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Which ionic channels of Pacemakers can work in very low frequencies in extrasystole?

Which ionic channels of Pacemakers can work in very low frequencies in extrasystole?


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At frequency 0-3 Hz. Like computer processors which can work at low frequencies and controlling under- and overvoltage.

Normal most significant channels are Ca2+ and K+ that are changing. However, I am not convinced that they can work with such a low frequencies. There must be some other channels that are triggering the extrasystole on.

Which ionic channels of Pacemakers can work in 2-3 Hz triggering extrasystole?


I think none. It is so specific frequency range that the possible sources are

  • autonomic nervous system and
  • some reflex arch.

Also, the frequency is logically low with autonomic triggering. My conjecture is that sympaticus starts up extrasystoles. I think it must go through some reflex arch to be so specific.


Ionic Channel Function in Action Potential Generation: Current Perspective

Over 50 years ago, Hodgkin and Huxley laid down the foundations of our current understanding of ionic channels. An impressive progress has been made during the following years that culminated in the revelation of the details of potassium channel structure. Nevertheless, even today, we cannot separate well currents recorded in central mammalian neurons. Many modern concepts about the function of sodium and potassium currents are based on experiments performed in nonmammalian cells. The recent recognition of the fast delayed rectifier current indicates that we need to reevaluate the biophysical role of sodium and potassium currents. This review will consider high quality voltage clamp data obtained from the soma of central mammalian neurons in the view of our current knowledge about proteins forming ionic channels. Fast sodium currents and three types of outward potassium currents, the delayed rectifier, the subthreshold A-type, and the D-type potassium currents, are discussed here. An updated current classification with biophysical role of each current subtype is provided. This review shows that details of kinetics of both sodium and outward potassium currents differ significantly from the classical descriptions and these differences may be of functional significance.

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Abstract

Electric pacemaker activity drives peristaltic and segmental contractions in the gastrointestinal tract. Interstitial cells of Cajal (ICC) are responsible for spontaneous pacemaker activity. ICC remain rhythmic in culture and generate voltage-independent inward currents via a nonselective cation conductance. Ca 2+ release from endoplasmic reticulum and uptake by mitochondria initiates pacemaker currents. This novel mechanism provides the basis for electric rhythmicity in gastrointestinal muscles.

The rhythmoneuromuscular apparatus of the gastrointestinal (GI) tract is more complicated than a syncytium of smooth muscle cells innervated by motor neurons. For many years, morphological studies of the tunica muscularis noted the presence of additional specialized cells that are commonly referred to as interstitial cells of Cajal (ICC). ICC were frequently found in close association with nerves, and in many cases they were described as “intercalated” between nerve terminals and smooth muscle cells (2). ICC were also observed to form gap junction connections with each other and with neighboring smooth muscle cells. Thus the electric syncytium of the tunica muscularis of the GI tract is composed of at least two cell types. Morphology also suggested that the innervation of the smooth muscle might be indirect and mainly occur via synapse-like structures between nerves and ICC. These studies were interesting and provocative, but it was only possible to speculate about the function of ICC from morphological analyses.

Intensive work on animal models (primarily mouse, guinea pig, and dog) during the past decade has provided physiological evidence that ICC provide the pacemaker activity typical of phasic GI muscles of the stomach, small bowel, and colon (i.e., electric slow waves cf. Ref. 9). Pacemaker ICC are generally found in the region of the myenteric plexus in the space between the circular and longitudinal muscle layers. We refer to the cells in the myenteric region as IC-MY. ICC along the submucosal surface of the circular muscle layer in the colon (IC-SM) are also able to generate pacemaker activity, particularly in larger animals such as the dog. IC-MY and IC-SM form extensive networks within pacemaker regions. These cells also extend into the bulk of the muscle layers in the septa that divide bundles of smooth muscle cells. Thus pacemaker activity is not necessarily confined to the myenteric and submucosal pacemaker regions, but these pacemakers are dominant in intact muscles. Fine processes of pacemaker ICC interconnect via gap junctions, and electric connections are also made with neighboring smooth muscle cells. Thus electric events occurring in ICC are capable of conducting to smooth muscle cells. Simultaneous recordings of electric activity from IC-MY and nearby smooth muscle cells have demonstrated that electric activity occurs first in IC-MY and then initiates electric responses in the smooth muscle cells (3). Connections between ICC are necessary for regenerative propagation of slow waves, and extension of ICC networks into the septa between muscle bundles may provide propagation pathways for transmission of slow waves through the tunica muscularis (perhaps analogous to the Purkinje fibers in the heart). Networks of IC-MY and some of the ultrastructural features of IC-MY are shown in Fig. 1 .

FIGURE 1. Morphological features of pacemaker interstitial cells of Cajal (ICC) and ICC involved in neurotransmission. A: network of myenteric ICC (IC-MY) in murine gastric antrum immunostained with an anti-Kit antibody. Multiple processes extend from cell bodies (arrows). B: low-power electron micrograph (EM) showing position of IC-MY within the region of the myenteric plexus. A large nerve trunk (mg) is likely to be an interganglionic connective of the myenteric plexus. CM, circular muscle layer arrow, ICC running adjacent to the CM. A large number of mitochondrial profiles fill the imaged portion of the IC-MY. C: higher-power EM of a portion of the IC-MY in B. Note large number of mitochondrial (m) profiles and very close associations between mitochondria and the plasma membrane. Note also the sarcoplasmic reticulum (SR arrowheads) and the frequent close contacts between SR and mitochondria. D: pacemaker ICC in culture double labeled with Kit antibody (red) and MitoTracker green FM (green). Pixels with both labels appear yellow. Mitochondria are extensively distributed throughout cell bodies (arrows) and processes (arrowheads) of pacemaker ICC. E: Intramuscular ICC (IC-IM) of murine gastric fundus double labeled with antibodies to Kit (green arrows) and vesicular acetylcholine transporter (red arrowheads). Note the close association between cholinergic motor neurons and IC-IM. A single neural process innervates multiple IC-IM (*). F: montage EM of an IC-IM and its relationship to a nerve terminal that contains nitric oxide synthase (NOS *). Note the very close synapse-like contact between NOS neurons and the IC-IM (arrow). Also shown is a gap junction between the IC-IM and a neighboring smooth muscle cell (arrowhead). G: higher-power EM detailing gap junction connection between IC-IM in F and smooth muscle cell. H: higher-power image of synaptic-like structure between the IC-IM and a NOS-containing motor nerve terminal (arrow) shown in F. I: similar synaptic-like connection (arrow) between an IC-IM and a motor neuron containing vesicular acetylcholine transporter-like immunoreactivity (*). F—I are reproduced from Ref. 14.

Other types of ICC can also be found in GI muscles. ICC are intermingled with the fibers of the circular and longitudinal muscle layers in the esophagus, stomach, colon, and sphincters. We have called these intramuscular ICC (IC-IM). IC-IM are extensively and closely associated with nerve fibers of the enteric nervous system (1) and form very close (<20 nm) synapse-like connections with varicose nerve terminals of excitatory and inhibitory motor neurons. Cells with similar characteristics, called IC-DMP, are likely to be a specialized type of IC-IM and are found in the region of the deep muscular plexus in the small intestine. IC-IM and associations with enteric neurons are illustrated in Fig. 1 , E–I.

