A kinetic model of single and clustered IP3 receptors in the absence of Ca2+ feedback

A structure-based computational model of IP3R1 incorporating Ca and IP3 regulation

The inositol 1,4,5-triphosphate receptor (IP3R) mediates Ca release in many cell types and is pivotal to a wide range of cellular processes. High-resolution cryoelectron microscopy studies have provided new structural details of IP3R type 1 (IP3R1), showing that channel function is determined by the movement of various domains within and between each of its four subunits. Channel properties are regulated by ligands, such as Ca and IP3, which bind at specific sites and control the interactions between these domains. However, it is not known how the various ligand-binding sites on IP3R1 interact to control the opening of the channel. In this study, we present a coarse-grained model of IP3R1 that accounts for the channel architecture and the location of specific Ca- and IP3-binding sites. This computational model accounts for the domain-domain interactions within and between the four subunits that form IP3R1, and it also describes how ligand binding regulates these interactions. Using a kinetic model, we explore how two Ca-binding sites on the cytosolic side of the channel interact with the IP3-binding site to regulate the channel open probability. Our primary finding is that the bell-shaped open probability of IP3R1 provides constraints on the relative strength of these regulatory binding sites. In particular, we argue that a specific Ca-binding site, whose function has not yet been established, is very likely a channel antagonist. Additionally, we apply our model to show that domain-domain interactions between neighboring subunits exert control over channel cooperativity and dictate the nonlinear response of the channel to Ca concentration. This suggests that specific domain-domain interactions play a pivotal role in maintaining the channel's stability, and a disruption of these interactions may underlie disease states associated with Ca dysregulation.

Mechanisms of synapse-to-nucleus calcium signalling in striatal neurons and impairments in Huntington's disease

Huntington's disease (HD) is a monogenic disorder with autosomal dominant inheritance. In HD patients, neurons in the striatum and cortex degenerate, leading to motor, psychiatric and cognitive disorders. Dysregulated synaptic function and calcium handling are common in many neurodegenerative diseases, including HD. N-methyl-D-aspartate (NMDA) receptor function is enhanced in HD at extrasynaptic sites, altering the balance of calcium-dependent neuronal survival versus death signalling pathways. Endoplasmic reticulum (ER) calcium handling is also abnormal in HD. The ER, which is continuous with the nuclear envelope, is purportedly involved in nuclear calcium signalling; based on this, we hypothesised that nuclear calcium signalling is altered in HD. We explored this hypothesis with calcium imaging techniques, including simultaneous epifluorescent imaging of cytosolic and nuclear calcium using jRCaMP1b and GCaMP3 sensors, respectively, in striatal spiny projection neurons in cortical-striatal co-cultures from the YAC128 mouse model of HD. Our data show contributions from a variety of calcium channels to nuclear calcium signalling. NMDA receptors (NMDARs) play an essential role in initiating action potential-dependent calcium signalling to the nucleus, and ryanodine receptors (RyR) contribute to both cytosolic and nuclear calcium signals. Unlike previous reports in glutamatergic hippocampal and cortical neurons, we found that in GABAergic striatal neurons, L-type voltage-gated calcium channels (CaV) contribute to cytosolic, but not nuclear calcium signalling. Calcium imaging also suggests impairments in nuclear calcium signalling in HD striatal neurons, where spontaneous action potential-dependent calcium transients in the nucleus were smaller in YAC128 striatal neurons compared to those of wild-type (WT). Our results elucidate mechanisms involved in action potential-dependent nuclear calcium signalling in GABAergic striatal neurons, and have revealed a clear deficit in this signalling in HD.

On the Ca2＋ elevation in vascular endothelial cells due to inositol trisphosphate-sensitive store receptors activation: A data-driven modeling approach

Agonist-induced Ca2+ signaling is essential for the regulation of many vital functions in endothelial cells (ECs). A broad range of stimuli elevate the cytosolic Ca2＋ concentration by promoting a pathway mediated by inositol 1,4,5 trisphosphate (IP3) which causes Ca2＋ release from intracellular stores. Despite its importance, there are very few studies focusing on the quantification of such dynamics in the vascular endothelium. Here, by using data from isolated ECs, we established a minimalistic modeling framework able to quantitatively capture the main features (averaged over a cell population) of the cytosolic Ca2＋ response to different IP3 stimulation levels. A suitable description of Ca2＋-regulatory function of inositol 1,4,5 trisphosphate receptors (IP3Rs) and corresponding parameter space are identified by comparing the different model variants against experimental mean population data. The same approach is used to numerically assess the relevance of cytosolic Ca2＋ buffering, as well as Ca2＋ store IP3-sensitivity in the overall cell dynamics. The variability in the dynamics' features observed across the population can be explained (at least in part) through variation of certain model parameters (such as buffering capacity or Ca2＋ store sensitivity to IP3). The results, in terms of experimental fitting and validation, support the proposed minimalistic model as a reference framework for the quantification of the EC Ca2＋ dynamics induced by IP3Rs activation.

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.

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.

