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

Ca2+ dynamics in interstitial cells: foundational mechanisms for the motor patterns in the gastrointestinal tract

The gastrointestinal (GI) tract displays multiple motor patterns that move nutrients and wastes through the body. Smooth muscle cells (SMCs) provide the forces necessary for GI motility, but interstitial cells, electrically coupled to SMCs, tune SMC excitability, transduce inputs from enteric motor neurons, and generate pacemaker activity that underlies major motor patterns, such as peristalsis and segmentation. The interstitial cells regulating SMCs are interstitial cells of Cajal (ICC) and PDGF receptor (PDGFR)α+ cells. Together these cells form the SIP syncytium. ICC and PDGFRα+ cells express signature Ca2+-dependent conductances: ICC express Ca2+-activated Cl- channels, encoded by Ano1, that generate inward current, and PDGFRα+ cells express Ca2+-activated K+ channels, encoded by Kcnn3, that generate outward current. The open probabilities of interstitial cell conductances are controlled by Ca2+ release from the endoplasmic reticulum. The resulting Ca2+ transients occur spontaneously in a stochastic manner. Ca2+ transients in ICC induce spontaneous transient inward currents and spontaneous transient depolarizations (STDs). Neurotransmission increases or decreases Ca2+ transients, and the resulting depolarizing or hyperpolarizing responses conduct to other cells in the SIP syncytium. In pacemaker ICC, STDs activate voltage-dependent Ca2+ influx, which initiates a cluster of Ca2+ transients and sustains activation of ANO1 channels and depolarization during slow waves. Regulation of GI motility has traditionally been described as neurogenic and myogenic. Recent advances in understanding Ca2+ handling mechanisms in interstitial cells and how these mechanisms influence motor patterns of the GI tract suggest that the term "myogenic" should be replaced by the term "SIPgenic," as this review discusses.

α-Synuclein-dependent increases in PIP5K1γ drive inositol signaling to promote neurotoxicity

Anomalous aggregation of α-synuclein (α-Syn) is a pathological hallmark of many degenerative synucleinopathies including Lewy body dementia (LBD) and Parkinson's disease (PD). Despite its strong link to disease, the precise molecular mechanisms that link α-Syn aggregation to neurodegeneration have yet to be elucidated. Here, we find that elevated α-Syn leads to an increase in the plasma membrane (PM) phosphoinositide PI(4,5)P2, which precipitates α-Syn aggregation and drives toxic increases in mitochondrial Ca2+ and reactive oxygen species leading to neuronal death. Upstream of this toxic signaling pathway is PIP5K1γ, whose abundance and localization is enhanced at the PM by α-Syn-dependent increases in ARF6. Selective inhibition of PIP5K1γ or knockout of ARF6 in neurons rescues α-Syn aggregation and cellular phenotypes of toxicity. Collectively, our data suggest that modulation of phosphoinositide metabolism may be a therapeutic target to slow neurodegeneration for PD and other related neurodegenerative disorders.

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 Homeostasis, Transporters, and Blockers in Health and Diseases of the Cardiovascular System

Calcium is a highly positively charged ionic species. It regulates all cell types' functions and is an important second messenger that controls and triggers several mechanisms, including membrane stabilization, permeability, contraction, secretion, mitosis, intercellular communications, and in the activation of kinases and gene expression. Therefore, controlling calcium transport and its intracellular homeostasis in physiology leads to the healthy functioning of the biological system. However, abnormal extracellular and intracellular calcium homeostasis leads to cardiovascular, skeletal, immune, secretory diseases, and cancer. Therefore, the pharmacological control of calcium influx directly via calcium channels and exchangers and its outflow via calcium pumps and uptake by the ER/SR are crucial in treating calcium transport remodeling in pathology. Here, we mainly focused on selective calcium transporters and blockers in the cardiovascular system.

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.

Tonic Calcium-Activated Chloride Current Sustained by ATP Release and Highly Desensitizing Human P2X1 Receptors

Extracellular adenosine triphosphate (ATP) participates in maintaining the vascular tone in the CNS, particularly in the retina, via the tonic activity of ligand gated activated P2X1 receptors. P2X1 receptors are characterized by their high affinity for ATP and their strong desensitization to concentrations of ATP that are 200-fold lower than their EC₅₀. The mechanism behind P2X1 tonic activity remains unclear. In this study, we expressed human P2X1 (hP2X1) homomeric receptors in Xenopus oocytes to explore the relationship between ATP release from oocytes at rest, hP2X1, and Ca²⁺-activated Cl^- channels. Our results indicate that Xenopus oocytes release ATP at rest via vesicular exocytosis, and this process is a constitutive phenomenon independent of extracellular Ca²⁺. Our results also indicate that hP2X1 receptors are able to sustain a tonic activity of Ca²⁺-activated Cl^- channels. In the presence of extracellular Ca²⁺ the activity of hP2X1 receptors is greatly amplified by its coupling with Ca²⁺-activated Cl^- channels. Future studies addressing the relationship between hP2X1 receptors and Ca²⁺-activated Cl^- channels in vascular smooth muscle cells should provide information about additional mechanisms that regulate the vascular tone and their potential as pharmaceutical targets. This article is part of a Special Issue entitled: Honoring Ricardo Miledi - outstanding neuroscientist of XX-XXI centuries.

Intracellular calcium stores mediate metaplasticity at hippocampal dendritic spines

Key points

Calcium (Ca²⁺) entry mediated by NMDA receptors is considered central to the induction of activity‐dependent synaptic plasticity in hippocampal area CA1; this description does not, however, take into account the potential contribution of endoplasmic reticulum (ER) Ca²⁺ stores.

The ER has a heterogeneous distribution in CA1 dendritic spines, and may introduce localized functional differences in Ca²⁺ signalling between synapses, as suggested by experiments on metabotropic receptor‐dependent long‐term depression.

A physiologically detailed computational model of Ca²⁺ dynamics at a CA3–CA1 excitatory synapse characterizes the contribution of spine ER via metabotropic signalling during plasticity induction protocols.

ER Ca²⁺ release via IP₃ receptors modulates NMDA receptor‐dependent plasticity in a graded manner, to selectively promote synaptic depression with relatively diminished effect on LTP induction; this may temper further strengthening at the stronger synapses which are preferentially associated with ER‐containing spines.