IC-IM and IC-DMP are functionally innervated and appear to mediate a significant part of the motor input from the enteric nervous system. In mutant mice lacking IC-IM, field stimulation of intrinsic neurons in the stomach resulted in greatly reduced postjunctional responses to cholinergic and nitrergic nerve stimulation (1, 14). Although the role of ICC in neurotransmission is extremely important in GI motility, this short review will focus on new findings about how ICC generate electric rhythmicity. IC-IM and IC-DMP may or may not have the capability of generating pacemaker-like currents, but these cells play an extremely important role in regulating the smooth muscle response to pacemaker activity.


Abstract : Interaction between a membrane oscillator generated by voltage-dependent ion channels and an intracellular calcium signal oscillator was present in the earliest models (1984 to 1985) using representations of the sarcoplasmic reticulum. Oscillatory release of calcium is inherent in the calcium-induced calcium release process. Those historical results fully support the synthesis proposed in the articles in this review series. The oscillator mechanisms do not primarily compete with each they entrain each other. However, there is some asymmetry: the membrane oscillator can continue indefinitely in the absence of the calcium oscillator. The reverse seems to be true only in pathological conditions. Studies from tissue-level work and on the development of the heart also provide valuable insights into the integrative action of the cardiac pacemaker.

The earliest models of cardiac rhythm, beginning with that of Noble, 1 were restricted to interactions between surface membrane ion channels. The first cardiac cell model to incorporate the intracellular calcium signaling system involved in excitation-contraction coupling was that of DiFrancesco and Noble. 2 That model was developed for sheep Purkinje fibers, and it was the first to predict a large role for sodium/calcium exchange current during the action potential. In fact it identified the slower components of inward current that had previously been attributed to calcium channel current as being attributable instead to the exchanger. Pacemaker activity in that model was attributed almost entirely to the slow onset of the nonspecific cation current, if, activated by hyperpolarization. The exchange current was not predicted to play any role in pacemaker rhythm in that case.

However, the DiFrancesco-Noble Purkinje fiber model was almost immediately developed to create the first mathematical model to reproduce voltage waveforms similar to those observed in rabbit sinoatrial node (SAN) cells. 3 It was also developed later to create the first models of rabbit atrial cells. 4,5 For the intracellular calcium signaling mechanisms, the 1980s models were based on the work of Fabiato on calcium-induced calcium release. 6

The experimental basis of the SAN model was the work of Brown et al, 7,8 which revealed the presence of very slow components of inward current similar to that predicted for the sodium/calcium exchange current during the action potential. In fact, the modeling gave confidence that these experimental recordings were not voltage-clamp artifacts.

One of the collaborators in that experimental work, Junko Kimura, later collaborated with Akinori Noma to measure the voltage and ion concentration dependence of the sodium/calcium exchange current under highly controlled conditions. 9,10 The results were in remarkable agreement with the equations used in the models. All subsequent developments of models of calcium signaling and of sodium/calcium exchange in the heart can be seen to derive from the models of the 1980s.

Among the experimental results on the rabbit SAN, there were 2 important findings that relate to the present controversies. The first was that, when investigating inward currents during voltage-clamp depolarizations, 2 clear components were often observed. Based on the modeling work, the first of these was attributed to activation of the L-type calcium current (called Isi in early work), whereas the second, much slower, component was attributed to activation of sodium/calcium exchange during calcium release following the onset of the action potential.

The computer model correctly reproduced these 2 components (see Figure 9 in Brown et al 8 ). Those original computations were done using OXSOFT HEART. We have repeated the computations for this article using the publicly available software COR (www.cor.physiol.ox.ac.uk) and the CellML encoded version of the model downloaded from the CellML model repository (www.cellml.org). The results are shown in Figure 1. They are very similar to the original figure but extend it by revealing the separate contributions of ICaL and INaCa. Later experimental work 11 fully confirmed the predictions of the models regarding sodium/calcium exchange current during the action potential.

Figure 1. Sodium/calcium exchange currents in the DiFrancesco-Noble (1985) model. 2 Top (A), Experimental results obtained by Kimura et al 1987 using guinea pig ventricular cells. 10 Exchange current in the inward mode (corresponding to sodium influx and calcium efflux) as a function of membrane potential at different concentrations of extracellular sodium ions. Top (B), Corresponding curves computed from the equations used for sodium/calcium exchange current in the model (note that these results were obtained before the experimental ones). Bottom, Variations of ionic currents (IK, ICa,f [now ICaL], If, and INaCa) during computed action and pacemaker potentials. Note the substantial inward exchange current predicted during the plateau of the action potential. This computation was performed for this article using COR and is exactly the same as that published in 1985.

Having established the performance of those models so far as the action potential is concerned, we now turn to the pacemaker depolarization. This is the critical question. During voltage-clamp depolarizations the sodium/calcium exchange current, reflecting the time course of the intracellular calcium transient invariably followed the onset and inactivation of the calcium channel current. By contrast, this time relationship was often reversed during the pacemaker depolarization. Figure 2 shows the experimental protocol used to reveal this in the 1984 work. The natural pacemaker depolarization was interrupted at various times by clamping the voltage to that achieved at the time of onset of the clamp. If this time was late enough (roughly, during the last third of the pacemaker depolarization), a slow inward current was recorded whose time course resembled the slow component recorded during standard voltage-clamp depolarizations. However, there was no visible preceding activation of the calcium current. This was interpreted to indicate the possibility that calcium release during sinus node pacemaker activity could precede activation of the calcium current, as observed by Lakatta et al. 12 Figure 2 shows new computations of this phenomenon using COR and the downloaded CellML file for the 1984 SAN model.

Figure 2. Calcium release preceding activation of ICaL. Top left, One of the experimental recordings made on rabbit sinoatrial node by Brown et al (Figure 9 in the article, 8 trace at −44 mV). The membrane potential was allowed to change spontaneously during an action potential and for most of the subsequent pacemaker depolarization. Near the end of this depolarization, but clearly before the upstroke of the action potential, the membrane potential was clamped at the potential reached. A slow transient inward current was recorded, the onset of which is much slower than that of the L-type calcium current. It requires ≈100 ms to reach its peak. Bottom left, Voltage protocol used to repeat the 1984 simulation of these results using the SAN model developed from the DiFrancesco-Noble model. Vertical scale is in millivolts. Horizontal scale is in seconds. Top right, Computed net ionic currents corresponding to the three levels of the clamp potential in the bottom left protocol. Clamping at the middle of the pacemaker depolarization simply generates a smooth development of net inward current corresponding to decay of IK and onset of If. The middle curve (interrupted) generates a slow transient inward current similar to that in the experimental trace (top left). The dotted curve generates a double peak as the L-type calcium current starts to be activated. Vertical scale is in nA horizontal scale in seconds. Bottom right, Computed variations in the sodium/calcium exchange current during the three voltage protocols.

The essence of the Lakatta hypothesis was therefore present in the very earliest simulations of calcium signaling in cardiac cells.

Why did Brown et al not attribute the pacemaker depolarization itself to this mechanism? The main reason was that, although slow inward ionic currents of this kind were often recorded in the experiments, they nearly always died out after 1 or 2 oscillations. The maintenance of the calcium signal oscillator was not therefore independent of the voltage-dependent ionic current oscillator.

Table 2. Non-standard Abbreviations and Acronyms

How Do the Different Oscillators Interact?

To investigate the contribution of the various ion currents, we compared the simulation results of the 6 mathematical models of SAN cells available in the CellML repository: Demir et al, 12a Dokos et al, 12b Kurata et al, 12c Maltsev and Lakatta, 12d Noble and Noble, 12e and Zhang et al. 12f For clarity of the figures, we show only the results of the latest 4 models in the figures but include the results of all models in the text.