Upregulated Ca2+ Release from the Endoplasmic Reticulum Leads to Impaired Presynaptic Function in Familial Alzheimer's Disease

Neurotransmitter release from presynaptic terminals is primarily regulated by rapid Ca2+ influx through membrane-resident voltage-gated Ca2+ channels (VGCCs). Moreover, accumulating evidence indicates that the endoplasmic reticulum (ER) is extensively present in axonal terminals of neurons and plays a modulatory role in synaptic transmission by regulating Ca2+ levels. Familial Alzheimer's disease (FAD) is marked by enhanced Ca2+ release from the ER and downregulation of Ca2+ buffering proteins. However, the precise consequence of impaired Ca2+ signaling within the vicinity of VGCCs (active zone (AZ)) on exocytosis is poorly understood. Here, we perform in silico experiments of intracellular Ca2+ signaling and exocytosis in a detailed biophysical model of hippocampal synapses to investigate the effect of aberrant Ca2+ signaling on neurotransmitter release in FAD. Our model predicts that enhanced Ca2+ release from the ER increases the probability of neurotransmitter release in FAD. Moreover, over very short timescales (30-60 ms), the model exhibits activity-dependent and enhanced short-term plasticity in FAD, indicating neuronal hyperactivity-a hallmark of the disease. Similar to previous observations in AD animal models, our model reveals that during prolonged stimulation (~450 ms), pathological Ca2+ signaling increases depression and desynchronization with stimulus, causing affected synapses to operate unreliably. Overall, our work provides direct evidence in support of a crucial role played by altered Ca2+ homeostasis mediated by intracellular stores in FAD.

Synapse Formation Activates a Transcriptional Program for Persistent Enhancement in the Bi-directional Transport of Mitochondria

Mechanisms that regulate the bi-directional transport of mitochondria in neurons for maintaining functional synaptic connections are poorly understood. Here, we show that in the pre-synaptic sensory neurons of the Aplysia gill withdrawal reflex, the formation of functional synapses leads to persistent enhancement in the flux of bi-directional mitochondrial transport. In the absence of a functional synapse, activation of cAMP signaling is sufficient to enhance bi-directional transport in sensory neurons. Furthermore, persistent enhancement in transport does not depend on NMDA and AMPA receptor signaling nor signaling from the post-synaptic neuronal cell body, but it is dependent on transcription and protein synthesis in the pre-synaptic neuron. We identified ∼4,000 differentially enriched transcripts in pre-synaptic neurons, suggesting a long-term change in the transcriptional program produced by synapse formation. These results provide insights into the regulation of bi-directional mitochondrial transport for synapse maintenance.

Anti-cross-correlation between the adjacent open and closed durations of Markovian channels

We show that a non-Markovian behavior can appear in a type of Markovian multimeric channel. Such a channel consists of N independent subunits, and each subunit has at least one open state and more than one closed state. Suppose the open state of the channel is defined as M out of N subunits in the open state with N>M>0. We show that, although the gating dynamics for each subunit between open and closed states is Markovian, the channel can show a memory behavior of weak anti-cross-correlation between the adjacent open and closed durations. Our study indicates that a non-Markovian binary time series can be obtained from a linear superposition of some independent channel subunits with Markovian gating dynamics.

A Statistical View on Calcium Oscillations

Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole-cell calcium oscillations are stochastic, which poses a significant challenge for modelling. In this review, we take a closer look at recently developed statistical approaches to calcium oscillations. These models describe the timing of whole-cell calcium spikes, yet their parametrisations reflect subcellular processes. We show how non-stationary calcium spike sequences, which e.g. occur during slow depletion of intracellular calcium stores or in the presence of time-dependent stimulation, can be analysed with the help of so-called intensity functions. By utilising Bayesian concepts, we demonstrate how values of key parameters of the statistical model can be inferred from single cell calcium spike sequences and illustrate what information whole-cell statistical models can provide about the subcellular mechanistic processes that drive calcium oscillations. In particular, we find that the interspike interval distribution of HEK293 cells under constant stimulation is captured by a Gamma distribution.

Parallel Stochastic Discrete Event Simulation of Calcium Dynamics in Neuron

The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g., spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in concentration (percentage-wise). These rare events can affect dynamics discretely in such a way that they cannot be evaluated by a deterministic and continuous simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a sequential deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic $\text{IP}_{3}\text{R}$IP3R structure.

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.

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.

Data-driven modeling of mitochondrial dysfunction in Alzheimer's disease

Intracellular accumulation of oligomeric forms of β amyloid (Aβ) are now believed to play a key role in the earliest phase of Alzheimer's disease (AD) as their rise correlates well with the early symptoms of the disease. Extensive evidence points to impaired neuronal Ca²⁺ homeostasis as a direct consequence of the intracellular Aβ oligomers. However, little is known about the downstream effects of the resulting Ca²⁺ rise on the many intracellular Ca²⁺-dependent pathways. Here we use multiscale modeling in conjunction with patch-clamp electrophysiology of single inositol 1,4,5-trisphosphate (IP₃) receptor (IP₃R) and fluorescence imaging of whole-cell Ca²⁺ response, induced by exogenously applied intracellular Aβ₄₂ oligomers to show that Aβ₄₂ inflicts cytotoxicity by impairing mitochondrial function. Driven by patch-clamp experiments, we first model the kinetics of IP₃R, which is then extended to build a model for the whole-cell Ca²⁺ signals. The whole-cell model is then fitted to fluorescence signals to quantify the overall Ca²⁺ release from the endoplasmic reticulum by intracellular Aβ₄₂ oligomers through G-protein-mediated stimulation of IP₃ production. The estimated IP₃ concentration as a function of intracellular Aβ₄₂ content together with the whole-cell model allows us to show that Aβ₄₂ oligomers impair mitochondrial function through pathological Ca²⁺ uptake and the resulting reduced mitochondrial inner membrane potential, leading to an overall lower ATP and increased production of reactive oxygen species and H₂O₂. We further show that mitochondrial function can be restored by the addition of Ca²⁺ buffer EGTA, in accordance with the observed abrogation of Aβ₄₂ cytotoxicity by EGTA in our live cells experiments.

