A multiple-oscillator mechanism underlies antigen-induced Ca2+ oscillations in Jurkat T-cells.

T-cell receptor stimulation triggers cytosolic Ca2+ signaling by inositol-1,4,5-trisphosphate (IP3)-mediated Ca2+ release from the endoplasmic reticulum (ER) and Ca2+ entry through Ca2+ release-activated Ca2+ (CRAC) channels gated by ER-located stromal-interacting molecules (STIM1/2). Physiologically, cytosolic Ca2+ signaling manifests as regenerative Ca2+ oscillations, which are critical for nuclear factor of activated T-cells-mediated transcription. In most cells, Ca2+ oscillations are thought to originate from IP3 receptor-mediated Ca2+ release, with CRAC channels indirectly sustaining them through ER refilling. Here, experimental and computational evidence support a multiple-oscillator mechanism in Jurkat T-cells whereby both IP3 receptor and CRAC channel activities oscillate and directly fuel antigen-evoked Ca2+ oscillations, with the CRAC channel being the major contributor. KO of either STIM1 or STIM2 significantly reduces CRAC channel activity. As such, STIM1 and STIM2 synergize for optimal Ca2+ oscillations and activation of nuclear factor of activated T-cells 1 and are essential for ER refilling. The loss of both STIM proteins abrogates CRAC channel activity, drastically reduces ER Ca2+ content, severely hampers cell proliferation and enhances cell death. These results clarify the mechanism and the contribution of STIM proteins to Ca2+ oscillations in T-cells.

A mathematical model of ENaC and Slc26a6 regulation by CFTR in salivary gland ducts.

Cystic fibrosis (CF) is a genetic disease caused by the mutations of cystic fibrosis transmembrane conductance regulator (CFTR), the cystic fibrosis transmembrane conductance regulator gene. Cftr is a critical ion channel expressed in the apical membrane of mouse salivary gland striated duct cells. Although Cftr is primarily a Cl- channel, its knockout leads to higher salivary Cl- and Na+ concentrations and lower pH. Mouse experiments show that the activation of Cftr upregulates epithelial Na+ channel (ENaC) protein expression level and Slc26a6 (a 1Cl-:2[Formula: see text] exchanger of the solute carrier family) activity. Experimentally, it is difficult to predict how much the coregulation effects of CFTR contribute to the abnormal Na+, Cl-, and [Formula: see text] concentrations and pH in CF saliva. To address this question, we construct a wild-type mouse salivary gland model and simulate CFTR knockout by altering the expression levels of CFTR, ENaC, and Slc26a6. By reproducing the in vivo and ex vivo final saliva measurements from wild-type and CFTR knockout animals, we obtain computational evidence that ENaC and Slc26a6 activities are downregulated in CFTR knockout in salivary glands.NEW & NOTEWORTHY This paper describes a salivary gland mathematical model simulating the ion exchange between saliva and the salivary gland duct epithelium. The novelty lies in the implementation of CFTR regulating ENaC and Slc26a6 in a CFTR knockout gland. By reproducing the experimental saliva measurements in wild-type and CFTR knockout glands, the model shows that CFTR regulates ENaC and Slc26a6 anion exchanger in salivary glands. The method could be used to understand the various cystic fibrosis phenotypes.

Emergence of broad cytosolic Ca2+ oscillations in the absence of CRAC channels: A model for CRAC-mediated negative feedback on PLC and Ca2+ oscillations through PKC.

The role of Ca2+ release-activated Ca2+ (CRAC) channels mediated by ORAI isoforms in calcium signalling has been extensively investigated. It has been shown that the presence or absence of different isoforms has a significant effect on store-operated calcium entry (SOCE). Yoast et al. (2020) showed that, in addition to the reported narrow-spike oscillations (whereby cytosolic calcium decreases quickly after a sharp increase), ORAI1 knockout HEK293 cells were able to oscillate with broad-spike oscillations (whereby cytosolic calcium decreases in a prolonged manner after a sharp increase) when stimulated with a muscarinic agonist. This suggests that Ca2+ influx through ORAI-mediated CRAC channels negatively regulates the duration of Ca2+ oscillations. We hypothesise that, through the activation of protein kinase C (PKC), ORAI1 negatively regulates phospholipase C (PLC) activity to decrease inositol 1,4,5-trisphosphate (IP3) production and limit the duration of agonist-evoked Ca2+ oscillations. Based on this hypothesis, we construct a new mathematical model, which shows that the formation of broad-spike oscillations is highly dependent on the absence of ORAI1. Predictions of this model are consistent with the experimental results.

