Calcium in close quarters: microdomain feedback in excitation-contraction coupling and other cell biological phenomena

Non-ionotropic voltage-gated calcium channel signaling

Voltage-gated calcium channels (VGCCs) are the major conduits for calcium ions (Ca2+) within excitable cells. Recent studies have highlighted the non-ionotropic functionality of VGCCs, revealing their capacity to activate intracellular pathways independently of ion flow. This non-ionotropic signaling mode plays a pivotal role in excitation-coupling processes, including gene transcription through excitation-transcription (ET), synaptic transmission via excitation-secretion (ES), and cardiac contraction through excitation-contraction (EC). However, it is noteworthy that these excitation-coupling processes require extracellular calcium (Ca2+) and Ca2+ occupancy of the channel ion pore. Analogous to the "non-canonical" characterization of the non-ionotropic signaling exhibited by the N-methyl-D-aspartate receptor (NMDA), which requires extracellular Ca2+ without the influx of ions, VGCC activation requires depolarization-triggered conformational change(s) concomitant with Ca2+ binding to the open channel. Here, we discuss the contributions of VGCCs to ES, ET, and EC coupling as Ca2+ binding macromolecules that transduces external stimuli to intracellular input prior to elevating intracellular Ca2+. We emphasize the recognition of calcium ion occupancy within the open ion-pore and its contribution to the excitation coupling processes that precede the influx of calcium. The non-ionotropic activation of VGCCs, triggered by the upstroke of an action potential, provides a conceptual framework to elucidate the mechanistic aspects underlying the microseconds nature of synaptic transmission, cardiac contractility, and the rapid induction of first-wave genes.

Integrating Bioelectrical Currents and Ca2+ Signaling with Biochemical Signaling in Development and Pathogenesis

Roles of bioelectrical signals are increasingly recognized in excitable and nonexcitable non-neural tissues. Diverse ion-selective channels, pumps, and gap junctions participate in bioelectrical signaling, including those transporting calcium ions (Ca2+). Ca2+ is the most versatile transported ion, because it serves as an electrical charge carrier and a biochemical regulator for multiple molecular binding, enzyme, and transcription activities. We aspire to learn how bioelectrical signals crosstalk to biochemical/biomechanical signals. In this study, we review four recent studies showing how bioelectrical currents and Ca2+ signaling affect collective dermal cell migration during feather bud elongation, affect chondrogenic differentiation in limb development, couple with mechanical tension in aligning gut smooth muscle, and affect mitochondrial function and skeletal muscle atrophy. We observe bioelectrical signals involved in several developmental and pathological conditions in chickens and mice at multiple spatial scales: cellular, cellular collective, and subcellular. These examples inspire novel concept and approaches for future basic and translational studies.

Calcium-induced calcium release in proximity to hair cell BK channels revealed by PKA activation

Large-conductance calcium-activated potassium (BK) channels play a critical role in electrical resonance, a mechanism of frequency selectivity in chicken hair cells. We determine that BK currents are dependent on inward flow of Ca2+ , and intracellular buffering of Ca2+ . Entry of Ca2+ is further amplified locally by calcium-induced Ca2+ release (CICR) in close proximity to plasma membrane BK channels. Ca2+ imaging reveals peripheral clusters of high concentrations of Ca2+ that are suprathreshold to that needed to activate BK channels. Protein kinase A (PKA) activation increases the size of BK currents likely by recruiting more BK channels due to spatial spread of high Ca2+ concentrations in turn from increasing CICR. STORM imaging confirms the presence of nanodomains with ryanodine and IP3 receptors in close proximity to the Slo subunit of BK channels. Together, these data require a rethinking of how electrical resonance is brought about and suggest effects of CICR in synaptic release. Both genders were included in this study.

Initial memory consolidation and the synaptic tagging and capture hypothesis

Everyday memories are retained automatically in the hippocampus and then decay very rapidly. Memory retention can be boosted when novel experiences occur shortly before or shortly after the time of memory encoding via a memory stabilization process called "initial memory consolidation." The dopamine release and new protein synthesis in the hippocampus during a novel experience are crucial for this novelty-induced memory boost. The mechanisms underlying initial memory consolidation are not well-understood, but the synaptic tagging and capture (STC) hypothesis provides a conceptual basis of synaptic plasticity events occurring during initial memory consolidation. In this review, we provide an overview of the STC hypothesis and its relevance to dopaminergic signalling, in order to explore the cellular and molecular mechanisms underlying initial memory consolidation in the hippocampus. We summarize electrophysiological STC processes based on the evidence from two-pathway experiments and a behavioural tagging hypothesis, which translates the STC hypothesis into a related behavioural hypothesis. We also discuss the function of two types of molecules, "synaptic tags" and "plasticity-related proteins," which have a crucial role in the STC process and initial memory consolidation. We describe candidate molecules for the roles of synaptic tag and plasticity-related proteins and interpret their candidacy based on evidence from two-pathway experiments ex vivo, behavioural tagging experiments in vivo and recent cutting-edge optical imaging experiments. Lastly, we discuss the direction of future studies to advance our understanding of molecular mechanisms underlying the STC process, which are critical for initial memory consolidation in the hippocampus.

Non-Differentiable Solution of Nonlinear Biological Population Model on Cantor Sets

The main objective of this study is to apply the local fractional homotopy analysis method (LFHAM) to obtain the non-differentiable solution of two nonlinear partial differential equations of the biological population model on Cantor sets. The derivative operator are taken in the local fractional sense. Two examples have been presented showing the effectiveness of this method in solving this model on Cantor sets.

Calcium-induced release of calcium in muscle: 50 years of work and the emerging consensus

Ryanodine-sensitive intracellular Ca2+ channels (RyRs) open upon binding Ca2+ at cytosolic-facing sites. This results in concerted, self-reinforcing opening of RyRs clustered in specialized regions on the membranes of Ca2+ storage organelles (endoplasmic reticulum and sarcoplasmic reticulum), a process that produces Ca2+-induced Ca2+ release (CICR). The process is optimized to achieve large but brief and localized increases in cytosolic Ca2+ concentration, a feature now believed to be critical for encoding the multiplicity of signals conveyed by this ion. In this paper, I trace the path of research that led to a consensus on the physiological significance of CICR in skeletal muscle, beginning with its discovery. I focus on the approaches that were developed to quantify the contribution of CICR to the Ca2+ increase that results in contraction, as opposed to the flux activated directly by membrane depolarization (depolarization-induced Ca2+ release [DICR]). Although the emerging consensus is that CICR plays an important role alongside DICR in most taxa, its contribution in most mammalian muscles appears to be limited to embryogenesis. Finally, I survey the relevance of CICR, confirmed or plausible, to pathogenesis as well as the multiple questions about activation of release channels that remain unanswered after 50 years.

Sensitized signalling between L-type Ca2+ channels and ryanodine receptors in the absence or inhibition of FKBP12.6 in cardiomyocytes

Aims

The heart contraction is controlled by the Ca2+-induced Ca2+ release (CICR) between L-type Ca2+ channels and ryanodine receptors (RyRs). The FK506-binding protein FKBP12.6 binds to RyR subunits, but its role in stabilizing RyR function has been debated for long. Recent reports of high-resolution RyR structure show that the HD2 domain that binds to the SPRY2 domain of neighbouring subunit in FKBP-bound RyR1 is detached and invisible in FKBP-null RyR2. The present study was to test the consequence of FKBP12.6 absence on the in situ activation of RyR2.

