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

A phenomenological cluster-based model of Ca2+ waves and oscillations for Inositol 1,4,5-trisphosphate receptor (IP3R) channels

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as Ca2+ puffs, waves, and oscillations that occur on multiple spatial and temporal scales. We introduce a minimal yet descriptive reaction-diffusion model of IP3 receptors for a saturating concentration of IP3 using a principled reduction of a detailed Markov chain description of individual channels. A dynamical systems analysis reveals the possibility of excitable, bistable and oscillatory dynamics of this model that correspond to three types of observed patterns of calcium release -- puffs, waves, and oscillations respectively. We explain the emergence of these patterns via a bifurcation analysis of a coupled two-cluster model, compute the phase diagram and quantify the speed of the waves and period of oscillations in terms of system parameters. We connect the termination of large-scale Ca2+ release events to IP3 unbinding or stochasticity.Comment: 18 pages, 10 figure

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

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

A deterministic model predicts the properties of stochastic calcium oscillations in airway smooth muscle cells

The inositol trisphosphate receptor ([Formula: see text]) is one of the most important cellular components responsible for oscillations in the cytoplasmic calcium concentration. Over the past decade, two major questions about the [Formula: see text] have arisen. Firstly, how best should the [Formula: see text] be modeled? In other words, what fundamental properties of the [Formula: see text] allow it to perform its function, and what are their quantitative properties? Secondly, although calcium oscillations are caused by the stochastic opening and closing of small numbers of [Formula: see text], is it possible for a deterministic model to be a reliable predictor of calcium behavior? Here, we answer these two questions, using airway smooth muscle cells (ASMC) as a specific example. Firstly, we show that periodic calcium waves in ASMC, as well as the statistics of calcium puffs in other cell types, can be quantitatively reproduced by a two-state model of the [Formula: see text], and thus the behavior of the [Formula: see text] is essentially determined by its modal structure. The structure within each mode is irrelevant for function. Secondly, we show that, although calcium waves in ASMC are generated by a stochastic mechanism, [Formula: see text] stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic [Formula: see text] models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified [Formula: see text] models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model

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

Markov chain models of calcium puffs and sparks

Localized cytosolic Ca2+ elevations known as puffs and sparks are important regulators of cellular function that arise due to the cooperative activity of Ca2+-regulated inositol 1,4,5-trisphosphate receptors (IP3Rs) or ryanodine receptors (RyRs) co-localized at Ca2+ release sites on the surface of the endoplasmic reticulum or sarcoplasmic reticulum. Theoretical studies have demonstrated that the cooperative gating of a cluster of Ca2+-regulated Ca 2+ channels modeled as a continuous-time discrete-state Markov chain may result in dynamics reminiscent of Ca2+ puffs and sparks. In such simulations, individual Ca2+-release channels are coupled via a mathematical representation of the local [Ca2+] and exhibit stochastic Ca2+ excitability where channels open and close in a concerted fashion. This dissertation uses Markov chain models of Ca 2+ release sites to advance our understanding of the biophysics connecting the microscopic parameters of IP3R and RyR gating to the collective phenomenon of puffs and sparks.;The dynamics of puffs and sparks exhibited by release site models that include both Ca2+ coupling and nearest-neighbor allosteric coupling are studied. Allosteric interactions are included in a manner that promotes the synchronous gating of channels by stabilizing neighboring closed-closed and/or open-open channel pairs. When the strength of Ca2+-mediated channel coupling is systematically varied, simulations that include allosteric interactions often exhibit more robust Ca2+ puffs and sparks. Interestingly, the changes in puff/spark duration, inter-event interval, and frequency observed upon the random removal of allosteric couplings that stabilize closed-closed channel pairs are qualitatively different than the changes observed when open-open channel pairs, or both open-open and closed-closed channel pairs are stabilized. The validity of a computationally efficient mean-field reduction applicable to the dynamics of a cluster of Ca2+-release Ca2+ channels coupled via the local [Ca2+] and allosteric interactions is also investigated.;Markov chain models of Ca2+ release sites composed of channels that are both activated and inactivated by Ca2+ are used to clarify the role of Ca2+ inactivation in the generation and termination of puffs and sparks. It is found that when the average fraction of inactivated channels is significant, puffs and sparks are often less sensitive to variations in the number of channels at release sites and the strength of Ca2+ coupling. While excessively fast Ca2+ inactivation can preclude puffs and sparks moderately fast Ca2+ inactivation often leads to time-irreversible puff/sparks whose termination is facilitated by the recruitment of inactivated channels throughout the duration of the puff/spark event. On the other hand, Ca2+ inactivation may be an important negative feedback mechanism even when its time constant is much greater than the duration of puffs and sparks. In fact, slow Ca 2+ inactivation can lead to release sites with a substantial fraction of inactivated channels that exhibit nearly time-reversible puffs and sparks that terminate without additional recruitment of inactivated channels

