Factors Determining the Recruitment of Inositol Trisphosphate Receptor Channels During Calcium Puffs

Puffs are localized, transient elevations in cytosolic Ca²⁺ that serve both as the building blocks of global cellular Ca²⁺ signals and as local signals in their own right. They arise from clustered inositol 1,4,5-trisphosphate receptor/channels (IP₃Rs), whose openings are coordinated by Ca²⁺-induced Ca²⁺ release (CICR). We utilized total internal reflection fluorescence imaging of Ca²⁺ signals in neuroblastoma cells with single-channel resolution to elucidate the mechanisms determining the triggering, amplitudes, kinetics, and spatial spread of puffs. We find that any given channel in a cluster has a mean probability of ∼66% of opening following opening of an initial “trigger” channel, and the probability of puff triggering thus increases steeply with increasing number of channels in a cluster (cluster size). Mean puff amplitudes scale with cluster size, but individual amplitudes vary widely, even at sites of similar cluster size, displaying similar proportions of events involving any given number of the channels in the cluster. Stochastic variation in numbers of Ca²⁺-inhibited IP₃Rs likely contributes to the variability of amplitudes of repeated puffs at a site but the amplitudes of successive puffs were uncorrelated, even though we observed statistical correlations between interpuff intervals and puff amplitudes. Initial puffs evoked following photorelease of IP₃—which would not be subject to earlier Ca²⁺-inhibition—also showed wide variability, indicating that mechanisms such as stochastic variation in IP₃ binding and channel recruitment by CICR further determine puff amplitudes. The mean termination time of puffs lengthened with increasing puff amplitude size, consistent with independent closings of channels after a given mean open time, but we found no correlation of termination time with cluster size independent of puff amplitude. The spatial extent of puffs increased with their amplitude, and puffs of similar size were of similar width, independent of cluster size.     

Factors Determining the Recruitment of Inositol Trisphosphate Receptor Channels During Calcium Puffs

Puffs are localized, transient elevations in cytosolic Ca²⁺ that serve both as the building blocks of global cellular Ca²⁺ signals and as local signals in their own right. They arise from clustered inositol 1,4,5-trisphosphate receptor/channels (IP₃Rs), whose openings are coordinated by Ca²⁺-induced Ca²⁺ release (CICR). We utilized total internal reflection fluorescence imaging of Ca²⁺ signals in neuroblastoma cells with single-channel resolution to elucidate the mechanisms determining the triggering, amplitudes, kinetics, and spatial spread of puffs. We find that any given channel in a cluster has a mean probability of ∼66% of opening following opening of an initial “trigger” channel, and the probability of puff triggering thus increases steeply with increasing number of channels in a cluster (cluster size). Mean puff amplitudes scale with cluster size, but individual amplitudes vary widely, even at sites of similar cluster size, displaying similar proportions of events involving any given number of the channels in the cluster. Stochastic variation in numbers of Ca²⁺-inhibited IP₃Rs likely contributes to the variability of amplitudes of repeated puffs at a site but the amplitudes of successive puffs were uncorrelated, even though we observed statistical correlations between interpuff intervals and puff amplitudes. Initial puffs evoked following photorelease of IP₃—which would not be subject to earlier Ca²⁺-inhibition—also showed wide variability, indicating that mechanisms such as stochastic variation in IP₃ binding and channel recruitment by CICR further determine puff amplitudes. The mean termination time of puffs lengthened with increasing puff amplitude size, consistent with independent closings of channels after a given mean open time, but we found no correlation of termination time with cluster size independent of puff amplitude. The spatial extent of puffs increased with their amplitude, and puffs of similar size were of similar width, independent of cluster size.     