Methods and results

Using whole-cell patch-clamp combined with confocal imaging, we applied a near threshold depolarization to activate a very small fraction of LCCs, which in turn activated RyR Ca2+ sparks stochastically. FKBP12.6-knockout and FK506/rapamycin treatments increased spark frequency and LCC-RyR coupling fidelity without altering LCC open probability. Neither FK506 nor rapamycin further altered LCC-RyR coupling fidelity in FKBP12.6-knockout cells. In loose-seal patch-clamp experiments, the LCC-RyR signalling kinetics, indexed by the delay for a LCC sparklet to trigger a RyR spark, was accelerated after FKBP12.6 knockout and FK506/rapamycin treatments. These results demonstrated that RyRs became more sensitive to Ca2+ triggers without FKBP12.6. Isoproterenol (1 μM) further accelerated the LCC-RyR signalling in FKBP12.6-knockout cells. The synergistic sensitization of RyRs by catecholaminergic signalling and FKBP12.6 dysfunction destabilized the CICR system, leading to chaotic Ca2+ waves and ventricular arrhythmias.

Conclusion

FKBP12.6 keeps the RyRs from over-sensitization, stabilizes the potentially regenerative CICR system, and thus may suppress the life-threatening arrhythmogenesis.

Membrane depolarization increases ryanodine sensitivity to Ca2+ release to the cytosol in L6 skeletal muscle cells: Implications for excitation-contraction coupling

The dihydropyridine receptor in the plasma membrane and the ryanodine receptor in the sarcoplasmic reticulum are known to physically interact in the process of excitation-contraction coupling. However, the mechanism for subsequent Ca(2+) release through the ryanodine receptor is unknown. Our lab has previously presented evidence that the dihydropyridine receptor and ryanodine receptor combine as a channel for the entry of Ca(2+) under resting conditions, known as store operated calcium entry. Here, we provide evidence that depolarization during excitation-contraction coupling causes the dihydropyridine receptor to disengage from the ryanodine receptor. The newly freed ryanodine receptor can then transport Ca(2+) from the sarcoplasmic reticulum to the cytosol. Experimentally, this should more greatly expose the ryanodine receptor to exogenous ryanodine. To examine this hypothesis, we titrated L6 skeletal muscle cells with ryanodine in resting and excited (depolarized) states. When L6 muscle cells were depolarized with high potassium or exposed to the dihydropyridine receptor agonist BAYK-8644, known to induce dihydropyridine receptor movement within the membrane, ryanodine sensitivity was enhanced. However, ryanodine sensitivity was unaffected when Ca(2+) was elevated without depolarization by the ryanodine receptor agonist chloromethylcresol, or by increasing Ca(2+) concentration in the media. Ca(2+) entry currents (from the extracellular space) during excitation were strongly inhibited by ryanodine, but Ca(2+) entry currents in the resting state were not. We conclude that excitation releases the ryanodine receptor from occlusion by the dihydropyridine receptor, enabling Ca(2+) release from the ryanodine receptor to the cytosol.

Basis for a neuronal version of Grover's quantum algorithm

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

Mechanisms underlying activation of transient BK current in rabbit urethral smooth muscle cells and its modulation by IP3-generating agonists

We used the perforated patch-clamp technique at 37°C to investigate the mechanisms underlying the activation of a transient large-conductance K(+) (tBK) current in rabbit urethral smooth muscle cells. The tBK current required an elevation of intracellular Ca(2+), resulting from ryanodine receptor (RyR) activation via Ca(2+)-induced Ca(2+) release, triggered by Ca(2+) influx through L-type Ca(2+) (CaV) channels. Carbachol inhibited tBK current by reducing Ca(2+) influx and Ca(2+) release and altered the shape of spike complexes recorded under current-clamp conditions. The tBK currents were blocked by iberiotoxin and penitrem A (300 and 100 nM, respectively) and were also inhibited when external Ca(2+) was removed or the CaV channel inhibitors nifedipine (10 μM) and Cd(2+) (100 μM) were applied. The tBK current was inhibited by caffeine (10 mM), ryanodine (30 μM), and tetracaine (100 μM), suggesting that RyR-mediated Ca(2+) release contributed to the activation of the tBK current. When IP3 receptors (IP3Rs) were blocked with 2-aminoethoxydiphenyl borate (2-APB, 100 μM), the amplitude of the tBK current was not reduced. However, when Ca(2+) release via IP3Rs was evoked with phenylephrine (1 μM) or carbachol (1 μM), the tBK current was inhibited. The effect of carbachol was abolished when IP3Rs were blocked with 2-APB or by inhibition of muscarinic receptors with the M3 receptor antagonist 4-diphenylacetoxy-N-methylpiperidine methiodide (1 μM). Under current-clamp conditions, bursts of action potentials could be evoked with depolarizing current injection. Carbachol reduced the number and amplitude of spikes in each burst, and these effects were reduced in the presence of 2-APB. In the presence of ryanodine, the number and amplitude of spikes were also reduced, and carbachol was without further effect. These data suggest that IP3-generating agonists can modulate the electrical activity of rabbit urethral smooth muscle cells and may contribute to the effects of neurotransmitters on urethral tone.

Calcium spike variability in cardiac myocytes results from activation of small cohorts of ryanodine receptor 2 channels

In mammalian cardiac myocytes, the elementary calcium releases triggered by step voltage stimuli manifest either as solitary or as twin spikes that vary widely in kinetics and amplitude for unknown reasons. Here we examined the variability of calcium spikes measured using line-scanning confocal microscopy in patch-clamped rat ventricular myocytes. Amplitude distributions of the single and of the first of twin spikes were broader than those of the second spikes. All could be best approximated by a sum of a few elementary Gaussian probability distribution functions. The latency distributions of the single and the first spikes were identical, much shorter and less variable than those of the second spikes. The multimodal distribution of spike amplitudes and the probability of occurrence of twin spikes were stochastically congruent with activation of only a few of the many RyR2 channels present in the release site cluster. The occurrence of twin release events was rare due to refractoriness of release, induced with a probability proportional to the number of RyR2s activated in the primary release event. We conclude that the variability of the elementary calcium release events supports a calcium signalling mechanism that arises from stochastics of RyR2 gating and from inactivation of local origin.

Coupled gating of skeletal muscle ryanodine receptors is modulated by Ca2+, Mg2+, and ATP

Coupled gating (synchronous openings and closures) of groups of skeletal muscle ryanodine receptors (RyR1), which mimics RyR1-mediated Ca(2+) release underlying Ca(2+) sparks, was first described by Marx et al. (Marx SO, Ondrias K, Marks AR. Science 281: 818-821, 1998). The nature of the RyR1-RyR1 interactions for coupled gating still needs to be characterized. Consequently, we defined planar lipid bilayer conditions where ∼25% of multichannel reconstitutions contain mixtures of coupled and independently gating RyR1. In ∼10% of the cases, all RyRs (2-10 channels; most frequently 3-4) gated in coupled fashion, allowing for quantification. Our results indicated that coupling required cytosolic solutions containing ATP/Mg(2+) and high (50 mM) luminal Ca(2+) (Ca(lum)) or Sr(2+) solutions. Bursts of coupled activity (events) started and ended abruptly, with all channels activating/deactivating within ∼300 μs. Coupled RyR1 were heterogeneous, where highly active RyR1 ("drivers") seemed open during the entire coupled event (P(o) = 1), while other RyR1s ("followers") displayed abundant flickering and smaller amplitude. Drivers mean open time increased with cytosolic Ca(2+) (Ca(cyt)) or caffeine, whereas followers flicker frequency was Ca(cyt) independent and more sensitive to inhibition by cytosolic Mg(2+). Coupled events were insensitive to varying lumen-to-cytosol Ca(2+) fluxes from ∼1 to 8 pA, which does not corroborate coupling of neighboring RyR1 by local Ca(2+)-induced Ca(2+) release. However, coupling requires specific Ca(lum) sites, as it was lost when Ca(lum) was replaced by luminal Ba(2+) or Mg(2+). In summary, coupled events reveal complex interactions among heterogeneous RyR1, differentially modulated by cytosolic ATP/Mg(2+), Ca(cyt), and Ca(lum,) which under cell-like ionic conditions may parallel synchronous RyR1 gating during Ca(2+) sparks.

