PACEMAKER OSCILLATIONS IN HEART AND BRAIN: A KEY ROLE FOR HYPERPOLARIZATION-ACTIVATED CATION CHANNELS

Rhythmic activity of single cells or multicellular networks is a common feature of all organisms. The oscillatory activity is characterized by time intervals of several seconds up to many hours. Cellular rhythms govern the beating of the heart, the swimming behavior of sperm, cycles of sleep and wakefulness, breathing, and the release of hormones. Many neurons in the brain and cardiac cells are characterized by endogenous rhythmic activity, which relies on a complex interplay between several distinct ion channels. In particular, one type of ion channel plays a prominent role in the control of rhythmic electrical activity since it determines the frequency of the oscillations. The activity of the channels is thus setting the “pace” of the oscillations; therefore, these channels are often referred to as “pacemaker” channels. Despite their obvious important physiological function, it was not until recently that genes encoding pacemaker channels have been identified. Because both hyperpolarization and cyclic nucleotides are key elements that control their activity, pacemaker channels have now been designated hyperpolarization-activated and cyclic nucleotide–gated (HCN) channels. The molecular identification of the channels and the upcoming studies on their properties in heterologous systems will certainly enhance our understanding of “pacemaking” in physiological systems. This review gives a brief insight into the physiological importance of these channels and sums up what we have learned since the first cloning of genes succeeded (for recent reviews, see also Clapham 1998; Luüthi and McCormick 1998a; Biel et al. 1999; Ludwig, Zong, Hofmann, et al. 1999; Santoro and Tibbs 1999). (Chronobiology International, 17(4), 453–469, 2000)     

Respiratory pattern generator model using Ca++-induced Ca++ release in neurons shows both pacemaker and reciprocal network properties

There are two contradictory explanations for central respiratory rhythmogenesis. One suggests that respiratory rhythm emerges from interaction between inspiratory and expiratory neural semicenters that inhibit each other and thereby provide reciprocal rhythmic activity (Brown 1914). The other uses bursting pacemaker activity of individual neurons to produce the rhythm (Feldman and Cleland 1982). Hybrid models have been developed to reconcile these two seemingly conflicting mechanisms (Smith et al. 2000; Rybak et al. 2001). Here we report computer simulations that demonstrate a unified mechanism of the two types of oscillator. In the model, we use the interaction of Ca⁺⁺-dependent K⁺ channels (Mifflin et al. 1985) with Ca⁺⁺-induced Ca⁺⁺ release from intracellular stores (McPherson and Campbell 1993), which was recently revealed in neurons (Hernandez-Cruz et al. 1997; Mitra and Slaughter 2002a,b; Scornik et al. 2001). Our computations demonstrate that uncoupled neurons with these intracellular mechanisms show conditional pacemaker properties (Butera et al. 1999) when exposed to steady excitatory inputs. Adding weak inhibitory synapses (based on increased K⁺ conductivity) between two model neural pools surprisingly synchronizes the activity of both neural pools. As inhibitory synaptic connections between the two pools increase from zero to higher values, the model produces first dissociated pacemaker activity of individual neurons, then periodic synchronous bursts of all neurons (inspiratory and expiratory), and finally reciprocal rhythmic activity of the neural pools.     

The ups and downs of daily life: profiling circadian gene expression in Drosophila

Circadian rhythms are responsible for 24-hour oscillations in diverse biological processes. While the central genes governing circadian pacemaker rhythmicity have largely been identified, clock-controlled output molecules responsible for regulating rhythmic behaviors remain largely unknown. Two recent reports from McDonald and Rosbash(1) and Claridge-Chang et al.2 address this issue. By identifying a large number of genes whose mRNA levels show circadian oscillations, the reports provide important new information on the biology of circadian rhythm. In addition, the reports illustrate both the power and limitations of microarray-based methods for profiling mRNA expression on a genomic scale.     