A Model for the Coexistence of Competing Mechanisms for Ca 2 + Oscillations in T-lymphocytes.

Ca 2 + is a ubiquitous signaling mechanism across different cell types. In T-cells, it is associated with cytokine production and immune function. Benson et al. have shown the coexistence of competing Ca 2 + oscillations during antigen stimulation of T-cell receptors, depending on the presence of extracellular Ca 2 + influx through the Ca 2 + release-activated Ca 2 + channel (Benson in J Biol Chem 29:105310, 2023). In this paper, we construct a mathematical model consisting of five ordinary differential equations and analyze the relationship between the competing oscillatory mechanisms.. We perform bifurcation analysis on two versions of our model, corresponding to the two oscillatory types, to find the defining characteristics of these two families.

Structural and functional analysis of salivary intercalated duct cells reveals a secretory phenotype.

Currently, all salivary ducts (intercalated, striated and collecting) are assumed to function broadly in a similar manner, reclaiming ions that were secreted by the secretory acinar cells while preserving fluid volume and delivering saliva to the oral cavity. Nevertheless, there has been minimal investigation into the structural and functional differences between distinct types of salivary duct cells. Therefore, in this study, the expression profile of proteins involved in stimulus-secretion coupling, as well as the function of the intercalated duct (ID) and striated duct cells, was examined. Particular focus was placed on defining differences between distinct duct cell populations. To accomplish this, immunohistochemistry and in situ hybridization were utilized to examine the localization and expression of proteins involved in reabsorption and secretion of ions and fluid. Further, in vivo calcium imaging was employed to investigate cellular function. Based on the protein expression profile and functional data, marked differences between the IDs and striated ducts were observed. Specifically, the ID cells express proteins native to the secretory acinar cells while lacking proteins specifically expressed in the striated ducts. Further, the ID and striated duct cells display different calcium signalling characteristics, with the IDs responding to a neural stimulus in a manner similar to the acinar cells. Overall, our data suggest that the IDs have a distinct role in the secretory process, separate from the reabsorptive striated ducts. Instead, based on our evidence, the IDs express proteins found in secretory cells, generate calcium signals in a manner similar to acinar cells, and, therefore, are likely secretory cells. KEY POINTS: Current studies examining salivary intercalated duct cells are limited, with minimal documentation of the ion transport machinery and the overall role of the cells in fluid generation. Salivary intercalated duct cells are presumed to function in the same manner as other duct cells, reclaiming ions, maintaining fluid volume and delivering the final saliva to the oral cavity. Here we systematically examine the structure and function of the salivary intercalated duct cells using immunohistochemistry, in situ hybridization and by monitoring in vivo Ca2+ dynamics. Structural data revealed that the intercalated duct cells lack proteins vital for reabsorption and express proteins necessary for secretion. Ca2+ dynamics in the intercalated duct cells were consistent with those observed in secretory cells and resulted from GPCR-mediated IP3 production.

The Mitochondrial Ca2+ uniporter is a central regulator of interorganellar Ca2+ transfer and NFAT activation.

