Mapping Interpuff Interval Distribution to the Properties of Inositol Trisphosphate Receptors

Modeling IP3-induced Ca2+ signaling based on its interspike interval statistics

Inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ signaling is a second messenger system used by almost all eukaryotic cells. Recent research demonstrated randomness of Ca2+ signaling on all structural levels. We compile eight general properties of Ca2+ spiking common to all cell types investigated and suggest a theory of Ca2+ spiking starting from the random behavior of IP3 receptor channel clusters mediating the release of Ca2+ from the endoplasmic reticulum capturing all general properties and pathway-specific behavior. Spike generation begins after the absolute refractory period of the previous spike. According to its hierarchical spreading from initiating channel openings to cell level, we describe it as a first passage process from none to all clusters open while the cell recovers from the inhibition which terminated the previous spike. Our theory reproduces the exponential stimulation response relation of the average interspike interval Tav and its robustness properties, random spike timing with a linear moment relation between Tav and the interspike interval SD and its robustness properties, sensitive dependency of Tav on diffusion properties, and nonoscillatory local dynamics. We explain large cell variability of Tav observed in experiments by variability of channel cluster coupling by Ca2+-induced Ca2+ release, the number of clusters, and IP3 pathway component expression levels. We predict the relation between puff probability and agonist concentration and [IP3] and agonist concentration. Differences of spike behavior between cell types and stimulating agonists are explained by the different types of negative feedback terminating spikes. In summary, the hierarchical random character of spike generation explains all of the identified general properties.

An integrate-and-fire approach to Ca2+ signaling. Part I: Renewal model

In computational neuroscience integrate-and-fire models capture the spike generation by a subthreshold dynamics supplemented by a simple fire-and-reset rule; they allow for a numerically efficient and analytically tractable description of stochastic single cell as well as network dynamics. Stochastic spiking is also a prominent feature of Ca2+ signaling which suggests to adopt the integrate-and-fire approach for this fundamental biophysical process. The model introduced here consists of two components describing 1) activity of clusters of inositol-trisphosphate receptor channels and 2) dynamics of the global Ca2+ concentrations in the cytosol. The cluster dynamics is given in terms of a cyclic Markov chain, capturing the puff, i.e., the punctuated release of Ca2+ from intracellular stores. The cytosolic Ca2+ concentration is described by an integrate-and-fire dynamics driven by the puff current. For the cyclic Markov chain we derive expressions for the statistics of the interpuff interval, the single-puff strength and the puff current assuming constant cytosolic Ca2+. The latter condition is often well approximated because cytosolic Ca2+ varies much slower than the cluster activity does. Furthermore, because the detailed two-component model is numerically expensive to simulate and difficult to treat analytically, we develop an analytical framework to approximate the driving puff current of the stochastic cytosolic Ca2+ dynamics by a temporally uncorrelated Gaussian noise. This approximation reduces our two-component system to an integrate-and-fire model with a nonlinear drift function and a multiplicative Gaussian white noise, a model that is known to generate a renewal spike train, i.e., a point process with statistically independent interspike intervals. The model allows for fast numerical simulations, permits to derive analytical expressions for the rate of Ca2+ spiking and the coefficient of variation of the interspike interval, and to approximate the interspike interval density and the spike train power spectrum. Comparison of these statistics to experimental data is discussed.