Analyzing optical imaging of Ca2+ signals via TIRF microscopy: The limits on resolution due to chemical rates and depth of the channels

High resolution total internal reflection (TIRF) microscopy (TIRFM) together with detailed computational modeling provides a powerful approach towards the understanding of a wide range of Ca²⁺ signals mediated by the ubiquitous inositol 1,4,5-trisphosphate (IP₃) receptor (IP₃R) channel. Exploiting this fruitful collaboration further requires close agreement between the models and observations. However, elementary Ca²⁺ release events, puffs, imaged through TIRFM do not show the rapid single-channel openings and closings during and between puffs as are present in simulated puffs using data-driven single channel models. TIRFM also shows a rapid equilibration of 10ms after a channel opens or closes which is not achievable in simulation using standard Ca²⁺ diffusion coefficients and reaction rates between indicator dye and Ca²⁺. Furthermore, TIRFM imaging cannot decipher the depth of the channel with respect to the microscope, which will affect the change in fluorescence that the microscope detects, thereby affecting its sensitivity to fast single-channel activity. Using the widely used Ca²⁺ diffusion coefficients and reaction rates, our simulations show equilibration rates that are eight times slower than TIRFM imaging. We show that to get equilibrium rates consistent with observed values, the diffusion coefficients and reaction rates have to be significantly higher than the values reported in the literature, and predict the channel depth to be 200-250nm. Finally, we show that with the addition of noise, short events due to 1-2ms opening and closing of channels that are observed in computational models can be missed in TIRFM.

IP3 receptor signaling and endothelial barrier function

The endothelium, a monolayer of endothelial cells lining vessel walls, maintains tissue-fluid homeostasis by restricting the passage of the plasma proteins and blood cells into the interstitium. The ion Ca²⁺, a ubiquitous secondary messenger, initiates signal transduction events in endothelial cells that is critical to control of vascular tone and endothelial permeability. The ion Ca²⁺ is stored inside the intracellular organelles and released into the cytosol in response to environmental cues. The inositol 1,4,5-trisphosphate (IP₃) messenger facilitates Ca²⁺ release through IP₃ receptors which are Ca²⁺-selective intracellular channels located within the membrane of the endoplasmic reticulum. Binding of IP₃ to the IP₃Rs initiates assembly of IP₃R clusters, a key event responsible for amplification of Ca²⁺ signals in endothelial cells. This review discusses emerging concepts related to architecture and dynamics of IP₃R clusters, and their specific role in propagation of Ca²⁺ signals in endothelial cells.

Clusters of calcium release channels harness the Ising phase transition to confine their elementary intracellular signals

Intracellular Ca signals represent a universal mechanism of cell function. Messages carried by Ca are local, rapid, and powerful enough to be delivered over the thermal noise. A higher signal-to-noise ratio is achieved by a cooperative action of Ca release channels such as IP3 receptors or ryanodine receptors arranged in clusters (release units) containing a few to several hundred release channels. The channels synchronize their openings via Ca-induced Ca release, generating high-amplitude local Ca signals known as puffs in neurons and sparks in muscle cells. Despite the positive feedback nature of the activation, Ca signals are strictly confined in time and space by an unexplained termination mechanism. Here we show that the collective transition of release channels from an open to a closed state is identical to the phase transition associated with the reversal of magnetic field in an Ising ferromagnet. Our simple quantitative criterion closely predicts the Ca store depletion level required for spark termination for each cluster size. We further formulate exact requirements that a cluster of release channels should satisfy in any cell type for our mapping to the Ising model and the associated formula to remain valid. Thus, we describe deterministically the behavior of a system on a coarser scale (release unit) that is random on a finer scale (release channels), bridging the gap between scales. Our results provide exact mapping of a nanoscale biological signaling model to an interacting particle system in statistical physics, making the extensive mathematical apparatus available to quantitative biology.

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

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

Regulation of glomerulotubular balance: flow-activated proximal tubule function

The purpose of this review is to summarize our knowledge and understanding of the physiological importance and the mechanisms underlying flow-activated proximal tubule transport. Since the earliest micropuncture studies of mammalian proximal tubule, it has been recognized that tubular flow is an important regulator of sodium, potassium, and acid-base transport in the kidney. Increased fluid flow stimulates Na⁺ and HCO₃^- absorption in the proximal tubule via stimulation of Na/H-exchanger isoform 3 (NHE3) and H⁺-ATPase. In the proximal tubule, brush border microvilli are the major flow sensors, which experience changes in hydrodynamic drag and bending moment as luminal flow velocity changes and which transmit the force of altered flow to cytoskeletal structures within the cell. The signal to NHE3 depends upon the integrity of the actin cytoskeleton; the signal to the H⁺-ATPase depends upon microtubules. We have demonstrated that alterations in fluid drag impact tubule function by modulating ion transporter availability within the brush border membrane of the proximal tubule. Beyond that, there is evidence that transporter activity within the peritubular membrane is also modulated by luminal flow. Secondary messengers that regulate the flow-mediated tubule function have also been delineated. Dopamine blunts the responsiveness of proximal tubule transporters to changes in luminal flow velocity, while a DA1 antagonist increases flow sensitivity of solute reabsorption. IP3 receptor-mediated intracellular Ca²⁺ signaling is critical to transduction of microvillus drag. In this review, we summarize our findings of the regulatory mechanism of flow-mediated Na⁺ and HCO₃^- transport in the proximal tubule and review available information about flow sensing and regulatory mechanism of glomerulotubular balance.