Ultrastructural remodelling of Ca(2+) signalling apparatus in failing heart cells

AIMS

The contraction of a heart cell is controlled by Ca(2+)-induced Ca(2+) release between L-type Ca(2+) channels (LCCs) in the cell membrane/T-tubules (TTs) and ryanodine receptors (RyRs) in the junctional sarcoplasmic reticulum (SR). During heart failure, LCC-RyR signalling becomes defective. The purpose of the present study was to reveal the ultrastructural mechanism underlying the defective LCC-RyR signalling and contractility.

METHODS AND RESULTS

In rat models of heart failure produced by transverse aortic constriction surgery, stereological analysis of transmission electron microscopic images showed that the volume density and the surface area of junctional SRs and those of SR-coupled TTs were both decreased in failing heart cells. The TT-SR junctions were displaced or missing from the Z-line areas. Moreover, the spatial span of individual TT-SR junctions was markedly reduced in failing heart cells. Numerical simulation and junctophilin-2 knockdown experiments demonstrated that the decrease in junction size (and thereby the constitutive LCC and RyR numbers) led to a scattered delay of Ca(2+) release activation.

CONCLUSIONS

The shrinking and eventual absence of TT-SR junctions are important mechanisms underlying the desynchronized and inhomogeneous Ca(2+) release and the decreased contractile strength in heart failure. Maintaining the nanoscopic integrity of TT-SR junctions thus represents a therapeutic strategy against heart failure and related cardiomyopathies.

The structure and functioning of the couplon in the mammalian cardiomyocyte

The couplons of the cardiomyocyte form nanospaces within the cell that place the L-type calcium channel (Ca(v)1.2), situated on the plasmalemma, in opposition to the type 2 ryanodine receptor (RyR2), situated on the sarcoplasmic reticulum. These two molecules, which form the basis of excitation-contraction coupling, are separated by a very limited space, which allows a few Ca(2+) ions passing through Ca(v)1.2 to activate the RyR2 at concentration levels that would be deleterious to the whole cell. The limited space also allows Ca(2+) inactivation of Ca(v)1.2. We have found that not all couplons are the same and that their properties are likely determined by their molecular partners which, in turn, determine their excitability. In particular, there are a class of couplons that lie outside the RyR2-Ca(v)1.2 dyad; in this case, the RyR2 is close to caveolin-3 rather than Ca(v)1.2. These extra-dyadic couplons are probably controlled by the multitude of molecules associated with caveolin-3 and may modulate contractile force under situations such as stress. It has long been assumed that like the skeletal muscle, the RyR2 in the couplon are arranged in a structured array with the RyR2 interacting with each other via domain 6 of the RyR2 molecule. This arrangement was thought to provide local control of RyR2 excitability. Using 3D electron tomography of the couplon, we show that the RyR2 in the couplon do not form an ordered pattern, but are scattered throughout it. Relatively few are in a checkerboard pattern--many RyR2 sit edge-to-edge, a configuration which might preclude their controlling each other's excitability. The discovery of this structure makes many models of cardiac couplon function moot and is a current avenue of further research.

Reduction of calcium release site models via moment fitting of phase-type distributions

Models of calcium (Ca(2 +)) release sites derived from continuous-time Markov chain (CTMC) models of intracellular Ca(2 +) channels exhibit collective gating reminiscent of the experimentally observed phenomenon of Ca(2 +) puffs and sparks. In order to overcome the state-space explosion that occurs in compositionally defined Ca(2 +) release site models, we have implemented an automated procedure for model reduction that replaces aggregated states of the full release site model with much simpler CTMCs that have similar within-group phase-type sojourn times and inter-group transitions. Error analysis based on comparison of full and reduced models validates the method when applied to release site models composed of 20 three-state channels that are both activated and inactivated by Ca(2 +). Although inspired by existing techniques for fitting moments of phase-type distributions, the automated reduction method for compositional Ca(2 +) release site models is unique in several respects and novel in this biophysical context.

Voltage-dependent modulation of cardiac ryanodine receptors (RyR2) by protamine

It has been reported that protamine (>10 µg/ml) blocks single skeletal RyR1 channels and inhibits RyR1-mediated Ca²⁺ release from sarcoplasmic reticulum microsomes. We extended these studies to cardiac RyR2 reconstituted into planar lipid bilayers. We found that protamine (0.02–20 µg/ml) added to the cytosolic surface of fully activated RyR2 affected channel activity in a voltage-dependent manner. At membrane voltage (V_m; SR lumen - cytosol) = 0 mV, protamine induced conductance transitions to several intermediate states (substates) as well as full block of RyR2. At V_m>10 mV, the substate with the highest level of conductance was predominant. Increasing V_m from 0 to +80 mV, decreased the number of transitions and residence of the channel in this substate. The drop in current amplitude (full opening to substate) had the same magnitude at 0 and +80 mV despite the ∼3-fold increase in amplitude of the full opening. This is more similar to rectification of channel conductance induced by other polycations than to the action of selective conductance modifiers (ryanoids, imperatoxin). A distinctive effect of protamine (which might be shared with polylysines and histones but not with non-peptidic polycations) is the activation of RyR2 in the presence of nanomolar cytosolic Ca²⁺ and millimolar Mg²⁺ levels. Our results suggest that RyRs would be subject to dual modulation (activation and block) by polycationic domains of neighboring proteins via electrostatic interactions. Understanding these interactions could be important as such anomalies may be associated with the increased RyR2-mediated Ca²⁺ leak observed in cardiac diseases.

Ryanodine receptor-mediated arrhythmias and sudden cardiac death

The cardiac ryanodine receptor-Ca²⁺ release channel (RyR2) is an essential sarcoplasmic reticulum (SR) transmembrane protein that plays a central role in excitation–contraction coupling (ECC) in cardiomyocytes. Aberrant spontaneous, diastolic Ca²⁺ leak from the SR due to dysfunctional RyR2 contributes to the formation of delayed after-depolarisations, which are thought to underlie the fatal arrhythmia that occurs in both heart failure (HF) and in catecholaminergic polymorphic ventricular tachycardia (CPVT). CPVT is an inherited disorder associated with mutations in either the RyR2 or a SR luminal protein, calsequestrin. RyR2 shows normal function at rest in CPVT but the RyR2 dysfunction is unmasked by physical exercise or emotional stress, suggesting abnormal RyR2 activation as an underlying mechanism. Several potential mechanisms have been advanced to explain the dysfunctional RyR2 observed in HF and CPVT, including enhanced RyR2 phosphorylation status, altered RyR2 regulation at luminal/cytoplasmic sites and perturbed RyR2 intra/inter-molecular interactions. This review considers RyR2 dysfunction in the context of the structural and functional modulation of the channel, and potential therapeutic strategies to stabilise RyR2 function in cardiac pathology.

Proper restoration of excitation-contraction coupling in the dihydropyridine receptor beta1-null zebrafish relaxed is an exclusive function of the beta1a subunit

The paralyzed zebrafish strain relaxed carries a null mutation for the skeletal muscle dihydropyridine receptor (DHPR) beta(1a) subunit. Lack of beta(1a) results in (i) reduced membrane expression of the pore forming DHPR alpha(1S) subunit, (ii) elimination of alpha(1S) charge movement, and (iii) impediment of arrangement of the DHPRs in groups of four (tetrads) opposing the ryanodine receptor (RyR1), a structural prerequisite for skeletal muscle-type excitation-contraction (EC) coupling. In this study we used relaxed larvae and isolated myotubes as expression systems to discriminate specific functions of beta(1a) from rather general functions of beta isoforms. Zebrafish and mammalian beta(1a) subunits quantitatively restored alpha(1S) triad targeting and charge movement as well as intracellular Ca(2+) release, allowed arrangement of DHPRs in tetrads, and most strikingly recovered a fully motile phenotype in relaxed larvae. Interestingly, the cardiac/neuronal beta(2a) as the phylogenetically closest, and the ancestral housefly beta(M) as the most distant isoform to beta(1a) also completely recovered alpha(1S) triad expression and charge movement. However, both revealed drastically impaired intracellular Ca(2+) transients and very limited tetrad formation compared with beta(1a). Consequently, larval motility was either only partially restored (beta(2a)-injected larvae) or not restored at all (beta(M)). Thus, our results indicate that triad expression and facilitation of 1,4-dihydropyridine receptor (DHPR) charge movement are common features of all tested beta subunits, whereas the efficient arrangement of DHPRs in tetrads and thus intact DHPR-RyR1 coupling is only promoted by the beta(1a) isoform. Consequently, we postulate a model that presents beta(1a) as an allosteric modifier of alpha(1S) conformation enabling skeletal muscle-type EC coupling.