Mitochondrial Ca2+ uptake tailors the strength of stimulation of plasma membrane phospholipase C-coupled receptors to that of cellular bioenergetics. However, how Ca2+ uptake by the mitochondrial Ca2+ uniporter (MCU) shapes receptor-evoked interorganellar Ca2+ signaling is unknown. Here, we used CRISPR/Cas9 gene knockout, subcellular Ca2+ imaging, and mathematical modeling to show that MCU is a universal regulator of intracellular Ca2+ signaling across mammalian cell types. MCU activity sustains cytosolic Ca2+ signaling by preventing Ca2+-dependent inactivation of store-operated Ca2+ release-activated Ca2+ channels and by inhibiting Ca2+ extrusion. Paradoxically, MCU knockout (MCU-KO) enhanced cytosolic Ca2+ responses to store depletion. Physiological agonist stimulation in MCU-KO cells led to enhanced frequency of cytosolic Ca2+ oscillations, endoplasmic reticulum Ca2+ refilling, nuclear translocation of nuclear factor for activated T cells transcription factors, and cell proliferation, without altering inositol-1,4,5-trisphosphate receptor activity. Our data show that MCU has dual counterbalancing functions at the cytosol-mitochondria interface, whereby the cell-specific MCU-dependent cytosolic Ca2+ clearance and buffering capacity of mitochondria reciprocally regulate interorganellar Ca2+ transfer and nuclear factor for activated T cells nuclear translocation during receptor-evoked signaling. These findings highlight the critical dual function of the MCU not only in the acute Ca2+ buffering by mitochondria but also in shaping endoplasmic reticulum and cytosolic Ca2+ signals that regulate cellular transcription and function.

Effect of Buffers with Multiple Binding Sites on Calcium Waves.

The existence and properties of intracellular waves of increased free cytoplasmic calcium concentration (calcium waves) are strongly affected by the binding and unbinding of calcium ions to a multitude of different buffers in the cell. These buffers can be mobile or immobile and, in general, have multiple binding sites that are not independent. Previous theoretical studies have focused on the case when each buffer molecule binds a single calcium ion. In this study, we analyze how calcium waves are affected by calcium buffers with two non-independent binding sites, and show that the interactions between the calcium binding sites can result in the emergence of new behaviors. In particular, for certain combinations of kinetic parameters, the profiles of buffer molecules with one calcium ion bound can be non-monotone.

A Mathematical Model of Salivary Gland Duct Cells.

Saliva is produced in two stages in the salivary glands: the secretion of primary saliva by the acinus and the modification of saliva composition to final saliva by the intercalated and striated ducts. In order to understand the saliva modification process, we develop a mathematical model for the salivary gland duct. The model utilises the realistic 3D structure of the duct reconstructed from an image stack of gland tissue. Immunostaining results show that TMEM16A and aquaporin are expressed in the intercalated duct cells and that ENaC is not. Based on this, the model predicts that the intercalated duct does not absorb Na[Formula: see text] and Cl[Formula: see text] like the striated duct but secretes a small amount of water instead. The input to the duct model is the time-dependent primary saliva generated by an acinar cell model. Our duct model produces final saliva output that agrees with the experimental measurements at various stimulation levels. It also shows realistic biological features such as duct cell volume, cellular concentrations and membrane potentials. Simplification of the model by omission of all detailed 3D structures of the duct makes a negligible difference to the final saliva output. This shows that saliva production is not sensitive to structural variation of the duct.

A Tale of two receptors.

Calcium (Ca2+) oscillations in hepatocytes have a wide dynamic range. In particular, recent experimental evidence shows that agonist stimulation of the P2Y family of receptors leads to qualitatively diverse Ca2+ oscillations. We present a new model of Ca2+ oscillations in hepatocytes based on these experiments to investigate the mechanisms controlling P2Y-activated Ca2+ oscillations. The model accounts for Ca2+ regulation of the IP3 receptor (IP3R), the positive feedback from Ca2+ on phospholipase C (PLC) and the P2Y receptor phosphorylation by protein kinase C (PKC). Furthermore, PKC is shown to control multiple cellular substrates. Utilising the model, we suggest the activity and intensity of PLC and PKC necessary to explain the qualitatively diverse Ca2+ oscillations in response to P2Y receptor activation.

Calcium Dynamics and Water Transport in Salivary Acinar Cells.

