Simulation of waves in calcium models with 3D spherical geometry (original) (raw)

Two-dimensional model of calcium waves reproduces the patterns observed in Xenopus oocytes

Biophysical Journal, 1992

Biological excitability enables the rapid transmission of physiological signals over distance. Using confocal fluorescence microscopy, we previously reported circular, planar, and spiral waves of Ca2+ in Xenopus laevis oocytes that annihilated one another upon collision (1). We present experimental evidence that the excitable process underlying wave propagation depends on Ca2+ diffusion and does not require oscillations in inositol (1, 4, 5) trisphosphate (1P3) concentration. Extending an existing ordinary differential equation (ODE) model of Ca2+ oscillations to two spatial dimensions, we develop a partial differential equation (PDE) model of Ca2+ excitability. The model assumes that cytosolic Ca2+ couples neighboring Ca2+ release sites. This simple PDE model qualitatively reproduces our experimental observations.

Simulation of the Fertilization Ca2+ Wave in Xenopus laevis Eggs

Biophysical Journal, 1998

present detailed measurements of the shape and speed of the fertilization Ca 2ϩ 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 Ca 2ϩ 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 (IP 3) receptor/Ca 2ϩ channels and sarcoendoplasmic reticulum calcium ATPase (SERCA) pumps. When combined with buffered diffusion of Ca 2ϩ in the cytoplasm, our simulations show that inhomogeneities in the Ca 2ϩ 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 IP 3 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 Ca 2ϩ fertilization wave front.

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

Biophysical chemistry, 1998

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 (IP 3 R) 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 Ca 2+ 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.

Calcium waves occur as Drosophila oocytes activate

Proceedings of the National Academy of Sciences, 2015

Significance This paper reports the first visualization of calcium dynamics in Drosophila eggs in vivo and in vitro, demonstrating that a calcium wave is a conserved feature of egg activation (the process by which a mature egg becomes able to initiate embryo development). In vertebrates and echinoderms, the fertilizing sperm triggers egg activation by inducing calcium release from the egg’s internal stores, causing wave(s) of increased calcium to sweep across the egg. However, insect eggs activate without fertilization. We show that a wave of increased calcium occurs during activation of Drosophila eggs. The wave is induced during ovulation by influx of calcium into the egg through mechanosensitive ion channels. Release of calcium from intracellular stores is required for wave propagation.

Abortive and propagating intracellular calcium waves: analysis from a hybrid model

PloS one, 2015

The functional properties of inositol(1,4,5)-triphosphate (IP3) receptors allow a variety of intracellular Ca2+ phenomena. In this way, global phenomena, such as propagating and abortive Ca2+ waves, as well as local events such as puffs, have been observed. Several experimental studies suggest that many features of global phenomena (e.g., frequency, amplitude, speed wave) depend on the interplay of biophysical processes such as diffusion, buffering, efflux and influx rates, which in turn depend on parameters such as buffer concentration, Ca2+ pump density, cytosolic IP3 level, and intercluster distance. Besides, it is known that cells are able to modify some of these parameters in order to regulate the Ca2+ signaling. By using a hybrid model, we analyzed different features of the hierarchy of calcium events as a function of two relevant parameters for the calcium signaling, the intercluster distance and the pump strength or intensity. In the space spanned by these two parameters, we...

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

Proceedings of the National Academy of Sciences, 1999

When Ca 2؉ 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 Ca 2؉ release wave in immature Xenopus oocytes and cardiac myocytes is saltatory, whereas the fertilization wave in the mature oocyte is continuous.

A membrane model for cytosolic calcium oscillations. A study using Xenopus oocytes

Biophysical Journal, 1992

Cytosolic calcium oscillations occur in a wide variety of cells and are involved in different cellular functions. We describe these calcium oscillations by a mathematical model based on the putative electrophysiological properties of the endoplasmic reticulum (ER) membrane. The salient features of our membrane model are calcium-dependent calcium channels and calcium pumps in the ER membrane, constant entry of calcium into the cytosol, calcium dependent removal from the cytosol, and buffering by cytoplasmic calcium binding proteins. Numerical integration of the model allows us to study the fluctuations in the cytosolic calcium concentration, the ER membrane potential, and the concentration of free calcium binding sites on a calcium binding protein. The model demonstrates the physiological features necessary for calcium oscillations and suggests that the level of calcium flux into the cytosol controls the frequency and amplitude of oscillations. The model also suggests that the level of buffering affects the frequency and amplitude of the oscillations. The model is supported by experiments indirectly measuring cytosolic calcium by calcium-induced chloride currents in Xenopus oocytes as well as cytosolic calcium oscillations observed in other preparations.

Propagated and Nonpropagated Calcium Transients during Egg Activation in the Annelid,Chaetopterus

Developmental Biology, 1995

Transient waves of Ca 2/ release cross-fertilizing deuterostome eggs from the point of sperm entry to its antipode and provide much of the activating stimulus for the egg. Based on several indirect lines of experimental evidence, it was proposed that protostome eggs are activated by a prolonged uptake of Ca 2/ from the medium due to sperm-induced membrane depolarization and that this uptake then starts an activation wave similar to those in deuterostomes, except that it moves inward from the whole surface rather than through the egg from pole to pole. To test these hypotheses, we microinjected oocytes of the polychaete annelid, Chaetopterus pergamentaceus, with semisynthetic recombinant aequorins and measured light emission in response to both fertilization and artificial activation by excess K / . Both fertilization and K / -activation induced multiple, brief Ca 2/ transients in the eggs. The first transient did not propagate, but it was followed by a series of globally propagated Ca 2/ waves interspersed with additional nonpropagated pulses. The waves traversed the egg at about 30 mm/sec. Sequential propagated waves and nonpropagated pulses generally originated at different regions on the egg surface, except the last few, which originated in the same ''pacemaker'' region. These new data are consistent with the hypothesis that the activation of protostome eggs is initiated by Ca 2/ waves. However, the fact that these waves propagated from pole to pole like those in deuterostome eggs refutes the notion that Ca 2/ waves in activating protostome eggs move inward from the whole surface. ᭧ 1995 Academic Press, Inc.