Acquisition of spine ER may thus represent a local, biophysically plausible ‘metaplastic switch’ at potentiated CA1 synapses, contributing to the plasticity–stability balance in neural circuits.

Abstract

Long‐term plasticity mediated by NMDA receptors supports input‐specific, Hebbian forms of learning at excitatory CA3–CA1 connections in the hippocampus. There exists an additional layer of stabilizing mechanisms that act globally as well as locally over multiple time scales to ensure that plasticity occurs in a constrained manner. Here, we investigated the role of calcium (Ca²⁺) stores associated with the endoplasmic reticulum (ER) in the local regulation of plasticity at individual CA1 synapses. Our study was spurred by (1) the curious observation that ER is sparsely distributed in dendritic spines, but over‐represented in larger spines that are likely to have undergone activity‐dependent strengthening, and (2) evidence suggesting that ER motility at synapses can be rapid, and accompany activity‐regulated spine remodelling. We constructed a physiologically realistic computational model of an ER‐bearing CA1 spine, and examined how IP₃‐sensitive Ca²⁺ stores affect spine Ca²⁺ dynamics during activity patterns mimicking the induction of long‐term potentiation and long‐term depression (LTD). Our results suggest that the presence of ER modulates NMDA receptor‐dependent plasticity in a graded manner that selectively enhances LTD induction. We propose that ER may locally tune Ca²⁺‐based plasticity, providing a braking mechanism to mitigate runaway strengthening at potentiated synapses. Our study provides a biophysically accurate description of postsynaptic Ca²⁺ regulation, and suggests that ER in the spine may promote the re‐use of hippocampal synapses with saturated strengths.

Calcium (Ca²⁺) entry mediated by NMDA receptors is considered central to the induction of activity‐dependent synaptic plasticity in hippocampal area CA1; this description does not, however, take into account the potential contribution of endoplasmic reticulum (ER) Ca²⁺ stores.

The ER has a heterogeneous distribution in CA1 dendritic spines, and may introduce localized functional differences in Ca²⁺ signalling between synapses, as suggested by experiments on metabotropic receptor‐dependent long‐term depression.

A physiologically detailed computational model of Ca²⁺ dynamics at a CA3–CA1 excitatory synapse characterizes the contribution of spine ER via metabotropic signalling during plasticity induction protocols.

ER Ca²⁺ release via IP₃ receptors modulates NMDA receptor‐dependent plasticity in a graded manner, to selectively promote synaptic depression with relatively diminished effect on LTP induction; this may temper further strengthening at the stronger synapses which are preferentially associated with ER‐containing spines.

Acquisition of spine ER may thus represent a local, biophysically plausible ‘metaplastic switch’ at potentiated CA1 synapses, contributing to the plasticity–stability balance in neural circuits.

Insemination or phosphatidic acid induces an outwardly spiraling disk of elevated Ca2+ to produce the Ca2+ wave during Xenopus laevis fertilization

During Xenopus fertilization, the initial intracellular calcium ((Ca²⁺)_i) release at the sperm-egg binding site (hot spot) has not been described without the use of inhibitors, nor related to underlying ER structure. Without inhibitors, we now report that sperm induce an initial hot spot after sperm addition to Xenopus eggs that was ~25 µm. This area is consistent with the size of ER patches and clusters of IP3 receptors that have enhanced activity. Furthermore, we find a new mechanism for the fertilization (Ca²⁺)_i wave; instead of outward diffusion of inositol 1,4,5-trisphosphate (IP₃), we find that the wave was generated by an outward, clockwise rotation of a ~63 µm disk of elevated (Ca²⁺)_i moving very rapidly at ~65 µm/s. We also suggest a new mechanism for the acceleration of the fertilization (Ca²⁺)_i wave as the disk accelerated and was joined by other rotating disks (some rotating counterclockwise) at a time when the speed of the (Ca²⁺)_i wave increases. To examine the role of phosphatidic acid (PA) in the release of (Ca²⁺)_i during Xenopus fertilization, we find that two inhibitors of PA production delayed the appearance of fertilization hot spots by ~9-12 min but did not reduce the size of hot spots and actually accelerated the later (Ca²⁺)_i wave. Surprisingly, global addition of PA to Xenopus eggs induced localized hot spots at a time and size that was similar to those induced after sperm addition. In contrast, sperm induce a rapid (Ca²⁺)_i wave (~4 µm/s) within ~30 s after hot spot appearance, whereas hot spots induced by PA required an ~32 min to induce a very slow (~1 µm/s) (Ca²⁺)_i wave with a lower peak of (Ca²⁺)_i. Thus, PA may not be required for the initial release of (Ca²⁺)_i at the sperm-egg binding site, but mimics sperm by inducing a similarly sized localized (Ca²⁺)_i release. As compared with sperm, PA may induce a weak, slow (Ca²⁺)_i wave by slowly increasing IP3 receptor clustering. Addition of PA to Xenopus oocytes, or Ca²⁺ ionophore to either Xenopus oocytes or eggs, did not induce hot spots but a global (Ca²⁺)_i wave that rapidly moved at ~12 µm/s.

Deterministic Limit of Intracellular Calcium Spikes

In nonexcitable cells, global Ca^{2+} spikes emerge from the collective dynamics of clusters of Ca^{2+} channels that are coupled by diffusion. Current modeling approaches have opposed stochastic descriptions of these systems to purely deterministic models, while both paradoxically appear compatible with experimental data. Combining fully stochastic simulations and mean-field analyses, we demonstrate that these two approaches can be reconciled. Our fully stochastic model generates spike sequences that can be seen as noise-perturbed oscillations of deterministic origin, while displaying statistical properties in agreement with experimental data. These underlying deterministic oscillations arise from a phenomenological spike nucleation mechanism.

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⁺.

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.