Figure 3 shows the membrane potential, the intracellular calcium concentration and the inward currents the models have in common: Ca 2+ L-type current (ICaL), Na + /Ca 2+ exchanger (INaCa), funny current (If), and background sodium current (IbNa).

Figure 3. Overview of models, oscillations, and underlying currents. Note that If(solid line in bottom graphs) is always the smallest of the inward currents (ICaL, INaCa, IbNa, and If).

The ICaL shows the largest amplitude of the currents in all the models, and the maximum INaCa current is larger than If and IbNa, except in the Zhang model, which has a constant intracellular calcium concentration for model simplification. If is in all models smaller than the IbNa.

When we now block the various currents, one at a time (see Figure 4), what happens to the membrane potential (and calcium) oscillations in the SAN cell models? All the models (Demir, Zhang, Maltsev, Dokos, Noble, Kurata) agree on the importance of ICaL: without activation of this calcium current, the SAN oscillations do not occur. The models are in accord with the experimental observation that without calcium uptake or release from the sarcoplasmic reticulum (SR) the oscillations do not stop (and a 2% increase in background sodium current leads to no missing beats in the Maltsev model). In addition, complete block of If does not stop the oscillations in any of the models.

Figure 4. The voltage traces when one or several model currents are fully blocked at t=2 seconds. The rows denote block of ICaL and ICaT, of INaCa, of background currents (see below), of If, and of Iup. The missing beats in the Maltsev model at block of SERCA disappear when IbNa is increased by 2%. “Background currents” blocked in respective models: Maltsev (IbCa and IbNa), Kurata (IbNa and IstNa), Zhang (IbCa and IbNa), Dokos (IbNa and INa).

So, is only ICaL necessary for the oscillations? What is actually causing the oscillations in the models? In all models, there exist a number of background or sustained inward currents (IbNa, IbCa, Ist), and setting them to zero abolishes or diminishes the oscillations in 4 of the models (Kurata, Maltsev, Noble, Demir) does that mean that the background currents might be more important than If and intracellular Ca 2+ cycling? Clearly, we are dealing here with a multifactorial system in which even ionic currents that show no intrinsic dynamic properties (which is the definition of a “background” current) or currents that have yet to be characterized completely (such as Ist) play an important quantitative role. Ist has been first characterized by Guo et al (1995) as sustained Na + inward current, which is active during the depolarization phase, but because of unavailability of a specific blocker, it has been impossible to investigate the importance of this current in whole SAN cells.

The removal of INaCa abolishes the oscillations as well (in all models but the Zhang model which has fixed ion concentrations). INaCa is most of the time an inward current extruding Ca 2+ from the cell (see Figure 4). When additionally setting the SR Ca 2+ concentration to constant the block of INaCa does only change the frequency, but does not abolish the oscillations completely. Therefore, it is the resulting Ca 2+ overload with full INaCa block that leads to the termination of the oscillations. As there exist also other pumps and exchangers in SAN cells to extrude Ca 2+ from the cell (avoiding Ca 2+ overload), which are not present in the mathematical models it is unclear whether complete block of INaCa would abolish the oscillations in real cells.

Sensitivity analysis of the SAN period with respect to block of ion currents and pumps was performed at steady state of the model (300 seconds after the change). The Table shows that the models consistently show an increase in period of 0.7 to 1.87%, 0.77 to 4.82%, 0.14 to 0.83%, and 0.83 to 1.34% with a 10% block of ICaT, IbNa, If, and Ist, respectively. Currents and pumps related to the intracellular calcium system show rather diverse results for the different models (block of ICaL, INaCa, and Iup led to a decrease in period in Demir versus and increase in Maltsev). We assume that this lack of consistency is attributable to the differences in calcium handling in the models.

Table 1. Sensitivity Analysis of the SAN Period

In general, the largest sensitivities can be observed for IbNa/Ist and second comes ICaT (ignoring the inconsistent values for ICaL). The Maltsev model provides an exception, with Iup inducing the largest change in period (followed by IbNa and ICaT).

A bifurcation analysis would be able to provide further information on the dynamic behavior of the models but would be beyond the scope of this article. Note also that all detailed results have to be interpreted with caution because the models have not been tuned and built for these kind of investigations, ie, the analysis could be out of the predictive range of the models.

The models would suggest 3 important features of concerted action leading to and maintaining the oscillations in the SAN cells: the slow depolarization phase via inward currents (If, Ist, [IbNa]), activation of the inward calcium currents (ICaL, ICaT), extrusion of calcium (INaCa, IpCa?). The importance of SR release could lie in the stabilization of the oscillations across frequencies as indicated by Maltsev and Lakatta, 12d but in their article, they also show that the SR release is not actually driving the oscillations (see Figure 5C in their article).

Insights From Tissue Studies and From Development of the Heart

The studies on which we have commented so far focus at the level of ion channels and the integration of their activity at the level of single cells. The other contributions to this issue make valuable contributions to the debate at the tissue level, particularly concerning the use of imaging with voltage- or calcium-sensitive indicators 13 and the insights that come from studying the development of pacemaker tissues. 14

These studies show that integrative physiology of pacemaker activity does not end with analysis of cellular activity. In fact, it has been evident since the first electrophysiological mapping work that the sinus node acts as more than just a few thousand cells beating in synchrony. Depending on the precise physiological conditions, the apparent origin of pacemaker activity can shift from one region of the node to another. 15–17 We refer to “apparent origin” because it would be an oversimplification to suppose that the area leading the depolarization uniquely determines what happens (see also elsewhere 18 ). Electric current flows between any two connected cells that are at different potentials, and this current must influence the leading cells (by slowing them down) as much as they influence the follower cells (by speeding them up). The earliest computations of cell-to-cell interaction in the sinus node using parallel computers showed that even very low connectivity (just a few connexin channels between each cell) could synchronize cells with inherently different rhythms. 19–21 These computations also revealed that the cells with an intrinsically rapid rhythm, located at the periphery of the node, and which would therefore ‘lead’ the depolarization in an isolated node, become the follower cells when the node is connected to the atrium. Boyett and colleagues showed experimentally and computationally 22 that isolating the sinus node alters the direction of propagation, with the leading cells shifting from the center to the periphery, and more recent work from Boyett and colleagues has further emphasized how the architecture of the node influences its function. 23 Anatomy and physiology necessarily interact at the tissue level. A valuable set of insights from the debate between Efimov and Federov versus Joung and Lin in Circulation Research 13 is that the origin of the impulse is multicentric and that single cells and the intact node react differently to drugs and to genetic changes.

Does work at the tissue level shed any light on the relative roles of membrane and calcium-generated oscillations? This is the central focus of the debate between Efimov and Federov versus Joung and Lin. In principle, using voltage-sensitive markers to search for multiple waveforms could make an important contribution. And indeed, the voltage-sensitive dyes do give results that differ from microelectrode recordings. Efimov and Federov attribute this to the fact that the dyes record from an extended region that can include cells and tissues of different types, and so necessarily give composite results. Against this, Joung and Lin point to the fact that confocal calcium imaging can sometimes show calcium changes leading voltage changes toward the end of the pacemaker depolarization, particularly in the presence of isoproterenol. Dissecting out such a complicated set of interrelationships will be difficult. We concur with the remark that future work will “require close collaboration between the mathematical modelers and experimenters to dissect the role of the individual components” 13 but would add that “dissect” already biases the analysis. In nonlinear interactive systems, attributing relative roles to different components may be misleading. It is the “integrative” function that matters. As also noted in that study, the different mechanisms work synergistically. Because of nonlinearity, this necessarily means that attribution of the quantitative contributions of individual components depends on the physiological and pathological context. This context includes the fact that information flow between the genome and the phenotype is not one way. The phenotype is not a static product of its genes (reviewed elsewhere 24,25 ). There is feedback downward from the phenotype to control gene expression. Good examples are available in this review series, including, notably, the downregulation of 2 important pacemaker currents, If and IKs, during atrial tachyarrhythmias. Activity in the atrium can therefore remodel the gene expression profile in the sinus node.

