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

Ca2+ puffs underlie adhesion-triggered Ca2+ microdomains in T cells

Ca2+ signalling is pivotal in T cell activation, an essential process in adaptive immune responses. Key to this activation are Ca2+ microdomains, which are transient increases in cytosolic Ca2+ concentration occurring within narrow regions between the endoplasmic reticulum (ER) and the plasma membrane (PM), lasting a few tens of milliseconds. Adhesion Dependent Ca2+ Microdomains (ADCM) rely on store-operated Ca2+ entry (SOCE) via the ORAI/STIM system. The nanometric scale at which these microdomains form poses challenges for direct experimental observation. Following the previous work of Gil et al. [1], which introduced a three-dimensional model of the ER-PM junction, this study combines a detailed description of the Ca2+ fluxes at the junction with stochastic dynamics of a cluster of D-myo-inositol 1,4,5 trisphosphate receptors (IP3R) located in the ER surrounding the junction. Because the consideration of Ca2+ release through the IP3R calls for the simulation of a portion of the cytoplasm considerably larger than the junction, our study also investigates the spatial distribution of PMCAs, revealing their likely localization outside the ER-PM junction. Simulations indicate that Ca2+ puffs implying the opening of 2-6 IP3Rs create ADCMs by provoking local depletions of ER Ca2+ stimulating Ca2+ entry through the ORAI1 channels. Such conditions allow the reproduction of the amplitude, duration and spatial extent of the observed ADCMs. By integrating advanced computational techniques with insights from experimental studies, our approach provides valuable information on the mechanisms governing early Ca2+ signalling in T cell activation, paving the way for a deeper understanding of immune responses.

Modeling IP3-induced Ca2+ signaling based on its interspike interval statistics

Inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ signaling is a second messenger system used by almost all eukaryotic cells. Recent research demonstrated randomness of Ca2+ signaling on all structural levels. We compile eight general properties of Ca2+ spiking common to all cell types investigated and suggest a theory of Ca2+ spiking starting from the random behavior of IP3 receptor channel clusters mediating the release of Ca2+ from the endoplasmic reticulum capturing all general properties and pathway-specific behavior. Spike generation begins after the absolute refractory period of the previous spike. According to its hierarchical spreading from initiating channel openings to cell level, we describe it as a first passage process from none to all clusters open while the cell recovers from the inhibition which terminated the previous spike. Our theory reproduces the exponential stimulation response relation of the average interspike interval Tav and its robustness properties, random spike timing with a linear moment relation between Tav and the interspike interval SD and its robustness properties, sensitive dependency of Tav on diffusion properties, and nonoscillatory local dynamics. We explain large cell variability of Tav observed in experiments by variability of channel cluster coupling by Ca2+-induced Ca2+ release, the number of clusters, and IP3 pathway component expression levels. We predict the relation between puff probability and agonist concentration and [IP3] and agonist concentration. Differences of spike behavior between cell types and stimulating agonists are explained by the different types of negative feedback terminating spikes. In summary, the hierarchical random character of spike generation explains all of the identified general properties.

IP3 receptors: An "elementary" journey from structure to signals

Inositol 1,4,5-trisphosphate receptors (IP3Rs) are large tetrameric channels which sit mostly in the membrane of the endoplasmic reticulum (ER) and mediate Ca2+ release from intracellular stores in response to extracellular stimuli in almost all cells. Dual regulation of IP3Rs by IP3 and Ca2+ itself, upstream "licensing", and the arrangement of IP3Rs into small clusters in the ER membrane, allow IP3Rs to generate spatially and temporally diverse Ca2+ signals. The characteristic biphasic regulation of IP3Rs by cytosolic Ca2+ concentration underpins regenerative Ca2+ signals by Ca2+-induced Ca2+-release, while also preventing uncontrolled explosive Ca2+ release. In this way, cells can harness a simple ion such as Ca2+ as a near-universal intracellular messenger to regulate diverse cellular functions, including those with conflicting outcomes such as cell survival and cell death. High-resolution structures of the IP3R bound to IP3 and Ca2+ in different combinations have together started to unravel the workings of this giant channel. Here we discuss, in the context of recently published structures, how the tight regulation of IP3Rs and their cellular geography lead to generation of "elementary" local Ca2+ signals known as Ca2+ "puffs", which form the fundamental bottleneck through which all IP3-mediated cytosolic Ca2+ signals must first pass.

