trisphosphate receptor for which the biphasic activation and inhibition of its activity by Ca2+ are sufficient to produce oscillations. Results for this model are compared with those based on Ca2+(-)induced Ca2+ release alone in the bullfrog sympathetic neuron. This kinetic model should be suitable for analyzing phenomena associated with "Ca2+ sparks," including their merger into Ca2+ waves in cardiac myocytes.

Animals↗

PubMed1996

Validity of the rapid buffering approximation near a point source of calcium ions.

In the presence of rapid buffers the full reaction-diffusion equations describing Ca2+ transport can be reduced using the rapid buffering approximation to a single transport equation for [Ca2+]. Here we simulate the full and reduced equations, exploring the conditions necessary for the validity of the rapid buffering approximation for an isolated Ca2+ channel or a cluster of channels. Using a point source and performing numerical simulations of different durations, we quantify the error of the rapid buffering approximation as a function of buffer and source parameters as well as the time and spatial scale set by the resolution of confocal microscopic measurements. We carry out simulations of Ca2+ "sparks" and "puffs," both with and without the indicator dye Ca2+ Green-1, and find that the rapid buffering approximation is excellent. These calculations also show that the traditional calculation of [Ca2+] from a fluorescence signal may grossly underestimate the true value of [Ca2+] near a source. Finally, we use the full model to simulate the transient Ca2+ domain near the pore of an open Ca2+ channel in a cell dialyzed with millimolar concentrations of 1,2-bis(2-aminophenoxy)ethane-N,N,N,N-tetraacetic acid or EGTA. In this regime, where the rapid buffering approximation is poor. Neher's equation for the steady-state Ca2+ profile is shown to be a reliable approximation adjacent to the pore.

Biophysical Phenomena↗

PubMed1996

Effect of Ca2+ influx on intracellular free Ca2+ responses in antigen-stimulated RBL-2H3 cells.

We undertake a quantitative investigation of changes in intracellular free Ca2+ concentration ([Ca2+]i) in antigen-stimulated rat basophilic leukemia (RBL-2H3) cells, which include contributions of both Ca2+ store release and Ca2+ influx from the medium. Following Keizer and De Young (J. Keizer and G. De Young. Biophys. J. 61: 649-660, 1992), we develop a highly constrained mathematical model for [Ca2+]i oscillations in RBL-2H3 cells, which includes activation of the inositol trisphosphate receptor (IP3R) by inositol 1,4,5-trisphospate, indirect Ca2+ activation of the IP3R via Ca2+ -dependent activity of phospholipase C-gamma, slow inhibition of the IP3R by cytosolic Ca2+, refilling of Ca2+ stores by a Ca2+ -ATPase (SERCA)-type pump, and a simple representation of the dependence of plasma membrane (PM) fluxes on experimental conditions. Using this full (open cell) model, we simulate [Ca2+]i responses for protocols in which antigen concentration and external Ca2+ are manipulated and compare out calculations with experimental data. In protocol A, cells are stimulated in the presence of external Ca2+, in protocols B and C, cells are stimulated in the absence of external Ca2+, with external Ca2+ later reapplied in protocol C. We are able to reproduce quantitatively the important features of all three protocols, including the dose response of protocol B, the [Ca2+]i response to thapsigargin, and lag time results, and we provide qualitative explanations for the responses derived from our calculations. We also develop a simplified (closed cell) version of the model in which PM fluxes are neglected and total free Ca2+ concentration ([Ca2+]T) is a slowly varying parameter. This permits us to explain in a simple graphical fashion how PM fluxes may influence [Ca2+]i responses in RBH-2H3 cells through modulation of [Ca2+]T.

Animals↗

PubMed1995

Enzymological differences of AChE and diazinon hepatic metabolism: correlation of in vitro data with the selective toxicity of diazinon to fish species.