On the dynamical structure of calcium oscillations

Oscillations in the concentration of free cytosolic Ca²⁺ are an important and ubiquitous control mechanism in many cell types. It is thus correspondingly important to understand the mechanisms that underlie the control of these oscillations and how their period is determined. We show that Class I Ca²⁺ oscillations (i.e., oscillations that can occur at a constant concentration of inositol trisphosphate) have a common dynamical structure, irrespective of the oscillation period. This commonality allows the construction of a simple canonical model that incorporates this underlying dynamical behavior. Predictions from the model are tested, and confirmed, in three different cell types, with oscillation periods ranging over an order of magnitude. The model also predicts that Ca²⁺ oscillation period can be controlled by modulation of the rate of activation by Ca²⁺ of the inositol trisphosphate receptor. Preliminary experimental evidence consistent with this hypothesis is presented. Our canonical model has a structure similar to, but not identical to, the classic FitzHugh-Nagumo model. The characterization of variables by speed of evolution, as either fast or slow variables, changes over the course of a typical oscillation, leading to a model without globally defined fast and slow variables.

Comparison of gating dynamics of different IP3R channels with immune algorithm searching for channel parameter distributions

The gating properties of the inositol 1, 4, 5-trisphosphate (IP₃) receptor (IP₃R) are determined by the binding and unbinding capability of Ca²⁺ ions and IP₃ messengers. With the patch clamp experiments, the stationary properties have been discussed for Xenopus oocyte type-1 IP₃R (Oo-IP₃R1), type-3 IP₃R (Oo-IP₃R3) and Spodoptera frugiperda IP₃R (Sf-IP₃R). In this paper, in order to provide insights about the relation between the observed gating characteristics and the gating parameters in different IP₃Rs, we apply the immune algorithm to fit the parameters of a modified DeYoung-Keizer model. By comparing the fitting parameter distributions of three IP₃Rs, we suggest that the three types of IP₃Rs have the similar open sensitivity in responding to IP₃. The Oo-IP₃R3 channel is easy to open in responding to low Ca²⁺ concentration, while Sf-IP₃R channel is easily inhibited in responding to high Ca²⁺ concentration. We also show that the IP₃ binding rate is not a sensitive parameter for stationary gating dynamics for three IP₃Rs, but the inhibitory Ca²⁺ binding/unbinding rates are sensitive parameters for gating dynamics for both Oo-IP₃R1 and Oo-IP₃R3 channels. Such differences may be important in generating the spatially and temporally complex Ca²⁺ oscillations in cells. Our study also demonstrates that the immune algorithm can be applied for model parameter searching in biological systems.

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.

Emergence of ion channel modal gating from independent subunit kinetics

Many ion channels exhibit a slow stochastic switching between distinct modes of gating activity. This feature of channel behavior has pronounced implications for the dynamics of ionic currents and the signaling pathways that they regulate. A canonical example is the inositol 1,4,5-trisphosphate receptor (IP3R) channel, whose regulation of intracellular Ca(2+) concentration is essential for numerous cellular processes. However, the underlying biophysical mechanisms that give rise to modal gating in this and most other channels remain unknown. Although ion channels are composed of protein subunits, previous mathematical models of modal gating are coarse grained at the level of whole-channel states, limiting further dialogue between theory and experiment. Here we propose an origin for modal gating, by modeling the kinetics of ligand binding and conformational change in the IP3R at the subunit level. We find good agreement with experimental data over a wide range of ligand concentrations, accounting for equilibrium channel properties, transient responses to changing ligand conditions, and modal gating statistics. We show how this can be understood within a simple analytical framework and confirm our results with stochastic simulations. The model assumes that channel subunits are independent, demonstrating that cooperative binding or concerted conformational changes are not required for modal gating. Moreover, the model embodies a generally applicable principle: If a timescale separation exists in the kinetics of individual subunits, then modal gating can arise as an emergent property of channel behavior.

Analyzing and Quantifying the Gain-of-Function Enhancement of IP3 Receptor Gating by Familial Alzheimer's Disease-Causing Mutants in Presenilins

Familial Alzheimer’s disease (FAD)-causing mutant presenilins (PS) interact with inositol 1,4,5-trisphosphate (IP₃) receptor (IP₃R) Ca²⁺ release channels resulting in enhanced IP₃R channel gating in an amyloid beta (Aβ) production-independent manner. This gain-of-function enhancement of IP₃R activity is considered to be the main reason behind the upregulation of intracellular Ca²⁺ signaling in the presence of optimal and suboptimal stimuli and spontaneous Ca²⁺ signals observed in cells expressing mutant PS. In this paper, we employed computational modeling of single IP₃R channel activity records obtained under optimal Ca²⁺ and multiple IP₃ concentrations to gain deeper insights into the enhancement of IP₃R function. We found that in addition to the high occupancy of the high-activity (H) mode and the low occupancy of the low-activity (L) mode, IP₃R in FAD-causing mutant PS-expressing cells exhibits significantly longer mean life-time for the H mode and shorter life-time for the L mode, leading to shorter mean close-time and hence high open probability of the channel in comparison to IP₃R in cells expressing wild-type PS. The model is then used to extrapolate the behavior of the channel to a wide range of IP₃ and Ca²⁺ concentrations and quantify the sensitivity of IP₃R to its two ligands. We show that the gain-of-function enhancement is sensitive to both IP₃ and Ca²⁺ and that very small amount of IP₃ is required to stimulate IP₃R channels in the presence of FAD-causing mutant PS to the same level of activity as channels in control cells stimulated by significantly higher IP₃ concentrations. We further demonstrate with simulations that the relatively longer time spent by IP₃R in the H mode leads to the observed higher frequency of local Ca²⁺ signals, which can account for the more frequent global Ca²⁺ signals observed, while the enhanced activity of the channel at extremely low ligand concentrations will lead to spontaneous Ca²⁺ signals in cells expressing FAD-causing mutant PS.

