Importance of cell variability for calcium signaling in rat airway myocytes

Heterogeneity and Delayed Activation as Hallmarks of Self-Organization and Criticality in Excitable Tissue

Self-organized critical dynamics is assumed to be an attractive mode of functioning for several real-life systems and entails an emergent activity in which the extent of observables follows a power-law distribution. The hallmarks of criticality have recently been observed in a plethora of biological systems, including beta cell populations within pancreatic islets of Langerhans. In the present study, we systematically explored the mechanisms that drive the critical and supercritical behavior in networks of coupled beta cells under different circumstances by means of experimental and computational approaches. Experimentally, we employed high-speed functional multicellular calcium imaging of fluorescently labeled acute mouse pancreas tissue slices to record calcium signals in a large number of beta cells simultaneously, and with a high spatiotemporal resolution. Our experimental results revealed that the cellular responses to stimulation with glucose are biphasic and glucose-dependent. Under physiological as well as under supraphysiological levels of stimulation, an initial activation phase was followed by a supercritical plateau phase with a high number of global intercellular calcium waves. However, the activation phase displayed fingerprints of critical behavior under lower stimulation levels, with a progressive recruitment of cells and a power-law distribution of calcium wave sizes. On the other hand, the activation phase provoked by pathophysiologically high glucose concentrations, differed considerably and was more rapid, less continuous, and supercritical. To gain a deeper insight into the experimentally observed complex dynamical patterns, we built up a phenomenological model of coupled excitable cells and explored empirically the model’s necessities that ensured a good overlap between computational and experimental results. It turned out that such a good agreement between experimental and computational findings was attained when both heterogeneous and stimulus-dependent time lags, variability in excitability levels, as well as a heterogeneous cell-cell coupling were included into the model. Most importantly, since our phenomenological approach involved only a few parameters, it naturally lends itself not only for determining key mechanisms of self-organized criticality at the tissue level, but also points out various features for comprehensive and realistic modeling of different excitable systems in nature.

Endothelial cells decode VEGF-mediated Ca2+ signaling patterns to produce distinct functional responses

A single extracellular stimulus can promote diverse behaviors among isogenic cells by differentially regulated signaling networks. We examined Ca(2+) signaling in response to VEGF (vascular endothelial growth factor), a growth factor that can stimulate different behaviors in endothelial cells. We found that altering the amount of VEGF signaling in endothelial cells by stimulating them with different VEGF concentrations triggered distinct and mutually exclusive dynamic Ca(2+) signaling responses that correlated with different cellular behaviors. These behaviors were cell proliferation involving the transcription factor NFAT (nuclear factor of activated T cells) and cell migration involving MLCK (myosin light chain kinase). Further analysis suggested that this signal decoding was robust to the noisy nature of the signal input. Using probabilistic modeling, we captured both the stochastic and deterministic aspects of Ca(2+) signal decoding and accurately predicted cell responses in VEGF gradients, which we used to simulate different amounts of VEGF signaling. Ca(2+) signaling patterns associated with proliferation and migration were detected during angiogenesis in developing zebrafish.

Strategy for NSAID administration to aspirin-intolerant asthmatics in combination with PGE2 analogue: a theoretical approach

Aspirin-induced asthma (AIA) is a severe inflammatory disease, which affects aspirin-intolerant patients after ingestion of aspirin or other non-steroidal anti-inflammatory drugs (NSAIDs). In this article, a mathematical model describing arachidonic acid metabolism and its interaction with NSAIDs, is used to study the strategy for safe managing of NSAIDs to AIA patients. Three different AIA patient populations are taken into consideration. First, the values of aspirin and ibuprofen limiting doses that might induce symptoms of AIA are calculated and compared to experimentally observed threshold doses to enlighten which AIA patient population is susceptible to aspirin and ibuprofen. Second, the methodology of NSAID administration is studied on AIA populations susceptible to aspirin and ibuprofen by using 1,000 mg dose of aspirin and 200 or 400 mg dose of ibuprofen followed by PGE(2) analogue dosing. Our model results show that successive doses of PGE(2) analogue applied at appropriate time after aspirin or ibuprofen ingestion would enable administration of both NSAIDs to AIA patients. PGE(2) analogue doses and the corresponding times of their applications are calculated. The model is also used to estimate the duration of symptoms of AIA for different aspirin and ibuprofen doses.