Models of spatially restricted biochemical reaction systems

Many reactions within the cell occur only in specific intracellular regions. Such local reaction networks give rise to microdomains of activated signaling components. The dynamics of microdomains can be visualized by live cell imaging. Computational models using partial differential equations provide mechanistic insights into the interacting factors that control microdomain dynamics. The mathematical models show that, for membrane-initiated signaling, the ratio of the surface area of the plasma membrane to the volume of the cytoplasm, the topology of the signaling network, the negative regulators, and kinetic properties of key components together define microdomain dynamics. Thus, patterns of locally restricted signaling reaction systems can be considered an emergent property of the cell.

Markov chain models of coupled calcium channels: Kronecker representations and iterative solution methods

Mathematical models of calcium release sites derived from Markov chain models of intracellular calcium channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic calcium excitability (i.e., calcium puffs and sparks). 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. We present a Kronecker-structured representation for calcium release site models and perform benchmark stationary distribution calculations using both exact and approximate iterative numerical solution techniques that leverage this structure. 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. In particular, multi-level methods provide excellent convergence with modest additional memory requirements for the Kronecker representation of calcium release site models. 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. This suggests approximate methods with multi-level iterative engines as a promising avenue of future research for large-scale calcium release site models.

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

Localized intracellular Ca(2+) elevations known as puffs and sparks arise from the cooperative activity of inositol 1,4,5-trisphosphate receptor Ca(2+) channels (IP(3)Rs) and ryanodine receptor Ca(2+) channels (RyRs) clustered at Ca(2+) release sites on the surface of the endoplasmic reticulum or sarcoplasmic reticulum. When Markov chain models of these intracellular Ca(2+)-regulated Ca(2+) channels are coupled via a mathematical representation of a Ca(2+) microdomain, simulated Ca(2+) release sites may exhibit the phenomenon of "stochastic Ca(2+) excitability" reminiscent of Ca(2+) puffs and sparks where channels open and close in a concerted fashion. To clarify the role of Ca(2+) inactivation of IP(3)Rs and RyRs in the dynamics of puffs and sparks, we formulate and analyze Markov chain models of Ca(2+) release sites composed of 10-40 three-state intracellular Ca(2+) channels that are inactivated as well as activated by Ca(2+). We study how the statistics of simulated puffs and sparks depend on the kinetics and dissociation constant of Ca(2+) inactivation and find that puffs and sparks are often less sensitive to variations in the number of channels at release sites and strength of coupling via local [Ca(2+)] when the average fraction of inactivated channels is significant. Interestingly, we observe that the single channel kinetics of Ca(2+) inactivation influences the thermodynamic entropy production rate of Markov chain models of puffs and sparks. While excessively fast Ca(2+) inactivation can preclude puffs and sparks, moderately fast Ca(2+) inactivation often leads to time-irreversible puffs and sparks whose termination is facilitated by the recruitment of inactivated channels throughout the duration of the puff/spark event. On the other hand, Ca(2+) 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 puffs and sparks that are nearly time-reversible and terminate without additional recruitment of inactivated channels.

Ryanodine receptor allosteric coupling and the dynamics of calcium sparks

Puffs and sparks are localized intracellular Ca(2+) elevations that arise from the cooperative activity of Ca(2+)-regulated inositol 1,4,5-trisphosphate receptors and ryanodine receptors clustered at Ca(2+) release sites on the surface of the endoplasmic reticulum or the sarcoplasmic reticulum. While the synchronous gating of Ca(2+)-regulated Ca(2+) channels can be mediated entirely though the buffered diffusion of intracellular Ca(2+), interprotein allosteric interactions also contribute to the dynamics of ryanodine receptor (RyR) gating and Ca(2+) sparks. In this article, Markov chain models of Ca(2+) release sites are used to investigate how the statistics of Ca(2+) spark generation and termination are related to the coupling of RyRs via local [Ca(2+)] changes and allosteric interactions. 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 Ca(2+)-mediated channel coupling is systematically varied (e.g., by changing the Ca(2+) buffer concentration), simulations that include synchronizing allosteric interactions often exhibit more robust Ca(2+) sparks; however, for some Ca(2+) coupling strengths the sparks are less robust. We find no evidence that the distribution of spark durations can be used to distinguish between allosteric interactions that stabilize closed channel pairs, open channel pairs, or both in a balanced fashion. On the other hand, the changes in spark duration, interspark interval, and frequency observed when allosteric interactions that stabilize closed channel pairs are gradually removed from simulations are qualitatively different than the changes observed when open or both closed and open channel pairs are stabilized. Thus, our simulations clarify how changes in spark statistics due to pharmacological washout of the accessory proteins mediating allosteric coupling may indicate the type of synchronizing allosteric interactions exhibited by physically coupled RyRs. We also investigate the validity of a mean-field reduction applicable to the dynamics of a ryanodine receptor cluster coupled via local [Ca(2+)] and allosteric interactions. In addition to facilitating parameter studies of the effect of allosteric coupling on spark statistics, the derivation of the mean-field model establishes the correct functional form for cooperativity factors representing the coupled gating of RyRs. This mean-field formulation is well suited for use in computationally efficient whole cell simulations of excitation-contraction coupling.

A mathematical model of fatigue in skeletal muscle force contraction

The ability for muscle to repeatedly generate force is limited by fatigue. The cellular mechanisms behind muscle fatigue are complex and potentially include breakdown at many points along the excitation-contraction pathway. In this paper we construct a mathematical model of the skeletal muscle excitation-contraction pathway based on the cellular biochemical events that link excitation to contraction. The model includes descriptions of membrane voltage, calcium cycling and crossbridge dynamics and was parameterised and validated using the response characteristics of mouse skeletal muscle to a range of electrical stimuli. This model was used to uncover the complexities of skeletal muscle fatigue. We also parameterised our model to describe force kinetics in fast and slow twitch fibre types, which have a number of biochemical and biophysical differences. How these differences interact to generate different force/fatigue responses in fast- and slow- twitch fibres is not well understood and we used our modelling approach to bring new insights to this relationship.

Sub-plasmalemmal [Ca2+]i upstroke in myocytes of the guinea-pig small intestine evoked by muscarinic stimulation: IP3R-mediated Ca2+ release induced by voltage-gated Ca2+ entry

Membrane depolarization triggers Ca²⁺ release from the sarcoplasmic reticulum (SR) in skeletal muscles via direct interaction between the voltage-gated L-type Ca²⁺ channels (the dihydropyridine receptors; VGCCs) and ryanodine receptors (RyRs), while in cardiac muscles Ca²⁺ entry through VGCCs triggers RyR-mediated Ca²⁺ release via a Ca²⁺-induced Ca²⁺ release (CICR) mechanism. Here we demonstrate that in phasic smooth muscle of the guinea-pig small intestine, excitation evoked by muscarinic receptor activation triggers an abrupt Ca²⁺ release from sub-plasmalemmal (sub-PM) SR elements enriched with inositol 1,4,5-trisphosphate receptors (IP₃Rs) and poor in RyRs. This was followed by a lesser rise, or oscillations in [Ca²⁺]_i. The initial abrupt sub-PM [Ca²⁺]_i upstroke was all but abolished by block of VGCCs (by 5 μM nicardipine), depletion of intracellular Ca²⁺ stores (with 10 μM cyclopiazonic acid) or inhibition of IP₃Rs (by 2 μM xestospongin C or 30 μM 2-APB), but was not affected by block of RyRs (by 50–100 μM tetracaine or 100 μM ryanodine). Inhibition of either IP₃Rs or RyRs attenuated phasic muscarinic contraction by 73%. Thus, in contrast to cardiac muscles, excitation–contraction coupling in this phasic visceral smooth muscle occurs by Ca²⁺ entry through VGCCs which evokes an initial IP₃R-mediated Ca²⁺ release activated via a CICR mechanism.