Saliva is secreted from the acinar cells of the salivary glands, using mechanisms that are similar to other types of water-transporting epithelial cells. Using a combination of theoretical and experimental techniques, over the past 20 years we have continually developed and modified a quantitative model of saliva secretion, and how it is controlled by the dynamics of intracellular calcium. However, over approximately the past 5 years there have been significant developments both in our understanding of the underlying mechanisms and in the way these mechanisms should best be modelled. Here, we review the traditional understanding of how saliva is secreted, and describe how our work has suggested important modifications to this traditional view. We end with a brief description of the most recent data from living animals and discuss how this is now contributing to yet another iteration of model construction and experimental investigation.

Dual mechanisms of Ca2+ oscillations in hepatocytes.

Calcium (Ca2+) oscillations in hepatocytes control many critical cellular functions, including glucose metabolism and bile secretion. The mechanisms underlying repetitive Ca2+ oscillations and how these mechanisms regulate these oscillations is not fully understood. Recent experimental evidence has shown that both Ca2+ regulation of the inositol 1,4,5-trisphosphate (IP3) receptor and IP3 metabolism generate Ca2+ oscillations and co-exist in hepatocytes. To investigate the effects of these feedback mechanisms on the Ca2+ response, we construct a mathematical model of the Ca2+ signalling network in hepatocytes. The model accounts for the biphasic regulation of Ca2+ on the IP3 receptor (IP3R) and the positive feedback from Ca2+ on IP3 metabolism, via activation of phospholipase C (PLC) by agonist and Ca2+. Model simulations show that Ca2+ oscillations exist for both constant [IP3] and for [IP3] changing dynamically. We show, both experimentally and in the model, that as agonist concentration increases, Ca2+ oscillations transition between simple narrow-spike oscillations and complex broad-spike oscillations. The model predicts that narrow-spike oscillations persist when Ca2+ transport across the plasma membrane is blocked. This prediction has been experimentally validated. In contrast, broad-spike oscillations are terminated when plasma membrane transport is blocked. We conclude that multiple feedback mechanisms participate in regulating Ca2+ oscillations in hepatocytes.

A Multicellular Model of Primary Saliva Secretion in the Parotid Gland.

We construct a three-dimensional anatomically accurate multicellular model of a parotid gland acinus to investigate the influence that the topology of its lumen has on primary fluid secretion. Our model consists of seven individual cells, coupled via a common lumen and intercellular signalling. Each cell is equipped with the intracellular calcium ([Formula: see text])-signalling model developed by Pages et al, Bull Math Biol 81: 1394-1426, 2019. https://doi.org/10.1007/s11538-018-00563-z and the secretion model constructed by Vera-Sigüenza et al., Bull Math Biol 81: 699-721, 2019. https://doi.org/10.1007/s11538-018-0534-z. The work presented here is a continuation of these studies. While previous mathematical research has proven invaluable, to the best of our knowledge, a multicellular modelling approach has never been implemented. Studies have hypothesised the need for a multiscale model to understand the primary secretion process, as acinar cells do not operate on an individual basis. Instead, they form racemous clusters that form intricate water and protein delivery networks that join the acini with the gland's ducts-questions regarding the extent to which the acinus topology influences the efficiency of primary fluid secretion to persist. We found that (1) The topology of the acinus has almost no effect on fluid secretion. (2) A multicellular spatial model of secretion is not necessary when modelling fluid flow. Although the inclusion of intercellular signalling introduces vastly more complex dynamics, the total secretory rate remains fundamentally unchanged. (3) To obtain an acinus, or better yet a gland flow rate estimate, one can multiply the output of a well-stirred single-cell model by the total number of cells required.

On the dynamical structure of calcium oscillations.

Oscillations in the concentration of free cytosolic Ca2+ 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 Ca2+ 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 Ca2+ oscillation period can be controlled by modulation of the rate of activation by Ca2+ 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.

A Mathematical Model of Fluid Transport in an Accurate Reconstruction of Parotid Acinar Cells.