An integrate-and-fire approach to Ca2+ signaling. Part I: Renewal model

In computational neuroscience integrate-and-fire models capture the spike generation by a subthreshold dynamics supplemented by a simple fire-and-reset rule; they allow for a numerically efficient and analytically tractable description of stochastic single cell as well as network dynamics. Stochastic spiking is also a prominent feature of Ca2+ signaling which suggests to adopt the integrate-and-fire approach for this fundamental biophysical process. The model introduced here consists of two components describing 1) activity of clusters of inositol-trisphosphate receptor channels and 2) dynamics of the global Ca2+ concentrations in the cytosol. The cluster dynamics is given in terms of a cyclic Markov chain, capturing the puff, i.e., the punctuated release of Ca2+ from intracellular stores. The cytosolic Ca2+ concentration is described by an integrate-and-fire dynamics driven by the puff current. For the cyclic Markov chain we derive expressions for the statistics of the interpuff interval, the single-puff strength and the puff current assuming constant cytosolic Ca2+. The latter condition is often well approximated because cytosolic Ca2+ varies much slower than the cluster activity does. Furthermore, because the detailed two-component model is numerically expensive to simulate and difficult to treat analytically, we develop an analytical framework to approximate the driving puff current of the stochastic cytosolic Ca2+ dynamics by a temporally uncorrelated Gaussian noise. This approximation reduces our two-component system to an integrate-and-fire model with a nonlinear drift function and a multiplicative Gaussian white noise, a model that is known to generate a renewal spike train, i.e., a point process with statistically independent interspike intervals. The model allows for fast numerical simulations, permits to derive analytical expressions for the rate of Ca2+ spiking and the coefficient of variation of the interspike interval, and to approximate the interspike interval density and the spike train power spectrum. Comparison of these statistics to experimental data is discussed.

Computational investigation of IP3 diffusion

Inositol 1,4,5-trisphosphate (IP₃) plays a key role in calcium signaling. After stimulation, it diffuses from the plasma membrane where it is produced to the endoplasmic reticulum where its receptors are localized. Based on in vitro measurements, IP₃ was long thought to be a global messenger characterized by a diffusion coefficient of ~ 280 μm²s^-1. However, in vivo observations revealed that this value does not match with the timing of localized Ca²⁺ increases induced by the confined release of a non-metabolizable IP₃ analog. A theoretical analysis of these data concluded that in intact cells diffusion of IP₃ is strongly hindered, leading to a 30-fold reduction of the diffusion coefficient. Here, we performed a new computational analysis of the same observations using a stochastic model of Ca²⁺ puffs. Our simulations concluded that the value of the effective IP₃ diffusion coefficient is close to 100 μm²s^-1. Such moderate reduction with respect to in vitro estimations quantitatively agrees with a buffering effect by non-fully bound inactive IP₃ receptors. The model also reveals that IP₃ spreading is not much affected by the endoplasmic reticulum, which represents an obstacle to the free displacement of molecules, but can be significantly increased in cells displaying elongated, 1-dimensional like geometries.

Inositol 1,4,5-trisphosphate receptors in cardiomyocyte physiology and disease

The contraction of cardiac muscle underlying the pumping action of the heart is mediated by the process of excitation-contraction coupling (ECC). While triggered by Ca²⁺ entry across the sarcolemma during the action potential, it is the release of Ca²⁺ from the sarcoplasmic reticulum (SR) intracellular Ca²⁺ store via ryanodine receptors (RyRs) that plays the major role in induction of contraction. Ca²⁺ also acts as a key intracellular messenger regulating transcription underlying hypertrophic growth. Although Ca²⁺ release via RyRs is by far the greatest contributor to the generation of Ca²⁺ transients in the cardiomyocyte, Ca²⁺ is also released from the SR via inositol 1,4,5-trisphosphate (InsP₃) receptors (InsP₃Rs). This InsP₃-induced Ca²⁺ release modifies Ca²⁺ transients during ECC, participates in directing Ca²⁺ to the mitochondria, and stimulates the transcription of genes underlying hypertrophic growth. Central to these specific actions of InsP₃Rs is their localization to responsible signalling microdomains, the dyad, the SR-mitochondrial interface and the nucleus. In this review, the various roles of InsP₃R in cardiac (patho)physiology and the mechanisms by which InsP₃ signalling selectively influences the different cardiomyocyte cell processes in which it is involved will be presented.

This article is part of the theme issue ‘The cardiomyocyte: new revelations on the interplay between architecture and function in growth, health, and disease’.

KRAP is required for diffuse and punctate IP3-mediated Ca2+ liberation and determines the number of functional IP3R channels within clusters