FCS experiments to quantify Ca2+ diffusion and its interaction with buffers

Ca²⁺ signals are ubiquitous. One of the key factors for their versatility is the variety of spatio-temporal distributions that the cytosolic Ca²⁺ can display. In most cell types Ca²⁺ signals not only depend on Ca²⁺ entry from the extracellular medium but also on Ca²⁺ release from internal stores, a process which is in turn regulated by cytosolic Ca²⁺ itself. The rate at which Ca²⁺ is transported, the fraction that is trapped by intracellular buffers, and with what kinetics are thus key features that affect the time and spatial range of action of Ca²⁺ signals. The quantification of Ca²⁺ diffusion in intact cells is quite challenging because the transport rates that can be inferred using optical techniques are intricately related to the interaction of Ca²⁺ with the dye that is used for its observation and with the cellular buffers. In this paper, we introduce an approach that uses Fluorescence Correlation Spectroscopy (FCS) experiments performed at different conditions that in principle allows the quantification of Ca²⁺ diffusion and of its reaction rates with unobservable (non-fluorescent) Ca²⁺ buffers. To this end, we develop the necessary theory to interpret the experimental results and then apply it to FCS experiments performed in a set of solutions containing Ca²⁺, a single wavelength Ca²⁺ dye, and a non-fluorescent Ca²⁺ buffer. We show that a judicious choice of the experimental conditions and an adequate interpretation of the fitting parameters can be combined to extract information on the free diffusion coefficient of Ca²⁺ and of some of the properties of the unobservable buffer. We think that this approach can be applied to other situations, particularly to experiments performed in intact cells.

Calcium waves in a grid of clustered channels with synchronous IP3 binding and unbinding

Calcium signals in cells occur at multiple spatial scales and variable temporal duration. However, a physical explanation for transitions between long-lasting global oscillations and localized short-term elevations (puffs) of cytoplasmic Ca²⁺ is still lacking. Here we introduce a phenomenological, coarse-grained model for the calcium variable, which is represented by ordinary differential equations. Due to its small number of parameters, and its simplicity, this model allows us to numerically study the interplay of multi-scale calcium concentrations with stochastic ion channel gating dynamics even in larger systems. We apply this model to a single cluster of inositol trisphosphate (IP ₃) receptor channels and find further evidence for the results presented in earlier work: a single cluster may be capable of producing different calcium release types, where long-lasting events are accompanied by unbinding of IP ₃ from the receptor (Rückl et al., PLoS Comput. Biol. 11, e1003965 (2015)). Finally, we show the practicability of the model in a grid of 64 clusters which is computationally intractable with previous high-resolution models. Here long-lasting events can lead to synchronized oscillations and waves, while short events stay localized. The frequency of calcium releases as well as their coherence can thereby be regulated by the amplitude of IP ₃ stimulation. Finally the model allows for a new explanation of oscillating [IP ₃], which is not based on metabolic production and degradation of IP ₃.

Determining the Roles of Inositol Trisphosphate Receptors in Neurodegeneration: Interdisciplinary Perspectives on a Complex Topic

It is well known that calcium (Ca²⁺) is involved in the triggering of neuronal death. Ca²⁺ cytosolic levels are regulated by Ca²⁺ release from internal stores located in organelles, such as the endoplasmic reticulum. Indeed, Ca²⁺ transit from distinct cell compartments follows complex dynamics that are mediated by specific receptors, notably inositol trisphosphate receptors (IP3Rs). Ca²⁺ release by IP3Rs plays essential roles in several neurological disorders; however, details of these processes are poorly understood. Moreover, recent studies have shown that subcellular location, molecular identity, and density of IP3Rs profoundly affect Ca²⁺ transit in neurons. Therefore, regulation of IP3R gene products in specific cellular vicinities seems to be crucial in a wide range of cellular processes from neuroprotection to neurodegeneration. In this regard, microRNAs seem to govern not only IP3Rs translation levels but also subcellular accumulation. Combining new data from molecular cell biology with mathematical modelling, we were able to summarize the state of the art on this topic. In addition to presenting how Ca²⁺ dynamics mediated by IP3R activation follow a stochastic regimen, we integrated a theoretical approach in an easy-to-apply, cell biology-coherent fashion. Following the presented premises and in contrast to previously tested hypotheses, Ca²⁺ released by IP3Rs may play different roles in specific neurological diseases, including Alzheimer's disease and Parkinson's disease.

Mode switching of Inositol 1,4,5-trisphosphate receptor channel shapes the Spatiotemporal scales of Ca2+ signals

The inositol 1,4,5-trisphosphate (InsP3) receptor (InsP3R) channel is crucial for the generation and modulation of highly specific intracellular Ca2+ signals performing numerous functions in animal cells. However, the single channel behavior during Ca2+ signals of different spatiotemporal scales is not well understood. To elucidate the correlation between the gating dynamics of single InsP3Rs and spatiotemporal Ca2+ patterns, we simulate a cluster of InsP3Rs under varying ligand concentrations and extract comprehensive gating statistics of all channels during events of different sizes and durations. Our results show that channels gating predominantly in the low activity mode with negligible occupancy of intermediate and high modes leads to single channel Ca2+ release event blips. Increasing occupancies of intermediate and high modes results in events with increasing size. When the channel has more than 50% probability of gating in the intermediate and high modes, the cluster generates very large puffs that would most likely result in global Ca2+ signals. The size, duration and frequency of Ca2+ signals all increase linearly with the total probability of channel gating in the intermediate and high modes. To our knowledge, this is the first study that quantitatively relates the modal characteristics of InsP3R to the shaping of different spatiotemporal scales of Ca2+ signals.

Accurate Langevin approaches to simulate Markovian channel dynamics

The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lu's classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed.

The role of IP3 receptor channel clustering in Ca2+ wave propagation during oocyte maturation

During oocyte maturation, the calcium-signaling machinery undergoes a dramatic remodeling resulting in distinctly different calcium-release patterns on all organizational scales from puffs to waves. The dynamics of the Ca(2+) release wave in mature as compared to immature oocytes are defined by a slower propagation speed and longer duration of the high Ca(2+) plateau. In this chapter, we use computational modeling to identify the changes in the signaling machinery, which contribute most significantly to the alterations observed in Ca(2+) wave propagation during Xenopus oocyte maturation. In addition to loss of store-operated calcium entry and internalization of plasma membrane pumps, we propose that spatial reorganization of the IP3 receptors in the plane of the ER membrane is a key factor for the observed signaling changes in Ca(2+) wave propagation.

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.