Rhythmically firing (20–50 Hz) neurons in monkey primary somatosensory cortex: Activity patterns during initiation of vibratory-cued hand movements

The activity patterns of rhythmically firing neurons in monkey primary somatosensory cortex (SI) were studied during trained wrist movements that were performed in response to palmar vibration. Of 1,222 neurons extracellularly recorded in SI, 129 cells (11%) discharged rhythmically (at 30 Hz) during maintained wrist position. During the initiation of vibratory-cued movements, neuronal activity usually decreased at 25 ms after vibration onset followed by an additional decrease in activity at 60 ms prior to movement onset. Rhythmically firing neurons are not likely to be integrate-and-fire neurons because, during activity changes, their rhythmic firing pattern was disrupted rather than modulated. The activity pattern of rhythmically firing neurons was complimentary to that of quickly adapting SI neurons recorded during the performance of this task (Nelson et al., 1991). Moreover, disruptions of rhythmic activity of individual SI neurons were similar to those reported previously for local field potential (LFP) oscillations in sensorimotor cortex during trained movements (Sanes and Donoghue, 1993). However, rhythmic activity of SI neurons did not wax and wane like LFP oscillations (Murthy and Fetz, 1992; Sanes and Donoghue, 1993). It has been suggested that fast (20–50 Hz) cortical oscillations may be initiated by inhibitory interneurons (Cowan and Wilson, 1994; Llinas et al., 1991; Stern and Wilson, 1994). We suggest that rhythmically firing neurons may tonically inhibit quickly adapting neurons and release them from the inhibition at go-cue onsets and prior to voluntary movements. It is possible that rhythmically active neurons may evoke intermittent oscillations in other cortical neurons and thus regulate cortical population oscillations.     

Characterization of in vitro gutlike organ formed from mouse embryonic stem cells

Using an embryoid body (EB) culture system, we have made a functional organlike cluster: the "gut" from embryonic stem (ES) cells (ES gut). There are many types of ES clusters, because ES cells have a pluripotent ability to develop into a wide range of cell types. Before inducing specific differentiation by exogenously added factors, we characterized comprehensive physiological and morphological properties of ES guts. Each ES gut has a hemispherical (or cystic) structure and exhibits spontaneous contractions [mean frequency: 13.5 ± 8.8 cycles per min (cpm)]. A dense distribution of interstitial cells of Cajal (ICC) was identified by c-Kit immunoreactivity, and specific subcellular structures of ICC and smooth muscle cells were identified with electron microscopy. ICC frequently formed close contacts with the neighboring smooth muscle cells and occasionally formed gap junctions with other ICC. Widely propagating intracellular Ca²⁺ concentration oscillations were generated in the ES gut from the aggregates of c-Kit immunopositive cells. Plateau potentials, possibly pacemaker potentials in ICC, and electrical slow waves were recorded for the first time. These events were nifedipine insensitive, as in the mouse gut. Our present results indicate that the rhythmic pacemaker activity generated in ICC efficiently spreads to smooth muscle cells and drives spontaneous rhythmic contractions of the ES gut. The present characterization of physiological and morphological properties of ES gut paves the way for making appropriate models to investigate the origin of rhythmicity in the gut. intracellular calcium concentration oscillation; interstitial cells of Cajal; peristalsis     

Oscillations in calcium-cyclic AMP control loops form the basis of pacemaker activity and other high frequency biological rhythms.

In this paper theoretical and experimental evidence is presented which indicates that oscillations in internal calcium and cyclic AMP concentrations due to an instability in their common control loops are possible and indeed may be widespread. Further, it is demonstrated that fluctuations in various cellular properties, in particular membrane potential, are a direct consequence of these second messenger oscillations. Given the central importance of calcium and cyclic AMP to the regulation of metabolism, these oscillations would influence most metabolic processes especially rhythmic behaviour. We propose that these oscillations form the basis of several biological rhythms including, potential oscillations in cardiac pacemaker cells, neurones and insulin secreting β-cells, the minute rhythm in smooth muscle, cyclic AMP pulses in Dictyostelium, rhythmical cytoplasmic streaming in Physarum and transepitheliel potential oscillations in Calliphora salivary gland. This model makes possible an explanation of the frequency and amplitude effects of hormones.     