KRas-induced actin-interacting protein (KRAP) has been identified as crucial for the appropriate localization and functioning of the inositol trisphosphate receptors (IP₃Rs) that mediate Ca²⁺ release from the endoplasmic reticulum. Here, we used siRNA knockdown of KRAP expression in HeLa and HEK293 cells to examine the roles of KRAP in the generation of IP₃-mediated local Ca²⁺ puffs and global, cell-wide Ca²⁺ signals. High resolution Ca²⁺ imaging revealed that the mean amplitude of puffs was strongly reduced by KRAP knockdown, whereas the Ca²⁺ flux during openings of individual IP₃R channels was little affected. In both control and KRAP knockdown cells the numbers of functional channels in the clusters underlying puff sites were stochastically distributed following a Poisson relationship, but the mean number of functional channels per site was reduced by about two thirds by KRAP knockdown. We conclude that KRAP is required for activity of IP₃R channels at puff sites and stochastically 'licenses' the function of individual channels on a one-to-one basis, rather than determining the functioning of the puff site as a whole. In addition to puff activity ('punctate' Ca²⁺ release), global, cell-wide Ca²⁺ signals evoked by higher levels of IP₃ are further composed from a discrete 'diffuse' mode of Ca²⁺ release. By applying fluctuation analysis to isolate the punctate component during global Ca²⁺ signals, we find that KRAP knockdown suppresses to similar extents punctate and diffuse Ca²⁺ release in wild-type cells and in HEK293 cells exclusively expressing type 1 and type 3 IP3Rs. Thus, KRAP appears essential for the functioning of the IP₃Rs involved in diffuse Ca²⁺ release as well as the clustered IP₃Rs that generate local Ca²⁺ puffs.

Mechanisms and Physiological Implications of Cooperative Gating of Ion Channels Clusters

Ion channels play a central role in the regulation of nearly every cellular process. Dating back to the classic 1952 Hodgkin-Huxley model of the generation of the action potential, ion channels have always been thought of as independent agents. A myriad of recent experimental findings exploiting advances in electrophysiology, structural biology, and imaging techniques, however, have posed a serious challenge to this long-held axiom as several classes of ion channels appear to open and close in a coordinated, cooperative manner. Ion channel cooperativity ranges from variable-sized oligomeric cooperative gating in voltage-gated, dihydropyridine-sensitive Ca_v1.2 and Ca_v1.3 channels to obligatory dimeric assembly and gating of voltage-gated Na_v1.5 channels. Potassium channels, transient receptor potential channels, hyperpolarization cyclic nucleotide-activated channels, ryanodine receptors (RyRs), and inositol trisphosphate receptors (IP₃Rs) have also been shown to gate cooperatively. The implications of cooperative gating of these ion channels range from fine tuning excitation-contraction coupling in muscle cells to regulating cardiac function and vascular tone, to modulation of action potential and conduction velocity in neurons and cardiac cells, and to control of pace-making activity in the heart. In this review, we discuss the mechanisms leading to cooperative gating of ion channels, their physiological consequences and how alterations in cooperative gating of ion channels may induce a range of clinically significant pathologies.

Termination of Ca2+ puffs during IP3-evoked global Ca2+ signals

We previously described that cell-wide cytosolic Ca²⁺ transients evoked by inositol trisphosphate (IP₃) are generated by two modes of Ca²⁺ liberation from the ER; 'punctate' release via an initial flurry of transient Ca²⁺ puffs from local clusters of IP₃ receptors, succeeded by a spatially and temporally 'diffuse' Ca²⁺ liberation. Those findings were derived using statistical fluctuation analysis to monitor puff activity which is otherwise masked as global Ca²⁺ levels rise. Here, we devised imaging approaches to resolve individual puffs during global Ca²⁺ elevations to better investigate the mechanisms terminating the puff flurry. We find that puffs contribute about 40% (∼90 attomoles) of the total Ca²⁺ liberation, largely while the global Ca²⁺ signal rises halfway to its peak. The major factor terminating punctate Ca²⁺ release is an abrupt decline in puff frequency. Although the amplitudes of large puffs fall during the flurry, the amplitudes of more numerous small puffs remain steady, so overall puff amplitudes decline only modestly (∼30%). The Ca²⁺ flux through individual IP₃ receptor/channels does not measurably decline during the flurry, or when puff activity is depressed by pharmacological lowering of Ca²⁺ levels in the ER lumen, indicating that the termination of punctate release is not a simple consequence of reduced driving force for Ca²⁺ liberation. We propose instead that the gating of IP₃ receptors at puff sites is modulated such that their openings become suppressed as the bulk [Ca²⁺] in the ER lumen falls during global Ca²⁺ signals.

IP3R-driven increases in mitochondrial Ca2+ promote neuronal death in NPC disease

Ca2+ is the most ubiquitous second messenger in neurons whose spatial and temporal elevations are tightly controlled to initiate and orchestrate diverse intracellular signaling cascades. Numerous neuropathologies result from mutations or alterations in Ca2+ handling proteins; thus, elucidating molecular pathways that shape Ca2+ signaling is imperative. Here, we report that loss-of-function, knockout, or neurodegenerative disease-causing mutations in the lysosomal cholesterol transporter, Niemann-Pick Type C1 (NPC1), initiate a damaging signaling cascade that alters the expression and nanoscale distribution of IP3R type 1 (IP3R1) in endoplasmic reticulum membranes. These alterations detrimentally increase Gq-protein coupled receptor-stimulated Ca2+ release and spontaneous IP3R1 Ca2+ activity, leading to mitochondrial Ca2+ cytotoxicity. Mechanistically, we find that SREBP-dependent increases in Presenilin 1 (PS1) underlie functional and expressional changes in IP3R1. Accordingly, expression of PS1 mutants recapitulate, while PS1 knockout abrogates Ca2+ phenotypes. These data present a signaling axis that links the NPC1 lysosomal cholesterol transporter to the damaging redistribution and activity of IP3R1 that precipitates cell death in NPC1 disease and suggests that NPC1 is a nanostructural disease.