Remodeling of gene expression naturally takes us on to consider the other major contribution to this focused issue of the journal because, as Christoffels et al 14 show, the development of the heart depends on suppression of gene expression as the embryo develops into the adult. All cardiac myocytes in the early embryo show pacemaker rhythm. The change to the adult forms occurs through repression of the gene expression patterns that develop to enable adult working myocardial cells to differentiate. As a consequence, the adult pacemaker cells resemble those of the early embryo. The identification of the transcriptional repressors involved is therefore an important goal. As Christoffels et al show, this is a rapidly developing area, and it contains the promise that we will eventually know the molecular basis of embryonic development of the heart. These insights will also be important in understanding adult function because there is continuous turnover of gene expression. Variations in expression levels during the turnover of ion channels have recently been shown by Ponard et al 18 to play a role in heart rate variability using a combination of myocyte cultures and computer modeling.

Conclusions

Experimental data and the in silico modeling work show the complexity of the multifactorial system of SAN excitation. The contribution of If and its importance as a pharmaceutical target has been proven by the successful development of ivabradine and is delineated further in the review article by DiFrancesco 26 in this review series. Further currents seem to be involved in the depolarization phase (Ist, mechanosensitive currents 27 and others) whose relative contributions are still to be determined.

It appears almost obvious that also the fast upstroke at the end of the depolarization phase has a large impact on the depolarization frequency by adjustment of the activation threshold. The evidence presented by Lakatta et al 12 in this review series underlines also the influence of SR Ca 2+ release in generation of the upstroke (besides ICaT and ICaL), in the extreme showing similarities to delayed afterdepolarizations.

Already, earliest modeling and experimental work showed (consistent with current findings) that neither If nor spontaneous Ca 2+ release from the SR on its own is or can be driving the pacemaking activity there is always concerted action necessary and interplay between the various ion channels. Also, the heart rate regulation via cAMP is influenced by and influences multiple ion channels, pumps, and exchangers, thereby creating a robust and stable, but still flexible, system that maintains the billions of heart beats in a normal life.

Future work will most probably discover even further mechanisms influencing heart rate that might be even more relevant targets in specific diseases and pathologies than the currently known pathways.

Original received February 12, 2010 revision received April 27, 2010 accepted April 28, 2010.

Sources of Funding

Work in the laboratory of the authors is financed by the European Union (Framework 6, BioSim, and Framework 7, VPH-PreDiCT) and the British Heart Foundation.


RESULTS

Single-channel kinetics of GIRK1/5 and GIRK1/4 channels

Injection of GIRK1 RNA causes the appearance of functional GIRK channels in Xenopus oocytes ( Dascal et al. 1993 Kubo et al. 1993 ), due to the presence of endogenous GIRK5 protein which forms heteromers with GIRK1 ( Hedin et al. 1996 ). The GIRK1/5 channels are a convenient model for investigation because their low density in oocyte membrane, most probably the result of a limited availability of GIRK5, allows the selection of records with a single channel. Therefore, we started this study with a kinetic analysis of GIRK1/5. Oocytes were injected with 500–1000 pg GIRK1 RNA, which always gave a maximal attainable expression of GIRK1/5 current in whole-cell recordings ( Vorobiov et al. 1998 data not shown). GIRK activity was measured in inside-out patches with ∼150 mM KCl on both sides of the membrane, and with 6 mM NaCl, 4 mM MgCl2 and 2 mM ATP in the bath. These conditions ensure that there will be no ‘rundown’ of the membrane phosphatidylinositol bisphosphate (PIP2), which is necessary for channel activity ( Sui et al. 1998 Huang et al. 1998 ). It should be noted that recordings in cell-attached patches with ACh in the pipette (data not shown) revealed two features that undermined a meaningful single-channel analysis. First, even when the patch appeared to be a single-channel one, further excision into bath solution containing GTPγS or Gβγ increased the channel open probability (Po) and usually revealed the presence of more than one channel. Second, at high concentrations of ACh (10 μM) the Po was often lower, and the mean closed time longer, than with low concentrations of ACh (10–100 nM), suggesting the involvement of an agonist-evoked desensitization process, which has been well described both in atrial cells and in oocytes ( Bunemann et al. 1996 Vorobiov et al. 1998 ). Therefore, we chose to analyse channel gating in excised patches using purified Gβγ, which did not cause time-dependent desensitization (see below, Figs 1 and 2) and gave a higher Po, ensuring real single-channel recordings (see Discussion).

Analysis of the kinetics of a GIRK1/4 channel activated by 20 nM Gβγ in a representative patch

A, record of channel activity after activation by 20 nM Gβγ. Gβγ was applied about 1 min before the beginning of the upper trace. The end of the upper trace corresponds to the time when the experiment was terminated. The middle and lower traces show segments of the record on an expanded time scale. B, open time distribution in the p.d.f. form. A total of > 5500 events were analysed. For one-exponential fit, τ= 2.58 ms for two-exponential fit, τo1= 0.69 ms, ao1= 0.451 τo2= 4.14 ms, ao2= 0.548. C, closed time distribution. Total of > 5500 events were analysed. The closed time histogram with logarithmic time bins was drawn using the parameters of the p.d.f. fit (see inset), as explained in Fig. 1C. The inset shows a probability density plot and four- and five-exponential fits in the p.d.f. form. For four-exponential fit, τc1= 0.63 ms, ac1= 0.417 τc2= 8.56 ms, ac2= 0.302 τc3= 129.5 ms, ac3= 0.231 τc4= 1085 ms, ac4= 0.049 for five-exponential fit, τc1= 0.564 ms, ac1= 0.377 τc2= 4.58 ms, ac2= 0.235 τc3= 26.32 ms, ac3= 0.172 τc4= 190 ms, ac4= 0.183 τc5= 1352 ms, ac5= 0.033. D, open probabilities of GIRK1/5 and GIRK1/4 channels activated by 20 nM Gβγ. E, contribution of components of distributions of open and closed times to total open and closed times. In D and E, the asterisks indicate statistically significant differences ( P < 0.05 ).

Both in the cell-attached configuration and after patch excision, without any agonist in the pipette, very low levels of basal activity were observed. In patches later verified as containing a single channel, as few as one to four openings per minute were often observed. Addition of 20 nM purified recombinant Gβ1γ2 was followed, after 0.2–2 min, by a robust activation of the channel (Fig. 1A cf. Schreibmayer et al. 1996 ) characterized by bursts of openings separated by periods of variable duration during which no openings were detected (Fig. 1Ab and Ac). After full activation by Gβγ (as judged by eye), the recording was continued without interruption at -80 mV for 6–11 min. Zero to four channels were usually present per patch, with electrodes of 1–1.8 MΩ resistance (inner diameter, 3.5–2.5 μm). Thirteen out of fifty patches that showed activation by Gβγ contained a single channel.