Inositol trisphosphate receptor Ca2+ release channels

The inositol 1,4,5-trisphosphate (InsP3) receptors (InsP3Rs) are a family of Ca2+ release channels localized predominately in the endoplasmic reticulum of all cell types. They function to release Ca2+ into the cytoplasm in response to InsP3 produced by diverse stimuli, generating complex local and global Ca2+ signals that regulate numerous cell physiological processes ranging from gene transcription to secretion to learning and memory. The InsP3R is a calcium-selective cation channel whose gating is regulated not only by InsP3, but by other ligands as well, in particular cytoplasmic Ca2+. Over the last decade, detailed quantitative studies of InsP3R channel function and its regulation by ligands and interacting proteins have provided new insights into a remarkable richness of channel regulation and of the structural aspects that underlie signal transduction and permeation. Here, we focus on these developments and review and synthesize the literature regarding the structure and single-channel properties of the InsP3R.

Determining calcium concentration in heterogeneous model systems using multiple indicators

Intracellular free calcium concentrations ([Ca2+]i) are assessed by measuring indicator fluorescence in entire cells or subcellular regions using fluorescence microscopy. [Ca2+]i is calculated using equations which link fluorescence intensities (or intensity ratios) to calcium concentrations [G. Grynkiewicz, M. Poenie, R.Y. Tsien, A new generation of Ca2+ indicators with greatly improved fluorescence properties, J. Biol. Chem. 260 (1985) 3440-3450]. However, if calcium ions are heterogeneously distributed within a region of interest, then the observed average fluorescence intensity may not reflect average [Ca2+]i. We assessed potential calcium determination errors in mathematical and experimental models consisting of 'low' and 'high' calcium compartments, using indicators with different affinity for calcium. [Ca2+] calculated using average fluorescence intensity was lower than the actual mean concentrations. Low affinity indicators reported higher (more accurate) values than their high affinity counterparts. To estimate compartment dimensions and respective [Ca2+], we extended the standard approach by using different indicator responses to the same [Ca2+]. While two indicators were sufficient to provide a partial characterization of two-compartment model systems, the use of three or more indicators offered full description of the model provided compartmental [Ca2+] were within the indicator sensitivity ranges. These results show that uneven calcium distribution causes underestimation of actual [Ca2+], and offers novel approaches to estimating calcium heterogeneity.

Modification of cytosolic calcium signaling by subplasmalemmal microdomains

To investigate the hypothesis that Na(+) concentration in subplasmalemmal microdomains regulates Ca(2+) concentrations in cellular microdomains ([Ca](md)), the cytosol ([Ca](cyt)), and sarcoplasmic reticulum (SR; [Ca](sr)), we modeled transport events in those compartments. Inputs to the model were obtained from published measurements in descending vasa recta pericytes and other smooth muscle cells. The model accounts for major classes of ion channels, Na(+)/Ca(2+) exchange (NCX), and the distributions of Na(+)-K(+)-ATPase alpha(1)- and alpha(2)-isoforms in the plasma membrane. Ca(2+) release from SR stores is assumed to occur via ryanodine (RyR) and inositol trisphosphate (IP(3)R) receptors. The model shows that the requisite existence of a significant Na(+) concentration difference between the cytosol ([Na](cyt)) and microdomains ([Na](md)) necessitates restriction of intercompartmental diffusion. Accepting the latter, the model predicts resting ion concentrations that are compatible with experimental measurements and temporal changes in [Ca](cyt) similar to those observed on NCX inhibition. An important role for NCX in the regulation of Ca(2+) signaling is verified. In the resting state, NCX operates in "forward mode," with Na(+) entry and Ca(2+) extrusion from the cell. Inhibition of NCX respectively raises and reduces [Ca](cyt) and [Na](cyt) by 40 and 30%. NCX translates variations in Na(+)-K(+)-ATPase activity into changes in [Ca](md), [Ca](sr), and [Ca](cyt). Taken together, the model simulations verify the feasibility of the central hypothesis that modulation of [Na](md) can influence both the loading of Ca(2+) into SR stores and [Ca(2+)](cyt) variation.

The dynamics of luminal depletion and the stochastic gating of Ca2+-activated Ca2+ channels and release sites

Single channel models of intracellular calcium (Ca(2+)) channels such as the 1,4,5-trisphosphate receptor and ryanodine receptor often assume that Ca(2+)-dependent transitions are mediated by constant background cytosolic [Ca(2+)]. This assumption neglects the fact that Ca(2+) released by open channels may influence subsequent gating through the processes of Ca(2+)-activation or inactivation. Similarly, the influence of the dynamics of luminal depletion on the stochastic gating of intracellular Ca(2+) channels is often neglected, in spite of the fact that the sarco/endoplasmic reticulum [Ca(2+)] near the luminal face of intracellular Ca(2+) channels influences the driving force for Ca(2+), the rate of Ca(2+) release, and the magnitude and time course of the consequent increase in cytosolic domain [Ca(2+)]. Here we analyze how the steady-state open probability of several minimal Ca(2+)-regulated Ca(2+) channel models depends on the conductance of the channel and the time constants for the relaxation of elevated cytosolic [Ca(2+)] and depleted luminal [Ca(2+)] to the bulk [Ca(2+)] of both compartments. Our approach includes Monte Carlo simulation as well as numerical solution of a system of advection-reaction equations for the multivariate probability density of elevated cytosolic [Ca(2+)] and depleted luminal [Ca(2+)] conditioned on each state of the stochastically gating channel. Both methods are subsequently used to study the role of luminal depletion in the dynamics of Ca(2+) puff/spark termination in release sites composed of Ca(2+) channels that are activated, but not inactivated, by cytosolic Ca(2+). The probability density approach shows that such minimal Ca(2+) release site models may exhibit puff/spark-like dynamics in either of two distinct parameter regimes. In one case, puffs/spark termination is due to the process of stochastic attrition and facilitated by rapid Ca(2+) domain collapse [cf. DeRemigio, H., Smith, G., 2005. The dynamics of stochastic attrition viewed as an absorption time on a terminating Markov chain. Cell Calcium 38, 73-86]. In the second case, puff/spark termination is promoted by the local depletion of luminal Ca(2+).

Kinetics of calcium spikes in rat cardiac myocytes

The local calcium release flux signals (calcium spikes) evoked by membrane depolarization were recorded at high temporal resolution (2000 lines s(-1)) in isolated ventricular myocytes of male rats, using combination of scanning confocal microscopy and the patch-clamp technique. The kinetic properties of calcium spikes were investigated. The time course of calcium spike activation could be described reliably by a model with higher-order (n = 3) kinetics, but not by a first-order exponential process. A model of calcium spike with calcium release termination coupled to its activation was preferential to a model with the release termination independent of its activation. Three fluorescent calcium dyes (OG-5N, fluo-3, and fluo-4) were compared for calcium spike measurements. Experimental measurements as well as simulations showed that the occurrence and latency of calcium spikes could be measured faithfully with all indicators, while the kinetics of calcium spikes was reliably traced only with OG-5N. Calcium spikes evoked by a step depolarization from -50 to 0 mV commenced with a mean latency of 4.1 +/- 0.2 ms and peaked 6.7 +/- 0.2 ms later. Their full amplitudes were normally distributed. The activation time constant of calcium spikes was 3.1 +/- 0.1 ms, and the time constant of termination was 5.5 +/- 0.2 ms. A negative correlation was observed between the observed amplitude of calcium spikes and their time constant of activation, but there was no correlation between their observed amplitude and time constant of termination, in agreement with the concept of steep calcium-dependent activation and fateful inactivation of calcium release flux.