The in vitro hepatic metabolism of diazinon, as well as the sensitivity of the brain acetylcholine esterase, to diazoxon inhibitory action have been studied in order to explain the different toxicity of diazinon to Oncorhynchus mykiss (rainbow trout), Poecilia reticulata (guppy), Brachydanio rerio (zebra fish) and Cyprinus carpio (carp). In spite of a very sensitive acetylcholine esterase the carp is very resistant to diazinon toxicity because of its very low rate of bioactivation and relatively high activity of detoxicating enzymes. The trout is very sensitive towards diazinon in spite of its low activity of bioactivation, because of its lack of detoxicating enzymes and a very sensitive acetylcholine esterase. Diazinon is very toxic for the guppy, because this fish combines a relatively sensitive acetylcholine esterase with a high rate of bioactivation. The zebra fish has the most insensitive acetylcholine esterase, associated with a limited activation rate, thus resulting a rather resistant species. The results obtained indicate that diazinon toxicity differences among the fish species studied can largely be explained in relation to metabolic balances in the liver and with the features of the target enzyme.

Acetylcholinesterase↗

PubMed1995

Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells.

Oscillatory secretion of insulin has been observed in many different experimental preparations ranging from pancreatic islets to the whole pancreas. Here we examine the mathematical features underlying a possible model for oscillatory secretion from the perifused, insulin-secreting cell line, HIT-15. The model includes the kinetics of uptake of glucose by GLUT transporters, the rate of glucose metabolism within the cell, and the effect of glucose on the rate of insulin secretion. Putative feedback by insulin on the rate of glucose transport into the cells is treated phenomenologically and leads to insulin oscillations similar to those observed experimentally in HIT cells. The resulting set of ordinary differential equations is simplified by time-scale analysis to a two-variable set of ordinary differential equations. Because of this simplification we can explore, in great detail, the characteristics of the oscillations and their sensitivity to parameter variation using phase plane analysis.

Animals↗

PubMed1995

On the roles of Ca2+ diffusion, Ca2+ buffers, and the endoplasmic reticulum in IP3-induced Ca2+ waves.

We have investigated the effects of Ca2+ diffusion, mobile and stationary Ca2+ buffers in the cytosol, and Ca2+ handling by the endoplasmic reticulum on inositol 1,4,5-trisphosphate-induced Ca2+ wave propagation. Rapid equilibration of free and bound Ca2+ is used to describe Ca2+ sequestration by buffers in both the cytosol and endoplasmic reticulum (ER) lumen. Cytosolic Ca2+ regulation is based on a kinetic model of the inositol 1,4,5-trisphosphate (IP3) receptor of De Young and Keizer that includes activation and inhibition of the IP3 receptor Ca2+ channel in the ER membrane and SERCA Ca2+ pumps in the ER. Diffusion of Ca2+ in the cytosol and the ER and the breakdown and diffusion of IP3 are also included in our calculations. Although Ca2+ diffusion is severely limited because of buffering, when conditions are chosen just below the threshold for Ca2+ oscillations, a pulse of IP3 or Ca2+ results in a solitary trigger wave that requires diffusion of Ca2+ for its propagation. In the oscillatory regime repetitive wave trains are observed, but for this type of wave neither the wave shape nor the speed is strongly dependent on the diffusion of Ca2+. Local phase differences lead to waves that are predominately kinematic in nature, so that the wave speed (c) is related to the wavelength (lambda) and the period of the oscillations (tau) approximately by the formula c = lambda/tau. The period is determined by features that control the oscillations, including [IP3] and pump activity, which are related to recent experiments. Both solitary waves and wave trains are accompanied by a Ca2+ depletion wave in the ER lumen, similar to that observed in cortical preparations from sea urchin eggs. We explore the effect of endogenous and exogenous Ca2+ buffers on wave speed and wave shape, which can be explained in terms of three distinct effects of buffering, and show that exogenous buffers or Ca2+ dyes can have considerable influence on the amplitude and width of the waves.

Animals↗