Puff-wave transition in an inhomogeneous model for calcium signals

Ca2+-calmodulin signalling at the host-pathogen interface

Multiple eukaryotic cell processes are modulated by calcium ions (Ca²⁺). As such, Ca²⁺ is emerging as a crucial regulator of innate immunity in multicellular organisms. In particular, recent studies have identified roles of Ca²⁺ signalling at the host-bacteria interface. Following microbial exposure, Ca²⁺ signals mobilised from the extracellular milieu or intracellular stores are transduced into cell physiological responses. However, during infection with host-adapted pathogens, Ca²⁺ signals are often atypical, due to the activities of virulence factors, with varied consequences for both the pathogen and the host cell. In this review, we describe the Ca²⁺-dependent host factors regulating antibacterial immunity, in addition to bacterial effectors that promote, inhibit, or co-opt Ca²⁺-calmodulin signalling to promote infection.

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.

Suppressing effect of Ca^{2+} blips on puff amplitudes by inhibiting channels to prevent recovery

As local signals, calcium puffs arise from the concerted opening of a few nearby inositol 1,4,5-trisphospate receptor channels to release Ca^{2+} ions from the endoplasmic reticulum. Although Ca^{2+} puffs have been well studied, little is known about the modulation of cytosolic basal Ca^{2+} concentration ([Ca^{2+}]_{Basal}) on puff dynamics. In this paper we consider a puff model to study how the statistical properties of puffs are modulated by [Ca^{2+}]_{Basal}. The puff frequency and lifetime trivially increase with the increasing [Ca^{2+}]_{Basal}, but an unexpected result is that the puff amplitude and the maximum open-channel number of the puff show decreasing relationship with the increasing [Ca^{2+}]_{Basal}. The underlying dynamics is related not only to the increasing puff frequency which gives a shorter recovery time, but also to the increasing frequency of blips with only one channel open. We indicate that Ca^{2+} blips cause the channels to be inhibited and prevent their recovery during interpuff intervals, resulting in the suppressing effect on puff amplitudes. With increasing [Ca^{2+}]_{Basal}, more blips occur to cause more channels to be inhibited, leaving fewer channels available for puff events. This study shows that the blips may play relevant functions in global Ca^{2+} waves through modulating puff dynamics.

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.

Quantifying the uncertainty of spontaneous Ca2+ oscillations in astrocytes: particulars of Alzheimer's disease

The quantification of spontaneous calcium (Ca(2+)) oscillations (SCOs) in astrocytes presents a challenge because of the large irregularities in the amplitudes, durations, and initiation times of the underlying events. In this article, we use a stochastic context to account for such SCO variability, which is based on previous models for cellular Ca(2+) signaling. First, we found that passive Ca(2+) influx from the extracellular space determine the basal concentration of this ion in the cytosol. Second, we demonstrated the feasibility of estimating both the inositol 1,4,5-trisphosphate (IP(3)) production levels and the average number of IP(3) receptor channels in the somatic clusters from epifluorescent Ca(2+) imaging through the combination of a filtering strategy and a maximum-likelihood criterion. We estimated these two biophysical parameters using data from wild-type adult mice and age-matched transgenic mice overexpressing the 695-amino-acid isoform of human Alzheimer β-amyloid precursor protein. We found that, together with an increase in the passive Ca(2+) influx, a significant reduction in the sensitivity of G protein-coupled receptors might lie beneath the abnormalities in the astrocytic Ca(2+) signaling, as was observed in rodent models of Alzheimer's disease. This study provides new, to our knowledge, indices for a quantitative analysis of SCOs in normal and pathological astrocytes.