'Trigger' events precede calcium puffs in Xenopus oocytes

The liberation of calcium ions sequestered in the endoplasmic reticulum through inositol 1,4,5-trisphosphate receptors/channels (IP₃Rs) results in a spatiotemporal hierarchy of calcium signaling events that range from single-channel openings to local Ca²⁺ puffs believed to arise from several to tens of clustered IP₃Rs to global calcium waves. Using high-resolution confocal linescan imaging and a sensitive Ca²⁺ indicator dye (fluo-4-dextran), we show that puffs are often preceded by small, transient Ca²⁺ elevations that we christen “trigger events”. The magnitude of triggers is consistent with their arising from the opening of a single IP₃ receptor/channel, and we propose that they initiate puffs by recruiting neighboring IP₃Rs within the cluster by a regenerative process of Ca²⁺-induced Ca²⁺ release. Puff amplitudes (fluorescence ratio change) are on average ~6 times greater than that of the triggers, suggesting that at least six IP₃Rs may simultaneously be open during a puff. Trigger events have average durations of ~12 ms, as compared to 19 ms for the mean rise time of puffs, and their spatial extent is ~3 times smaller than puffs (respective widths at half peak amplitude 0.6 and 1.6 μm). All these parameters were relatively independent of IP₃ concentration, although the proportion of puffs showing resolved triggers was greatest (~80%) at low [IP₃]. Because Ca²⁺ puffs constitute the building blocks from which cellular IP₃-mediated Ca²⁺ signals are constructed, the events that initiate them are likely to be of fundamental importance for cell signaling. Moreover, the trigger events provide a useful yardstick by which to derive information regarding the number and spatial arrangement of IP₃Rs within clusters.     

Termination of calcium puffs and coupled closings of inositol trisphosphate receptor channels

Calcium puffs are localized Ca²⁺ signals mediated by Ca²⁺ release from the endoplasmic reticulum (ER) through clusters of inositol trisphosphate receptor (IP₃R) channels. The recruitment of IP₃R channels during puffs depends on Ca²⁺-induced Ca²⁺ release, a regenerative process that must be terminated to maintain control of cell signaling and prevent Ca²⁺ cytotoxicity. Here, we studied puff termination using total internal reflection microscopy to resolve the gating of individual IP₃R channels during puffs in intact SH-SY5Y neuroblastoma cells. We find that the kinetics of IP₃R channel closing differ from that expected for independent, stochastic gating, in that multiple channels tend to remain open together longer than predicted from their individual open lifetimes and then close in near-synchrony. This behavior cannot readily be explained by previously proposed termination mechanisms, including Ca²⁺-inhibition of IP₃Rs and local depletion of Ca²⁺ in the ER lumen. Instead, we postulate that the gating of closely adjacent IP₃Rs is coupled, possibly via allosteric interactions, suggesting an important mechanism to ensure robust puff termination in addition to Ca²⁺-inactivation.     

Inositol (1,4,5)-Trisphosphate Receptor Microarchitecture Shapes Ca Puff Kinetics

Inositol (1,4,5)-trisphosphate receptors (IP₃Rs) release intracellular Ca²⁺ as localized Ca²⁺ signals (Ca²⁺ puffs) that represent the activity of small numbers of clustered IP₃Rs spaced throughout the endoplasmic reticulum. Although much emphasis has been placed on estimating the number of active Ca²⁺ release channels supporting Ca²⁺ puffs, less attention has been placed on understanding the role of cluster microarchitecture. This is important as recent data underscores the dynamic nature of IP₃R transitions between heterogeneous cellular architectures and the differential behavior of IP₃Rs socialized into clusters. Here, we applied a high-resolution model incorporating stochastically gating IP₃Rs within a three-dimensional cytoplasmic space to demonstrate: 1), Ca²⁺ puffs are supported by a broad range of clustered IP₃R microarchitectures; 2), cluster ultrastructure shapes Ca²⁺ puff characteristics; and 3), loosely corralled IP₃R clusters (>200 nm interchannel separation) fail to coordinate Ca²⁺ puffs, owing to inefficient triggering and impaired coupling due to reduced Ca²⁺-induced Ca²⁺ release microwave velocity (<10 nm/s) throughout the channel array. Dynamic microarchitectural considerations may therefore influence Ca²⁺ puff occurrence/properties in intact cells, contrasting with a more minimal role for channel number over the same simulated conditions in shaping local Ca²⁺ dynamics.     