Aberrant Ca²⁺ signaling caused by IP₃R gating dysregulation is implicated in many neurodegenerative diseases such as Alzheimer’s, Huntington’s, Spinocerebellar ataxias, and endoplasmic reticulum stress-induced brain damage. Thus understanding IP₃R dysfunction is important for the etiology of these diseases. It was previously shown that FAD-causing mutant PS interacts with the IP₃R, leading to its gain-of-function enhancement in optimal Ca²⁺ and sub-saturating IP₃ concentrations. Here, we use data-driven modeling to provide deeper insights into the upregulation of IP₃R gating in a wide range of ligand concentrations and quantify the sensitivity of the channel to its ligands in the presence of mutant PS. Our simulations demonstrate that these changes can alter the statistics of local Ca²⁺ events and we speculate that they lead to Ca²⁺ signaling dysregulations at the whole cell level observed in FAD cells. These models will provide the foundation for future data-driven computational framework for local and global Ca²⁺ signals that will be used to judiciously isolate the primary pathways causing Ca²⁺ dysregulation in FAD from those that are downstream, and to study the effects of upregulation of IP₃R activity on cell function.

Picomolar sensitivity to inositol trisphosphate in Xenopus oocytes

Ca(2+) liberation from the endoplasmic reticulum mediated by inositol trisphosphate receptor/channels (IP3Rs) in response to production of the second messenger IP3 regulates numerous signaling pathways. However, estimates of resting and physiologically relevant cytosolic concentrations of IP3 vary appreciably. Here we directly address this question, taking advantage of the large size of Xenopus oocytes to image Ca(2+) liberation evoked by bolus intracellular injections of known concentrations of IP3. Our principal finding is that IP3 evokes both global and local Ca(2+) signals in freshly isolated oocytes at concentrations as low as a few pM. A corollary is that basal, resting [IP3] must be even lower, given the absence of detectable Ca(2+) signals before injection. The dose/response curve for IP3-activation of Ca(2+) liberation suggests that freshly isolated oocytes express two distinct functional populations of IP3 receptors with EC50 values around 200 pM and tens of nM, whereas the high-affinity receptors are not apparent in oocytes examined later than about 3 days after isolation from the ovary.

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.

Exact stochastic simulation of a calcium microdomain reveals the impact of Ca²⁺ fluctuations on IP₃R gating

In this study, we numerically analyzed the nonlinear Ca(2+)-dependent gating dynamics of a single, nonconducting inositol 1,4,5-trisphosphate receptor (IP₃R) channel, using an exact and fully stochastic simulation algorithm that includes channel gating, Ca(2+) buffering, and Ca(2+) diffusion. The IP₃R is a ubiquitous intracellular Ca(2+) release channel that plays an important role in the formation of complex spatiotemporal Ca(2+) signals such as waves and oscillations. Dynamic subfemtoliter Ca(2+) microdomains reveal low copy numbers of Ca(2+) ions, buffer molecules, and IP₃Rs, and stochastic fluctuations arising from molecular interactions and diffusion do not average out. In contrast to models treating calcium dynamics deterministically, the stochastic approach accounts for this molecular noise. We varied Ca(2+) diffusion coefficients and buffer reaction rates to tune the autocorrelation properties of Ca(2+) noise and found a distinct relation between the autocorrelation time τac, the mean channel open and close times, and the resulting IP₃R open probability PO. We observed an increased PO for shorter noise autocorrelation times, caused by increasing channel open times and decreasing close times. In a pure diffusion model the effects become apparent at elevated calcium concentrations, e.g., at [Ca(2+)] = 25 μM, τac = 0.082 ms, the IP₃R open probability increased by ≈20% and mean open times increased by ≈4 ms, compared to a zero noise model. We identified the inactivating Ca(2+) binding site of IP₃R subunits as the primarily noise-susceptible element of the De Young and Keizer model. Short Ca(2+) noise autocorrelation times decrease the probability of Ca(2+) association and consequently increase IPvR activity. These results suggest a functional role of local calcium noise properties on calcium-regulated target molecules such as the ubiquitous IP₃R. This finding may stimulate novel experimental approaches analyzing the role of calcium noise properties on microdomain behavior.

An allosteric model of the inositol trisphosphate receptor with nonequilibrium binding

The inositol trisphosphate receptor (IPR) is a crucial ion channel that regulates the Ca(2+) influx from the endoplasmic reticulum (ER) to the cytoplasm. A thorough study of the IPR channel contributes to a better understanding of calcium oscillations and waves. It has long been observed that the IPR channel is a typical biological system which performs adaptation. However, recent advances on the physical essence of adaptation show that adaptation systems with a negative feedback mechanism, such as the IPR channel, must break detailed balance and always operate out of equilibrium with energy dissipation. Almost all previous IPR models are equilibrium models assuming detailed balance and thus violate the dissipative nature of adaptation. In this article, we constructed a nonequilibrium allosteric model of single IPR channels based on the patch-clamp experimental data obtained from the IPR in the outer membranes of isolated nuclei of the Xenopus oocyte. It turns out that our model reproduces the patch-clamp experimental data reasonably well and produces both the correct steady-state and dynamic properties of the channel. Particularly, our model successfully describes the complicated bimodal [Ca(2+)] dependence of the mean open duration at high [IP3], a steady-state behavior which fails to be correctly described in previous IPR models. Finally, we used the patch-clamp experimental data to validate that the IPR channel indeed breaks detailed balance and thus is a nonequilibrium system which consumes energy.