Lessons from the Endoplasmic Reticulum Ca2+ Transporters-A Cancer Connection

Ca2+ is an integral mediator of intracellular signaling, impacting almost every aspect of cellular life. The Ca2+-conducting transporters located on the endoplasmic reticulum (ER) membrane shoulder the responsibility of constructing the global Ca2+ signaling landscape. These transporters gate the ER Ca2+ release and uptake, sculpt signaling duration and intensity, and compose the Ca2+ signaling rhythm to accommodate a plethora of biological activities. In this review, we explore the mechanisms of activation and functional regulation of ER Ca2+ transporters in the establishment of Ca2+ homeostasis. We also contextualize the aberrant alterations of these transporters in carcinogenesis, presenting Ca2+-based therapeutic interventions as a means to tackle malignancies.

Noise analysis of cytosolic calcium image data

Cellular Ca²⁺ signals are often constrained to cytosolic micro- or nano-domains where stochastic openings of Ca²⁺ channels cause large fluctuations in local Ca²⁺ concentration (Ca²⁺ 'noise'). With the advent of TIRF microscopy to image the fluorescence of Ca²⁺-sensitive probes from attoliter volumes it has become possible to directly monitor these signals, which closely track the gating of plasmalemmal and ER Ca²⁺-permeable channels. Nevertheless, it is likely that many physiologically important Ca²⁺ signals are too small to resolve as discrete events in fluorescence recordings. By analogy with noise analysis of electrophysiological data, we explore here the use of statistical approaches to detect and analyze such Ca²⁺ noise in images obtained using Ca²⁺-sensitive indicator dyes. We describe two techniques - power spectrum analysis and spatio-temporal correlation - and demonstrate that both effectively identify discrete, spatially localized calcium release events (Ca²⁺ puffs). Moreover, we show they are able to detect localized noise fluctuations in a case where discrete events cannot directly be resolved.

Simulation of calcium signaling in fine astrocytic processes: Effect of spatial properties on spontaneous activity

Astrocytes, a glial cell type of the central nervous system, have emerged as detectors and regulators of neuronal information processing. Astrocyte excitability resides in transient variations of free cytosolic calcium concentration over a range of temporal and spatial scales, from sub-microdomains to waves propagating throughout the cell. Despite extensive experimental approaches, it is not clear how these signals are transmitted to and integrated within an astrocyte. The localization of the main molecular actors and the geometry of the system, including the spatial organization of calcium channels IP3R, are deemed essential. However, as most calcium signals occur in astrocytic ramifications that are too fine to be resolved by conventional light microscopy, most of those spatial data are unknown and computational modeling remains the only methodology to study this issue. Here, we propose an IP3R-mediated calcium signaling model for dynamics in such small sub-cellular volumes. To account for the expected stochasticity and low copy numbers, our model is both spatially explicit and particle-based. Extensive simulations show that spontaneous calcium signals arise in the model via the interplay between excitability and stochasticity. The model reproduces the main forms of calcium signals and indicates that their frequency crucially depends on the spatial organization of the IP3R channels. Importantly, we show that two processes expressing exactly the same calcium channels can display different types of calcium signals depending on the spatial organization of the channels. Our model with realistic process volume and calcium concentrations successfully reproduces spontaneous calcium signals that we measured in calcium micro-domains with confocal microscopy and predicts that local variations of calcium indicators might contribute to the diversity of calcium signals observed in astrocytes. To our knowledge, this model is the first model suited to investigate calcium dynamics in fine astrocytic processes and to propose plausible mechanisms responsible for their variability.

Spatial-temporal patterning of Ca2+ signals by the subcellular distribution of IP3 and IP3 receptors

The patterning of cytosolic Ca²⁺ signals in space and time underlies their ubiquitous ability to specifically regulate numerous cellular processes. Signals mediated by liberation of Ca²⁺ sequestered in the endoplasmic reticulum (ER) through inositol trisphosphate receptor (IP₃R) channels constitute a hierarchy of events; ranging from openings of individual IP₃ channels, through the concerted openings of several clustered IP₃Rs to generate local Ca²⁺ puffs, to global Ca²⁺ waves and oscillations that engulf the entire cell. Here, we review recent progress in elucidating how this hierarchy is shaped by an interplay between the functional gating properties of IP₃Rs and their spatial distribution within the cell. We focus in particular on the subset of IP₃Rs that are organized in stationary clusters and are endowed with the ability to preferentially liberate Ca²⁺.