Ca²⁺ images obtained in different experimental conditions shed light on the spatial distribution of IP₃ receptors that underlie Ca²⁺ puffs

Many intracellular Ca(2+) signals involve Ca(2+) release from the endoplasmic reticulum through inositol 1,4,5-trisphosphate receptors (IP3Rs). The open probability of IP3Rs depends on cytosolic Ca(2+) so that these signals involve Ca(2+)-induced Ca(2+)-release (CICR). IP3Rs are organized in clusters. The signals they mediate are observed using single-wavelength dyes and, often, a slow Ca(2+) buffer (EGTA) is added to disrupt CICR between clusters and keep the signals spatially restricted. It is assumed that the presence of the dye or of EGTA does not alter the intra-cluster Ca(2+) dynamics. In this paper we analyze this issue combining experiments and numerical simulations. We compare the properties of local signals known as puffs observed with different dyes and EGTA concentrations. We determine that although the dye or EGTA does not alter the intra-cluster dynamics, the set of observable events is different depending on the degree of inter-cluster uncoupling of the experiment. An analysis of the observations shows that the events that are missed for insufficient inter-cluster uncoupling are those of fastest amplitude growth rate. This agrees with a spatial organization in which the largest amplitude events correspond to clusters with densely packed active IP3Rs.

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.

Basis for a neuronal version of Grover's quantum algorithm

Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church–Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical “subroutines” involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N^1/2)) needed to find some “target” solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca²⁺ response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca²⁺-induced Ca²⁺ release and the search (or signaling) velocity of Ca²⁺ wave propagation. As chemical processes, such as the duration of Ca²⁺ mobilization, become rate-limiting over interstore distances, Ca²⁺ waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca²⁺ diffusion coefficient, D^1/2, matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca²⁺ signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response regulation choices.

Fluorescence fluctuations and equivalence classes of Ca²⁺ imaging experiments

release into the cytosol through inositol 1,4,5-trisphosphate receptors (IP₃Rs) plays a relevant role in numerous physiological processes. IP₃R-mediated signals involve -induced -release (CICR) whereby release through one open IP₃R induces the opening of other channels. IP₃Rs are apparently organized in clusters. The signals can remain localized (i.e., puffs) if CICR is limited to one cluster or become waves that propagate between clusters. puffs are the building blocks of waves. Thus, there is great interest in determining puff properties, especially in view of the current controversy on the spatial distribution of activatable IP₃Rs. puffs have been observed in intact cells with optical techniques proving that they are intrinsically stochastic. Obtaining a correct picture of their dynamics then entails being able to detect the whole range of puff sizes. puffs are observed using visible single-wavelength dyes, slow exogenous buffers (e.g., EGTA) to disrupt inter-cluster CICR and UV-photolyzable caged IP₃. Single-wavelength dyes increase their fluorescence upon calcium binding producing images that are strongly dependent on their kinetic, transport and photophysical properties. Determining the artifacts that the imaging setting introduces is particularly relevant when trying to analyze the smallest signals. In this paper we introduce a method to estimate the expected signal-to-noise ratio of imaging experiments that use single-wavelength dyes. The method is based on the Number and Brightness technique. It involves the performance of a series of experiments and their subsequent analysis in terms of a fluorescence fluctuation model with which the model parameters are quantified. Using the model, the expected signal-to-noise ratio is then computed. Equivalence classes between different experimental conditions that produce images with similar signal-to-noise ratios can then be established. The method may also be used to estimate the smallest signals that can reliably be observed with each setting.

Quantitative properties and receptor reserve of the DAG and PKC branch of G(q)-coupled receptor signaling

G_q protein–coupled receptors (G_qPCRs) of the plasma membrane activate the phospholipase C (PLC) signaling cascade. PLC cleaves the membrane lipid phosphatidylinositol 4,5-bisphosphate (PIP₂) into the second messengers diacylgycerol (DAG) and inositol 1,4,5-trisphosphate (IP₃), leading to calcium release, protein kinase C (PKC) activation, and in some cases, PIP₂ depletion. We determine the kinetics of each of these downstream endpoints and also ask which is responsible for the inhibition of KCNQ2/3 (K_V7.2/7.3) potassium channels in single living tsA-201 cells. We measure DAG production and PKC activity by Förster resonance energy transfer–based sensors, and PIP₂ by KCNQ2/3 channels. Fully activating endogenous purinergic receptors by uridine 5′triphosphate (UTP) leads to calcium release, DAG production, and PKC activation, but no net PIP₂ depletion. Fully activating high-density transfected muscarinic receptors (M₁Rs) by oxotremorine-M (Oxo-M) leads to similar calcium, DAG, and PKC signals, but PIP₂ is depleted. KCNQ2/3 channels are inhibited by the Oxo-M treatment (85%) and not by UTP (<1%), indicating that depletion of PIP₂ is required to inhibit KCNQ2/3 in response to receptor activation. Overexpression of A kinase–anchoring protein (AKAP)79 or calmodulin (CaM) does not increase KCNQ2/3 inhibition by UTP. From these results and measurements of IP₃ and calcium presented in our companion paper (Dickson et al. 2013. J. Gen. Physiol.http://dx.doi.org/10.1085/jgp.201210886), we extend our kinetic model for signaling from M₁Rs to DAG/PKC and IP₃/calcium signaling. We conclude that calcium/CaM and PKC-mediated phosphorylation do not underlie dynamic KCNQ2/3 channel inhibition during G_qPCR activation in tsA-201 cells. Finally, our experimental data provide indirect evidence for cleavage of PI(4)P by PLC in living cells, and our modeling revisits/explains the concept of receptor reserve with measurements from all steps of G_qPCR signaling.

Ca2+ sparks and puffs are generated and interact in rat hippocampal CA1 pyramidal neuron dendrites

1,4,5-Inositol trisphosphate receptors (IP3Rs) and ryanodine receptors (RyRs) mediate release of Ca(2+) from internal stores in many neurons. The details of the spatial and temporal characteristics of these signals and their interactions in dendrites remain to be clarified. We found that localized Ca(2+) release events, with no associated change in membrane potential, occurred spontaneously in the dendrites of rat hippocampal CA1 pyramidal neurons. Their rate, but not their amplitude or time course, could be modulated by changes in membrane potential. Together, these results suggest that the spontaneous events are similar to RyR-dependent Ca(2+) "sparks" found in cardiac myocytes. In addition, we found that we could generate another kind of localized Ca(2+) release event by either a synaptic tetanus in the presence of 3-((R)-2-carboxypiperazine-4-yl)-propyl-1-phosphonic acid and CNQX or by uncaging IP3. These events had slower rise times and decay times than sparks and were more heterogeneous. These properties are similar to Ca(2+) "puffs" found in oocytes. These two localized signals interact. Low-intensity tetanic synaptic stimulation or uncaging of IP3 increased the decay time of spontaneous Ca(2+) events without changing their rise time or amplitude. Pharmacological experiments suggest that this event widening is attributable to a delayed IP3R-mediated release of Ca(2+) triggered by the synergistic action of IP3 and Ca(2+) released by RyRs. The actions of IP3 appear to be confined to the main apical dendrite because uncaging IP3 in the oblique dendrites has no effect on the time course of localized events or backpropagating action potential-evoked Ca(2+) signals in this region.

