Global noise and oscillations in clustered excitable media

Astrocyte calcium signaling: Interplay between structural and dynamical patterns

Inspired by calcium activity in astrocytes, which is different in the cell body and thick branches on the one hand and thin branchlets and leaflets on the other hand, we formulate a concept of spatially partitioned oscillators. These are inhomogeneous media with regions having different excitability properties, with a global dynamics governed by spatial configuration of such regions. Due to a high surface-to-volume ratio, calcium dynamics in astrocytic leaflets is dominated by transmembrane currents, while somatic calcium dynamics relies on exchange with intracellular stores, mediated by IP 3 , which is in turn synthesized in the space nearby the plasma membrane. Reciprocal coupling via diffusion of calcium and IP 3 between the two regions makes the spatial configuration an essential contributor to overall dynamics. Due to these features, the mechanisms governing the pattern formation of calcium dynamics differ from classical excitable systems with noise or from networks of clustered oscillators. We show how geometrical inhomogeneity can play an ordering role allowing for stable scenarios for calcium wave initiation and propagation.

Wave failure at strong coupling in intracellular Ca^{2+} signaling system with clustered channels

As an important intracellular signal, Ca^{2+} ions control diverse cellular functions. In this paper, we discuss the Ca^{2+} signaling with a two-dimensional model in which the inositol 1,4,5-trisphosphate (IP_{3}) receptor channels are distributed in clusters on the endoplasmic reticulum membrane. The wave failure at large Ca^{2+} diffusion coupling is discussed in detail in the model. We show that with varying model parameters the wave failure is a robust behavior with either deterministic or stochastic channel dynamics. We suggest that the wave failure should be a general behavior in inhomogeneous diffusing systems with clustered excitable regions and may occur in biological Ca^{2+} signaling systems.

Accurate Langevin approaches to simulate Markovian channel dynamics

The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lu's classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed.

Modeling the spontaneous Ca2+ oscillations in astrocytes: Inconsistencies and usefulness

Spontaneous calcium (Ca2+) oscillations (SCOs) in astrocytes might be a crucial signaling for the multipurpose role of this type of cell in several brain functions. To interpret experimental data of astrocytic SCOs, which has been largely observed in the last decade, several groups have attempted to accommodate biophysical models that were developed in the past for Ca2+ signaling in other cell types. In most of the cases, only predictive strategies were used to estimate specific parameters of these modified models from actual experiments. In this study, we discuss the most remarkable models used to describe Ca2+ signaling in astrocytes. At the same time, we aim to revise the particulars of applying these models to interpret epifluorescent time series obtained from large regions of interest. Specially, we developed a detailed model for global Ca2+ signaling in the somata of astrocytes. In order to estimate some of the parameters in our model, we propose a deductive reasoning strategy, i.e., a statistical inference method that results from combining a filtering technique and a maximum likelihood principle. By means of computer simulations, we evaluate the accuracy of this estimation's strategy. Finally, we use the new model, in combination with a recent experimental findings by our group, to estimate the degree of cluster coupling inside the soma during the genesis of global Ca2+ events.

Using Jensen's inequality to explain the role of regular calcium oscillations in protein activation

Oscillations of cytosolic Ca(2 +) are very important for cellular signalling in excitable and non-excitable cells. The information of various extracellular stimuli is encoded into oscillating patterns of Ca(2 +) that subsequently lead to the activation of different Ca(2 +)-sensitive target proteins in the cell. The question remains, however, why this information is transmitted by means of an oscillating rather than a constant signal. Here we show that, in fact, Ca(2 +) oscillations can achieve a better activation of target proteins than a comparable constant signal with the same amount of Ca(2 +) used. For this we use Jensen's inequality that describes the relation between the function value of the average of a set of argument values and the average of the function values of the arguments from that set. We analyse the role of the cooperativity of the binding of Ca(2 +) and of zero-order ultrasensitivity, which are two properties that are often observed in experiments on the activation of Ca(2 +)-sensitive target proteins. Our results apply to arbitrary oscillation shapes and a very general decoding model, thus generalizing the observations of several previous studies. We compare our results with data from experimental studies investigating the activation of nuclear factor of activated T cells (NFAT) and Ras by oscillatory and constant signals. Although we are restricted to specific approximations due to the lack of detailed kinetic data, we find good qualitative agreement with our theoretical predictions.