All three IP3 receptor isoforms generate Ca2+ puffs that display similar characteristics

Inositol 1,4,5-trisphosphate (IP₃) evokes Ca²⁺ release through IP₃ receptors (IP₃Rs) to generate both local Ca²⁺ puffs arising from concerted openings of clustered IP₃Rs and cell-wide Ca²⁺ waves. Imaging Ca²⁺ puffs with single-channel resolution yields information on the localization and properties of native IP₃Rs in intact cells, but interpretation has been complicated because cells express varying proportions of three structurally and functionally distinct isoforms of IP₃Rs. Here, we used TIRF and light-sheet microscopy to image Ca²⁺ puffs in HEK-293 cell lines generated by CRISPR-Cas9 technology to express exclusively IP₃R type 1, 2, or 3. Photorelease of the IP₃ analog i-IP₃ in all three cell lines evoked puffs with largely similar mean amplitudes, temporal characteristics, and spatial extents. Moreover, the single-channel Ca²⁺ flux was similar among isoforms, indicating that clusters of different IP₃R isoforms contain comparable numbers of active channels. Our results show that all three IP₃R isoforms cluster to generate local Ca²⁺ puffs and, contrary to findings of divergent properties from in vitro electrophysiological studies, display similar conductances and gating kinetics in intact cells.

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.

Ca2+ signals initiate at immobile IP3 receptors adjacent to ER-plasma membrane junctions

IP₃ receptors (IP₃Rs) release Ca²⁺ from the ER when they bind IP₃ and Ca²⁺. The spatial organization of IP₃Rs determines both the propagation of Ca²⁺ signals between IP₃Rs and the selective regulation of cellular responses. Here we use gene editing to fluorescently tag endogenous IP₃Rs, and super-resolution microscopy to determine the geography of IP₃Rs and Ca²⁺ signals within living cells. We show that native IP₃Rs cluster within ER membranes. Most IP₃R clusters are mobile, moved by diffusion and microtubule motors. Ca²⁺ signals are generated by a small population of immobile IP₃Rs. These IP₃Rs are licensed to respond, but they do not readily mix with mobile IP₃Rs. The licensed IP₃Rs reside alongside ER-plasma membrane junctions where STIM1, which regulates store-operated Ca²⁺ entry, accumulates after depletion of Ca²⁺ stores. IP₃Rs tethered close to ER-plasma membrane junctions are licensed to respond and optimally placed to be activated by endogenous IP₃ and to regulate Ca²⁺ entry.

IP₃ receptors mediate Ca²⁺ release from the endoplasmic reticulum. Here the authors show that only a small fraction of IP₃ receptors initiate Ca²⁺ signals; these immobile IP₃ receptors adjacent to the plasma membrane are optimally placed to control STIM1-dependent Ca²⁺ entry.

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 (r_low). By varying [IP₃] and r_low 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 r_low. 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.

Hindered cytoplasmic diffusion of inositol trisphosphate restricts its cellular range of action

The range of action of intracellular messengers is determined by their rates of diffusion and degradation. Previous measurements in oocyte cytoplasmic extracts indicated that the Ca²⁺-liberating second messenger inositol trisphosphate (IP₃) diffuses with a coefficient (~280 μm² s^-1) similar to that in water, corresponding to a range of action of ~25 μm. Consequently, IP₃ is generally considered a "global" cellular messenger. We reexamined this issue by measuring local IP₃-evoked Ca²⁺ puffs to monitor IP₃ diffusing from spot photorelease in neuroblastoma cells. Fitting these data by numerical simulations yielded a diffusion coefficient (≤10 μm² s^-1) about 30-fold slower than that previously reported. We propose that diffusion of IP₃ in mammalian cells is hindered by binding to immobile, functionally inactive receptors that were diluted in oocyte extracts. The predicted range of action of IP₃ (<5 μm) is thus smaller than the size of typical mammalian cells, indicating that IP₃ should better be considered as a local rather than a global cellular messenger.