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.

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.

Microdomains of muscarinic acetylcholine and Ins(1,4,5)P₃ receptors create 'Ins(1,4,5)P₃ junctions' and sites of Ca²+ wave initiation in smooth muscle

Increases in cytosolic Ca²⁺ concentration ([Ca²⁺]_c) mediated by inositol (1,4,5)-trisphosphate [Ins(1,4,5)P₃, hereafter InsP₃] regulate activities that include division, contraction and cell death. InsP₃-evoked Ca²⁺ release often begins at a single site, then regeneratively propagates through the cell as a Ca²⁺ wave. The Ca²⁺ wave consistently begins at the same site on successive activations. Here, we address the mechanisms that determine the Ca²⁺ wave initiation site in intestinal smooth muscle cells. Neither an increased sensitivity of InsP₃ receptors (InsP₃R) to InsP₃ nor regional clustering of muscarinic receptors (mAChR3) or InsP₃R1 explained the selection of an initiation site. However, examination of the overlap of mAChR3 and InsP₃R1 localisation, by centre of mass analysis, revealed that there was a small percentage (∼10%) of sites that showed colocalisation. Indeed, the extent of colocalisation was greatest at the Ca²⁺ wave initiation site. The initiation site might arise from a selective delivery of InsP₃ from mAChR3 activity to particular InsP₃Rs to generate faster local [Ca²⁺]_c increases at sites of colocalisation. In support of this hypothesis, a localised subthreshold ‘priming’ InsP₃ concentration applied rapidly, but at regions distant from the initiation site, shifted the wave to the site of the priming. Conversely, when the Ca²⁺ rise at the initiation site was rapidly and selectively attenuated, the Ca²⁺ wave again shifted and initiated at a new site. These results indicate that Ca²⁺ waves initiate where there is a structural and functional coupling of mAChR3 and InsP₃R1, which generates junctions in which InsP₃ acts as a highly localised signal by being rapidly and selectively delivered to InsP₃R1.

Multi-scale data-driven modeling and observation of calcium puffs

The spatiotemporal dynamics of elementary Ca(2+) release events, such as "blips" and "puffs" shapes the hierarchal Ca(2+) signaling in many cell types. Despite being the building blocks of Ca(2+) patterning, the mechanism responsible for the observed properties of puffs, especially their termination is incompletely understood. In this paper, we employ a data-driven approach to gain insights into the complex dynamics of blips and puffs. We use a model of inositol 1,4,5-trisphosphate (IP(3)) receptor (IP(3)R) derived directly from single channel patch clamp data taken at 10 μM concentration of IP(3) to simulate calcium puffs. We first reproduce recent observations regarding puffs and blips and then investigate the mechanism of puff termination. Our model suggests that during a puff, IP(3)R s proceed around a loop through kinetic states from "rest" to "open" to "inhibited" and back to "rest". A puff terminates because of self-inhibition. Based on our simulations, we rule out the endoplasmic reticulum (ER) Ca(2+) depletion as a possible cause for puff termination. The data-driven approach also enables us to estimate the current through a single IP(3)R and the peak Ca(2+) concentration near the channel pore.

Modeling the spontaneous Ca2+ oscillations in astrocytes: Inconsistencies and usefulness

Spontaneous calcium (Ca2+) oscillations (SCOs) in astrocytes might be a crucial signaling for the multipurpose role of this type of cell in several brain functions. To interpret experimental data of astrocytic SCOs, which has been largely observed in the last decade, several groups have attempted to accommodate biophysical models that were developed in the past for Ca2+ signaling in other cell types. In most of the cases, only predictive strategies were used to estimate specific parameters of these modified models from actual experiments. In this study, we discuss the most remarkable models used to describe Ca2+ signaling in astrocytes. At the same time, we aim to revise the particulars of applying these models to interpret epifluorescent time series obtained from large regions of interest. Specially, we developed a detailed model for global Ca2+ signaling in the somata of astrocytes. In order to estimate some of the parameters in our model, we propose a deductive reasoning strategy, i.e., a statistical inference method that results from combining a filtering technique and a maximum likelihood principle. By means of computer simulations, we evaluate the accuracy of this estimation's strategy. Finally, we use the new model, in combination with a recent experimental findings by our group, to estimate the degree of cluster coupling inside the soma during the genesis of global Ca2+ events.

Mitochondrial organization and Ca2+ uptake

Mitochondria may function as multiple separate organelles or as a single electrically coupled continuum to modulate changes in [Ca2+]c (cytoplasmic Ca2+ concentration) in various cell types. Mitochondria may also be tethered to the internal Ca2+ store or plasma membrane in particular parts of cells to facilitate the organelles modulation of local and global [Ca2+]c increases. Differences in the organization and positioning contributes significantly to the at times apparently contradictory reports on the way mitochondria modulate [Ca2+]c signals. In the present paper, we review the organization of mitochondria and the organelles role in Ca2+ signalling.

Inositol trisphosphate receptors in smooth muscle cells

Inositol 1,4,5-trisphosphate receptors (IP(3)Rs) are a family of tetrameric intracellular calcium (Ca(2+)) release channels that are located on the sarcoplasmic reticulum (SR) membrane of virtually all mammalian cell types, including smooth muscle cells (SMC). Here, we have reviewed literature investigating IP(3)R expression, cellular localization, tissue distribution, activity regulation, communication with ion channels and organelles, generation of Ca(2+) signals, modulation of physiological functions, and alterations in pathologies in SMCs. Three IP(3)R isoforms have been identified, with relative expression and cellular localization of each contributing to signaling differences in diverse SMC types. Several endogenous ligands, kinases, proteins, and other modulators control SMC IP(3)R channel activity. SMC IP(3)Rs communicate with nearby ryanodine-sensitive Ca(2+) channels and mitochondria to influence SR Ca(2+) release and reactive oxygen species generation. IP(3)R-mediated Ca(2+) release can stimulate plasma membrane-localized channels, including transient receptor potential (TRP) channels and store-operated Ca(2+) channels. SMC IP(3)Rs also signal to other proteins via SR Ca(2+) release-independent mechanisms through physical coupling to TRP channels and local communication with large-conductance Ca(2+)-activated potassium channels. IP(3)R-mediated Ca(2+) release generates a wide variety of intracellular Ca(2+) signals, which vary with respect to frequency, amplitude, spatial, and temporal properties. IP(3)R signaling controls multiple SMC functions, including contraction, gene expression, migration, and proliferation. IP(3)R expression and cellular signaling are altered in several SMC diseases, notably asthma, atherosclerosis, diabetes, and hypertension. In summary, IP(3)R-mediated pathways control diverse SMC physiological functions, with pathological alterations in IP(3)R signaling contributing to disease.