Flavonoid Regulation of HCN2 Channels

The hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels are pacemaker channels whose currents contribute to rhythmic activity in the heart and brain. HCN channels open in response to hyperpolarizing voltages, and the binding of cAMP to their cyclic nucleotide-binding domain (CNBD) facilitates channel opening. Here, we report that, like cAMP, the flavonoid fisetin potentiates HCN2 channel gating. Fisetin sped HCN2 activation and shifted the conductance-voltage relationship to more depolarizing potentials with a half-maximal effective concentration (EC₅₀) of 1.8 μm. When applied together, fisetin and cAMP regulated HCN2 gating in a nonadditive fashion. Fisetin did not potentiate HCN2 channels lacking their CNBD, and two independent fluorescence-based binding assays reported that fisetin bound to the purified CNBD. These data suggest that the CNBD mediates the fisetin potentiation of HCN2 channels. Moreover, binding assays suggest that fisetin and cAMP partially compete for binding to the CNBD. NMR experiments demonstrated that fisetin binds within the cAMP-binding pocket, interacting with some of the same residues as cAMP. Together, these data indicate that fisetin is a partial agonist for HCN2 channels.     

Connexin Genes in the Mouse and Human Genome

Gap junctions serve for direct intercellular communication by docking of two hemichannels in adjacent cells thereby forming conduits between the cytoplasmic compartments of adjacent cells. Connexin genes code for subunit proteins of gap junction channels and are members of large gene families in mammals. So far, 17 connexin (Cx) genes have been described and characterized in the murine genome. For most of them, orthologues in the human genome have been found (see White and Paul 1999; Manthey et al. 1999; Teubner et al. 2001; Söhl et al. 2001). We have recently performed searches for connexin genes in murine and human gene libraries available at EMBL/Heidelberg, NCBI and the Celera company that have increased the number of identified connexins to 19 in mouse and 20 in humans. For one mouse connexin gene and two human connexin genes we did not find orthologues in the other genome. Here we present a short overview on distinct connexin genes which we found in the mouse and human genome and which may include all members of this gene family, if no further connexin gene will be discovered in the remaining non-sequenced parts (about 1-5%) of the genomes.     

A single histidine residue determines the pH sensitivity of the pacemaker channel HCN2

Hyperpolarization-activated cyclic nucleotide-gated (HCN) cation channels control the rhythmic activity of heart and neuronal networks. The activation of these channels is regulated in a complex manner by hormones and neurotransmitters. In addition it was suggested that the channels may be controlled by the pH of the cytosol. Here we demonstrate that HCN2, a member of the HCN channel family, is directly modulated by the intracellular pH in the physiological range. Protons inhibit HCN2 channels by shifting the voltage dependence of channel activation to more negative voltages. By using site-directed mutagenesis, we have identified a single histidine residue (His-321) localized at the boundary between the voltage-sensing S4 helix and the cytoplasmic S4-S5 linker of the channel that is a major determinant of pH sensitivity. Replacement of His-321 by either arginine, glutamine, or glutamate results in channels that are no longer sensitive to shifts in intracellular pH. In contrast, cAMP-mediated modulation is completely intact in mutant channels indicating that His-321 is not involved in the molecular mechanism that controls modulation of HCN channel activity by cyclic nucleotides. Because His-321 is conserved in all four HCN channels known so far, regulation by intracellular pH is likely to constitute a general feature of both cardiac and neuronal pacemaker channels.     

Nature of rhythmic discharges in ventral spinal cord roots]

Rhythmic "locomotor discharges" recorded in the ventral spinal roots by Perret et al proved to increase during asphyxia and disappeared during apnea. Thus, rhythmic discharges in the ventral spinal roots depended on irradiation from the respiratory centre and could not confirm the fact of existence of a special "locomotor pacemaker".     

Connexin genes in the mouse and human genome

Gap junctions serve for direct intercellular communication by docking of two hemichannels in adjacent cells thereby forming conduits between the cytoplasmic compartments of adjacent cells. Connexin genes code for subunit proteins of gap junction channels and are members of large gene families in mammals. So far, 17 connexin (Cx) genes have been described and characterized in the murine genome. For most of them, orthologues in the human genome have been found (see White and Paul 1999; Manthey et al. 1999; Teubner et al. 2001; S?hl et al. 2001). We have recently performed searches for connexin genes in murine and human gene libraries available at EMBL/Heidelberg, NCBI and the Celera company that have increased the number of identified connexins to 19 in mouse and 20 in humans. For one mouse connexin gene and two human connexin genes we did not find orthologues in the other genome. Here we present a short overview on distinct connexin genes which we found in the mouse and human genome and which may include all members of this gene family, if no further connexin gene will be discovered in the remaining non-sequenced parts (about 1-5%) of the genomes.     