Translating intracellular calcium signaling into models

The rich experimental data on intracellular calcium has put theoreticians in an ideal position to derive models of intracellular calcium signaling. Over the last 25 years, a large number of modeling frameworks have been suggested. Here, I will review some of the milestones of intracellular calcium modeling with a special emphasis on calcium-induced calcium release (CICR) through inositol-1,4,5-trisphosphate and ryanodine receptors. I will highlight key features of CICR and how they are represented in models as well as the challenges that theoreticians face when translating our current understanding of calcium signals into equations. The selected examples demonstrate that a successful model provides mechanistic insights into the molecular machinery of the Ca²⁺ signaling toolbox and determines the contribution of local Ca²⁺ release to global Ca²⁺ patterns, which at the moment cannot be resolved experimentally.

Nicotine elicits prolonged calcium signaling along ventral hippocampal axons

Presynaptic nicotinic acetylcholine receptors (nAChRs) have long been implicated in the modulation of CNS circuits. We previously reported that brief exposure to low concentrations of nicotine induced sustained potentiation of glutamatergic transmission at ventral hippocampal (vHipp)-striatal synapses. Here, we exploited nAChR subtype-selective antagonists and agonists and α7*nAChR knockout mutant mice (α7-/-) to elucidate the signaling mechanisms underlying nAChR-mediated modulation of synaptic transmission. Using a combination of micro-slices culture from WT and α7-/-mice, calcium imaging, and immuno-histochemical techniques, we found that nicotine elicits localized and oscillatory increases in intracellular Ca(2+) along vHipp axons that persists for up to 30 minutes. The sustained phase of the nicotine-induced Ca(2+) response was blocked by α-BgTx but not by DHβE and was mimicked by α7*nAChR agonists but not by non-α7*nAChR agonists. In vHipp slices from α7-/- mice, nicotine elicited only transient increases of axonal Ca(2+) signals and did not activate CaMKII. The sustained phase of the nicotine-induced Ca(2+) response required localized activation of CaMKII, phospholipase C, and IP3 receptor mediated Ca(2+)-induced Ca(2+) release (CICR). In conclusion, activation of presynaptic nAChRs by nicotine elicits Ca(2+) influx into the presynaptic axons, the sustained phase of the nicotine-induced Ca(2+) response requires that axonal α7*nAChR activate a downstream signaling network in the vHipp axons.

Activation of Src and release of intracellular calcium by phosphatidic acid during Xenopus laevis fertilization

We report a new step in the fertilization in Xenopus laevis which has been found to involve activation of Src tyrosine kinase to stimulate phospholipase C-γ (PLC-γ) which increases inositol 1,4,5-trisphosphate (IP3) to release intracellular calcium ([Ca](i)). Molecular species analysis and mass measurements suggested that sperm activate phospholipase D (PLD) to elevate phosphatidic acid (PA). We now report that PA mass increased 2.7 fold by 1 min after insemination and inhibition of PA production by two methods inhibited activation of Src and PLCγ, increased [Ca](i) and other fertilization events. As compared to 14 other lipids, PA specifically bound Xenopus Src but not PLCγ. Addition of synthetic PA activated egg Src (an action requiring intact lipid rafts) and PLCγ as well as doubling the amount of PLCγ in rafts. In the absence of elevated [Ca](i), PA addition elevated IP3 mass to levels equivalent to that induced by sperm (but twice that achieved by calcium ionophore). Finally, PA induced [Ca](i) release that was blocked by an IP3 receptor inhibitor. As only PLD1b message was detected, and Western blotting did not detect PLD2, we suggest that sperm activate PLD1b to elevate PA which then binds to and activates Src leading to PLCγ stimulation, IP3 elevation and [Ca](i) release. Due to these and other studies, PA may also play a role in membrane fusion events such as sperm-egg fusion, cortical granule exocytosis, the elevation of phosphatidylinositol 4,5-bisphosphate and the large, late increase in sn 1,2-diacylglycerol in fertilization.

Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels

A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation of mesoscopic properties from the knowledge of microscopic Markovian transition probabilities. We show how exact analytic formulae for the first and second moments of resident time distributions in mesostates can be derived from microscopic resident times and transition probabilities even for systems with a large number of microstates. We apply our formalism to models of the inositol trisphosphate receptor, which plays a key role in generating calcium signals triggering a wide variety of cellular responses. We demonstrate how experimentally accessible quantities, such as opening and closing times and the coefficient of variation of inter-spike intervals, and other, more elaborated, quantities can be analytically calculated from the underlying microscopic Markovian dynamics. A virtue of our approach is that we do not need to follow the detailed time evolution of the whole system, as we derive the relevant properties of its steady state without having to take into account the often extremely complicated transient features. We emphasize that our formulae fully agree with results obtained by stochastic simulations and approaches based on a full determination of the microscopic system's time evolution. We also illustrate how experiments can be devised to discriminate between alternative molecular models of the inositol trisphosphate receptor. The developed approach is applicable to any system described by a Markov process and, owing to the analytic nature of the resulting formulae, provides an easy way to characterize also rare events that are of particular importance to understand the intermittency properties of complex dynamic systems.