Salivary gland acinar cells use the calcium ([Formula: see text]) ion as a signalling messenger to regulate a diverse range of intracellular processes, including the secretion of primary saliva. Although the underlying mechanisms responsible for saliva secretion are reasonably well understood, the precise role played by spatially heterogeneous intracellular [Formula: see text] signalling in these cells remains uncertain. In this study, we use a mathematical model, based on new and unpublished experimental data from parotid acinar cells (measured in excised lobules of mouse parotid gland), to investigate how the structure of the cell and the spatio-temporal properties of [Formula: see text] signalling influence the production of primary saliva. We combine a new [Formula: see text] signalling model [described in detail in a companion paper: Pages et al. in Bull Math Biol 2018, submitted] with an existing secretion model (Vera-Sigüenza et al. in Bull Math Biol 80:255-282, 2018. https://doi.org/10.1007/s11538-017-0370-6 ) and solve the resultant model in an anatomically accurate three-dimensional cell. Our study yields three principal results. Firstly, we show that spatial heterogeneities of [Formula: see text] concentration in either the apical or basal regions of the cell have no significant effect on the rate of primary saliva secretion. Secondly, in agreement with previous work (Palk et al., in J Theor Biol 305:45-53, 2012. https://doi.org/10.1016/j.jtbi.2012.04.009 ) we show that the frequency of [Formula: see text] oscillation has no significant effect on the rate of primary saliva secretion, which is determined almost entirely by the mean (over time) of the apical and basal [Formula: see text]. Thirdly, it is possible to model the rate of primary saliva secretion as a quasi-steady-state function of the cytosolic [Formula: see text] averaged over the entire cell when modelling the flow rate is the only interest, thus ignoring all the dynamic complexity not only of the fluid secretion mechanism but also of the intracellular heterogeneity of [Formula: see text]. Taken together, our results demonstrate that an accurate multiscale model of primary saliva secretion from a single acinar cell can be constructed by ignoring the vast majority of the spatial and temporal complexity of the underlying mechanisms.

A Model of [Formula: see text] Dynamics in an Accurate Reconstruction of Parotid Acinar Cells.

We have constructed a spatiotemporal model of [Formula: see text] dynamics in parotid acinar cells, based on new data about the distribution of inositol trisphophate receptors (IPR). The model is solved numerically on a mesh reconstructed from images of a cluster of parotid acinar cells. In contrast to our earlier model (Sneyd et al. in J Theor Biol 419:383-393. https://doi.org/10.1016/j.jtbi.2016.04.030 , 2017b), which cannot generate realistic [Formula: see text] oscillations with the new data on IPR distribution, our new model reproduces the [Formula: see text] dynamics observed in parotid acinar cells. This model is then coupled with a fluid secretion model described in detail in a companion paper: A mathematical model of fluid transport in an accurate reconstruction of a parotid acinar cell (Vera-Sigüenza et al. in Bull Math Biol. https://doi.org/10.1007/s11538-018-0534-z , 2018b). Based on the new measurements of IPR distribution, we show that Class I models (where [Formula: see text] oscillations can occur at constant [[Formula: see text]]) can produce [Formula: see text] oscillations in parotid acinar cells, whereas Class II models (where [[Formula: see text]] needs to oscillate in order to produce [Formula: see text] oscillations) are unlikely to do so. In addition, we demonstrate that coupling fluid flow secretion with the [Formula: see text] signalling model changes the dynamics of the [Formula: see text] oscillations significantly, which indicates that [Formula: see text] dynamics and fluid flow cannot be accurately modelled independently. Further, we determine that an active propagation mechanism based on calcium-induced calcium release channels is needed to propagate the [Formula: see text] wave from the apical region to the basal region of the acinar cell.

New saliva secretion model based on the expression of Na+-K+ pump and K+ channels in the apical membrane of parotid acinar cells.