Molecular and Biochemical Characterization of AtPAP15, a Purple Acid Phosphatase with Phytase Activity,in Arabidopsis

Purple acid phosphatase (PAP) catalyzes the hydrolysis of phosphate monoesters and anhydrides to release phosphate within an acidic pH range. Among the 29 PAP-like proteins in Arabidopsis (Arabidopsis thaliana), AtPAP15 (At3g07130) displays a greater degree of amino acid identity with soybean (Glycine max; GmPHY) and tobacco (Nicotiana tabacum) PAP (NtPAP) with phytase activity than the other AtPAPs. In this study, transgenic Arabidopsis that expressed an AtPAP15 promoter∷β-glucuronidase (GUS) fusion protein showed that AtPAP15 expression was developmentally and temporally regulated, with strong GUS staining at the early stages of seedling growth and pollen germination. The expression was also organ/tissue specific, with strongest GUS staining in the vasculature, pollen grains, and roots. The recombinant AtPAP purified from transgenic tobacco exhibited broad substrate specificity with moderate phytase activity. AtPAP15 T-DNA insertion lines exhibited a lower phytase and phosphatase activity in seedling and germinating pollen and lower pollen germination rate compared with the wild type and their complementation lines. Therefore, AtPAP15 likely mobilizes phosphorus reserves in plants, particularly during seed and pollen germination. Since AtPAP15 is not expressed in the root hair or in the epidermal cells, it is unlikely to play any role in external phosphorus assimilation.At pH in the range of 4 to 7, purple acid phosphatases (PAPs) catalyze the hydrolysis of a wide range of activated phosphoric acid monoesters and diesters and anhydrides (Klabunde et al., 1996). They are distinguished from the other phosphatases by their insensitivity to l-(+) tartrate inhibition and therefore are also known as tartrate-resistant acid phosphatases. Their characteristic pink or purple color derives from a charge transfer transition between a Tyr residue and the “chromophoric” ferric ion in the binuclear Fe(III)-Me(II) center, where the metal (Me) is iron, zinc, or manganese (Schenk et al., 1999). PAP proteins are also characterized by seven conserved amino acid residues (shown in boldface) in the five conserved motifs DXG, GDXXY, GNH(D/E), VXXH, and GHXH, which are involved in the coordination of the dimetal nuclear center (Li et al., 2002).PAPs are widespread in mammals, fungi, bacteria, and plants. Interestingly, while only a few copies of PAP-like genes are present in mammalian and fungal genomes (Mullaney and Ullah, 2003; Flanagan et al., 2006), multiple copies are present in plant genomes (Schenk et al., 2000). For example, 29 PAP-like genes have been identified in the Arabidopsis (Arabidopsis thaliana) genome (Li et al., 2002). It is intriguing that so many PAP-like genes are required for plant metabolism; this diverse portfolio of PAP-like genes implies differential functions for them. Plant PAPs are generally considered to mediate phosphorus acquisition and redistribution based on their ability to hydrolyze phosphorus compounds (Cashikar et al., 1997; Bozzo et al., 2004; Lung et al., 2008). However, additional biological roles have been reported for some plant PAPs. For example, the PAPs AtACP5 (AtPAP17), SAP1, and SAP2 (del Pozo et al., 1999; Bozzo et al., 2002) display not only phosphatase but also peroxidase activity, suggesting their involvement in the removal of reactive oxygen compounds in plant organs. GmPAP3, isolated from salted-stressed soybean (Glycine max), reportedly mediates salt tolerance via NaCl and oxidative stress inductions but not by phosphorus starvation (Liao et al., 2003).Some PAP members can hydrolyze phytic acid (myoinositol hexakisphosphate [InsP6]) to inorganic phosphate and free or lower phosphoric esters of myoinositol. Since the major storage form of phosphorus in plant seeds and pollen grains is phytate, PAPs with phytase activity may play a role in seed and pollen germination. However, not all PAPs exhibit phytase activity. The first plant phytase PAP, GmPHY, was isolated from the cotyledon of germinating soybean seedlings (Hegeman and Grabau, 2001). A tobacco (Nicotiana tabacum) root PAP phytase was identified more recently that is likely involved in mobilizing external organic phosphorus in soil (Lung et al., 2008).Relatively little is known about the biochemical properties and physiological roles of the 29 PAP-like Arabidopsis genes (del Pozo et al., 1999; Veljanovski et al., 2006). An enzyme assay involving the glutathione S-transferase (GST)-AtPAP23 fusion protein revealed that the Arabidopsis PAP AtPAP23 exhibits phytase activity (Zhu et al., 2005). A GUS study showed that AtPAP23 is exclusively expressed in the flower of the Arabidopsis plant. In a recent report, a recombinant AtPAP15 expressed in Escherichia coli was also found to exhibit phytase activity; this PAP potentially modulates plant ascorbate synthesis through supply of myoinositol from the phytate hydrolysis reaction (Zhang et al., 2008). However, the possible physiological roles of AtPAP15 in phosphorus mobilization have not been examined.In this study, AtPAP15 expressed in a plant (tobacco) system was biochemically characterized, and its temporal and spatial expression patterns in Arabidopsis were examined. The physiological roles of AtPAP15 in phosphorus mobilization were also delineated.     