Superresolution Localization of Single Functional IP3R Channels Utilizing Ca Flux as a Readout

The subcellular localization of membrane Ca²⁺ channels is crucial for their functioning, but is difficult to study because channels may be distributed more closely than the resolution of conventional microscopy is able to detect. We describe a technique, stochastic channel Ca²⁺ nanoscale resolution (SCCaNR), employing Ca²⁺-sensitive fluorescent dyes to localize stochastic openings and closings of single Ca²⁺-permeable channels within <50 nm, and apply it to examine the clustered arrangement of inositol trisphosphate receptor (IP₃R) channels underlying local Ca²⁺ puffs. Fluorescence signals (blips) arising from single functional IP₃Rs are almost immotile (diffusion coefficient <0.003 μm² s⁻¹), as are puff sites over prolonged periods, suggesting that the architecture of this signaling system is stable and not subject to rapid, dynamic rearrangement. However, rapid stepwise changes in centroid position of fluorescence are evident within the durations of individual puffs. These apparent movements likely result from asynchronous gating of IP₃Rs distributed within clusters that have an overall diameter of ∼400 nm, indicating that the nanoscale architecture of IP₃R clusters is important in shaping local Ca²⁺ signals. We anticipate that SCCaNR will complement superresolution techniques such as PALM and STORM for studies of Ca²⁺ channels as it obviates the need for photoswitchable labels and provides functional as well as spatial information.     

Modulation of Elementary Calcium Release Mediates a Transition from Puffs to Waves in an IP3R Cluster Model

The oscillating concentration of intracellular calcium is one of the most important examples for collective dynamics in cell biology. Localized releases of calcium through clusters of inositol 1,4,5-trisphosphate receptor channels constitute elementary signals called calcium puffs. Coupling by diffusing calcium leads to global releases and waves, but the exact mechanism of inter-cluster coupling and triggering of waves is unknown. To elucidate the relation of puffs and waves, we here model a cluster of IP₃R channels using a gating scheme with variable non-equilibrium IP₃ binding. Hybrid stochastic and deterministic simulations show that puffs are not stereotyped events of constant duration but are sensitive to stimulation strength and residual calcium. For increasing IP₃ concentration, the release events become modulated at a timescale of minutes, with repetitive wave-like releases interspersed with several puffs. This modulation is consistent with experimental observations we present, including refractoriness and increase of puff frequency during the inter-wave interval. Our results suggest that waves are established by a random but time-modulated appearance of sustained release events, which have a high potential to trigger and synchronize activity throughout the cell.     

Single-Molecule Tracking of Inositol Trisphosphate Receptors Reveals Different Motilities and Distributions

Puffs are local Ca²⁺ signals that arise by Ca²⁺ liberation from the endoplasmic reticulum through the concerted opening of tightly clustered inositol trisphosphate receptors/channels (IP₃Rs). The locations of puff sites observed by Ca²⁺ imaging remain static over several minutes, whereas fluorescence recovery after photobleaching (FRAP) experiments employing overexpression of fluorescently tagged IP₃Rs have shown that the majority of IP₃Rs are freely motile. To address this discrepancy, we applied single-molecule imaging to locate and track type 1 IP₃Rs tagged with a photoswitchable fluorescent protein and expressed in COS-7 cells. We found that ∼70% of the IP₃R1 molecules were freely motile, undergoing random walk motility with an apparent diffusion coefficient of ∼0.095 μm s⁻¹, whereas the remaining molecules were essentially immotile. A fraction of the immotile IP₃Rs were organized in clusters, with dimensions (a few hundred nanometers across) comparable to those previously estimated for the IP₃R clusters underlying functional puff sites. No short-term (seconds) changes in overall motility or in clustering of immotile IP₃Rs were apparent following activation of IP₃/Ca²⁺ signaling. We conclude that stable clusters of small numbers of immotile IP₃Rs may underlie local Ca²⁺ release sites, whereas the more numerous motile IP₃Rs appear to be functionally silent.     