Data-driven modeling of mitochondrial dysfunction in Alzheimer's disease

Intracellular accumulation of oligomeric forms of β amyloid (Aβ) are now believed to play a key role in the earliest phase of Alzheimer's disease (AD) as their rise correlates well with the early symptoms of the disease. Extensive evidence points to impaired neuronal Ca²⁺ homeostasis as a direct consequence of the intracellular Aβ oligomers. However, little is known about the downstream effects of the resulting Ca²⁺ rise on the many intracellular Ca²⁺-dependent pathways. Here we use multiscale modeling in conjunction with patch-clamp electrophysiology of single inositol 1,4,5-trisphosphate (IP₃) receptor (IP₃R) and fluorescence imaging of whole-cell Ca²⁺ response, induced by exogenously applied intracellular Aβ₄₂ oligomers to show that Aβ₄₂ inflicts cytotoxicity by impairing mitochondrial function. Driven by patch-clamp experiments, we first model the kinetics of IP₃R, which is then extended to build a model for the whole-cell Ca²⁺ signals. The whole-cell model is then fitted to fluorescence signals to quantify the overall Ca²⁺ release from the endoplasmic reticulum by intracellular Aβ₄₂ oligomers through G-protein-mediated stimulation of IP₃ production. The estimated IP₃ concentration as a function of intracellular Aβ₄₂ content together with the whole-cell model allows us to show that Aβ₄₂ oligomers impair mitochondrial function through pathological Ca²⁺ uptake and the resulting reduced mitochondrial inner membrane potential, leading to an overall lower ATP and increased production of reactive oxygen species and H₂O₂. We further show that mitochondrial function can be restored by the addition of Ca²⁺ buffer EGTA, in accordance with the observed abrogation of Aβ₄₂ cytotoxicity by EGTA in our live cells experiments.

High expression of type I inositol 1,4,5-trisphosphate receptor in the kidney of rats with hepatorenal syndrome

AIM

To detect the expression of type I inositol 1,4,5-trisphosphate receptor (IP3RI) in the kidney of rats with hepatorenal syndrome (HRS).

METHODS

One hundred and twenty-five Sprague-Dawley rats were randomly divided into four groups to receive an intravenous injection of D-galactosamine (D-GalN) plus lipopolysaccharide (LPS; group G/L, n = 50), D-GalN alone (group G, n = 25), LPS alone (group L, n = 25), and normal saline (group NS, n = 25), respectively. At 3, 6, 9, 12, and 24 h after injection, blood, liver, and kidney samples were collected. Hematoxylin-eosin staining of liver tissue was performed to assess hepatocyte necrosis. Electron microscopy was used to observe ultrastructural changes in the kidney. Western blot analysis and real-time PCR were performed to detect the expression of IP3RI protein and mRNA in the kidney, respectively.

RESULTS

Hepatocyte necrosis was aggravated gradually, which was most significant at 12 h after treatment with D-galactosamine/lipopolysaccharide, and was characterized by massive hepatocyte necrosis. At the same time, serum levels of biochemical indicators including liver and kidney function indexes were all significantly changed. The structure of the renal glomerulus and tubules was normal at all time points. Western blot analysis indicated that IP3RI protein expression began to rise at 3 h (P < 0.05) and peaked at 12 h (P < 0.01). Real-time PCR demonstrated that IP3RI mRNA expression began to rise at 3 h (P < 0.05) and peaked at 9 h (P < 0.01).

CONCLUSION

IP3RI protein expression is increased in the kidney of HRS rats, and may be regulated at the transcriptional level.

On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling

The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems and is the basis of the predictive power of theoretical physics. While physicists have confidence in this correspondence, it is less recognized in cellular biophysics. On the one hand, the complex organization of cellular dynamics involving a plethora of interacting molecules and the basic observation of cell variability seem to question its possibility. The practical difficulties of deriving the equations describing cellular behaviour from first principles support these doubts. On the other hand, ignoring such a correspondence would severely limit the possibility of predictive quantitative theory in biophysics. Additionally, the existence of functional modules (like pathways) across cell types suggests also the existence of mathematical structures with comparable universality. Only a few cellular systems have been sufficiently investigated in a variety of cell types to follow up these basic questions. IP₃ induced Ca²⁺signalling is one of them, and the mathematical structure corresponding to it is subject of ongoing discussion. We review the system's general properties observed in a variety of cell types. They are captured by a reaction diffusion system. We discuss the phase space structure of its local dynamics. The spiking regime corresponds to noisy excitability. Models focussing on different aspects can be derived starting from this phase space structure. We discuss how the initial assumptions on the set of stochastic variables and phase space structure shape the predictions of parameter dependencies of the mathematical models resulting from the derivation.