Ca(2+) signalling by IP(3) receptors

The Ca(2) (+) signals evoked by inositol 1,4,5-trisphosphate (IP(3)) are built from elementary Ca(2) (+) release events involving progressive recruitment of IP(3) receptors (IP(3)R), intracellular Ca(2) (+) channels that are expressed in almost all animal cells. The smallest events ('blips') result from opening of single IP(3)R. Larger events ('puffs') reflect the near-synchronous opening of a small cluster of IP(3)R. These puffs become more frequent as the stimulus intensity increases and they eventually trigger regenerative Ca(2) (+) waves that propagate across the cell. This hierarchical recruitment of IP(3)R is important in allowing Ca(2) (+) signals to be delivered locally to specific target proteins or more globally to the entire cell. Co-regulation of IP(3)R by Ca(2) (+) and IP(3), the ability of a single IP(3)R rapidly to mediate a large efflux of Ca(2) (+) from the endoplasmic reticulum, and the assembly of IP(3)R into clusters are key features that allow IP(3)R to propagate Ca(2) (+) signals regeneratively. We review these properties of IP(3)R and the structural basis of IP(3)R behavior.

Fundamental properties of Ca2+ signals

BACKGROUND

Ca2+ is a ubiquitous and versatile second messenger that transmits information through changes of the cytosolic Ca2+ concentration. Recent investigations changed basic ideas on the dynamic character of Ca2+ signals and challenge traditional ideas on information transmission.

SCOPE OF REVIEW

We present recent findings on key characteristics of the cytosolic Ca2+ dynamics and theoretical concepts that explain the wide range of experimentally observed Ca2+ signals. Further, we relate properties of the dynamical regulation of the cytosolic Ca2+ concentration to ideas about information transmission by stochastic signals.

MAJOR CONCLUSIONS

We demonstrate the importance of the hierarchal arrangement of Ca2+ release sites on the emergence of cellular Ca2+ spikes. Stochastic Ca2+ signals are functionally robust and adaptive to changing environmental conditions. Fluctuations of interspike intervals (ISIs) and the moment relation derived from ISI distributions contain information on the channel cluster open probability and on pathway properties.

GENERAL SIGNIFICANCE

Robust and reliable signal transduction pathways that entail Ca2+ dynamics are essential for eukaryotic organisms. Moreover, we expect that the design of a stochastic mechanism which provides robustness and adaptivity will be found also in other biological systems. Ca2+ dynamics demonstrate that the fluctuations of cellular signals contain information on molecular behavior. This article is part of a Special Issue entitled Biochemical, biophysical and genetic approaches to intracellular calcium signaling.

Mean field strategies induce unrealistic non-linearities in calcium puffs

Mean field models are often useful approximations to biological systems, but sometimes, they can yield misleading results. In this work, we compare mean field approaches with stochastic models of intracellular calcium release. In particular, we concentrate on calcium signals generated by the concerted opening of several clustered channels (calcium puffs). To this end we simulate calcium puffs numerically and then try to reproduce features of the resulting calcium distribution using mean field models were all the channels open and close simultaneously. We show that an unrealistic non-linear relationship between the current and the number of open channels is needed to reproduce the simulated puffs. Furthermore, a single channel current which is five times smaller than the one of the stochastic simulations is also needed. Our study sheds light on the importance of the stochastic kinetics of the calcium release channel activity to estimate the release fluxes.

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.

Observable effects of Ca2+ buffers on local Ca2+ signals

Calcium signals participate in a large variety of physiological processes. In many instances, they involve calcium entry through inositol 1,4,5-trisphosphate (IP(3)) receptors (IP(3)Rs), which are usually organized in clusters. Recent high-resolution optical experiments by Smith & Parker have provided new information on Ca(2+) release from clustered IP(3)Rs. In the present paper, we use the model recently introduced by Solovey & Ponce Dawson to determine how the distribution of the number of IP(3)Rs that become open during a localized release event may change by the presence of Ca(2+) buffers, substances that react with Ca(2+), altering its concentration and transport properties. We then discuss how buffer properties could be extracted from the observation of local signals.

Unitary Ca(2+) current through recombinant type 3 InsP(3) receptor channels under physiological ionic conditions

The ubiquitous inositol 1,4,5-trisphosphate (InsP(3)) receptor (InsP(3)R) channel, localized primarily in the endoplasmic reticulum (ER) membrane, releases Ca(2+) into the cytoplasm upon binding InsP(3), generating and modulating intracellular Ca(2+) signals that regulate numerous physiological processes. Together with the number of channels activated and the open probability of the active channels, the size of the unitary Ca(2+) current (i(Ca)) passing through an open InsP(3)R channel determines the amount of Ca(2+) released from the ER store, and thus the amplitude and the spatial and temporal nature of Ca(2+) signals generated in response to extracellular stimuli. Despite its significance, i(Ca) for InsP(3)R channels in physiological ionic conditions has not been directly measured. Here, we report the first measurement of i(Ca) through an InsP(3)R channel in its native membrane environment under physiological ionic conditions. Nuclear patch clamp electrophysiology with rapid perfusion solution exchanges was used to study the conductance properties of recombinant homotetrameric rat type 3 InsP(3)R channels. Within physiological ranges of free Ca(2+) concentrations in the ER lumen ([Ca(2+)](ER)), free cytoplasmic [Ca(2+)] ([Ca(2+)](i)), and symmetric free [Mg(2+)] ([Mg(2+)](f)), the i(Ca)-[Ca(2+)](ER) relation was linear, with no detectable dependence on [Mg(2+)](f). i(Ca) was 0.15 +/- 0.01 pA for a filled ER store with 500 microM [Ca(2+)](ER). The i(Ca)-[Ca(2+)](ER) relation suggests that Ca(2+) released by an InsP(3)R channel raises [Ca(2+)](i) near the open channel to approximately 13-70 microM, depending on [Ca(2+)](ER). These measurements have implications for the activities of nearby InsP(3)-liganded InsP(3)R channels, and they confirm that Ca(2+) released by an open InsP(3)R channel is sufficient to activate neighboring channels at appropriate distances away, promoting Ca(2+)-induced Ca(2+) release.