A Stochastic Model of Calcium Puffs Based on Single-Channel Data

Calcium puffs are local transient Ca²⁺ releases from internal Ca²⁺ stores such as the endoplasmic reticulum or the sarcoplasmic reticulum. Such release occurs through a cluster of inositol 1,4,5-trisphosphate receptors (IP₃Rs). Based on the IP₃R model (which is determined by fitting to stationary single-channel data) and nonstationary single-channel data, we construct a new IP₃R model that includes time-dependent rates of mode switches. A point-source model of Ca²⁺ puffs is then constructed based on the new IP₃R model and is solved by a hybrid Gillespie method with adaptive timing. Model results show that a relatively slow recovery of an IP₃R from Ca²⁺ inhibition is necessary to reproduce most of the experimental outcomes, especially the nonexponential interpuff interval distributions. The number of receptors in a cluster could be severely underestimated when the recovery is sufficiently slow. Furthermore, we find that, as the number of IP₃Rs increases, the average duration of puffs initially increases but then becomes saturated, whereas the average decay time keeps increasing linearly. This gives rise to the observed asymmetric puff shape.     

Comparison of Ca2+ puffs evoked by extracellular agonists and photoreleased IP3

The inositol trisphosphate (IP₃) signaling pathway evokes local Ca²⁺ signals (Ca²⁺ puffs) that arise from the concerted openings of clustered IP₃ receptor/channels in the ER membrane. Physiological activation is triggered by binding of agonists to G-protein-coupled receptors (GPCRs) on the cell surface, leading to cleavage of phosphatidyl inositol bisphosphate and release of IP₃ into the cytosol. Photorelease of IP₃ from a caged precursor provides a convenient and widely employed means to study the final stage of IP₃-mediated Ca²⁺ liberation, bypassing upstream signaling events to enable more precise control of the timing and relative concentration of cytosolic IP₃. Here, we address whether Ca²⁺ puffs evoked by photoreleased IP₃ fully replicate those arising from physiological agonist stimulation. We imaged puffs in individual SH-SY5Y neuroblastoma cells that were sequentially stimulated by picospritzing extracellular agonist (carbachol, CCH or bradykinin, BK) followed by photorelease of a poorly-metabolized IP₃ analog, i-IP₃. The centroid localizations of fluorescence signals during puffs evoked in the same cells by agonists and photorelease substantially overlapped (within ∼1 μm), suggesting that IP₃ from both sources accesses the same, or closely co-localized clusters of IP₃Rs. Moreover, the time course and spatial spread of puffs evoked by agonists and photorelease matched closely. Because photolysis generates IP₃ uniformly throughout the cytoplasm, our results imply that IP₃ generated in SH-SY5Y cells by activation of receptors to CCH and BK also exerts broadly distributed actions, rather than specifically activating a subpopulation of IP₃Rs that are scaffolded in close proximity to cell surface receptors to form a signaling nanodomain.     

Frequency and Relative Prevalence of Calcium Blips and Puffs in a Model of Small IP3R Clusters

In this work, we model the local calcium release from clusters with a few inositol 1,4,5-trisphosphate receptor (IP₃R) channels, focusing on the stochastic process in which an open channel either triggers other channels to open (as a puff) or fails to cause any channel to open (as a blip). We show that there are linear relations for the interevent interval (including blips and puffs) and the first event latency against the inverse cluster size. However, nonlinearity is found for the interpuff interval and the first puff latency against the inverse cluster size. Furthermore, the simulations indicate that the blip fraction among all release events and the blip frequency are increasing with larger basal [Ca²⁺], with blips in turn giving a growing contribution to basal [Ca²⁺]. This result suggests that blips are not just lapses to trigger puffs, but they may also possess a biological function to contribute to the initiation of calcium waves by a preceding increase of basal [Ca²⁺] in cells that have small IP₃R clusters.     

Frequency and Relative Prevalence of Calcium Blips and Puffs in a Model of Small IP3R Clusters

In this work, we model the local calcium release from clusters with a few inositol 1,4,5-trisphosphate receptor (IP₃R) channels, focusing on the stochastic process in which an open channel either triggers other channels to open (as a puff) or fails to cause any channel to open (as a blip). We show that there are linear relations for the interevent interval (including blips and puffs) and the first event latency against the inverse cluster size. However, nonlinearity is found for the interpuff interval and the first puff latency against the inverse cluster size. Furthermore, the simulations indicate that the blip fraction among all release events and the blip frequency are increasing with larger basal [Ca²⁺], with blips in turn giving a growing contribution to basal [Ca²⁺]. This result suggests that blips are not just lapses to trigger puffs, but they may also possess a biological function to contribute to the initiation of calcium waves by a preceding increase of basal [Ca²⁺] in cells that have small IP₃R clusters.     