Direct in vivo monitoring of sarcoplasmic reticulum Ca2+ and cytosolic cAMP dynamics in mouse skeletal muscle

Skeletal muscle contraction depends on the release of Ca(2+) from the sarcoplasmic reticulum (SR), but the dynamics of the SR free Ca(2+) concentration ([Ca(2+)](SR)), its modulation by physiological stimuli such as catecholamines, and the concomitant changes in cAMP handling have never been directly determined. We used two-photon microscopy imaging of GFP-based probes expressed in mouse skeletal muscles to monitor, for the first time in a live animal, the dynamics of [Ca(2+)](SR) and cAMP. Our data, which were obtained in highly physiological conditions, suggest that free [Ca(2+)](SR) decreases by approximately 50 microM during single twitches elicited through nerve stimulation. We also demonstrate that cAMP levels rise upon beta-adrenergic stimulation, leading to an increased efficacy of the Ca(2+) release/reuptake cycle during motor nerve stimulation.

Three-dimensional distribution of ryanodine receptor clusters in cardiac myocytes

The clustering of ryanodine receptors (RyR2) into functional Ca2+ release units is central to current models for cardiac excitation-contraction (E-C) coupling. Using immunolabeling and confocal microscopy, we have analyzed the distribution of RyR2 clusters in rat and ventricular atrial myocytes. The resolution of the three-dimensional structure was improved by a novel transverse sectioning method as well as digital deconvolution. In contrast to earlier reports, the mean RyR2 cluster transverse spacing was measured 1.05 microm in ventricular myocytes and estimated 0.97 microm in atrial myocytes. Intercalated RyR2 clusters were found interspersed between the Z-disks on the cell periphery but absent in the interior, forming double rows flanking the local Z-disks on the surface. The longitudinal spacing between the adjacent rows of RyR2 clusters on the Z-disks was measured to have a mean value of 1.87 microm in ventricular and 1.69 microm in atrial myocytes. The measured RyR2 cluster distribution is compatible with models of Ca2+ wave generation. The size of the typical RyR2 cluster was close to 250 nm, and this suggests that approximately 100 RyR2s might be present in a cluster. The importance of cluster size and three-dimensional spacing for current E-C coupling models is discussed.

A 3D Monte Carlo analysis of the role of dyadic space geometry in spark generation

In multiple biological systems, vital intracellular signaling processes occur locally in minute periplasmic subspaces often referred to as signaling microdomains. The number of signaling molecules in these microdomains is small enough to render the notion of continuous concentration changes invalid, such that signaling events are better described using stochastic rather than deterministic methods. Of particular interest is the dyadic cleft in the cardiac myocyte, where short-lived, local increases in intracellular Ca2+ known as Ca2+ sparks regulate excitation-contraction coupling. The geometry of dyadic spaces can alter in disease and development and display significant interspecies variability. We created and studied a 3D Monte Carlo model of the dyadic cleft, specifying the spatial localization of L-type Ca2+ channels and ryanodine receptors. Our analysis revealed how reaction specificity and efficiency are regulated by microdomain geometry as well as the physical separation of signaling molecules into functional complexes. The spark amplitude and rise time were found to be highly dependent on the concentration of activated channels per dyadic cleft and on the intermembrane separation, but not very sensitive to other cleft dimensions. The role of L-type Ca2+ channel and ryanodine receptor phosphorylation was also examined. We anticipate that this modeling approach may be applied to other systems (e.g., neuronal growth cones and chemotactic cells) to create a general description of stochastic events in Ca2+ signaling.

Concerted vs. sequential. Two activation patterns of vast arrays of intracellular Ca2+ channels in muscle

To signal cell responses, Ca²⁺ is released from storage through intracellular Ca²⁺ channels. Unlike most plasmalemmal channels, these are clustered in quasi-crystalline arrays, which should endow them with unique properties. Two distinct patterns of local activation of Ca²⁺ release were revealed in images of Ca²⁺ sparks in permeabilized cells of amphibian muscle. In the presence of sulfate, an anion that enters the SR and precipitates Ca²⁺, sparks became wider than in the conventional, glutamate-based solution. Some of these were “protoplatykurtic” (had a flat top from early on), suggesting an extensive array of channels that activate simultaneously. Under these conditions the rate of production of signal mass was roughly constant during the rise time of the spark and could be as high as 5 μm³ ms⁻¹, consistent with a release current >50 pA since the beginning of the event. This pattern, called “concerted activation,” was observed also in rat muscle fibers. When sulfate was combined with a reduced cytosolic [Ca²⁺] (50 nM) these sparks coexisted (and interfered) with a sequential progression of channel opening, probably mediated by Ca²⁺-induced Ca²⁺ release (CICR). Sequential propagation, observed only in frogs, may require parajunctional channels, of RyR isoform β, which are absent in the rat. Concerted opening instead appears to be a property of RyR α in the amphibian and the homologous isoform 1 in the mammal.

Spatial microenvironment defines Ca2+ entry and Ca2+ release in salivary gland cells

The difference of Ca(2+) mobilization induced by muscarinic receptor activation between parotid acinar and duct cells was examined. Oxotremorine, a muscarinic-cholinergic agonist, induced intracellular Ca(2+) release and extracellular Ca(2+) entry through store-operated Ca(2+) entry (SOC) and non-SOC channels in acinar cells, but it activated only Ca(2+) entry from non-SOC channels in duct cells. RT-PCR experiments showed that both types of cells expressed the same muscarinic receptor, M3. Given that ATP activated the intracellular Ca(2+) stores, the machinery for intracellular Ca(2+) release was intact in the duct cells. By immunocytochemical experiments, IP(3)R2 colocalized with M3 receptors in the plasma membrane area of acinar cells; in duct cells, IP(3)R2 resided in the region on the opposite side of the M3 receptors. On the other hand, purinergic P2Y2 receptors were found in the apical area of duct cells where they colocalized with IP(3)R2. These results suggest that the expression of the IP(3)Rs near G-protein-coupled receptors is necessary for the activation of intracellular Ca(2+) stores. Therefore, the microenvironment probably affects intracellular Ca(2+) release and Ca(2+) entry.

Propagation of Ca2+ release in cardiac myocytes: role of mitochondria

Factors contributing to "local control" of Ca2+ release in cardiac myocytes are incompletely understood. We induced local release of Ca2+ by regional exposure of mouse atrial and ventricular myocytes to 10mM caffeine for 500 ms using a rapid solution switcher. Propagation of Ca2+ release was imaged by means of a Nipkow confocal microscope, and fluo-3. Under physiologic conditions, a local release of Ca2+ propagated in atrial myocytes, not in ventricular myocytes. Inhibition of SR Ca2+ uptake (500 nM thapsigargin), and of Ca2+ extrusion via Na/Ca exchange (5mM Ni2+), did not result in propagation in ventricular myocytes. The density of mitochondria was greater in ventricular than in atrial myocytes, although the abundance of ryanodine receptors and myofilaments was similar. Partial inhibition of Ca2+ uptake via the mitochondrial Ca2+ uniporter (5 microM Ru360) caused an increase in the [Ca2+]i transient in paced ventricular myocytes, and consistently resulted in propagation of Ca2+ release. This effect of Ru360 did not appear to be due to altered SR Ca2+ content. These data indicate that Ca2+ uptake via the mitochondrial uniporter occurs on a beat-to-beat basis, and may contribute to local control of Ca2+ release. Propagation of Ca2+ release in atrial myocytes may result in part from the relatively low density of mitochondria present.

