Theoretical insights into the mechanism of spiral Ca2+ wave initiation in Xenopus oocytes

Ca2+ spiral waves in a spatially discrete and random medium

It is well known that the spatial distribution of the calcium ion channels in the endoplasmic reticulum is discrete. We study the Ca(2+) spiral pattern formation based on a model in which ion channels are discretely and randomly distributed. Numerical simulations are performed on different types of media with the Ca(2+) release sites uniformly distributed, discretely and uniformly arranged, or discretely and randomly arranged. The comparisons among the different media show that random distribution is necessary for spontaneous initiation of Ca(2+) spiral waves, and the discrete and random distribution is of significance for spiral waves under physiologically reasonable conditions. The period and velocity of spiral waves are also calculated, and they are not prominently changed by varying the type of medium.

Calcium sparks

The calcium ion (Ca(2+)) is the simplest and most versatile intracellular messenger known. The discovery of Ca(2+) sparks and a related family of elementary Ca(2+) signaling events has revealed fundamental principles of the Ca(2+) signaling system. A newly appreciated "digital" subsystem consisting of brief, high Ca(2+) concentration over short distances (nanometers to microns) comingles with an "analog" global Ca(2+) signaling subsystem. Over the past 15 years, much has been learned about the theoretical and practical aspects of spark formation and detection. The quest for the spark mechanisms [the activation, coordination, and termination of Ca(2+) release units (CRUs)] has met unexpected challenges, however, and raised vexing questions about CRU operation in situ. Ample evidence shows that Ca(2+) sparks catalyze many high-threshold Ca(2+) processes involved in cardiac and skeletal muscle excitation-contraction coupling, vascular tone regulation, membrane excitability, and neuronal secretion. Investigation of Ca(2+) sparks in diseases has also begun to provide novel insights into hypertension, cardiac arrhythmias, heart failure, and muscular dystrophy. An emerging view is that spatially and temporally patterned activation of the digital subsystem confers on intracellular Ca(2+) signaling an exquisite architecture in space, time, and intensity, which underpins signaling efficiency, stability, specificity, and diversity. These recent advances in "sparkology" thus promise to unify the simplicity and complexity of Ca(2+) signaling in biology.

A kinetic Monte Carlo simulation study of inositol 1,4,5-trisphosphate receptor (IP3R) calcium release channel

Most of the previously theoretical studies about the stochastic nature of the IP3R calcium release channel gating use the chemical master equation (CME) approach. Because of the limitations of this approach we have used a stochastic simulation algorithm (SSA) presented by Gillespie. A single subunit of De Young-Keizer (DYK) model was simulated using Gillespie algorithm. The model has been considered in its complete form with eight states. We investigate the conditions which affect the open state of the model. Calcium concentrations were the subject of fluctuation in the previous works while in this study the population of the states is the subject of stochastic fluctuations. We found out that decreasing open probability is a function of Ca(2+) concentration in fast time domain, while in slow time domain it is a function of IP3 concentration. Studying the population of each state shows a time dependent reaction pattern in fast and medium time domains (10(-4) and 10(-3)s). In this pattern the state of X(010) has a determinative role in selecting the open state path. Also, intensity and frequency of fluctuations and Ca(2+) inhibitions have been studied. The results indicate that Gillespie algorithm can be a better choice for studying such systems, without using any approximation or elimination while having acceptable accuracy. In comparison with the chemical master equation, Gillespie algorithm is also provides a wide area for studying biological systems from other points of view.

Modeling the dependence of the period of intracellular Ca2+ waves on SERCA expression

Contrary to intuitive expectations, overexpression of sarco-endoplasmic reticulum (ER) Ca(2+) ATPases (SERCAs) in Xenopus oocytes leads to a decrease in the period and an increase in the amplitude of intracellular Ca(2+) waves. Here we examine these experimental findings by modeling Ca(2+) release using a modified Othmer-Tang-model. An increase in the period and a reduction in the amplitude of Ca(2+) wave activity are obtained when increases in SERCA density are simulated while keeping all other parameters of the model constant. However, Ca(2+) wave period can be reduced and the wave amplitude and velocity can be significantly increased when an increase in the luminal ER Ca(2+) concentration due to SERCA overexpression is incorporated into the model. Increased luminal Ca(2+) occurs because increased SERCA activity lowers cytosolic Ca(2+), which is partially replenished by Ca(2+) influx across the plasma membrane. These simulations are supported by experimental data demonstrating higher luminal Ca(2+) levels, decreased periods, increased amplitude, and increased velocity of Ca(2+) waves in response to increased SERCA density.

Simulation of waves in calcium models with 3D spherical geometry

Waves of calcium ions are present in fertilized eggs of many species. Models for pulse and tidal wave propagation have usually been studied in one or two spatial coordinates only. We examine in three spatial coordinates some established models, based on Ca(2+)-induced Ca(2+)-release from both (assumed) continuously or heterogeneously distributed stores of endoplasmic reticulum (ER) through channels activated by inositol triphosphate (IP(3)). With continuous IP(3) distribution decreasing radially towards the interior, we obtain concave pulse shapes for waves penetrating the interior. Concave waves are also recorded in systems with ER confined to distributions of small spheres (microdomains) inside the cell, which we simulate for front waves (tides) in bistable systems.