On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling

The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems, and is the basis of the predictive power of theoretical physics. While physicists have confidence in this correspondence, it is less recognized in cellular biophysics. On the one hand, the complex organization of cellular dynamics involving a plethora of interacting molecules and the basic observation of cell variability seem to question its possibility. The practical difficulties of deriving the equations describing cellular behaviour from first principles support these doubts. On the other hand, ignoring such a correspondence would severely limit the possibility of predictive quantitative theory in biophysics. Additionally, the existence of functional modules (like pathways) across cell types suggests also the existence of mathematical structures with comparable universality. Only a few cellular systems have been sufficiently investigated in a variety of cell types to follow up these basic questions. IP3 induced Ca2+ signalling is one of them, and the mathematical structure corresponding to it is subject of ongoing discussion. We review the system’s general properties observed in a variety of cell types. They are captured by a reaction diffusion system. We discuss the phase space structure of its local dynamics. The spiking regime corresponds to noisy excitability. Models focussing on different aspects can be derived starting from this phase space structure. We discuss how the initial assumptions on the set of stochastic variables and phase space structure shape the predictions of parameter dependencies of the mathematical models resulting from the derivation

High-resolution optical analyses of IP3-evoked Ca2+ signals

Ca2+ is a universal intracellular messenger that regulates many cellular responses. Most cells express inositol 1,4,5-trisphosphate receptors (IP3R) that mediate Ca2+ release from the endoplasmic reticulum (ER) when they bind IP3 produced after activation of cell-surface receptors. Vertebrate genomes encode three closely related subtypes of IP3R (IP3R1-3). High-resolution optical analyses have revealed a hierarchy of IP3-evoked Ca2+ signals that are thought to arise from the co-regulation of IP3Rs by IP3 and Ca2+. The smallest events (‘blips’) report the opening of single IP3Rs, Ca2+ ‘puffs’ report the almost simultaneous opening of a few clustered IP3Rs, and as stimulus intensities increase further Ca2+ signals propagate regeneratively as Ca2+ waves. The aim of this study was to establish whether all three IP3R subtypes can generate Ca2+ puffs. I first used a haploid cell line (HAP1 cells) to generate, using CRISPR/Cas9, a line lacking all endogenous IP3Rs. However, for analyses of Ca2+ puffs, I used HEK cells that had been engineered, using CRISPR/Cas9 to disrupt endogenous genes, to express single IP3R subtypes. Local Ca2+ signals evoked by flash-photolysis of caged- IP3 were recorded using Cal520 and total internal reflection fluorescence (TIRF) microscopy in human embryonic kidney (HEK) cells. The Flika algorithm was used, and validated, for automated detection of Ca2+ puffs and to measure their properties. IP3 evoked Ca2+ puffs in wild-type HEK cells and in cells expressing single IP3R subtypes. In wild-type cells, the Ca2+ signals invariably propagated regeneratively to give global increases in cytosolic [Ca2+]. This occurred less frequently in cells expressing single IP3R subtypes, commensurate with their lower overall levels of IP3R expression. The properties of the Ca2+ puffs, including their rise and decay times, durations, the size of the unitary fluorescence steps as channels closed channel during the falling phase, and the estimated number of active IP3Rs in each Ca2+ puff, were broadly similar in each of the four cell lines. The latter observation suggests that despite lower overall levels of IP3R expression (~30%) in cells with single subtypes relative to WT cells, there is a mechanism that ensures formation of similarly sized IP3R clusters. The only significant differences between cell lines were the slower kinetics of the Ca2+ puffs evoked by IP3R2, which may suggest dissociation of IP3 from its receptor contributes to the termination of Ca2+ puffs. My results demonstrate, for the first time, that all three IP3R subtypes can generate Ca2+ puffs. I conclude that Ca2+ puffs are fundamental building blocks of all IP3-evoked Ca2+ signals.Biotechnology and Biological Sciences Research Council (BBSRC