Dynamic regulation of IP3 receptor clustering and activity by IP3

Inositol 1,4,5-trisphosphate receptors (IP₃Rs) are intracellular Ca²⁺ channels. Their regulation by both IP₃ and Ca²⁺ allows interactions between IP₃Rs to generate a hierarchy of intracellular Ca²⁺ release events. These can progress from openings of single IP₃R, through near-synchronous opening of a few IP₃Rs within a cluster to much larger signals that give rise to regenerative Ca²⁺ waves that can invade the entire cell. We have used patch-clamp recording from excised nuclear membranes of DT40 cells expressing only IP₃R3 and shown that low concentrations of IP₃ rapidly and reversibly cause IP₃Rs to assemble into small clusters. In addition to bringing IP₃Rs close enough to allow Ca²⁺ released by one IP₃R to regulate the activity of its neighbors, clustering also retunes the regulation of IP₃Rs by IP₃ and Ca²⁺. At resting cytosolic [Ca²⁺], lone IP₃R are more sensitive to IP₃ and the mean channel open time (~10ms) is twice as long as for clustered IP₃R. When the cytosolic free [Ca²⁺] is increased to 1µM, to mimic the conditions that might prevail when an IP₃R within a cluster opens, clustered IP₃R are no longer inhibited and their gating becomes coupled. IP₃, by dynamically regulating IP₃R clustering, both positions IP₃R for optimal interactions between them and it serves to exaggerate the effects of Ca²⁺ within a cluster. During the course of these studies, we have observed that nuclear IP₃R stably express one of two single channel K ⁺ conductances (γ_K ~120 or 200pS). Here we demonstrate that for both states of the IP₃R, the effects of IP₃ on clustering are indistinguishable. These observations reinforce our conclusion that IP₃ dynamically regulates assembly of IP₃Rs into clusters that underlie the hierarchical recruitment of elementary Ca²⁺ release events.     

Timescales of IP3-Evoked Ca Spikes Emerge from Ca Puffs Only at the Cellular Level

The behavior of biological systems is determined by the properties of their component molecules, but the interactions are usually too complex to understand fully how molecular behavior generates cellular behavior. Ca²⁺ signaling by inositol trisphosphate receptors (IP₃R) offers an opportunity to understand this relationship because the cellular behavior is defined largely by Ca²⁺-mediated interactions between IP₃R. Ca²⁺ released by a cluster of IP₃R (giving a local Ca²⁺ puff) diffuses and ignites the behavior of neighboring clusters (to give repetitive global Ca²⁺ spikes). We use total internal reflection fluorescence microscopy of two mammalian cell lines to define the temporal relationships between Ca²⁺ puffs (interpuff intervals, IPI) and Ca²⁺ spikes (interspike intervals) evoked by flash photolysis of caged IP₃. We find that IPI are much shorter than interspike intervals, that puff activity is stochastic with a recovery time that is much shorter than the refractory period of the cell, and that IPI are not periodic. We conclude that Ca²⁺ spikes do not arise from oscillatory dynamics of IP₃R clusters, but that repetitive Ca²⁺ spiking with its longer timescales is an emergent property of the dynamics of the whole cluster array.     

Modeling of the Modulation by Buffers of Ca Release through Clusters of IP3 Receptors

Intracellular Ca²⁺ release is a versatile second messenger system. It is modeled here by reaction-diffusion equations for the free Ca²⁺ and Ca²⁺ buffers, with spatially discrete clusters of stochastic IP₃ receptor channels (IP₃Rs) controlling the release of Ca²⁺ from the endoplasmic reticulum. IP₃Rs are activated by a small rise of the cytosolic Ca²⁺ concentration and inhibited by large concentrations. Buffering of cytosolic Ca²⁺ shapes global Ca²⁺ transients. Here we use a model to investigate the effect of buffers with slow and fast reaction rates on single release spikes. We find that, depending on their diffusion coefficient, fast buffers can either decouple clusters or delay inhibition. Slow buffers have little effect on Ca²⁺ release, but affect the time course of the signals from the fluorescent Ca²⁺ indicator mainly by competing for Ca²⁺. At low [IP₃], fast buffers suppress fluorescence signals, slow buffers increase the contrast between bulk signals and signals at open clusters, and large concentrations of buffers, either fast or slow, decouple clusters.     