Calcium domains around single and clustered IP3 receptors and their modulation by buffers

We study Ca(2+) release through single and clustered IP(3) receptor channels on the ER membrane under presence of buffer proteins. Our computational scheme couples reaction-diffusion equations and a Markovian channel model and allows our investigating the effects of buffer proteins on local calcium concentrations and channel gating. We find transient and stationary elevations of calcium concentrations around active channels and show how they determine release amplitude. Transient calcium domains occur after closing of isolated channels and constitute an important part of the channel's feedback. They cause repeated openings (bursts) and mediate increased release due to Ca(2+) buffering by immobile proteins. Stationary domains occur during prolonged activity of clustered channels, where the spatial proximity of IP(3)Rs produces a distinct [Ca(2+)] scale (0.5-10 microM), which is smaller than channel pore concentrations (>100 microM) but larger than transient levels. While immobile buffer affects transient levels only, mobile buffers in general reduce both transient and stationary domains, giving rise to Ca(2+) evacuation and biphasic modulation of release amplitude. Our findings explain recent experiments in oocytes and provide a general framework for the understanding of calcium signals.

Superresolution localization of single functional IP3R channels utilizing Ca2+ 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 microm2 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 approximately 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.

Stochastic fire-diffuse-fire model with realistic cluster dynamics

Living organisms use waves that propagate through excitable media to transport information. Ca2+ waves are a paradigmatic example of this type of processes. A large hierarchy of Ca2+ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, Ca2+ release occurs trough inositol 1,4,5-trisphosphate receptors (IP3Rs) which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of IP3R 's that replicates the experimental observations reported in [D. Fraiman, Biophys. J. 90, 3897 (2006)]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the IP3 concentration is increased.

Recording single-channel activity of inositol trisphosphate receptors in intact cells with a microscope, not a patch clamp

Optical single-channel recording is a novel tool for the study of individual Ca2+-permeable channels within intact cells under minimally perturbed physiological conditions. As applied to the functioning and spatial organization of IP3Rs, this approach complements our existing knowledge, which derives largely from reduced systems - such as reconstitution into lipid bilayers and patch clamping of IP3Rs on the membrane of excised nuclei - where the spatial arrangement and interactions among IP3Rs via CICR are disrupted. The ability to image the activity of single IP3R channels with millisecond resolution together with localization of their positions with a precision of a few tens of nanometers both raises several intriguing questions and holds promise of answers. In particular, what mechanism underlies the anchoring of puffs and blips to static locations; why do these Ca2+ release events appear to involve only a very small fraction of the IP3Rs within a cell; and how can we reconcile the relative immotility of functional IP3Rs with numerous studies reporting free diffusion of IP3R protein in the ER membrane?

Visualization of inositol 1,4,5-trisphosphate receptors on the nuclear envelope outer membrane by freeze-drying and rotary shadowing for electron microscopy

The receptors for the second messenger InsP(3) comprise a family of closely related ion channels that release Ca(2+) from intracellular stores, most prominently the endoplasmic reticulum and its extension into the nuclear envelope. The precise sub-cellular localization of InsP(3)Rs and the spatial relationships among them are important for the initiation, spatial and temporal properties and propagation of local and global Ca(2+) signals, but the spatial organization of InsP(3)Rs in Ca(2+) stores is poorly characterized. Using nuclei isolated from insect Sf9 cells and freeze-dry rotary shadowing, we have addressed this by directly visualizing the cytoplasmic domain of InsP(3)R located on the cytoplasmic side of the nuclear envelope. Identification of approximately 15 nm structures as the cytoplasmic domain of InsP(3)R was indirectly supported by a marked increase in their frequency after transient transfections with cDNAs for rat types 1 and 3 InsP(3)R, and directly confirmed by gold labeling either with heparin or a specific anti-InsP(3)R antibody. Over-expression of InsP(3)R did not result in the formation of arrays or clusters with channels touching each other. Gold-labeling suggests that the channel amino terminus resides near the center of the cytoplasmic tetrameric quaternary structure. The combination of nuclear isolation with freeze-drying and rotary shadow techniques allows direct visualization of InsP(3)Rs in native nuclear envelopes and can be used to determine their spatial distribution and density.

Puff-wave transition in an inhomogeneous model for calcium signals

In many cell types, calcium ion channels on the endoplasmic reticulum membrane occur in a clustered distribution. The channels generate either localized puffs, each comprising channels of only one cluster, or global calcium waves. In this work we model the calcium system as a two-dimensional lattice of active elements distributed regularly in an otherwise passive space. We address an important feature of the puff-wave transition, which is the difference in lifetime of puffs at a few hundred milliseconds and long-lived global waves with periods of several seconds. We show that such a lifetime difference between puffs and waves can be understood with strongly reduced ordinary differential equations modified by a time-scale factor that takes into account the coupling strength of active and passive regions determined by the Ca2+ diffusion coefficient. Furthermore, we show that the point model can also describe very well the dependence of Ca2+ oscillation characteristics on the cluster-cluster distance in the case of large diffusivity.

Intra-cluster percolation of calcium signals

Calcium signals are involved in a large variety of physiological processes. Their versatility relies on the diversity of spatio-temporal behaviors that the calcium concentration can display. Calcium entry through inositol 1,4,5-trisphosphate (IP) receptors (IPR's) is a key component that participates in both local signals such as “puffs” and in global waves. IPR's are usually organized in clusters on the membrane of the endoplasmic reticulum and their spatial distribution has important effects on the resulting signal. Recent high resolution observations [1] of Ca puffs offer a window to study intra-cluster organization. The experiments give the distribution of the number of IPR's that open during each puff without much processing. Here we present a simple model with which we interpret the experimental distribution in terms of two stochastic processes: IP binding and unbinding and Ca-mediated inter-channel coupling. Depending on the parameters of the system, the distribution may be dominated by one or the other process. The transition between both extreme cases is similar to a percolation process. We show how, from an analysis of the experimental distribution, information can be obtained on the relative weight of the two processes. The largest distance over which Ca-mediated coupling acts and the density of IP-bound IPR's of the cluster can also be estimated. The approach allows us to infer properties of the interactions among the channels of the cluster from statistical information on their emergent collective behavior.