The dynamics of stochastic attrition viewed as an absorption time on a terminating Markov chain

Localized Ca(2+) elevations known as Ca(2+) puffs and sparks are cellular signals that arise from the cooperative activity of clusters of inositol 1,4,5-trisphosphate receptors and ryanodine receptors clustered at Ca(2+) release sites on the surface of the endoplasmic reticulum or sarcoplasmic reticulum. When Markov chain models of these intracellular Ca(2+)-regulated Ca(2+) channels are coupled via a mathematical representation of Ca(2+) microdomain, simulated Ca(2+) release sites may exhibit the phenomenon of "stochastic Ca(2+) excitability" where the inositol 1,4,5-trisphosphate receptors (IP(3)Rs) or ryanodine receptors (RyRs) open and close in a concerted fashion. Interestingly, under some conditions simulated puffs and sparks can be observed even when the single-channel model used does not include slow Ca(2+) inactivation or, indeed, any long-lived closed/refractory state [V. Nguyen, R. Mathias, G. Smith, Stochastic automata network descriptor for Markov chain models of instantaneously-coupled intracellular Ca(2+) channels, Bull. Math. Biol. 67 (2005) 393-432]. In this case, termination of the localized Ca(2+) elevation occurs when all of the intracellular channels at a release site simultaneously close through a process referred to as stochastic attrition [M. Stern, Theory of excitation-contraction coupling in cardiac muscle, Biophys. J. 63 (1992) 497-517]. In this paper, we investigate the statistical properties of stochastic attrition viewed as an absorption time on a terminating Markov chain that represents a Ca(2+) release site composed of N two-state channels that are activated by Ca(2+). Assuming that the local [Ca(2+)] experienced by a channel depends only on the number of open channels at the Ca(2+) release site (i.e., instantaneous mean-field coupling [ibid.], we derive the probability distribution function for the time until stochastic attrition occurs and present an analytical formula for the expectation of this random variable. We explore how the contribution of stochastic attrition to the termination of Ca(2+) puffs and sparks depends on the number of channels at a release site, the source amplitude of the channels (i.e., the strength of the coupling), the background [Ca(2+)], channel kinetics, and the cooperactivity of Ca(2+) binding. Because we explicitly model the Ca(2+) regulation of the intracellular channels, our results differ markedly from (and in fact generalize) preliminary analyses that assume the intracellular Ca(2+) channels are uncoupled and consequently independent.

Inactivation of Ca2+ transients in amphibian and mammalian muscle fibres

MagFluo-4 fluorescence (Ca2+) transients associated with action potentials were measured in intact muscle fibres, manually dissected from toads ( Leptodactylus insularis ) or enzymatically dissociated from mice. In toads, the decay phase of the Ca2+ transients is described by a single exponential with a time constant ( tau ) of about 7 ms. In mice, a double exponential function with tau 's of 1.5 and 15.5 ms, respectively gives a better fit. In both species the amplitude of Ca2+ transients diminished during repetitive stimulation: in amphibian muscle fibres, the decrease was about 20% with 1 Hz stimulation and 55% at 10 Hz. In mammalian fibres, repetitive stimulation causes a less conspicuous decrease of the transient amplitude: 10% at 1 Hz and 15% at 10 Hz. During tetanic stimulation at 100 Hz the transient amplitude decays to 20% in toad fibres and 40% in mouse fibres. This decrease could be associated with the phenomenon of inactivation of Ca2+ release, described by other authors. Recovery from inactivation, studied by a double stimuli protocol also indicates that in toad fibres the ability to release Ca2+ is abolished to a greater extent than in mouse fibres. In fact the ratio between the amplitudes of the second and first transient, when they are separated by a 10 ms interval, is 0.29 for toad and 0.58 for mouse fibres. In toad fibres, recovery from inactivation, to about 80 % of the initial value, occurs with a tau of 32 ms at 22 degrees C; while in mouse fibres recovery from inactivation is almost complete and occurs with a tau of 36 ms under the same conditions. The results indicate that Ca2+ release in enzymatically dissociated mammalian muscle fibres inactivates to a smaller extent than in intact amphibian muscle fibres.

Optical single-channel recording: imaging Ca2+ flux through individual ion channels with high temporal and spatial resolution

Developments in imaging technology now enable visualization of the functioning of individual ion channels in living cells: something previously possible only by the electrophysiological patch-clamp technique. We review techniques that track channel gating via changes in intracellular [Ca2+] resulting from openings of Ca(2+)-permeable channels. Spatial and temporal resolution are optimized by monitoring Ca2+ close to the channel mouth, and we describe the use of two imaging modalities: confocal laser scan microscopy (linescan CLSM) and total internal reflection fluorescence microscopy (TIRFM). Both currently achieve a kinetic resolution of <10 ms, provide a simultaneous and independent readout from many channels, and enable their locations to be mapped with submicrometer resolution. TIRFM provides 2-D images from a very thin (approximately 100 nm) optical section, but it is restricted to channels in the plasma membrane of cells adhering close to a cover glass. In contrast, CLSM can image channels in intracellular membranes but, to achieve good temporal resolution, has been utilized only in a linescan mode with limited spatial information. We anticipate that imaging techniques will develop as a useful adjunct to patch-clamping for single-channel studies, with capabilities including simultaneous readout from multiple channels, high-resolution mapping of channel location, and mobility that is inaccessible by electrophysiological means. Optical single-channel recording is applicable to diverse voltage- and ligand-gated Ca(2+)-permeable channels and has potential for high-throughput functional analysis.

Modulation of the voltage sensor of L-type Ca2+ channels by intracellular Ca2+

Both intracellular calcium and transmembrane voltage cause inactivation, or spontaneous closure, of L-type (CaV1.2) calcium channels. Here we show that long-lasting elevations of intracellular calcium to the concentrations that are expected to be near an open channel (>/=100 microM) completely and reversibly blocked calcium current through L-type channels. Although charge movements associated with the opening (ON) motion of the channel's voltage sensor were not altered by high calcium, the closing (OFF) transition was impeded. In two-pulse experiments, the blockade of calcium current and the reduction of gating charge movements available for the second pulse developed in parallel during calcium load. The effect depended steeply on voltage and occurred only after a third of the total gating charge had moved. Based on that, we conclude that the calcium binding site is located either in the channel's central cavity behind the voltage-dependent gate, or it is formed de novo during depolarization through voltage-dependent rearrangements just preceding the opening of the gate. The reduction of the OFF charge was due to the negative shift in the voltage dependence of charge movement, as previously observed for voltage-dependent inactivation. Elevation of intracellular calcium concentration from approximately 0.1 to 100-300 microM sped up the conversion of the gating charge into the negatively distributed mode 10-100-fold. Since the "IQ-AA" mutant with disabled calcium/calmodulin regulation of inactivation was affected by intracellular calcium similarly to the wild-type, calcium/calmodulin binding to the "IQ" motif apparently is not involved in the observed changes of voltage-dependent gating. Although calcium influx through the wild-type open channels does not cause a detectable negative shift in the voltage dependence of their charge movement, the shift was readily observable in the Delta1733 carboxyl terminus deletion mutant, which produces fewer nonconducting channels. We propose that the opening movement of the voltage sensor exposes a novel calcium binding site that mediates inactivation.