Suppressing effect of Ca^{2+} blips on puff amplitudes by inhibiting channels to prevent recovery

As local signals, calcium puffs arise from the concerted opening of a few nearby inositol 1,4,5-trisphospate receptor channels to release Ca^{2+} ions from the endoplasmic reticulum. Although Ca^{2+} puffs have been well studied, little is known about the modulation of cytosolic basal Ca^{2+} concentration ([Ca^{2+}]_{Basal}) on puff dynamics. In this paper we consider a puff model to study how the statistical properties of puffs are modulated by [Ca^{2+}]_{Basal}. The puff frequency and lifetime trivially increase with the increasing [Ca^{2+}]_{Basal}, but an unexpected result is that the puff amplitude and the maximum open-channel number of the puff show decreasing relationship with the increasing [Ca^{2+}]_{Basal}. The underlying dynamics is related not only to the increasing puff frequency which gives a shorter recovery time, but also to the increasing frequency of blips with only one channel open. We indicate that Ca^{2+} blips cause the channels to be inhibited and prevent their recovery during interpuff intervals, resulting in the suppressing effect on puff amplitudes. With increasing [Ca^{2+}]_{Basal}, more blips occur to cause more channels to be inhibited, leaving fewer channels available for puff events. This study shows that the blips may play relevant functions in global Ca^{2+} waves through modulating puff dynamics.

On the Adjacency Matrix of RyR2 Cluster Structures

In the heart, electrical stimulation of cardiac myocytes increases the open probability of sarcolemmal voltage-sensitive Ca2+ channels and flux of Ca2+ into the cells. This increases Ca2+ binding to ligand-gated channels known as ryanodine receptors (RyR2). Their openings cause cell-wide release of Ca2+, which in turn causes muscle contraction and the generation of the mechanical force required to pump blood. In resting myocytes, RyR2s can also open spontaneously giving rise to spatially-confined Ca2+ release events known as "sparks." RyR2s are organized in a lattice to form clusters in the junctional sarcoplasmic reticulum membrane. Our recent work has shown that the spatial arrangement of RyR2s within clusters strongly influences the frequency of Ca2+ sparks. We showed that the probability of a Ca2+ spark occurring when a single RyR2 in the cluster opens spontaneously can be predicted from the precise spatial arrangements of the RyR2s. Thus, "function" follows from "structure." This probability is related to the maximum eigenvalue (λ1) of the adjacency matrix of the RyR2 cluster lattice. In this work, we develop a theoretical framework for understanding this relationship. We present a stochastic contact network model of the Ca2+ spark initiation process. We show that λ1 determines a stability threshold for the formation of Ca2+ sparks in terms of the RyR2 gating transition rates. We recapitulate these results by applying the model to realistic RyR2 cluster structures informed by super-resolution stimulated emission depletion (STED) microscopy. Eigendecomposition of the linearized mean-field contact network model reveals functional subdomains within RyR2 clusters with distinct sensitivities to Ca2+. This work provides novel perspectives on the cardiac Ca2+ release process and a general method for inferring the functional properties of transmembrane receptor clusters from their structure.

A comparison of fluorescent Ca²⁺ indicators for imaging local Ca²⁺ signals in cultured cells

Localized subcellular changes in Ca(2+) serve as important cellular signaling elements, regulating processes as diverse as neuronal excitability and gene expression. Studies of cellular Ca(2+) signaling have been greatly facilitated by the availability of fluorescent Ca(2+) indicators. The respective merits of different indicators to monitor bulk changes in cellular Ca(2+) levels have been widely evaluated, but a comprehensive comparison for their use in detecting and analyzing local, subcellular Ca(2+) signals is lacking. Here, we evaluated several fluorescent Ca(2+) indicators in the context of local Ca(2+) signals (puffs) evoked by inositol 1,4,5-trisphosphate (IP3) in cultured human neuroblastoma SH-SY5Y cells, using high-speed video-microscopy. Altogether, nine synthetic Ca(2+) dyes (Fluo-4, Fluo-8, Fluo-8 high affinity, Fluo-8 low affinity, Oregon Green BAPTA-1, Cal-520, Rhod-4, Asante Calcium Red, and X-Rhod-1) and three genetically-encoded Ca(2+)-indicators (GCaMP6-slow, -medium and -fast variants) were tested; criteria include the magnitude, kinetics, signal-to-noise ratio and detection efficiency of local Ca(2+) puffs. Among these, we conclude that Cal-520 is the optimal indicator for detecting and faithfully tracking local events; that Rhod-4 is the red-emitting indicator of choice; and that none of the GCaMP6 variants are well suited for imaging subcellular Ca(2+) signals.

Shared functional defect in IP₃R-mediated calcium signaling in diverse monogenic autism syndromes

Autism spectrum disorder (ASD) affects 2% of children, and is characterized by impaired social and communication skills together with repetitive, stereotypic behavior. The pathophysiology of ASD is complex due to genetic and environmental heterogeneity, complicating the development of therapies and making diagnosis challenging. Growing genetic evidence supports a role of disrupted Ca(2+) signaling in ASD. Here, we report that patient-derived fibroblasts from three monogenic models of ASD-fragile X and tuberous sclerosis TSC1 and TSC2 syndromes-display depressed Ca(2+) release through inositol trisphosphate receptors (IP3Rs). This was apparent in Ca(2+) signals evoked by G protein-coupled receptors and by photoreleased IP3 at the levels of both global and local elementary Ca(2+) events, suggesting fundamental defects in IP3R channel activity in ASD. Given the ubiquitous involvement of IP3R-mediated Ca(2+) signaling in neuronal excitability, synaptic plasticity, gene expression and neurodevelopment, we propose dysregulated IP3R signaling as a nexus where genes altered in ASD converge to exert their deleterious effect. These findings highlight potential pharmaceutical targets, and identify Ca(2+) screening in skin fibroblasts as a promising technique for early detection of individuals susceptible to ASD.