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.published_or_final_versio

Markov chain models of instantaneously coupled intracellular calcium channels

Localized calcium elevations known as calcium puffs or sparks are cellular signals arising from cooperative activity of clusters of inositol 1,4,5-trisphosphate receptors (IP3Rs) or ryanodine receptors (RyRs) located at calcium release sites on the endoplasmic or sarcoplasmic reticulum membrane. When Markov chain models of these intracellular calcium-regulated calcium channels are coupled via a mathematical representation of the calcium microdomain, simulated calcium release sites may exhibit the phenomenon of stochastic calcium excitability where the IP3Rs or RyRs open and close in a concerted fashion. Although the biophysical theory relating the kinetics of single channels to the collective phenomena of puffs and sparks is only beginning to be developed, Markov chain models of coupled intracellular channels give insight into the dynamics of calcium puffs and sparks.;Interestingly, under some conditions simulated puffs and sparks can be observed even when the single channel model used does not include slow calcium inactivation or any long-lived closed state. In this case termination of the localized calcium elevation occurs when all of the intracellular channels at a release site simultaneously close through a process called stochastic attrition. This dissertation investigates the statistical properties of stochastic attrition viewed as an absorption time on a terminating Markov chain that represents a calcium release site composed of two-state channels that are activated by calcium. Assuming that the local calcium concentration experienced by a channel depends only on the number of open channels at the calcium release site, the probability distribution function for the time until stochastic attrition occurs is derived and an analytical formula for the expectation of this random variable is presented. Also explored is how the contribution of stochastic attrition to the termination of calcium puffs and sparks depends on the number of channels at a release site, the source amplitude of the channels, the background calcium concentration, channel kinetics, and the cooperativity of calcium binding.;This dissertation also studies whether single channel models with calcium inactivation are less sensitive to the details of release site ultrastructure than models that lack a slow calcium-inactivation process. Release site dynamics obtained from simulated calcium release sites composed of instantaneously coupled calcium-regulated calcium channels whose random spatial locations were chosen from a uniform distribution on a disc of specified radius are compared to simulations with channels arranged on hexagonal lattices. Analysis of puff/spark statistics confirms that puffs and sparks are less sensitive to the spatial organization of release sites when the single channel model includes a slow inactivation process. The validity of several different mean-field reductions that do not explicitly account for the details of release site ultrastructure is also investigated.;Calcium release site models are stochastic automata networks that involve many functional transitions, that is, the transition probabilities of each channel depend on the local calcium concentration and thus the state of the other channels. A Kronecker structured representation for calcium release site models is presented and benchmark stationary distribution calculations using both exact and approximate iterative numerical solution techniques that leverage this structure are performed. When it is possible to obtain an exact solution, response measures such as the number of channels in a particular state converge more quickly using the iterative numerical methods than occupation measures calculated via Monte Carlo simulation. When an exact solution is not feasible, iterative approximate methods based on the Power method may be used, with performance similar to Monte Carlo estimates