The number and spatial distribution of IP3 receptors underlying calcium puffs in Xenopus oocytes

Calcium puffs are local Ca(2+) release events that arise from a cluster of inositol 1,4,5-trisphosphate receptor channels (IP(3)Rs) and serve as a basic "building block" from which global Ca(2+) waves are generated. Important questions remain as to the number of IP(3)Rs that open during a puff, their spatial distribution within a cluster, and how much Ca(2+) current flows through each channel. The recent discovery of "trigger" events-small Ca(2+) signals that immediately precede puffs and are interpreted to arise through opening of single IP(3)R channels-now provides a useful yardstick by which to calibrate the Ca(2+) flux underlying puffs. Here, we describe a deterministic numerical model to simulate puffs and trigger events. Based on confocal linescan imaging in Xenopus oocytes, we simulated Ca(2+) release in two sequential stages; representing the trigger by the opening of a single IP(3)R in the center of a cluster for 12 ms, followed by the concerted opening of some number of IP(3)Rs for 19 ms, representing the rising phase of the puff. The diffusion of Ca(2+) and Ca(2+)-bound indicator dye were modeled in a three-dimensional cytosolic volume in the presence of immobile and mobile Ca(2+) buffers, and were used to predict the observed fluorescence signal after blurring by the microscope point-spread function. Optimal correspondence with experimental measurements of puff spatial width and puff/trigger amplitude ratio was obtained assuming that puffs arise from the synchronous opening of 25-35 IP(3)Rs, each carrying a Ca(2+) current of approximately 0.4 pA, with the channels distributed through a cluster 300-800 nm in diameter.     

The probability of triggering calcium puffs is linearly related to the number of inositol trisphosphate receptors in a cluster

Puffs are local Ca(2+) signals that arise by Ca(2+) liberation from the endoplasmic reticulum through concerted opening of tightly clustered inositol trisphosphate receptor/channels (IP(3)R). They serve both local signaling functions and trigger global Ca(2+) waves. The numbers of functional IP(3)R within clusters differ appreciably between different puff sites, and we investigated how the probability of puff occurrence varies with cluster size. We imaged puffs in SH-SY5Y cells using total internal fluorescence microscopy, and estimated cluster sizes from the magnitude of the largest puff observed at each site relative to the signal from a single channel. We find that the initial triggering rate of puffs following photorelease of IP(3), and the average frequency of subsequent repetitive puffs, vary about linearly with cluster size. These data accord well with stochastic simulations in which opening of any individual IP(3)R channel within a cluster triggers a puff via Ca(2+)-induced Ca(2+) release. An important consequence is that the signaling power of a puff site (average amount of Ca(2+) released per puff × puff frequency) varies about the square of cluster size, implying that large clusters contribute disproportionately to cellular signaling and, because of their higher puff frequency, preferentially act as pacemakers to initiate Ca(2+) waves.     

Inositol (1,4,5)-trisphosphate receptor microarchitecture shapes Ca2+ puff kinetics