Quantifying calcium fluxes underlying calcium puffs in Xenopus laevis oocytes

We determine the calcium fluxes through inositol 1,4,5-trisphosphate receptor/channels underlying calcium puffs of Xenopus laevis oocytes using a simplified version of the algorithm of Ventura et al. An analysis of 130 puffs obtained with Fluo-4 indicates that Ca2+ release comes from a region of width approximately 450 nm, that the release duration is peaked around 18 s and that the underlying Ca2+ currents range between 0.12 and 0.95 pA. All these parameters are independent of IP(3) concentration. We explore what distributions of channels that open during a puff, N(p), and what relations between current and number of open channels, I(N(p)), are compatible with our findings and with the distribution of puff-to-trigger amplitude ratio reported in Rose et al. To this end, we use simple "mean field" models in which all channels open and close simultaneously. We find that the variability among clusters plays an important role in shaping the observed puff amplitude distribution and that a model for which I(N(p)) approximately N(p) for small N(p) and I(N(p)) approximately N(p)(1/alpha) (alpha > 1) for large N(p), provides the best agreement. Simulations of more detailed models in which channels open and close stochastically show that this nonlinear behavior can be attributed to the limited time resolution of the observations and to the averaging procedure that is implicit in the mean-field models. These conclusions are also compatible with observations of approximately 400 puffs obtained using the dye Oregon green.

Ca(2+) puffs originate from preestablished stable clusters of inositol trisphosphate receptors

Intracellular calcium ion (Ca(2+)) signaling crucially depends on the clustered organization of inositol trisphosphate receptors (IP(3)Rs) in the endoplasmic reticulum (ER) membrane. These ligand-gated ion channels liberate Ca(2+) to generate local signals known as Ca(2+) puffs. We tested the hypothesis that IP(3) itself elicits rapid clustering of IP(3)Rs by using flash photolysis of caged IP(3) in conjunction with high-resolution Ca(2+) imaging to monitor the activity and localization of individual IP(3)Rs within intact mammalian cells. Our results indicate that Ca(2+) puffs arising with latencies as short as 100 to 200 ms after photorelease of IP(3) already involve at least four IP(3)R channels, and that this number does not subsequently grow. Moreover, single active IP(3)Rs show limited mobility, and stochastic simulations suggest that aggregation of IP(3)Rs at puff sites by a diffusional trapping mechanism would require many seconds. We thus conclude that puff sites represent preestablished, stable clusters of IP(3)Rs and that functional IP(3)Rs are not readily diffusible within the ER membrane.

IP3 receptors: some lessons from DT40 cells

Inositol-1,4,5-trisphosphate receptors (IP3Rs) are intracellular Ca2+ channels that are regulated by IP3 and Ca2+ and are modulated by many additional signals. These properties allow them to initiate and, via Ca2+-induced Ca2+ release, regeneratively propagate Ca2+ signals evoked by receptors that stimulate formation of IP3. The ubiquitous expression of IP3R highlights their importance, but it also presents problems when attempting to resolve the behavior of defined IP3R. DT40 cells are a pre-B-lymphocyte cell line in which high rates of homologous recombination afford unrivalled opportunities to disrupt endogenous genes. DT40-knockout cells with both alleles of each of the three IP3R genes disrupted provide the only null-background for analysis of homogenous recombinant IP3R. We review the properties of DT40 cells and consider three areas where they have contributed to understanding IP3R behavior. Patch-clamp recording from the nuclear envelope and Ca2+ release from intracellular stores loaded with a low-affinity Ca2+ indicator address the mechanisms leading to activation of IP(3)R. We show that IP3 causes intracellular IP3R to cluster and re-tune their responses to IP3 and Ca2+, better equipping them to mediate regenerative Ca2+ signals. Finally, we show that DT40 cells reliably count very few IP3R into the plasma membrane, where they mediate about half the Ca2+ entry evoked by the B-cell antigen receptor.

Mitochondrial Ca2+ uptake increases Ca2+ release from inositol 1,4,5-trisphosphate receptor clusters in smooth muscle cells

Smooth muscle activities are regulated by inositol 1,4,5-trisphosphate (InsP(3))-mediated increases in cytosolic Ca2+ concentration ([Ca2+](c)). Local Ca2+ release from an InsP(3) receptor (InsP(3)R) cluster present on the sarcoplasmic reticulum is termed a Ca2+ puff. Ca2+ released via InsP(3)R may diffuse to adjacent clusters to trigger further release and generate a cell-wide (global) Ca2+ rise. In smooth muscle, mitochondrial Ca2+ uptake maintains global InsP(3)-mediated Ca2+ release by preventing a negative feedback effect of high [Ca2+] on InsP(3)R. Mitochondria may regulate InsP(3)-mediated Ca2+ signals by operating between or within InsP(3)R clusters. In the former mitochondria could regulate only global Ca2+ signals, whereas in the latter both local and global signals would be affected. Here whether mitochondria maintain InsP(3)-mediated Ca2+ release by operating within (local) or between (global) InsP(3)R clusters has been addressed. Ca2+ puffs evoked by localized photolysis of InsP(3) in single voltage-clamped colonic smooth muscle cells had amplitudes of 0.5-4.0 F/F(0), durations of approximately 112 ms at half-maximum amplitude, and were abolished by the InsP(3)R inhibitor 2-aminoethoxydiphenyl borate. The protonophore carbonyl cyanide 3-chloropheylhydrazone and complex I inhibitor rotenone each depolarized DeltaPsi(M) to prevent mitochondrial Ca2+ uptake and attenuated Ca2+ puffs by approximately 66 or approximately 60%, respectively. The mitochondrial uniporter inhibitor, RU360, attenuated Ca2+ puffs by approximately 62%. The "fast" Ca2+ chelator 1,2-bis(o-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid acted like mitochondria to prolong InsP(3)-mediated Ca2+ release suggesting that mitochondrial influence is via their Ca2+ uptake facility. These results indicate Ca2+ uptake occurs quickly enough to influence InsP(3)R communication at the intra-cluster level and that mitochondria regulate both local and global InsP(3)-mediated Ca2+ signals.