The Na(+)-K(+)-ATPase alpha2-subunit isoform modulates contractility in the perinatal mouse diaphragm

This study uses genetically altered mice to examine the contribution of the Na(+)-K(+)-ATPase alpha2 catalytic subunit to resting potential, excitability, and contractility of the perinatal diaphragm. The alpha2 protein is reduced by 38% in alpha2-heterozygous and absent in alpha2-knockout mice, and alpha1-isoform is upregulated 1.9-fold in alpha2-knockout. Resting potentials are depolarized by 0.8-4.0 mV in heterozygous and knockout mice. Action potential threshold, overshoot, and duration are normal. Spontaneous firing, a developmental function, is impaired in knockout diaphragm, but this does not compromise its ability to fire evoked action potential trains, the dominant mode of activation near birth. Maximum tetanic force, rate of activation, force-frequency and force-voltage relationships, and onset and magnitude of fatigue are not changed. The major phenotypic consequence of reduced alpha2 content is that relaxation from contraction is 1.7-fold faster. This finding reveals a distinct cellular role of the alpha2-isoform at a step after membrane excitation, which cannot be restored simply by increasing alpha1 content. Na+/Ca2+ exchanger expression decreases in parallel with alpha2-isoform, suggesting that Ca2+ extrusion is affected by the altered alpha2 genotype. There are no major compensatory changes in expression of sarcoplasmic reticulum Ca(2+)-ATPase, phospholamban, or plasma membrane Ca(2+)-ATPase. These results demonstrate that the Na(+)-K(+)-ATPase alpha1-isoform alone is able to maintain equilibrium K+ and Na+ gradients and to substitute for alpha2-isoform in most cellular functions related to excitability and force. They further indicate that the alpha2-isoform contributes significantly less at rest than expected from its proportional content but can modulate contractility during muscle contraction.

Analysing cardiac excitation–contraction coupling with mathematical models of local control

Cardiac excitation-contraction (E-C) coupling describes the process that links sarcolemmal Ca2+ influx via L-type Ca2+ channels to Ca2+ release from the sarcoplasmic reticulum via ryanodine receptors (RyRs). This process has proven difficult to study experimentally, and complete descriptions of how the cell couples surface membrane and intracellular signal transduction proteins to achieve both stable and sensitive intracellular calcium release are still lacking. Mathematical models provide a framework to test our understanding of how this is achieved. While no single model is yet capable of describing all features of cardiac E-C coupling, models of increasing complexity are revealing unexpected subtlety in the process. In particular, modelling has established a general failure of 'common-pool' models and has emphasized the requirement for 'local control' so that microscopic sub-cellular domains can separate local behaviour from the whole-cell average (common-pool) behaviour. The micro-architecture of the narrow diadic cleft in which the local control takes place is a key factor in determining local Ca2+ dynamics. There is still considerable uncertainty about the number of Ca2+ ions required to open RyRs within the cleft and various gating models have been proposed, many of which are in reasonable agreement with available experimental data. However, not all models exhibit a realistic voltage dependence of E-C coupling gain. Furthermore, it is unclear which model features are essential to producing reasonable gain properties. Thus, despite the success of local-control models in explaining many features of cardiac E-C coupling, more work will be needed to provide a sound theoretical basis of cardiac E-C coupling.

Discrete intracellular signaling domains of soluble adenylyl cyclase: camps of cAMP?

Soluble adenylyl cyclase can function in the nucleus, defining a nuclear microdomain of adenosine 3',5'-monophosphate (cAMP) signaling. Bundey and Insel discuss the evidence for discrete signaling microdomains of cAMP, including the nucleus and caveolae, and conclude that such microdomains may be defined by the localized, subcellular expression of adenylyl cyclase isoforms.

Regulation of Ion Channel Expression

A potentially important mechanism controlling ion channel expression is homeostatic regulation, which can act to maintain a stable electrophysiological phenotype in cardiac myocytes as well as to provide plasticity in response to genetic, pathological, or pharmacological insults. The capabilities and limitations of the homeostatic regulatory mechanisms that contribute to the control of cardiac ion channel expression are the primary topic of this review.

Ryanodine Receptor Oligomeric Interaction

Specific interactions between adjacent ryanodine receptor (RyR) molecules to form ordered two-dimensional arrays in the membrane have been demonstrated using electron microscopy both in situ, in tissues and cells, and in vitro, with the purified protein. RyR interoligomeric association has also been inferred from observations of simultaneous channel gating during multi-RyR channel recordings in lipid bilayers. In this study, we report experiments designed to identify the region(s) of the RyR molecule, participating in this reciprocal interaction. Using epitope-specific antibodies, we identified a RyR tryptic fragment that specifically bound the intact immobilized RyR. Three overlapping RyR fragments encompassing this epitope, expressed using an in vitro mammalian expression system, were immunoprecipitated by RyR. To refine the binding regions, smaller RyR fragments were expressed as glutathione S-transferase (GST) fusion proteins, and their binding to RyR was monitored using a "sandwich" enzyme-linked immunosorbent assay. Three GST-RyR fusion proteins demonstrated specific binding, dependent upon ionic strength. Binding was greatest at 50-150 mm NaCl for two GST-RyR constructs, and a third GST-RyR construct demonstrated maximum binding between 150 and 450 mm NaCl. The binding at high NaCl concentration suggested involvement of a hydrophobic interaction. In silico analysis of secondary structure showed evidence of coil regions in two of these RyR fragment sequences, which might explain these data. In GST pull-down assays, these same three fragments captured RyR2, and two of them retained RyR1. These results identify a region at the center of the linear RyR (residues 2540-3207 of human RyR2) which is able to bind to the RyR oligomer. This region may constitute a specific subdomain participating in RyR-RyR interaction.

Localized effects of cAMP mediated by distinct routes of protein kinase A

More than 20% of the human genome encodes proteins involved in transmembrane and intracellular signaling pathways. The cAMP-protein kinase A (PKA) pathway is one of the most common and versatile signal pathways in eukaryotic cells and is involved in regulation of cellular functions in almost all tissues in mammals. Various extracellular signals converge on this signal pathway through ligand binding to G protein-coupled receptors, and the cAMP-PKA pathway is therefore tightly regulated at several levels to maintain specificity in the multitude of signal inputs. Ligand-induced changes in cAMP concentration vary in duration, amplitude, and extension into the cell, and cAMP microdomains are shaped by adenylyl cyclases that form cAMP as well as phosphodiesterases that degrade cAMP. Different PKA isozymes with distinct biochemical properties and cell-specific expression contribute to cell and organ specificity. A kinase anchoring proteins (AKAPs) target PKA to specific substrates and distinct subcellular compartments providing spatial and temporal specificity for mediation of biological effects channeled through the cAMP-PKA pathway. AKAPs also serve as scaffolding proteins that assemble PKA together with signal terminators such as phosphatases and cAMP-specific phosphodiesterases as well as components of other signaling pathways into multiprotein signaling complexes that serve as crossroads for different paths of cell signaling. Targeting of PKA and integration of a wide repertoire of proteins involved in signal transduction into complex signal networks further increase the specificity required for the precise regulation of numerous cellular and physiological processes.

An Excel-based model of Ca2+diffusion and fura 2 measurements in a spherical cell

We wrote a program that runs as a Microsoft Excel spreadsheet to calculate the diffusion of Ca2+in a spherical cell in the presence of a fixed Ca2+buffer and two diffusible Ca2+buffers, one of which is considered to be a fluorescent Ca2+indicator. We modeled Ca2+diffusion during and after Ca2+influx across the plasma membrane with parameters chosen to approximate amphibian sympathetic neurons, mammalian adrenal chromaffin cells, and rat dorsal root ganglion neurons. In each of these cell types, the model predicts that spatially averaged intracellular Ca2+activity ([Ca2+]avg) rises to a high peak and starts to decline promptly on the termination of Ca2+influx. We compared [Ca2+]avgwith predictions of ratiometric Ca2+measurements analyzed in two ways. Method 1 sums the fluorescence at each of the two excitation or emission wavelengths over the N compartments of the model, calculates the ratio of the summed signals, and converts this ratio to Ca2+([Ca2+]avg,M1). Method 2 sums the measured number of moles of Ca2+in each of the N compartments and divides by the volume of the cell ([Ca2+]avg,M2). [Ca2+]avg,M1peaks well after the termination of Ca2+influx at a value substantially less than [Ca2+]avgbecause the summed signals do not reflect the averaged free Ca2+if the signals come from compartments containing gradients in free Ca2+spanning nonlinear regions of the relationship between free Ca2+and the fluorescence signals. In contrast, [Ca2+]avg,M2follows [Ca2+]avgclosely.