Mathematical modelling of ca(2+) oscillations in airway smooth muscle cells

Numerical simulation of calcium dynamics dependent ATP degradation, IP3 and NADH production due to obesity in a hepatocyte cell

Calcium (Ca[Formula: see text]) signals have a crucial role in regulating various processes of almost every cell to maintain its structure and function. Calcium dynamics has been studied in various cells including hepatocytes by many researchers, but the mechanisms of calcium signals involved in regulation and dysregulation of various processes like ATP degradation rate, IP[Formula: see text] and NADH production rate respectively in normal and obese cells are still poorly understood. In this paper, a reaction diffusion equation of calcium is employed to propose a model of calcium dynamics by coupling ATP degradation rate, IP[Formula: see text] and NADH production rate in hepatocyte cells under normal and obese conditions. The processes like source influx, buffer, endoplasmic reticulum (ER), mitochondrial calcium uniporters (MCU) and Na[Formula: see text]/Ca[Formula: see text] exchanger (NCX) have been incorporated in the model. Linear finite element method is used along spatial dimension, and Crank-Nicolson method is used along temporal dimension for numerical simulation. The results have been obtained for the normal hepatocyte cells and for cells due to obesity. The comparative study of these results reveal significant difference caused due to obesity in Ca[Formula: see text] dynamics as well as in ATP degradation rate, IP[Formula: see text] and NADH production rate.

A dynamical model of TGF-β activation in asthmatic airways

Excessive activation of the regulatory cytokine transforming growth factor $\beta $ (TGF-$\beta $) via contraction of airway smooth muscle (ASM) is associated with the development of asthma. In this study, we develop an ordinary differential equation model that describes the change in density of the key airway wall constituents, ASM and extracellular matrix (ECM), and their interplay with subcellular signalling pathways leading to the activation of TGF-$\beta $. We identify bistable parameter regimes where there are two positive steady states, corresponding to either reduced or elevated TGF-$\beta $ concentration, with the latter leading additionally to increased ASM and ECM density. We associate the former with a healthy homeostatic state and the latter with a diseased (asthmatic) state. We demonstrate that external stimuli, inducing TGF-$\beta $ activation via ASM contraction (mimicking an asthmatic exacerbation), can perturb the system irreversibly from the healthy state to the diseased one. We show that the properties of the stimuli, such as their frequency or strength, and the clearance of surplus active TGF-$\beta $, are important in determining the long-term dynamics and the development of disease. Finally, we demonstrate the utility of this model in investigating temporal responses to bronchial thermoplasty, a therapeutic intervention in which ASM is ablated by applying thermal energy to the airway wall. The model predicts the parameter-dependent threshold damage required to obtain irreversible reduction in ASM content, suggesting that certain asthma phenotypes are more likely to benefit from this intervention.

Emerging concepts in smooth muscle contributions to airway structure and function: implications for health and disease

Airway structure and function are key aspects of normal lung development, growth, and aging, as well as of lung responses to the environment and the pathophysiology of important diseases such as asthma, chronic obstructive pulmonary disease, and fibrosis. In this regard, the contributions of airway smooth muscle (ASM) are both functional, in the context of airway contractility and relaxation, as well as synthetic, involving production and modulation of extracellular components, modulation of the local immune environment, cellular contribution to airway structure, and, finally, interactions with other airway cell types such as epithelium, fibroblasts, and nerves. These ASM contributions are now found to be critical in airway hyperresponsiveness and remodeling that occur in lung diseases. This review emphasizes established and recent discoveries that underline the central role of ASM and sets the stage for future research toward understanding how ASM plays a central role by being both upstream and downstream in the many interactive processes that determine airway structure and function in health and disease.

A deterministic model predicts the properties of stochastic calcium oscillations in airway smooth muscle cells

The inositol trisphosphate receptor () is one of the most important cellular components responsible for oscillations in the cytoplasmic calcium concentration. Over the past decade, two major questions about the have arisen. Firstly, how best should the be modeled? In other words, what fundamental properties of the allow it to perform its function, and what are their quantitative properties? Secondly, although calcium oscillations are caused by the stochastic opening and closing of small numbers of , is it possible for a deterministic model to be a reliable predictor of calcium behavior? Here, we answer these two questions, using airway smooth muscle cells (ASMC) as a specific example. Firstly, we show that periodic calcium waves in ASMC, as well as the statistics of calcium puffs in other cell types, can be quantitatively reproduced by a two-state model of the , and thus the behavior of the is essentially determined by its modal structure. The structure within each mode is irrelevant for function. Secondly, we show that, although calcium waves in ASMC are generated by a stochastic mechanism, stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model.

The inositol trisphosphate receptor () is one of the most important cellular components responsible for calcium oscillations. Over the past decade, two major questions about the have arisen. Firstly, what fundamental properties of the allow it to perform its function? Secondly, although calcium oscillations are caused by the stochastic properties of small numbers of is it possible for a deterministic model to be a reliable predictor of calcium dynamics? Using airway smooth muscle cells as an example, we show that calcium dynamics can be accurately modeled using simplified models, and, secondly, that deterministic models are qualitatively accurate predictors of calcium dynamics. These results are important for the study of calcium dynamics in many cell types.

Activation of store-operated calcium entry in airway smooth muscle cells: insight from a mathematical model

Intracellular dynamics of airway smooth muscle cells (ASMC) mediate ASMC contraction and proliferation, and thus play a key role in airway hyper-responsiveness (AHR) and remodelling in asthma. We evaluate the importance of store-operated entry (SOCE) in these dynamics by constructing a mathematical model of ASMC signaling based on experimental data from lung slices. The model confirms that SOCE is elicited upon sufficient depletion of the sarcoplasmic reticulum (SR), while receptor-operated entry (ROCE) is inhibited in such conditions. It also shows that SOCE can sustain agonist-induced oscillations in the absence of other influx. SOCE up-regulation may thus contribute to AHR by increasing the oscillation frequency that in turn regulates ASMC contraction. The model also provides an explanation for the failure of the SERCA pump blocker CPA to clamp the cytosolic of ASMC in lung slices, by showing that CPA is unable to maintain the SR empty of . This prediction is confirmed by experimental data from mouse lung slices, and strongly suggests that CPA only partially inhibits SERCA in ASMC.