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

The inositol trisphosphate receptor ([Formula: see text]) 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 [Formula: see text] have arisen. Firstly, how best should the [Formula: see text] be modeled? In other words, what fundamental properties of the [Formula: see text] 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 [Formula: see text], 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 [Formula: see text], and thus the behavior of the [Formula: see text] 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, [Formula: see text] stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic [Formula: see text] models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified [Formula: see text] models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model

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

A simple mechanochemical model for calcium signalling in embryonic epithelial cells

Calcium (Ca2+) signalling is one of the most important mechanisms of information propagation in the body. In embryogenesis the interplay between Ca2+ signalling and mechanical forces is critical to the healthy development of an embryo but poorly understood. Several types of embryonic cells exhibit calcium-induced contractions and many experiments indicate that Ca2+ signals and contractions are coupled via a two-way mechanochemical coupling. We present a new analysis of experimental data that supports the existence of this coupling during Apical Constriction in Neural Tube Closure. We then propose a mechanochemical model, building on early models that couple Ca2+ dynamics to cell mechanics and replace the bistable Ca2+ release with modern, experimentally validated Ca2+ dynamics. We assume that the cell is a linear viscoelastic material and model the Ca2+-induced contraction stress with a Hill function saturating at high Ca2+ levels. We also express, for the first time, the 'stretch-activation' Ca2+ flux in the early mechanochemical models as a bottom-up contribution from stretch-sensitive Ca2+ channels on the cell membrane. We reduce the model to three ordinary differential equations and analyse its bifurcation structure semi-analytically as the IP3 concentration, and the 'strength' of stretch activation, λ vary. The Ca2+ system (λ=0, no mechanics) exhibits relaxation oscillations for a certain range of IP3 values. As λ is increased the range of IP3 values decreases, the oscillation amplitude decreases and the frequency increases. Oscillations vanish for a sufficiently high value of λ. These results agree with experiments in embryonic cells that also link the loss of Ca2+ oscillations to embryo abnormalities. The work addresses a very important and understudied question on the coupling of chemical and mechanical signalling in embryogenesis

Data-Driven Modelling of the Inositol Trisphosphate Receptor (IPR) and its Role in Calcium-Induced Calcium Release (CICR)

We review the current state of the art of data-driven modelling of the inositol trisphosphate receptor (IPR). After explaining that the IPR plays a crucial role as a central regulator in calcium dynamics, several sources of relevant experimental data are introduced. Single ion channels are best studied by recording single-channel currents under different ligand concentrations via the patch-clamp technique. The particular relevance of modal gating, the spontaneous switching between different levels of channel activity that occur even at constant ligand concentrations, is highlighted. In order to investigate the interactions of IPRs, calcium release from small clusters of channels, so-called calcium puffs, can be used. We then present the mathematical framework common to all models based on single-channel data, aggregated continuous-time Markov models, and give a short review of statistical approaches for parameterising these models with experimental data. The process of building a Markov model that integrates various sources of experimental data is illustrated using two recent examples, the model by Ullah et al. and the “Park–Drive” model by Siekmann et al. (Biophys. J. 2012), the only models that account for all sources of data currently available. Finally, it is demonstrated that the essential features of the Park–Drive model in different models of calcium dynamics are preserved after reducing it to a two-state model that only accounts for the switching between the inactive “park” and the active “drive” modes. This highlights the fact that modal gating is the most important mechanism of ligand regulation in the IPR. It also emphasises that data-driven models of ion channels do not necessarily have to lead to detailed models but can be constructed so that relevant data is selected to represent ion channels at the appropriate level of complexity for a given application