A Deterministic Model Predicts the Properties of Stochastic Calcium Oscillations in Airway Smooth Muscle Cells

Cao, Pengxing; Tan, Xiahui; Donovan, Graham M.; Sanderson, Michael J.; Sneyd, James

doi:10.1371/journal.pcbi.1003783

Cited by 55 publications

(98 citation statements)

References 37 publications

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“…Instead of modeling this complex mechanism, we focused on qualitatively capturing the characteristic that SOC channels open after calcium is depleted from the ER. Therefore, as a simplified first step, we used a reverse Hill equation to model the activation of these channels, as in Cao et al (2014). Store-operated calcium entry is a subject of intense ongoing research, and the model will need to be re-evaluated and updated as more data becomes available.…”

Section: Discussionmentioning

confidence: 99%

Mathematical investigation of IP3-dependent calcium dynamics in astrocytes

et al. 2017

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We study evoked calcium dynamics in astrocytes, a major cell type in the mammalian brain. Experimental evidence has shown that such dynamics are highly variable between different trials, cells, and cell subcompartments. Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. Variation in the maximum flow in different calcium channels is also shown to determine the range of stable oscillations, as well as set the range of frequencies of the oscillations. Further, by conducting a randomized search through the parameter space and recording the resulting calcium responses, we create a database that can be used by experimentalists to help estimate the underlying channel distribution of their cells.

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Section: Discussionmentioning

confidence: 99%

Mathematical investigation of IP3-dependent calcium dynamics in astrocytes

et al. 2017

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“…However, in our canonical Ca 2+ oscillation model, the time scale, τ h , of the "slow" variable, h, is a decreasing function of c. This feature, which is derived from the previous modeling work of ref. 35, results in a model that gives more realistic Ca 2+ spikes than does the traditional FHN model. In this sense, our canonical model is similar to the models of refs.…”

Section: +mentioning

confidence: 99%

On the dynamical structure of calcium oscillations

Sneyd

Han

Wang

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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101

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Oscillations in the concentration of free cytosolic Ca 2+ are an important and ubiquitous control mechanism in many cell types. It is thus correspondingly important to understand the mechanisms that underlie the control of these oscillations and how their period is determined. We show that Class I Ca 2+ oscillations (i.e., oscillations that can occur at a constant concentration of inositol trisphosphate) have a common dynamical structure, irrespective of the oscillation period. This commonality allows the construction of a simple canonical model that incorporates this underlying dynamical behavior. Predictions from the model are tested, and confirmed, in three different cell types, with oscillation periods ranging over an order of magnitude. The model also predicts that Ca 2+ oscillation period can be controlled by modulation of the rate of activation by Ca 2+ of the inositol trisphosphate receptor. Preliminary experimental evidence consistent with this hypothesis is presented. Our canonical model has a structure similar to, but not identical to, the classic FitzHugh-Nagumo model. The characterization of variables by speed of evolution, as either fast or slow variables, changes over the course of a typical oscillation, leading to a model without globally defined fast and slow variables. ) are a ubiquitous signaling mechanism, occurring in many cell types and controlling a wide array of cellular functions (1-6). In many cases, the signal is carried by the oscillation frequency; for example, Ca 2+ oscillation frequency is known to control contraction of pulmonary and arteriole smooth muscle (7,8), as well as gene expression and differentiation (9-11). Although there are cell types where the frequency of Ca 2+ oscillation appears to be less important than the mean [Ca 2+ ] (12), an understanding of how Ca 2+ oscillation frequency is controlled remains critical to our understanding of many important cellular processes. Interestingly, it appears that the signal may not be carried by the absolute oscillation frequency but rather by a change in frequency (13), leading to a signaling system that is robust to intercellular variability, even within the same cell type. A concept similar to that of the Ca 2+ toolbox is important in the mathematical modeling of Ca 2+ dynamics. Models try to extract fundamental mechanisms, omitting less important details so that the basic skeleton-the basic toolbox components-can become clear. In the construction of such skeleton models, the concept of dynamical structure becomes important. The behavior of a model can be qualitatively described by a set of bifurcations and attracting or repelling sets, and this description is essentially independent of the exact model equations and parameters used to realize the underlying dynamical structure (in that there can be many different equations and parameters that have the same dynamical structure).One important question is how cells can generate Ca 2+ oscillations of widely differing periods, even though they appear to be using the same elements o...

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“…The recent work by Cao and colleagues [45] that proposed a deterministic model of IP3Rs that qualitatively predicts some stochastic Ca 2+ oscillation properties is very encouraging. This two-state model was constructed by reducing a 6-state stochastic IP3R model [46], where the six states were partitioned into two groups assuming time scale differences and the experimentally observed "two mode" property.…”

Section: Future Workmentioning

confidence: 90%

Reduction of calcium release site models via optimized state aggregation

Hao

2016

EPJ Nonlinear Biomed Phys

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Background: Markov chain models of calcium release sites in living cells exhibit stochastic dynamics reminiscent of the experimentally observed phenomenon of calcium puffs and sparks. Such models often take the form of stochastic automata networks in which the transition probabilities for each of a large number of intercellular channel models depend on the local calcium concentration and thus the state of nearby channels. The state-space size in such compositionally defined calcium release site models increases exponentially as the number of channels increases, which is referred to as "state-space explosion". Methods: In order to overcome the state-space explosion problem, we utilized the idea of "coarse graining" and implemented an automated procedure that reduces the state space by aggregating and lumping states of the full release site model. For a given state aggregation scheme, the transition rates between reduced states are chosen consistent with the conditional probability distribution among states within each group. A genetic algorithm-based approach is then applied to select the state aggregation schemes that lead to reduced models that approximate the observable behaviors of the full model. Results: The genetic algorithm-based approach is implemented in Matlab® and applied to two different release site models. The approach found reduced models that approximate the full model in the number of open channels, spark statistics, and the jump probability matrix as a function of time. Conclusions: A novel automated genetic algorithm-based searching technique is implemented to find reduced calcium release site models that approximate observable behaviors of the full Markov chain models that possess intractable state-spaces. As compared to the full model, the reduced models produce quantitatively similar results using significantly less computational resources.

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A Deterministic Model Predicts the Properties of Stochastic Calcium Oscillations in Airway Smooth Muscle Cells

Cited by 55 publications

References 37 publications

Mathematical investigation of IP3-dependent calcium dynamics in astrocytes

Mathematical investigation of IP3-dependent calcium dynamics in astrocytes

On the dynamical structure of calcium oscillations

Reduction of calcium release site models via optimized state aggregation

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