Single-molecule tracking of inositol trisphosphate receptors reveals different motilities and distributions

Puffs are local Ca(2+) signals that arise by Ca(2+) liberation from the endoplasmic reticulum through the concerted opening of tightly clustered inositol trisphosphate receptors/channels (IP3Rs). The locations of puff sites observed by Ca(2+) 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/Ca(2+) signaling. We conclude that stable clusters of small numbers of immotile IP3Rs may underlie local Ca(2+) release sites, whereas the more numerous motile IP3Rs appear to be functionally silent.

Optimal microdomain crosstalk between endoplasmic reticulum and mitochondria for Ca2+ oscillations

A Ca²⁺ signaling model is proposed to consider the crosstalk of Ca²⁺ ions between endoplasmic reticulum (ER) and mitochondria within microdomains around inositol 1, 4, 5-trisphosphate receptors (IP₃R) and the mitochondrial Ca²⁺ uniporter (MCU). Our model predicts that there is a critical IP₃R-MCU distance at which 50% of the ER-released Ca²⁺ is taken up by mitochondria and that mitochondria modulate Ca²⁺ signals differently when outside of this critical distance. This study highlights the importance of the IP₃R-MCU distance on Ca²⁺ signaling dynamics. The model predicts that when MCU are too closely associated with IP₃Rs, the enhanced mitochondrial Ca²⁺ uptake will produce an increase of cytosolic Ca²⁺ spike amplitude. Notably, the model demonstrates the existence of an optimal IP₃R-MCU distance (30–85 nm) for effective Ca²⁺ transfer and the successful generation of Ca²⁺ signals in healthy cells. We suggest that the space between the inner and outer mitochondria membranes provides a defense mechanism against occurrences of high [Ca²⁺]_Cyt. Our results also hint at a possible pathological mechanism in which abnormally high [Ca²⁺]_Cyt arises when the IP₃R-MCU distance is in excess of the optimal range.

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 [Ca(2+)], with blips in turn giving a growing contribution to basal [Ca(2+)]. 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 [Ca(2+)] in cells that have small IP3R clusters.

Factors determining the recruitment of inositol trisphosphate receptor channels during calcium puffs

Puffs are localized, transient elevations in cytosolic Ca(2+) that serve both as the building blocks of global cellular Ca(2+) 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 Ca(2+)-induced Ca(2+) release (CICR). We utilized total internal reflection fluorescence imaging of Ca(2+) 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 Ca(2+)-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 Ca(2+)-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.

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

Calcium puffs are localized Ca(2+) signals mediated by Ca(2+) release from the endoplasmic reticulum (ER) through clusters of inositol trisphosphate receptor (IP3R) channels. The recruitment of IP3R channels during puffs depends on Ca(2+)-induced Ca(2+) release, a regenerative process that must be terminated to maintain control of cell signaling and prevent Ca(2+) 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 Ca(2+)-inhibition of IP3Rs and local depletion of Ca(2+) 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 Ca(2+)-inactivation.

An algorithm for automated detection, localization and measurement of local calcium signals from camera-based imaging

Local Ca(2+) transients such as puffs and sparks form the building blocks of cellular Ca(2+) signaling in numerous cell types. They have traditionally been studied by linescan confocal microscopy, but advances in TIRF microscopy together with improved electron-multiplied CCD (EMCCD) cameras now enable rapid (>500 frames s(-1)) imaging of subcellular Ca(2+) signals with high spatial resolution in two dimensions. This approach yields vastly more information (ca. 1 Gb min(-1)) than linescan imaging, rendering visual identification and analysis of local events imaged both laborious and subject to user bias. Here we describe a routine to rapidly automate identification and analysis of local Ca(2+) events. This features an intuitive graphical user-interfaces and runs under Matlab and the open-source Python software. The underlying algorithm features spatial and temporal noise filtering to reliably detect even small events in the presence of noisy and fluctuating baselines; localizes sites of Ca(2+) release with sub-pixel resolution; facilitates user review and editing of data; and outputs time-sequences of fluorescence ratio signals for identified event sites along with Excel-compatible tables listing amplitudes and kinetics of events.

Excitability in a stochastic differential equation model for calcium puffs

Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.