For kinetic analysis, we selected nine recordings in which there was no overlap of openings during the whole time of the record. Selection by this criterion ensures, with a high level of confidence, the presence of a single channel in the patch (see Discussion). Each of the recordings was subjected to a kinetic analysis in the Matlab environment using the procedure described in the Methods. An example of such analysis is shown in Fig. 1. Open time distribution, presented as a probability density function (p.d.f.) histogram in Fig. 1B, could be well fitted to a biexponential function, with time constants (τo1 and τo2) of ∼0.8 and 5 ms (see Table 1 [link] for details). Fitting with a single exponential did not satisfactorily describe the data.

GIRK1/4
GIRK1/5 (9 cells) GIRK1/4 (4 cells) Burst mode Low-Pn mode GIRK1/4 + Gαi1(4 cells)
Open times
τo1 (ms) 0.81 ± 0.11 0.71 ± 0.01 1.24 0.50 0.57
to1 (ms) 0.23 ± 0.04 0.38 ± 0.05 0.86 0.41 0.35
ao1 0.30 ± 0.04 0.52 ± 0.06 0.698 0.81 0.605
τo2 (ms) 5.00 ± 0.80 2.86 ± 0.52 4.07 2.63 3.59
to2 (ms) 3.43 ± 0.52 1.40 ± 0.36* 1.23 0.50 1.42
ao2 0.70 ± 0.04 0.47 ± 0.06 0.302 0.19 0.395
Total to (ms) 3.85 ± 0.55 1.98 ± 0.32 2.09 0.91 1.77
Closed times
τc1 (ms) 0.54 ± 0.04 0.62 ± 0.02 0.67 0.93 0.78
tc1 (ms) 0.27 ± 0.03 0.22 ± 0.02 0.30 0.22 0.34
ac1 0.503 ± 0.046 0.355 ± 0.029 0.444 0.239 0.438
τc2 (ms) 3.97 ± 0.55 4.9 ± 0.95 5.67
tc2 (ms) 0.64 ± 0.08 1.41 ± 0.38 2.36
ac2 0.171 ± 0.018 0.279 ± 0.051* 0.415
τc3 (ms) 35.7 ± 5.05 31.4 ± 3.7 46.6 23.3 14.4
tc3 (ms) 8.33 ± 2.04 6.73 ± 1.42 5.83 8.29 4.66
ac3 0.208 ± 0.030 0.209 ± 0.019 0.125 0.356 0.324
τc4 (ms) 236 ± 61.4 240.4 ± 31 238.5 314.1
tc4 (ms) 18.6 ± 2.5 31.3 ± 7.2 84.1 48.5
ac4 0.104 ± 0.014 0.128 ± 0.026 0.352 0.154
τc5 (ms) 1432 ± 215 2200 ± 403 760 2637 6703
tc5 (ms) 15.2 ± 2.2 54.6 ± 19.4* 11.87 138.7 561.3
ac5 0.013 ± 0.002 0.029 ± 0.012 0.016 0.053 0.084
Total tc (ms) 43.4 ± 5.6 94.3 ± 25.2* 20.3 231.3 614.8
  • Data in the burst and low-Pn modes were pooled from all cells ( n= 4 ) before the analysis. *Statistically significant difference from GIRK1/5 ( P < 0.05 ).

The closed time distribution was significantly more complex. This distribution is presented in Fig. 1Ca in the form in which the actual fitting procedure was performed (with linear time bins of variable length see Methods) and in the more conventional form of a histogram with logarithmic time bins in Fig. 1Cb. Exponential fits of the data to a probability density function were done using a maximal likelihood algorithm with two, three, four or five exponents. At least four exponential components were required to describe this distribution, but the five-exponential fit was visibly better in most cells (Fig. 1Cb). The characteristic time constants τc1 to τc5 were, on average, approximately 0.5, 4, 36, 236 and 1432 ms (Table 1 [link]). (A few very long closures of > 10 s, such as the one in Fig. 1Aa, were excluded from the fit in a few cells. They might represent an additional population of closures, but were too infrequent for a reliable fit.)

GIRK1/4 channels were studied in oocytes injected with much smaller, equal amounts of GIRK1 and GIRK4 RNA (25–100 pg oocyte −1 ). It is important to emphasize that, when GIRK1 RNA was injected alone at these concentrations, the whole-cell currents were very small ( Vorobiov et al. 1998 ), and we were usually unable to detect any GIRK channel activity with patch electrodes of 1–1.8 MΩ resistance. In contrast, when GIRK4 was coexpressed, even these small amounts of RNA gave rise to whole-cell currents of several microamps (not shown). Several channels were usually activated by 20 nM Gβγ in small patches (pipettes of 1.5–2.5 MΩ resistance, 2.7–1.5 μm inner diameter), and single-channel records were obtained in only four out of > 70 patches. Each of the four single-channel records was analysed separately.

The general pattern of GIRK1/4 activity was similar to that of GIRK1/5 (Fig. 2A). Open time distribution could be satisfactorily fitted by a biexponential function with time constants of 0.7 and 2.9 ms (Fig. 2B and Table 1 [link]). Like GIRK1/5, at least four exponents were necessary to describe the closed time distribution, but the fit was substantially improved by using a five-exponential function (Fig. 2C). The values of the closed time constants τc1 to τc5 were similar to those of GIRK1/5. The fraction of the total area under the fitted curve (ak) of the second component was significantly different (Table 1 [link]).

The most striking difference between GIRK1/4 and GIRK1/5 was an ∼3-fold lower Po of GIRK1/4 (Fig. 2D). To understand the factors determining the low Po of GIRK1/4, the results were further processed as explained in the Methods (eqns (4)–(8)). In order to assess the contribution to Po of a kth population of events (exponential component) of an open or a closed time distribution, it was necessary to calculate the mean open and closed times of each population (to,k and tc,k, respectively). These mean times, as well as the total mean open and closed times of the whole record (to and tc, respectively), were calculated from the results of the exponential fits described above. The contribution of a population of openings to the total mean open time and thus to Po is given by to,k/to the same applies to closed times (eqns (8a) and (8b)). Since tk=akτk (eqn. (4)), using the fraction of total area under the fitted curve (ak) for estimating the contribution of a given exponential population to Po is misleading the scarcity of long events is compensated for by their long duration. It is also important to note that in a single exponential distribution mean time (t) equals the kinetic time constant (τ). In a multiexponential distribution, mean open or closed time of a kth exponential component (population of events) does not correspond to τk actually, they may differ by orders of magnitude (compare, for example, τc5 and tc5 in Table 1 [link]).

Figure 2E summarizes the contributions of the different exponential components to total open and closed times. In the open time distribution, GIRK1/5 and GIRK1/4 showed statistically significant differences: the population of events with longer τoo2) contributed more than 90 % of the total open time in GIRK1/5 and less than 75 % in GIRK1/4 correspondingly, the contributions of the population with shorter τoo1) showed an inverse relationship. In the closed time distributions, a noteworthy feature of both channel types was the outstanding contribution of the long closed times. The longest closures with a τc of about 1–2 s (τc5), which constituted only 1–3 % of all closed times by area (Table 1 [link]), contributed 30 % (GIRK1/5) to 55 % (GIRK1/4) of total closed time (Fig. 2E). In GIRK1/4, this population of closures contributed a significantly larger part of total closed time than in GIRK1/5. The second longest population of closures with a τc of ∼240 ms (τc4) contributed < 13 % by area but ∼33–44 % by time. The short closures with a τc of 0.5–0.6 and 4–4.9 ms contributed less than 5 %, although they were the most abundant by area.