Inositol (1,4,5)-trisphosphate receptors (IP(3)Rs) release intracellular Ca(2+) as localized Ca(2+) signals (Ca(2+) puffs) that represent the activity of small numbers of clustered IP(3)Rs spaced throughout the endoplasmic reticulum. Although much emphasis has been placed on estimating the number of active Ca(2+) release channels supporting Ca(2+) puffs, less attention has been placed on understanding the role of cluster microarchitecture. This is important as recent data underscores the dynamic nature of IP(3)R transitions between heterogeneous cellular architectures and the differential behavior of IP(3)Rs socialized into clusters. Here, we applied a high-resolution model incorporating stochastically gating IP(3)Rs within a three-dimensional cytoplasmic space to demonstrate: 1), Ca(2+) puffs are supported by a broad range of clustered IP(3)R microarchitectures; 2), cluster ultrastructure shapes Ca(2+) puff characteristics; and 3), loosely corralled IP(3)R clusters (>200 nm interchannel separation) fail to coordinate Ca(2+) puffs, owing to inefficient triggering and impaired coupling due to reduced Ca(2+)-induced Ca(2+) release microwave velocity (<10 nm/s) throughout the channel array. Dynamic microarchitectural considerations may therefore influence Ca(2+) puff occurrence/properties in intact cells, contrasting with a more minimal role for channel number over the same simulated conditions in shaping local Ca(2+) dynamics.     

An efficient reduced-lattice model of IP3R for probing Ca2+ dynamics

Numerous cellular processes are regulated by Ca²⁺ signals, and the endoplasmic reticulum (ER) membrane's inositol triphosphate receptor (IP₃R) is critical for modulating intracellular Ca²⁺ dynamics. The IP₃Rs are seen to be clustered in a variety of cell types. The combination of IP₃Rs clustering and IP₃Rs-mediated Ca²⁺-induced Ca²⁺ release results in the hierarchical organization of the Ca²⁺ signals, which challenges the numerical simulation given the multiple spatial and temporal scales that must be covered. The previous methods rather ignore the spatial feature of IP₃Rs or fail to coordinate the conflicts between the real biological relevance and the computational cost. In this work, a general and efficient reduced-lattice model is presented for the simulation of IP₃Rs-mediated multiscale Ca²⁺ dynamics. The model highlights biological details that make up the majority of the calcium events, including IP₃Rs clustering and calcium domains, and it reduces the complexity by approximating the minor details. The model's extensibility provides fresh insights into the function of IP₃Rs in producing global Ca²⁺ events and supports the research under more physiological circumstances. Our work contributes to a novel toolkit for modeling multiscale Ca²⁺ dynamics and advances knowledge of Ca²⁺ signals.     

Calcium-dependent inactivation and the dynamics of calcium puffs and sparks

Localized intracellular Ca²⁺ elevations known as puffs and sparks arise from the cooperative activity of inositol 1,4,5-trisphosphate receptor Ca²⁺ channels (IP₃Rs) and ryanodine receptor Ca²⁺ channels (RyRs) clustered at Ca²⁺ release sites on the surface of the endoplasmic reticulum or sarcoplasmic reticulum. When Markov chain models of these intracellular Ca²⁺-regulated Ca²⁺ channels are coupled via a mathematical representation of a Ca²⁺ microdomain, simulated Ca²⁺ release sites may exhibit the phenomenon of “stochastic Ca²⁺ excitability” reminiscent of Ca²⁺ puffs and sparks where channels open and close in a concerted fashion. To clarify the role of Ca²⁺ inactivation of IP₃Rs and RyRs in the dynamics of puffs and sparks, we formulate and analyze Markov chain models of Ca²⁺ release sites composed of 10–40 three-state intracellular Ca²⁺ channels that are inactivated as well as activated by Ca²⁺. We study how the statistics of simulated puffs and sparks depend on the kinetics and dissociation constant of Ca²⁺ inactivation and find that puffs and sparks are often less sensitive to variations in the number of channels at release sites and strength of coupling via local [Ca²⁺] when the average fraction of inactivated channels is significant. Interestingly, we observe that the single channel kinetics of Ca²⁺ inactivation influences the thermodynamic entropy production rate of Markov chain models of puffs and sparks. While excessively fast Ca²⁺ inactivation can preclude puffs and sparks, moderately fast Ca²⁺ inactivation often leads to time-irreversible puffs and sparks whose termination is facilitated by the recruitment of inactivated channels throughout the duration of the puff/spark event. On the other hand, Ca²⁺ inactivation may be an important negative feedback mechanism even when its time constant is much greater than the duration of puffs and sparks. In fact, slow Ca²⁺ inactivation can lead to release sites with a substantial fraction of inactivated channels that exhibit puffs and sparks that are nearly time-reversible and terminate without additional recruitment of inactivated channels.