Different Xanthines Cause Membrane Potential Oscillations in a Unicellular Green Alga Pointing to a Ryanodine/cADPR Receptor Ca2+ Channel

In the unicellular green alga Eremosphaera viridis caffeineinduces oscillations of cytosolic Ca²⁺ which cause membranepotential oscillations. Application of the caffeine analoguesisocaffeine, theophylline, and isotheophylline resulted in membranepotential oscillations with a structure-activity relationshipcomparable to isolated ryanodine/cyclic ADPribose (cADPR) receptorCa²⁺ channels from animal cells. (Received November 24, 1998; Accepted February 1, 1999)     

Rhythmic cortical neurons increase their oscillations and sculpt basal ganglia signaling during motor learning

The function and modulation of neural circuits underlying motor skill may involve rhythmic oscillations (Feller, 1999 ; Marder and Goaillard, 2006 ; Churchland et al., 2012 ). In the proposed pattern generator for birdsong, the cortical nucleus HVC, the frequency and power of oscillatory bursting during singing increases with development (Crandall et al., 2007 ; Day et al., 2009 ). We examined the maturation of cellular activity patterns that underlie these changes. Single unit ensemble recording combined with antidromic identification (Day et al., 2011 ) was used to study network development in anesthetized zebra finches. Autocovariance quantified oscillations within single units. A subset of neurons oscillated in the theta/alpha/mu/beta range (8–20 Hz), with greater power in adults compared to juveniles. Across the network, the normalized oscillatory power in the 8–20 Hz range was greater in adults than juveniles. In addition, the correlated activity between rhythmic neuron pairs increased with development. We next examined the functional impact of the oscillators on the output neurons of HVC. We found that the firing of oscillatory neurons negatively correlated with the activity of cortico‐basal ganglia neurons (HVC_Xs), which project to Area X (the song basal ganglia). If groups of oscillators work together to tonically inhibit and precisely control the spike timing of adult HVC_Xs with coordinated release from inhibition, then the activity of HVC_Xs in juveniles should be decreased relative to adults due to uncorrelated, tonic inhibition. Consistent with this hypothesis, HVC_Xs had lower activity in juveniles. These data reveal network changes that shape cortical‐to‐basal ganglia signaling during motor learning. © 2013 Wiley Periodicals, Inc. Develop Neurobiol 73: 754–768, 2013     

The end effector of circadian heart rate variation: the sinoatrial node pacemaker cell

Cardiovascular function is regulated by the rhythmicity of circadian, infradian and ultradian clocks. Specific time scales of different cell types drive their functions: circadian gene regulation at hours scale, activation-inactivation cycles of ion channels at millisecond scales, the heart''s beating rate at hundreds of millisecond scales, and low frequency autonomic signaling at cycles of tens of seconds. Heart rate and rhythm are modulated by a hierarchical clock system: autonomic signaling from the brain releases neurotransmitters from the vagus and sympathetic nerves to the heart’s pacemaker cells and activate receptors on the cell. These receptors activating ultradian clock functions embedded within pacemaker cells include sarcoplasmic reticulum rhythmic spontaneous Ca²⁺ cycling, rhythmic ion channel current activation and inactivation, and rhythmic oscillatory mitochondria ATP production. Here we summarize the evidence that intrinsic pacemaker cell mechanisms are the end effector of the hierarchical brain-heart circadian clock system. [BMB Reports 2015; 48(12): 677-684]     

The human gene coding for HCN2, a pacemaker channel of the heart.