Further examination of Table 1 [link] reveals that the total mean open time of GIRK1/4 was ∼1.9 times shorter and the total mean closed time was ∼2.2 times longer ( P < 0.05 ) than those of GIRK1/5. The longer to2 of GIRK1/5 is the sole factor underlying the difference in total open time the higher value of the longest closed time, tc5, of GIRK1/4 is the main reason for the longer total closed time of GIRK1/4. The differences in open and closed times explain, and contribute approximately equally to, the observed difference in Po values of the two channels. The long closures (tc4 and tc5) constitute 89 % of the total time of GIRK1/4 activity and explain the low value of Po.

Analysis of frequency of openings of GIRK1/4

Figure 3A shows the frequency diagram of a 100 s portion of a record after activation by Gβγ (out of a total of ∼460 s in this cell same patch as in Fig. 2). Similar to what has been observed in atrial cells ( Ivanova-Nikolova et al. 1998 ), this diagram demonstrates the presence of 400 ms segments with a large number of openings (high frequency of opening), probably reflecting the occurrence of bursts of openings, interspersed with segments of low frequency of opening. A similar pattern was observed during the whole time of recording in this patch and in the other three patches tested. To improve the accuracy and resolution of the further analysis, the data from all four patches were combined into one distribution (total recording time, 27 min). The fraction of ‘null’ segments (with no openings) was 0.48.

The frequency histogram was best fitted with three geometricals with characteristic frequencies of 0.6, 4 and 34.5 Hz (Fig. 3B) fitting with four geometricals did not give better results. Thus, like in atrial cells ( Ivanova-Nikolova et al. 1998 ), at least three populations of 400 ms segments with different frequency characteristics can be detected after activation by Gβγ.

Next, we analysed the distribution of open times within the 400 ms segments. Figure 3C shows an all-points presentation of this distribution. Interestingly, the segments with the lowest fo (i.e. those that showed one or a few openings per 400 ms) showed a wide range of open times, instead of having the shortest to as would be expected if they represented the activity of the channel with the lowest number of bound Gβγ and poorest opening ( Ivanova-Nikolova et al. 1998 ). Figure 3D shows that the averaged to, s values in the different frequency classes were quite similar along the whole range of frequencies. Importantly, these data are practically identical to those obtained by Ivanova-Nikolova et al. (1998) after activation of cardiac GIRK with Gβ1γ5, strongly supporting the relevance of studying GIRK1/4 in oocytes. The mean to was 1.77 ± 0.10 ms (1920 segments), very close to the value of 1.86 ± 0.09 ms obtained by Ivanova-Nikolova et al. (1998) with Gβ1γ5 (and also similar to 1.98 ± 0.32 ms calculated from the kinetic analysis Table 1 [link]).

Slow modal gating of GIRK1/4

From visual examination of our records it was apparent that the channel ‘cycles’ between periods of many seconds with bursting activity, and even longer periods dominated by single openings, long closures and scarce, short bursts. This is exemplified in Fig. 4 which shows a 320 s stretch of record from the same patch as in Figs 2 and 3A. This behaviour is a sign of modal gating, as found in voltage-dependent Ca 2+ and Na + channels ( Delcour & Tsien, 1993 Keynes, 1994 ).

GIRK1/4 activated by Gβγ ‘cycles’ between periods of low and high Po

A 320 s segment of the record of GIRK1/4 activity after activation by 20 nM Gβγ. The inverted triangles show the boundaries between clusters of burst and low-Po modes, as in Fig. 5A.

P o diaries with 0.4, 2 or 5 s bins (Fig. 5A 2 s bins) supported the impression that the channel cycles between long periods of a ‘burst’ mode of openings and a ‘low-Po’ mode. The 2 s bin data were chosen to select periods of the record (clusters, or runs) with either low or high Po, with the average Po of the whole record as the cut-off Po (null segments were included). The |Z| values were calculated as described by Colquhoun & Sakmann (1985) for each record and were in the range 5.8–7.3. Such values of |Z| suggest that segments with similar Po are unlikely to be randomly distributed and thus segments with similar Po probably cluster together. Although the runs analysis is a relatively crude indicator of modal gating ( Colquhoun & Sakmann, 1985 ), it further supports the assumption of modal behaviour of GIRK1/4 at a constant concentration of Gβγ on the long time scale.

For further analysis, clusters of segments with Po above the cut-off level were designated as belonging to the burst mode and the rest were classified as belonging to the low-Po mode separate event lists were made for each cluster. The process of selection is illustrated in Figs 4 and 5A, where the boundaries of burst/low-Po clusters are indicated by triangles. Some periods of the record were omitted because they were of low quality or for simplicity (e.g. relatively short burst or low-Po periods, usually less than 10 s, making the analysis very tedious). An example is the stretch between ∼310 and ∼365 s in the record of Fig. 5A (indicated by a dashed line between two triangles). The mean durations of the clusters were 19.8 ± 3.9 s ( n= 15 ) in the burst mode and 46.8 ± 7.6 s ( n= 16 ) in the low-Po mode. In all, data from ∼70 % of the total recording time were processed this contained 77.3 % of all openings. Data from burst mode clusters and from low-Po mode clusters from all four patches were combined, forming two sets of data that were analysed separately. The overall Po in the two sets of data was 0.102 in burst mode and 0.0034 in low-Po mode (Fig. 6C).

Kinetic analysis of GIRK1/4 gating within burst and low-Po modes

Data were pooled from four patches before the analysis. A, open time distributions (in the p.d.f. form) corresponding to burst and low-Po modes, shown superimposed. The continuous lines show the corresponding two-exponential fits. The parameters of the fit are shown in Table 1 [link]. B, closed time distributions (with logarithmic time bins) corresponding to burst and low-Po modes, shown superimposed. For presentation purposes only, the first two bins were subdivided into smaller ones, and the numbers of events in each bin were interpolated. The curves show the results of the standard fitting procedure to linear p.d.f. histograms (as explained in Figs 1C and 2C) with four exponents. The parameters of the fit are shown in Table 1 [link]. C, open probabilities in the two modes. D, contribution of the exponential components of distributions of open and closed times to total open and closed times in burst and low-Po modes.

Frequency analysis with 400 ms segments, as performed previously for the whole record, revealed striking differences between burst and low-Po modes. Two-hundred out of 712 segments in the burst mode (28 %), and 1244 out of 2130 segments in the low-Po mode (58 %) were empty, that is, contained no openings. The mean open times of the two sets of data were clearly different across the whole frequency range (Fig. 5B). In low-Po mode, to, s was always 2–3 times lower than in the corresponding frequency class of the burst mode in most frequency classes, the difference was statistically significant. Note especially the lowest frequency class, 2.5 Hz (one opening per 400 ms segment), which is supposed to be the lowest to class in the model of Ivanova-Nikolova et al. (1998) . It existed in both burst and low-Po modes though was more abundant in the low-Po mode, but the mean to, s differed greatly: 3.41 ± 0.58 ms (64 segments) vs. 1.14 ± 0.06 ms (468 segments, P < 0.001 ) for burst and low-Po mode, respectively. The average overall to was 2.74 ± 0.11 ms (502 segments) in the burst mode, and 1.24 ± 0.04 ms (886 segments) in the low-Po mode the 2.2-fold difference was highly significant ( P < 0.001 ). Most of the open time was contributed by the burst mode: 79 % of all openings appeared within the periods of burst mode, and only 21 % appeared in low-Po mode. Thus, low-Po and burst mode were characterized by different to values, which is usually considered an indication of different modalities of gating ( Delcour et al. 1993 ). The histograms of frequency of opening were also remarkably different between the two modes (Fig. 5C and D). In both cases, the frequency distributions could be fitted with two geometricals assuming three geometricals did not improve the fit. The two modes shared only the low frequency population with a characteristic frequency of 1.24–1.46 Hz. Each of the modes had only one additional frequency population: the burst mode had a characteristic frequency of 88.6 Hz, and the low-Po mode had a characteristic frequency of 10.7 Hz.