The plasma membrane of parotid acinar cells is functionally divided into apical and basolateral regions. According to the current model, fluid secretion is driven by transepithelial ion gradient, which facilitates water movement by osmosis into the acinar lumen from the interstitium. The osmotic gradient is created by the apical Cl- efflux and the subsequent paracellular Na+ transport. In this model, the Na+-K+ pump is located exclusively in the basolateral membrane and has essential role in salivary secretion, since the driving force for Cl- transport via basolateral Na+-K+-2Cl- cotransport is generated by the Na+-K+ pump. In addition, the continuous electrochemical gradient for Cl- flow during acinar cell stimulation is maintained by the basolateral K+ efflux. However, using a combination of single-cell electrophysiology and Ca2+-imaging, we demonstrate that photolysis of Ca2+ close to the apical membrane of parotid acinar cells triggered significant K+ current, indicating that a substantial amount of K+ is secreted into the lumen during stimulation. Nevertheless, the K+ content of the primary saliva is relatively low, suggesting that K+ might be reabsorbed through the apical membrane. Therefore, we investigated the localization of Na+-K+ pumps in acinar cells. We show that the pumps appear evenly distributed throughout the whole plasma membrane, including the apical pole of the cell. Based on these results, a new mathematical model of salivary fluid secretion is presented, where the pump reabsorbs K+ from and secretes Na+ to the lumen, which can partially supplement the paracellular Na+ pathway.

A mathematical model of calcium dynamics in HSY cells.

Saliva is an essential part of activities such as speaking, masticating and swallowing. Enzymes in salivary fluid protect teeth and gums from infectious diseases, and also initiate the digestion process. Intracellular calcium (Ca2+) plays a critical role in saliva secretion and regulation. Experimental measurements of Ca2+ and inositol trisphosphate (IP3) concentrations in HSY cells, a human salivary duct cell line, show that when the cells are stimulated with adenosine triphosphate (ATP) or carbachol (CCh), they exhibit coupled oscillations with Ca2+ spike peaks preceding IP3 spike peaks. Based on these data, we construct a mathematical model of coupled Ca2+ and IP3 oscillations in HSY cells and perform model simulations of three different experimental settings to forecast Ca2+ responses. The model predicts that when Ca2+ influx from the extracellular space is removed, oscillations gradually slow down until they stop. The model simulation of applying a pulse of IP3 predicts that photolysis of caged IP3 causes a transient increase in the frequency of the Ca2+ oscillations. Lastly, when Ca2+-dependent activation of PLC is inhibited, we see an increase in the oscillation frequency and a decrease in the amplitude. These model predictions are confirmed by experimental data. We conclude that, although concentrations of Ca2+ and IP3 oscillate, Ca2+ oscillations in HSY cells are the result of modulation of the IP3 receptor by intracellular Ca2+, and that the period is modulated by the accompanying IP3 oscillations.

A Mathematical Model Supports a Key Role for Ae4 (Slc4a9) in Salivary Gland Secretion.

We develop a mathematical model of a salivary gland acinar cell with the objective of investigating the role of two [Formula: see text] exchangers from the solute carrier family 4 (Slc4), Ae2 (Slc4a2) and Ae4 (Slc4a9), in fluid secretion. Water transport in this type of cell is predominantly driven by [Formula: see text] movement. Here, a basolateral [Formula: see text] adenosine triphosphatase pump (NaK-ATPase) and a [Formula: see text]-[Formula: see text]-[Formula: see text] cotransporter (Nkcc1) are primarily responsible for concentrating the intracellular space with [Formula: see text] well above its equilibrium potential. Gustatory and olfactory stimuli induce the release of [Formula: see text] ions from the internal stores of acinar cells, which triggers saliva secretion. [Formula: see text]-dependent [Formula: see text] and [Formula: see text] channels promote ion secretion into the luminal space, thus creating an osmotic gradient that promotes water movement in the secretory direction. The current model for saliva secretion proposes that [Formula: see text] anion exchangers (Ae), coupled with a basolateral [Formula: see text] ([Formula: see text]) (Nhe1) antiporter, regulate intracellular pH and act as a secondary [Formula: see text] uptake mechanism (Nauntofte in Am J Physiol Gastrointest Liver Physiol 263(6):G823-G837, 1992; Melvin et al. in Annu Rev Physiol 67:445-469, 2005. https://doi.org/10.1146/annurev.physiol.67.041703.084745 ). Recent studies demonstrated that Ae4 deficient mice exhibit an approximate [Formula: see text] decrease in gland salivation (Peña-Münzenmayer et al. in J Biol Chem 290(17):10677-10688, 2015). Surprisingly, the same study revealed that absence of Ae2 does not impair salivation, as previously suggested. These results seem to indicate that the Ae4 may be responsible for the majority of the secondary [Formula: see text] uptake and thus a key mechanism for saliva secretion. Here, by using 'in-silico' Ae2 and Ae4 knockout simulations, we produced mathematical support for such controversial findings. Our results suggest that the exchanger's cotransport of monovalent cations is likely to be important in establishing the osmotic gradient necessary for optimal transepithelial fluid movement.