Hyperpolarization-activated, cyclic nucleotide-gated (HCN) channels, underlying 'pacemaker' currents (I(f)/Ih), are involved in pacemaker activity of cardiac sinoatrial node myocytes and central neurons. Several cDNAs deriving from four different genes were recently identified which code for channels characterized by six transmembrane domains and a cyclic nucleotide binding domain. We report here the identification of the human HCN2 gene and show that its functional expression in a human kidney cell line generates a current with properties similar to the native pacemaker f-channel of the heart. The hHCN2 gene maps to the telomeric region of chromosome 19, band p13.3. This is the first identification of a genetic locus coding for an HCN channel.     

Pacemaker neurons and neuronal networks: an integrative view

Rhythmically active neuronal networks give rise to rhythmic motor activities but also to seemingly non-rhythmic behaviors such as sleep, arousal, addiction, memory and cognition. Many of these networks contain pacemaker neurons. The ability of these neurons to generate bursts of activity intrinsically lies in voltage- and time-dependent ion fluxes resulting from a dynamic interplay among ion channels, second messenger pathways and intracellular Ca2+ concentrations, and is influenced by neuromodulators and synaptic inputs. This complex intrinsic and extrinsic modulation of pacemaker activity exerts a dynamic effect on network activity. The nonlinearity of bursting activity might enable pacemaker neurons to facilitate the onset of excitatory states or to synchronize neuronal ensembles--an interactive process that is intimately regulated by synaptic and modulatory processes.     

An Optimal Frequency in Ca2+ Oscillations for Stomatal Closure Is an Emergent Property of Ion Transport in Guard Cells