In order to further characterize the differences between the two modes of gating we performed a full kinetic analysis of the high-Po and low-Po sets of data. The results are summarized in Fig. 6 and in Table 1 [link]. A visual examination of the open and closed time histograms shown in Fig. 6A and B reveals significant differences between burst and low-Po modes (the use of probability density plots, which show normalized frequencies of openings and closures, enables direct comparison of the different sets of data). Open time histograms (Fig. 6A) revealed a relative abundance of shorter openings in the low-Po mode (grey bars) compared to the burst mode (open bars). The open time distributions within each mode could not be satisfactorily fitted to a single-exponential function (not shown), and two exponentials were required in both cases (shown in Fig. 6A). Both open time constants, especially the shorter one, were substantially smaller in the low-Po mode than in the burst mode (Table 1 [link]). These results suggested that the total open time distribution, without separation into modes (Fig. 2), probably contained more than two exponential components despite the reasonable fit obtained with the two-exponential function. The mean open time was more than 2 times greater in the burst than in the low-Po mode (Table 1 [link]) however, this difference alone could not explain the 30-fold higher Po of the burst mode.

The differences between closed time distributions were even more striking (Fig. 6B) long closed times were obviously much more abundant in the low-Po mode (grey bars) than in the burst mode (open bars). Four exponential components were detected in both burst and low-Po modes (Fig. 6B Table 1 [link]). The use of five exponents did not improve the quality or the stability of the fit in either case. Furthermore, some of the characteristic time constants obtained in the four-exponential fits within modes showed striking similarities to the five closed time constants of the total distribution (Table 1 [link]). The shortest, τc1, was very similar in the total distribution of GIRK1/4 patches and in the two modes, being 0.6–0.9 ms. τc2 (∼5 ms) of the total distribution was boldly represented in the burst mode but absent from the low-Po mode. The next time constant, of 23 and 46 ms for the burst and low-Po mode, respectively, probably corresponds to τc3 of the total distribution (31 ms). The next population of closures, characterized by a τc4 of 240 ms, was undoubtedly contributed exclusively by a major subpopulation which is present in the low-Po mode ( τ= 238.5 ms ), but absent from the burst mode. Finally, the longest time constant, τc5, appeared smaller in the burst mode (760 ms) than in the total population or in the low-Po mode however, the estimate of this time constant was not very accurate because of the relative rarity of the long closures in the burst mode.

The total mean closed time in the low-Po mode was more than 10-fold greater than in the burst mode (Table 1 [link]), suggesting that the great difference in the Po was mainly due to this factor. Analysis of the contributions of the components of the exponential distributions in the two modes (Fig. 6D) showed that the populations with short and long open times contributed approximately equally to the total open time. Again, the differences between the modes in the closed times are remarkable. In the low-Po mode, the short closures are unimportant, and the two populations with the longest τ, τc4 and τc5 (∼240 and ∼2700 ms) account for > 95 % of the total closed time. In contrast, in the burst mode two out of the three shorter classes of closures (τc2 and τc3 ∼6 and 47 ms) make a substantial contribution (> 40 %) to the total closed time.

Modal behaviour of the GIRK1/5 channels

From visual inspection of the records and Po data (2 s segments) it appeared that modal behaviour is much less obvious in GIRK1/5 than in GIRK1/4 channels. However, runs analysis rendered |Z| values in the range 4–8.4, suggesting that clustering of segments with similar Po is unlikely to happen by chance. A more detailed analysis was therefore performed as for GIRK1/4 channels (to avoid the ambiguity of different sampling frequencies, 5 cells with a sampling frequency of 2.5 kHz were selected for the present analysis). Mean to values corresponding to the two presumptive modes were significantly different (4.37 ± 0.16 ms for burst mode and 2.73 ± 0.07 ms for low-Po mode, P < 0.001 ). The overall Po values in burst and low-Po mode were 0.122 and 0.029, respectively. Note that this ∼4-fold difference in mean Po was much smaller than in GIRK1/4 channels (∼30-fold).

Frequency analysis did not show explicit differences between modes in the same way as for GIRK1/4 channels. Both burst mode and low-Po mode frequency distributions could be well fitted with two geometricals which gave rather close values of characteristic frequencies (1.16 and 38.03 Hz for the burst mode, 1.09 and 18.66 Hz for the low-Po mode). Similarly, kinetic analysis of the high- and low-Po sets of data did not give as clear a picture as in the case of GIRK1/4. Open time distributions in both modes were satisfactorily fitted with two exponents, of which only the longer one appeared to diverge substantially between the modes (1.06 and 6.28 ms for the burst mode, 0.85 and 3.52 ms for the low-Po mode). According to closed time distribution analysis, it appeared that the low-Po mode probably contained all five closed time components that were found in the whole records. The burst mode closed time distribution could be fitted with four exponents, omitting the long exponent found in the low-Po mode.

GIRK1/4 gating after inhibition by Gαi1

GIRK1/5 channels are inhibited by GTPγS-activated, myristoylated Gαi1 with an IC50 close to 15 pM at 100 pM, the inhibition reaches 95 % ( Schreibmayer et al. 1996 ). This inhibition is not due to sequestration of Gβγ but to another, unknown mechanism. In rat atrial myocytes, inhibition was ∼85 %, apparently less than that of GIRK1/5 ( Schreibmayer et al. 1996 ). Although in the same work we also observed inhibition of GIRK1/4 channels expressed in the oocytes, neither channel kinetics nor the mechanism of inhibition by Gαi1 was analysed in detail. The pattern of channel activity in the presence of Gαi1 was characterized by long shut periods and low Po, resembling the low-Po mode and raising the possibility that Gαi1 may be one of the cellular factors controlling the modal behaviour of GIRK. Therefore, we decided to make a detailed analysis of Gαi1-induced inhibition of GIRK1/4.

The excised patches were exposed to 20 nM Gβγ alone or together with 25 or 100 pM Gαi1. As can be seen from Fig. 7A, in many patches the inhibitory effect of Gαi1 could be easily seen. However, in most cases a substantial activation of GIRK1/4 was still observed in the presence of Gαi1. To quantify the effects of Gβγ and Gαi1, the extent of activation by Gβγ in each patch was normalized to the basal activity in the same patch, by calculating NPo in the presence of Gβγ divided by basal NPo. NPo in the presence of Gβγ was measured during a 1 min period of maximal activity, between 2 and 7 min after addition of Gβγ. Basal NPo was measured during the second minute after patch excision. The estimation of NPo in patches with very low basal activity (less than 3–4 openings min −1 ) was unreliable, therefore patches with basal NPo < 0.00005 have been excluded from the analysis (4 out of 37 patches).

A summary of these experiments is shown in Fig. 7B. Gβγ alone activated the channel by > 770-fold. In the presence of GTPγS-activated Gαi1 the activation was attenuated by about 70 %, but was still very substantial at ∼200-fold. The inhibition could be easily overlooked if thorough comparisons with the control activation by Gβγ were not performed in the same oocyte batches.