A minimal model for the mitochondrial rapid mode of Ca²+ uptake mechanism

Mitochondria possess a remarkable ability to rapidly accumulate and sequester Ca²⁺. One of the mechanisms responsible for this ability is believed to be the rapid mode (RaM) of Ca²⁺ uptake. Despite the existence of many models of mitochondrial Ca²⁺ dynamics, very few consider RaM as a potential mechanism that regulates mitochondrial Ca²⁺ dynamics. To fill this gap, a novel mathematical model of the RaM mechanism is developed herein. The model is able to simulate the available experimental data of rapid Ca²⁺ uptake in isolated mitochondria from both chicken heart and rat liver tissues with good fidelity. The mechanism is based on Ca²⁺ binding to an external trigger site(s) and initiating a brief transient of high Ca²⁺ conductivity. It then quickly switches to an inhibited, zero-conductive state until the external Ca²⁺ level is dropped below a critical value (∼100–150 nM). RaM's Ca²⁺- and time-dependent properties make it a unique Ca²⁺ transporter that may be an important means by which mitochondria take up Ca²⁺in situ and help enable mitochondria to decode cytosolic Ca²⁺ signals. Integrating the developed RaM model into existing models of mitochondrial Ca²⁺ dynamics will help elucidate the physiological role that this unique mechanism plays in mitochondrial Ca²⁺-homeostasis and bioenergetics.

Denoising two-photon calcium imaging data

Two-photon calcium imaging is now an important tool for in vivo imaging of biological systems. By enabling neuronal population imaging with subcellular resolution, this modality offers an approach for gaining a fundamental understanding of brain anatomy and physiology. Proper analysis of calcium imaging data requires denoising, that is separating the signal from complex physiological noise. To analyze two-photon brain imaging data, we present a signal plus colored noise model in which the signal is represented as harmonic regression and the correlated noise is represented as an order autoregressive process. We provide an efficient cyclic descent algorithm to compute approximate maximum likelihood parameter estimates by combing a weighted least-squares procedure with the Burg algorithm. We use Akaike information criterion to guide selection of the harmonic regression and the autoregressive model orders. Our flexible yet parsimonious modeling approach reliably separates stimulus-evoked fluorescence response from background activity and noise, assesses goodness of fit, and estimates confidence intervals and signal-to-noise ratio. This refined separation leads to appreciably enhanced image contrast for individual cells including clear delineation of subcellular details and network activity. The application of our approach to in vivo imaging data recorded in the ferret primary visual cortex demonstrates that our method yields substantially denoised signal estimates. We also provide a general Volterra series framework for deriving this and other signal plus correlated noise models for imaging. This approach to analyzing two-photon calcium imaging data may be readily adapted to other computational biology problems which apply correlated noise models.

Effects of transmitters and amyloid-beta peptide on calcium signals in rat cortical astrocytes: Fura-2AM measurements and stochastic model simulations

Background

To better understand the complex molecular level interactions seen in the pathogenesis of Alzheimer's disease, the results of the wet-lab and clinical studies can be complemented by mathematical models. Astrocytes are known to become reactive in Alzheimer's disease and their ionic equilibrium can be disturbed by interaction of the released and accumulated transmitters, such as serotonin, and peptides, including amyloid- peptides (A). We have here studied the effects of small amounts of A25–35 fragments on the transmitter-induced calcium signals in astrocytes by Fura-2AM fluorescence measurements and running simulations of the detected calcium signals.

Methodology/Principal Findings

Intracellular calcium signals were measured in cultured rat cortical astrocytes following additions of serotonin and glutamate, or either of these transmitters together with A25–35. A25–35 increased the number of astrocytes responding to glutamate and exceedingly increased the magnitude of the serotonin-induced calcium signals. In addition to A25–35-induced effects, the contribution of intracellular calcium stores to calcium signaling was tested. When using higher stimulus frequency, the subsequent calcium peaks after the initial peak were of lower amplitude. This may indicate inadequate filling of the intracellular calcium stores between the stimuli. In order to reproduce the experimental findings, a stochastic computational model was introduced. The model takes into account the major mechanisms known to be involved in calcium signaling in astrocytes. Model simulations confirm the principal experimental findings and show the variability typical for experimental measurements.

Conclusions/Significance

Nanomolar A25–35 alone does not cause persistent change in the basal level of calcium in astrocytes. However, even small amounts of A25–35, together with transmitters, can have substantial synergistic effects on intracellular calcium signals. Computational modeling further helps in understanding the mechanisms associated with intracellular calcium oscillations. Modeling the mechanisms is important, as astrocytes have an essential role in regulating the neuronal microenvironment of the central nervous system.