Oscillations in cytosolic-free Ca²⁺ concentration ([Ca2+]_i) have been proposed to encode information that controls stomatal closure. [Ca2+]_i oscillations with a period near 10 min were previously shown to be optimal for stomatal closure in Arabidopsis (Arabidopsis thaliana), but the studies offered no insight into their origins or mechanisms of encoding to validate a role in signaling. We have used a proven systems modeling platform to investigate these [Ca2+]_i oscillations and analyze their origins in guard cell homeostasis and membrane transport. The model faithfully reproduced differences in stomatal closure as a function of oscillation frequency with an optimum period near 10 min under standard conditions. Analysis showed that this optimum was one of a range of frequencies that accelerated closure, each arising from a balance of transport and the prevailing ion gradients across the plasma membrane and tonoplast. These interactions emerge from the experimentally derived kinetics encoded in the model for each of the relevant transporters, without the need of any additional signaling component. The resulting frequencies are of sufficient duration to permit substantial changes in [Ca2+]_i and, with the accompanying oscillations in voltage, drive the K⁺ and anion efflux for stomatal closure. Thus, the frequency optima arise from emergent interactions of transport across the membrane system of the guard cell. Rather than encoding information for ion flux, these oscillations are a by-product of the transport activities that determine stomatal aperture.Stomata in the leaf epidermis are the main pathway both for CO₂ entry for photosynthesis and for foliar water loss by transpiration. Guard cells surround the stomatal pore and regulate the aperture, balancing the often conflicting demands for CO₂ and water conservation. Guard cells open and close the pore by expanding and contracting through the uptake and loss, respectively, of osmotic solutes, notably of K⁺, Cl⁻, and malate²⁻ (Mal²⁻; Pandey et al., 2007; Kim et al., 2010; Roelfsema and Hedrich, 2010; Lawson and Blatt, 2014). These transport processes comprise the final effectors of a regulatory network that coordinates transport across the plasma membrane and tonoplast, and maintains the homeostasis of the guard cell. A number of well-defined signals—including light, CO₂, drought and the water stress hormone abscisic acid (ABA)—act on this network, altering transport, solute content, turgor and cell volume, and ultimately stomatal aperture.Much research has focused on stomatal closure, underscoring both Ca²⁺-independent and Ca²⁺-dependent signaling. Of the latter, elevated cytosolic-free Ca²⁺ concentration ([Ca2+]_i) inactivates inward-rectifying K⁺ channels (I_K,in) to prevent K⁺ uptake and activates Cl⁻ (anion) channels (I_Cl) at the plasma membrane to depolarize the membrane and engage K⁺ efflux through outward-rectifying K⁺ channels (I_K,out; Keller et al., 1989; Blatt et al., 1990; Thiel et al., 1992; Lemtiri-Chlieh and MacRobbie, 1994). ABA, and most likely CO₂ (Kim et al., 2010), elevate [Ca2+]_i by facilitating Ca²⁺ entry at the plasma membrane to trigger Ca²⁺ release from endomembrane stores, a process often described as Ca²⁺-induced Ca²⁺ release (Grabov and Blatt, 1998, 1999). The hormone promotes Ca²⁺ influx by activating Ca²⁺ channels (I_Ca) at the plasma membrane, even in isolated membrane patches (Hamilton et al., 2000, 2001), which is linked to reactive oxygen species (Kwak et al., 2003; Wang et al., 2013). In parallel, cADP-ribose and nitric oxide promote endomembrane Ca²⁺ release and [Ca2+]_i elevation (Leckie et al., 1998; Neill et al., 2002; Garcia-Mata et al., 2003; Blatt et al., 2007). Best estimates indicate that endomembrane release accounts for more than 95% of the Ca²⁺ entering the cytosol to raise [Ca2+]_i (Chen et al., 2012; Wang et al., 2012).One feature of stomatal response to ABA, and indeed to a range of stimuli both hormonal as well as external, is its capacity for oscillations both in membrane voltage and [Ca2+]_i. Guard cell [Ca2+]_i at rest is typically around 100 to 200 nm, as it is in virtually all living cells. In response to ABA, [Ca2+]_i can rise above 1 μm—and locally, most likely above 10 μm—often in cyclic transients of tens of seconds to several minutes’ duration in association with oscillations in voltage and stomatal closure (Gradmann et al., 1993; McAinsh et al., 1995; Webb et al., 1996; Grabov and Blatt, 1998, 1999; Staxen et al., 1999; Allen et al., 2001). In principle, cycling in voltage and [Ca2+]_i arises as closure is accelerated with a controlled release of K⁺, Cl⁻, and Mal²⁻ from the guard cell and is subject to extracellular ion concentrations (Gradmann et al., 1993; Chen et al., 2012). However, it has been proposed that these, and similar oscillations in a variety of plant cell models, serve as physiological signals in their own right (McAinsh et al., 1995; Ehrhardt et al., 1996; Taylor et al., 1996). In support of such a signaling role, experiments designed to impose [Ca2+]_i (and voltage) oscillations in guard cells have yielded an optimal frequency for closure with a period near 10 min (Allen et al., 2001). Nonetheless, the studies offer no mechanistic explanation for this optimum that could validate a causal role in signaling, and none has been forthcoming since. Here we address questions of how such optimal frequencies in [Ca2+]_i oscillation arise and their relevance for stomatal closure, using quantitative systems analysis of guard cell transport and homeostasis. Our findings indicate that oscillations in voltage and [Ca2+]_i, and their optima associated with stomatal closure, are most simply explained as emerging from the interactions between ion transporters that drive stomatal closure. Thus, we conclude that these oscillations do not control, but are a by-product of the transport that determines stomatal aperture.     

Neural dynamics during anoxia and the "wave of death"

Recent experiments in rats have shown the occurrence of a high amplitude slow brain wave in the EEG approximately 1 minute after decapitation, with a duration of 5-15 s (van Rijn et al, PLoS One 6, e16514, 2011) that was presumed to signify the death of brain neurons. We present a computational model of a single neuron and its intra- and extracellular ion concentrations, which shows the physiological mechanism for this observation. The wave is caused by membrane potential oscillations, that occur after the cessation of activity of the sodium-potassium pumps has lead to an excess of extracellular potassium. These oscillations can be described by the Hodgkin-Huxley equations for the sodium and potassium channels, and result in a sudden change in mean membrane voltage. In combination with a high-pass filter, this sudden depolarization leads to a wave in the EEG. We discuss that this process is not necessarily irreversible.