Mapping Interpuff Interval Distribution to the Properties of Inositol Trisphosphate Receptors.

Tightly clustered inositol trisphosphate receptors (IP3Rs) control localized Ca2+ liberation from the endoplasmic reticulum to generate repetitive Ca2+ puffs. Distributions of the interpuff interval (IPI), i.e., the waiting time between successive puffs, are found to be well characterized by a probability density function involving only two parameters, λ and ξ, which represent the basal rate of puff generation and the recovery rate from refractoriness, respectively. However, how the two parameters depend on the kinetic parameters of single IP3Rs in a cluster is still unclear. In this article, using a stochastic puff model and a single-channel data-based IP3R model, we establish the dependencies of λ and ξ on two important IP3R model parameters, IP3 concentration ([IP3]) and the recovery rate from Ca2+ inhibition (rlow). By varying [IP3] and rlow in physiologically plausible ranges, we find that the ξ-λ plane is comprised of only two disjoint regions, a biologically impermissible region and a region where each parameter set (ξ, λ) can be caused by using two different combinations of [IP3] and rlow. The two combinations utilize very different mechanisms to maintain the same IPI distribution, and the mechanistic difference provides a way of identifying IP3R kinetic parameters by observing properties of the IPI.

The relative contributions of store-operated and voltage-gated Ca2+ channels to the control of Ca2+ oscillations in airway smooth muscle.

KEY POINTS: Agonist-dependent oscillations in the concentration of free cytosolic calcium are a vital mechanism for the control of airway smooth muscle contraction and thus are a critical factor in airway hyper-responsiveness. Using a mathematical model, closely tied to experimental work, we show that the oscillations in membrane potential accompanying the calcium oscillations have no significant effect on the properties of the calcium oscillations. In addition, the model shows that calcium entry through store-operated calcium channels is critical for calcium oscillations, but calcium entry through voltage-gated channels has much less effect. The model predicts that voltage-gated channels are less important than store-operated channels in the control of airway smooth muscle tone. ABSTRACT: Airway smooth muscle contraction is typically the key mechanism underlying airway hyper-responsiveness, and the strength of muscle contraction is determined by the frequency of oscillations of intracellular calcium (Ca2+ ) concentration. In airway smooth muscle cells, these Ca2+ oscillations are caused by cyclic Ca2+ release from the sarcoplasmic reticulum, although Ca2+ influx via plasma membrane channels is also necessary to sustain the oscillations over longer times. To assess the relative contributions of store-operated and voltage-gated Ca2+ channels to this Ca2+ influx, we generated a comprehensive mathematical model, based on experimental Ca2+ measurements in mouse precision-cut lung slices, to simulate Ca2+ oscillations and changes in membrane potential. Agonist-induced Ca2+ oscillations are accompanied by oscillations in membrane potential, although the membrane potential oscillations are too small to generate large Ca2+ currents through voltage-gated Ca2+ channels, and thus have little effect on the Ca2+ oscillations. Ca2+ entry through voltage-gated channels only becomes important when the cell is depolarized (e.g. by a high external K+ concentration). As a result, agonist-induced Ca2+ oscillations are critically dependent on Ca2+ entry through store-operated channels but do not depend strongly on Ca2+ entry though voltage-gated channels.