Intracellular calcium channels: inositol-1,4,5-trisphosphate receptors

The inositol-1,4,5-trisphosphate receptors (InsP3Rs) are the major intracellular Ca(2+)-release channels in cells. Activity of InsP3Rs is essential for elementary and global Ca(2+) events in the cell. There are three InsP3Rs isoforms that are present in mammalian cells. In this review we will focus primarily on InsP3R type 1. The InsP3R1 is a predominant isoform in neurons and it is the most extensively studied isoform. Combination of biophysical and structural methods revealed key mechanisms of InsP3R function and modulation. Cell biological and biochemical studies lead to identification of a large number of InsP3R-binding proteins. InsP3Rs are involved in the regulation of numerous physiological processes, including learning and memory, proliferation, differentiation, development and cell death. Malfunction of InsP3R1 play a role in a number of neurodegenerative disorders and other disease states. InsP3Rs represent a potentially valuable drug target for treatment of these disorders and for modulating activity of neurons and other cells. Future studies will provide better understanding of physiological functions of InsP3Rs in health and disease.

A stochastic model of calcium puffs based on single-channel data

Calcium puffs are local transient Ca(2+) releases from internal Ca(2+) 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 Ca(2+) 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 Ca(2+) 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.

Temperature dependence of IP3-mediated local and global Ca2+ signals

We examined the effect of temperature (12-40°C) on local and global Ca2+ signals mediated by inositol trisphosphate receptor/channels (IP3R) in human neuroblastoma (SH-SY5Y) cells. The amplitudes and spatial spread of local signals arising from single IP3R (blips) and clusters of IP3R (puffs) showed little temperature dependence, whereas their kinetics (durations and latencies) were markedly accelerated by increasing temperature. In contrast, the amplitude of global Ca2+ waves increased appreciably at lower temperatures, probably as a result of the longer duration of IP(3)R channel opening. Several parameters, including puff and blip durations, puff latency and frequency, and frequency of repetitive Ca2+ waves, showed a biphasic temperature dependence on Arrhenius plots. In all cases the transition temperature occurred at ∼25°C, possibly reflecting a phase transition in the lipids of the endoplasmic reticulum membrane. Although the IP3-evoked Ca2+ signals were qualitatively similar at 25°C and 36°C, one should consider the temperature sensitivity of IP3-mediated signal amplitudes when extrapolating from room temperature to physiological temperature. Conversely, further cooling may be advantageous to improve the optical resolution of channel gating kinetics.

Cytosolic [Ca2+] regulation of InsP3-evoked puffs

InsP3-mediated puffs are fundamental building blocks of cellular Ca2+ signalling, and arise through the concerted opening of clustered InsP3Rs (InsP3 receptors) co-ordinated via Ca2+-induced Ca2+ release. Although the Ca2+ dependency of InsP3Rs has been extensively studied at the single channel level, little is known as to how changes in basal cytosolic [Ca2+] would alter the dynamics of InsP3-evoked Ca2+ signals in intact cells. To explore this question, we expressed Ca2+-permeable channels (nicotinic acetylcholine receptors) in the plasma membrane of voltage-clamped Xenopus oocytes to regulate cytosolic [Ca2+] by changing the electrochemical gradient for extracellular Ca2+ entry, and imaged Ca2+ liberation evoked by photolysis of caged InsP3. Elevation of basal cytosolic [Ca2+] strongly increased the amplitude and shortened the latency of global Ca2+ waves. In oocytes loaded with EGTA to localize Ca2+ signals, the number of sites at which puffs were observed and the frequency and latency of puffs were strongly dependent on cytosolic [Ca2+], whereas puff amplitudes were only weakly affected. The results of the present study indicate that basal cytosolic [Ca2+] strongly affects the triggering of puffs, but has less of an effect on puffs once they have been initiated.

Hierarchic stochastic modelling applied to intracellular Ca(2+) signals

Important biological processes like cell signalling and gene expression have noisy components and are very complex at the same time. Mathematical analysis of such systems has often been limited to the study of isolated subsystems, or approximations are used that are difficult to justify. Here we extend a recently published method (Thurley and Falcke, PNAS 2011) which is formulated in observable system configurations instead of molecular transitions. This reduces the number of system states by several orders of magnitude and avoids fitting of kinetic parameters. The method is applied to Ca(2+) signalling. Ca(2+) is a ubiquitous second messenger transmitting information by stochastic sequences of concentration spikes, which arise by coupling of subcellular Ca(2+) release events (puffs). We derive analytical expressions for a mechanistic Ca(2+) model, based on recent data from live cell imaging, and calculate Ca(2+) spike statistics in dependence on cellular parameters like stimulus strength or number of Ca(2+) channels. The new approach substantiates a generic Ca(2+) model, which is a very convenient way to simulate Ca(2+) spike sequences with correct spiking statistics.