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.

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.

'Eventless' InsP3-dependent SR-Ca2+ release affecting atrial Ca2+ sparks

Augmented inositol 1,4,5-trisphosphate receptor (InsP3R) function has been linked to a variety of cardiac pathologies, including cardiac arrhythmia. The contribution of inositol 1,4,5-trisphosphate-induced Ca(2+) release (IP3ICR) in excitation-contraction coupling (ECC) under physiological conditions, as well as under cellular remodelling, remains controversial. Here we test the hypothesis that local IP3ICR directly affects ryanodine receptor (RyR) function and subsequent Ca(2+)-induced Ca(2+) release in atrial myocytes. IP3ICR was evoked by UV-flash photolysis of caged InsP3 under whole-cell configuration of the voltage-clamp technique in atrial myocytes isolated from C57/BL6 mice. Photolytic release of InsP3 was accompanied by a significant increase in the Ca(2+) release event frequency (4.14 ± 0.72 vs. 6.20 ± 0.76 events (100 μm)(-1) s(-1)). These individual photolytically triggered Ca(2+) release events were identified as Ca(2+) sparks, which originated from RyR openings. This was verified by Ca(2+) spark analysis and pharmacological separation between RyR and InsP3R-dependent sarcoplasmic reticulum (SR)-Ca(2+) release (2-aminoethoxydiphenyl borate, xestospongin C, tetracaine). Significant SR-Ca(2+) flux but eventless SR-Ca(2+) release through InsP3R were characterized using SR-Ca(2+) leak/SR-Ca(2+) load measurements. These results strongly support the idea that IP3ICR can effectively modulate RyR openings and Ca(2+) spark probability. We conclude that eventless and highly efficient InsP3-dependent SR-Ca(2+) flux is the main mechanism of functional cross-talk between InsP3Rs and RyRs, which may be an important factor in the modulation of ECC sensitivity.

A data-driven model of a modal gated ion channel: the inositol 1,4,5-trisphosphate receptor in insect Sf9 cells

The inositol 1,4,5-trisphosphate (IP(3)) receptor (IP(3)R) channel is crucial for the generation and modulation of intracellular Ca(2+) signals in animal cells. To gain insight into the complicated ligand regulation of this ubiquitous channel, we constructed a simple quantitative continuous-time Markov-chain model from the data. Our model accounts for most experimentally observed gating behaviors of single native IP(3)R channels from insect Sf9 cells. Ligand (Ca(2+) and IP(3)) dependencies of channel activity established six main ligand-bound channel complexes, where a complex consists of one or more states with the same ligand stoichiometry and open or closed conformation. Channel gating in three distinct modes added one complex and indicated that three complexes gate in multiple modes. This also restricted the connectivity between channel complexes. Finally, latencies of channel responses to abrupt ligand concentration changes defined a model with specific network topology between 9 closed and 3 open states. The model with 28 parameters can closely reproduce the equilibrium gating statistics for all three gating modes over a broad range of ligand concentrations. It also captures the major features of channel response latency distributions. The model can generate falsifiable predictions of IP(3)R channel gating behaviors and provide insights to both guide future experiment development and improve IP(3)R channel gating analysis. Maximum likelihood estimates of the model parameters and of the parameters in the De Young-Keizer model yield strong statistical evidence in favor of our model. Our method is simple and easily applicable to the dynamics of other ion channels and molecules.

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.

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.

Simulation of postsynaptic glutamate receptors reveals critical features of glutamatergic transmission

Activation of several subtypes of glutamate receptors contributes to changes in postsynaptic calcium concentration at hippocampal synapses, resulting in various types of changes in synaptic strength. Thus, while activation of NMDA receptors has been shown to be critical for long-term potentiation (LTP) and long term depression (LTD) of synaptic transmission, activation of metabotropic glutamate receptors (mGluRs) has been linked to either LTP or LTD. While it is generally admitted that dynamic changes in postsynaptic calcium concentration represent the critical elements to determine the direction and amplitude of the changes in synaptic strength, it has been difficult to quantitatively estimate the relative contribution of the different types of glutamate receptors to these changes under different experimental conditions. Here we present a detailed model of a postsynaptic glutamatergic synapse that incorporates ionotropic and mGluR type I receptors, and we use this model to determine the role of the different receptors to the dynamics of postsynaptic calcium with different patterns of presynaptic activation. Our modeling framework includes glutamate vesicular release and diffusion in the cleft and a glutamate transporter that modulates extracellular glutamate concentration. Our results indicate that the contribution of mGluRs to changes in postsynaptic calcium concentration is minimal under basal stimulation conditions and becomes apparent only at high frequency of stimulation. Furthermore, the location of mGluRs in the postsynaptic membrane is also a critical factor, as activation of distant receptors contributes significantly less to calcium dynamics than more centrally located ones. These results confirm the important role of glutamate transporters and of the localization of mGluRs in postsynaptic sites in their signaling properties, and further strengthen the notion that mGluR activation significantly contributes to postsynaptic calcium dynamics only following high-frequency stimulation. They also provide a new tool to analyze the interactions between metabotropic and ionotropic glutamate receptors.

