Excitability in a stochastic differential equation model for calcium puffs

Calcium waves in a grid of clustered channels with synchronous IP3 binding and unbinding

Calcium signals in cells occur at multiple spatial scales and variable temporal duration. However, a physical explanation for transitions between long-lasting global oscillations and localized short-term elevations (puffs) of cytoplasmic Ca²⁺ is still lacking. Here we introduce a phenomenological, coarse-grained model for the calcium variable, which is represented by ordinary differential equations. Due to its small number of parameters, and its simplicity, this model allows us to numerically study the interplay of multi-scale calcium concentrations with stochastic ion channel gating dynamics even in larger systems. We apply this model to a single cluster of inositol trisphosphate (IP ₃) receptor channels and find further evidence for the results presented in earlier work: a single cluster may be capable of producing different calcium release types, where long-lasting events are accompanied by unbinding of IP ₃ from the receptor (Rückl et al., PLoS Comput. Biol. 11, e1003965 (2015)). Finally, we show the practicability of the model in a grid of 64 clusters which is computationally intractable with previous high-resolution models. Here long-lasting events can lead to synchronized oscillations and waves, while short events stay localized. The frequency of calcium releases as well as their coherence can thereby be regulated by the amplitude of IP ₃ stimulation. Finally the model allows for a new explanation of oscillating [IP ₃], which is not based on metabolic production and degradation of IP ₃.

Determining the Roles of Inositol Trisphosphate Receptors in Neurodegeneration: Interdisciplinary Perspectives on a Complex Topic

It is well known that calcium (Ca²⁺) is involved in the triggering of neuronal death. Ca²⁺ cytosolic levels are regulated by Ca²⁺ release from internal stores located in organelles, such as the endoplasmic reticulum. Indeed, Ca²⁺ transit from distinct cell compartments follows complex dynamics that are mediated by specific receptors, notably inositol trisphosphate receptors (IP3Rs). Ca²⁺ release by IP3Rs plays essential roles in several neurological disorders; however, details of these processes are poorly understood. Moreover, recent studies have shown that subcellular location, molecular identity, and density of IP3Rs profoundly affect Ca²⁺ transit in neurons. Therefore, regulation of IP3R gene products in specific cellular vicinities seems to be crucial in a wide range of cellular processes from neuroprotection to neurodegeneration. In this regard, microRNAs seem to govern not only IP3Rs translation levels but also subcellular accumulation. Combining new data from molecular cell biology with mathematical modelling, we were able to summarize the state of the art on this topic. In addition to presenting how Ca²⁺ dynamics mediated by IP3R activation follow a stochastic regimen, we integrated a theoretical approach in an easy-to-apply, cell biology-coherent fashion. Following the presented premises and in contrast to previously tested hypotheses, Ca²⁺ released by IP3Rs may play different roles in specific neurological diseases, including Alzheimer's disease and Parkinson's disease.

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.

Modulation of elementary calcium release mediates a transition from puffs to waves in an IP3R cluster model

The oscillating concentration of intracellular calcium is one of the most important examples for collective dynamics in cell biology. Localized releases of calcium through clusters of inositol 1,4,5-trisphosphate receptor channels constitute elementary signals called calcium puffs. Coupling by diffusing calcium leads to global releases and waves, but the exact mechanism of inter-cluster coupling and triggering of waves is unknown. To elucidate the relation of puffs and waves, we here model a cluster of IP3R channels using a gating scheme with variable non-equilibrium IP3 binding. Hybrid stochastic and deterministic simulations show that puffs are not stereotyped events of constant duration but are sensitive to stimulation strength and residual calcium. For increasing IP3 concentration, the release events become modulated at a timescale of minutes, with repetitive wave-like releases interspersed with several puffs. This modulation is consistent with experimental observations we present, including refractoriness and increase of puff frequency during the inter-wave interval. Our results suggest that waves are established by a random but time-modulated appearance of sustained release events, which have a high potential to trigger and synchronize activity throughout the cell.