Kinetic behavior of the general modifier mechanism of Botts and Morales with non-equilibrium binding

In this paper, we perform a complete analysis of the kinetic behavior of the general modifier mechanism of Botts and Morales in both equilibrium steady states and non-equilibrium steady states (NESS). Enlightened by the non-equilibrium theory of Markov chains, we introduce the net flux into discussion and acquire an expression of the rate of product formation in NESS, which has clear biophysical significance. Up till now, it is a general belief that being an activator or an inhibitor is an intrinsic property of the modifier. However, we reveal that this traditional point of view is based on the equilibrium assumption. A modifier may no longer be an overall activator or inhibitor when the reaction system is not in equilibrium. Based on the regulation of enzyme activity by the modifier concentration, we classify the kinetic behavior of the modifier into three categories, which are named hyperbolic behavior, bell-shaped behavior, and switching behavior, respectively. We show that the switching phenomenon, in which a modifier may convert between an activator and an inhibitor when the modifier concentration varies, occurs only in NESS. Effects of drugs on the Pgp ATPase activity, where drugs may convert from activators to inhibitors with the increase of the drug concentration, are taken as a typical example to demonstrate the occurrence of the switching phenomenon.

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.

Enhanced ER Ca2+ store filling by overexpression of SERCA2b promotes IP3-evoked puffs

Liberation of Ca(2+) from the endoplasmic reticulum (ER) through inositol trisphosphate receptors (IP(3)R) is modulated by the ER Ca(2+) content, and overexpression of SERCA2b to accelerate Ca(2+) sequestration into the ER has been shown to potentiate the frequency and amplitude of IP(3)-evoked Ca(2+) waves in Xenopus oocytes. Here, we examined the effects of SERCA overexpression on the elementary IP(3)-evoked puffs to elucidate whether ER [Ca(2+)] may modulate IP(3)R function via luminal regulatory sites in addition to simply determining the size of the available store and electrochemical driving force for Ca(2+) release. SERCA2b and Ca(2+) permeable nicotinic plasmalemmal channels were expressed in oocytes, and hyperpolarizing pulses were delivered to induce Ca(2+) influx and thereby load ER stores. Puffs evoked by photoreleased IP(3) were significantly potentiated in terms of numbers of responding sites, frequency and amplitude following transient Ca(2+) influx in SERCA-overexpressing cells, whereas little change was evident with SERCA overexpression alone or following Ca(2+) influx in control cells not overexpressing SERCA. Intriguingly, we observed the appearance of a new population of puffs that arose after long latencies and had prolonged durations supporting the notion of luminal regulation of IP(3)R gating kinetics.

Intercellular calcium waves in glial cells with bistable dynamics

A two-dimensional model is proposed for intercellular calcium (Ca(2 +)) waves with Ca(2 +)-induced IP(3) regeneration and the diffusion of IP(3) through gap junctions. Many experimental observations in glial cells, i.e. responding to local mechanical stimulation, glutamate application, mechanical stimulation followed by ACh application, and glutamate followed by mechanical stimulation, are reproduced and classified by the model. We show that a glial cell model with bistable dynamics, i.e. a Ca(2 +) oscillation state coexisting with a fixed point, can cause a prolonged plateau of Ca(2 +) signals in the cells nearby the stimulated cell when the cell network responds to the local mechanical stimulation.

The role of agonist-independent conformational transformation (AICT) in IP₃ cluster behavior

Inositol 1,4,5-trisphosphate (IP(3)) receptor is a central unit in intracellular Ca(2+) signaling. Regulation of the IP₃ receptor by calcium is well characterized. High open probability values are reported for a single IP₃ receptor in nuclear patch clamp experiments. These experimental observations are in contrast with the lower open probability values of the lipid bilayer experiments. Most theoretical models do not account for high open probabilities of the receptor. But more recently, new models of the IP₃ receptor have been put forward which are constrained by single-channel nuclear patch clamp recordings, which generate the larger open probability with the aid of an additional agonist-independent conformational transformation (AICT)-'active' state. The main aim of this work is to constrain the AICT models with a wealth of experimental data characterizing calcium release from IP₃ receptor clusters. Our results suggest that consistency of cluster release between theory and experiments constrains the kinetics of the agonist-independent conformational transition rates (AICT) to values which lead to small open probabilities for the IP₃ receptor inconsistent with nuclear patch clamp experimental data.

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.

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.

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.

Modulation of endoplasmic reticulum Ca2+ store filling by cyclic ADP-ribose promotes inositol trisphosphate (IP3)-evoked Ca2+ signals

In addition to its well established function in activating Ca(2+) release from the endoplasmic reticulum (ER) through ryanodine receptors (RyR), the second messenger cyclic ADP-ribose (cADPR) also accelerates the activity of SERCA pumps, which sequester Ca(2+) into the ER. Here, we demonstrate a potential physiological role for cADPR in modulating cellular Ca(2+) signals via changes in ER Ca(2+) store content, by imaging Ca(2+) liberation through inositol trisphosphate receptors (IP(3)R) in Xenopus oocytes, which lack RyR. Oocytes were injected with the non-metabolizable analog 3-deaza-cADPR, and cytosolic [Ca(2+)] was transiently elevated by applying voltage-clamp pulses to induce Ca(2+) influx through expressed plasmalemmal nicotinic channels. We observed a subsequent potentiation of global Ca(2+) signals evoked by strong photorelease of IP(3), and increased numbers of local Ca(2+) puffs evoked by weaker photorelease. These effects were not evident with cADPR alone or following cytosolic Ca(2+) elevation alone, indicating that they did not arise through direct actions of cADPR or Ca(2+) on the IP(3)R, but likely resulted from enhanced ER store filling. Moreover, the appearance of a new population of puffs with longer latencies, prolonged durations, and attenuated amplitudes suggests that luminal ER Ca(2+) may modulate IP(3)R function, in addition to simply determining the size of the available store and the electrochemical driving force for release.

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.