In four patches activated by Gβγ in the presence of Gαi1, no overlaps of openings were observed during the whole time of the record (7–10 min after Gβγ application). Since there were relatively few openings in each of these records, data from these four patches were combined, and open and closed kinetics were analysed as previously. Open time distribution was fitted with two exponents (Fig. 7C and Table 1 [link]). Closed time distribution was fitted with four exponents (Fig. 7D), close but not identical to those of the low-Po mode (Table 1 [link]). Frequency analysis of GIRK1/4 gating in the presence of Gαi1 rendered characteristic frequencies of 1.13 and 7.47 Hz, similar to those found in the low-Po mode of GIRK1/4 (1.46 and 10.7 Hz).


3 ION CURRENT MODELS

Models of the cardiac AP are composed of several submodels, describing particular ionic currents through channels and transporters, diffusive fluxes between intracellular compartments, and calcium buffering and release in the sarcoplasmic reticulum. Of these components, the voltage-sensitive passive ion-channel currents were the first to be modeled, and the problem of fitting mathematical models to electrophysiology data from “whole-cell voltage-clamp” experiments has been particularly well studied in cardiac, neuronal, and general excitable-cell physiology.

3.1 Voltage-sensitive ion channels

(2)

3.1.1 Steady states and time constants

Several studies have focused on the problem of estimating steady-state currents and time constants of current decay/activation from whole-cell current recordings at particular voltages. While these analyses are often performed on synthetic data and can be highly mathematical, their results are relevant to experimenters as well as modelers, as time constants and steady states are still commonly used to report experimental results (although, for reasons that will become clear, we implore any experimenters who are reading to please also publish the current time courses in a digital format).

Many published studies consider the specific problem of fitting a two-gate Hodgkin–Huxley model (i.e., with an activation and an inactivation gate). Such models can be written in a form where each gate's kinetics are described by a voltage-dependent steady-state and time constant, and the fitting procedure involves extracting these quantities from current measurements independently for several voltages. Detailed examples of these analysis methods are given in the supplementary materials to Clerx, Beattie, et al. ( 2019 ). A model “fit” is then made by fitting (often somewhat arbitrary) curves through the resulting points, and inserting the resulting equation directly into a model. A schematic overview of this procedure is shown in Figure 5a.

A crucial point regarding this method was made by Beaumont, Roberge, and Leon ( 1993 ), who showed that the steady states can only be measured correctly if the time constants of the different gates (e.g., activation and inactivation) are “well-separated.” In other words, our ability to measure steady states of activation and inactivation at any voltage V, depends on there being a large difference in the time constants of activation and inactivation at that voltage. The same conclusion was reinforced by Willms, Baro, Harris-Warrick, and Guckenheimer ( 1999 ) and Lee, Smaill, and Smith ( 2006 ). Having well-separated time constants often means that one of the processes is either very fast (e.g., INa activation) or very slow (e.g., IKr activation). There is an interesting experimental consideration here, in that very fast processes are difficult to measure and may require specialized equipment (Sherman, Shrier, & Cooper, 1999 ), while for slow processes great care must be taken that the voltage steps are long enough (Clerx, Beattie, et al., 2019 Vandenberg et al., 2012 ), which poses difficulties if cells becomes unstable during measurement. It is preferable not to have to wait for steady states to arise to fit a model's parameters.

3.1.2 Hodgkin–Huxley model parameters

A second paper by Beaumont, Roberge, and Lemieux ( 1993 ) investigated the problem of finding the steady states of a HH model with nonseparable time constants. As part of their solution, which they termed an inversion procedure, they used a Boltzmann-curve to connect the steady states at all measured voltages (which provides a stronger constraint on the data than fitting each voltage independently) and then fitted it using the peak current and the time-to-peak, reasoning that these points provide the highest signal-to-noise ratio. The final parameters are then obtained using numerical optimization. A further extension of this method was presented in Wang and Beaumont ( 2004 ), which avoids numerical optimization, but requires an updated voltage-step protocol that is not well tolerated by all cell-types. The fourth paper in the series (Raba, Cordeiro, Antzelevitch, & Beaumont, 2013 ) provided an experimental confirmation of the need for an updated experimental protocol, and contained experiments on synthetic data showing an improved version of the Wang and Beaumont ( 2004 ) method.

Willms et al. ( 1999 ) and Lee et al. ( 2006 ) performed similar analyses of two-gate HH models, and both showed that estimating steady states and time constants independently (or “disjointly”) leads to an error in the estimate of steady-state activation that scales with the ratio of the time constants of activation and inactivation. The work by Lee et al. ( 2006 ) went on to recommend an approach that minimizes an error in peak currents, time-to-peak, and steady-state currents, while Willms et al. ( 1999 ) recommended fitting current traces directly (see Figure 5c). Both studies used simulations to show the superiority of their methods over a conventional approach.

A different approach was taken by Csercsik et al. ( 2010 ) and Csercsik, Hangos, and Szederkenyi ( 2012 ), who investigated the theoretical identifiability of steady states and time constants from a single voltage-step. For HH models with two gates, each with Exponent 1, they were able to show that time constants are identifiable, while the maximal conductance and steady states form an unidentifiable pair. This analysis was extended to general HH models (any number of gates with any exponents) by Walch and Eisenberg ( 2016 ), with the additional result that the exponents themselves are identifiable. This is valuable work for the analysis of single voltage steps, but the analysis has yet to be extended to multi-voltage-step protocols, where we know from practical identifiability experiments that knowledge of the relationship between parameters at different voltages can provide full identifiability of parameters (e.g., by assuming voltage-dependent rates of the form shown in Figure 1).

3.1.3 Markov models and optimization approaches

Many models postulate a more complicated kinetic scheme than independent HH gates, so that the system can no longer be described by a set of independent time constants and steady states. Instead, these models are fit by defining an error measure between experimental data and simulations using some initial guess for the parameters, and then iteratively adjusting the parameters until the error is minimized. Unlike the methods discussed in the previous sections, which are restricted to HH models, optimization-based methods can be used for any model of an ionic current.

A common method to use optimization for model calibration, is to simulate conventional voltage-clamp protocols, calculate steady states and time constants (temporarily assuming a HH formalism), and then adjust parameters until the difference between simulated and experimental values is minimized (see Figure 5b). This method has the advantage that it requires only steady states and time constants as input, which are easy to find in the experimental literature, but it can lead to large errors and an unnecessarily complex fitting procedure (Clerx, Beattie, et al., 2019 ).

An alternative method, shown in Figure 5c, is to compare the recorded and simulated currents directly. An early example of this method was shown in Balser, Roden, and Bennett ( 1990 ), who simulated channel open probability in a three-state Markov model (with Eyring rates) and fitted this to the estimated open probability from macroscopic whole-cell recordings. They showed the applicability of their method to measurements in Guinea pig ventricular myocytes, but also verified its performance on a simulated set of 90 virtual “cells.”

Identifiability of Markov model parameters has focused on local analysis which starts from a known solution in parameter space. If the model is found to be unidentifiable at this point this proves a lack of global identifiability, but no guarantees can be given for the global identifiability of locally identifiable results. Several models and voltage protocols were tested for local identifiability by Fink and Noble ( 2009 ), who used it to highlight several unidentifiable parameters in published Markov models. An extension of this method based on singular value decomposition was later presented in Sher et al. ( 2013 ) and used to create reduced models by eliminating redundant parameters. Note that even a practical identifiability analysis based on global optimization is still local with respect to the single set of parameters that generated the synthetic data, and so repeating these exercises with multiple possible parameter sets is also recommended.

3.1.4 Protocol design

Practical identifiability analysis has been used as a tool to design voltage-clamp protocols. For example, Fink and Noble ( 2009 ) analyzed and shortened popular voltage-clamp protocols by removing steps that did not affect parameter identifiability. Zhou et al. ( 2009 ) also tested various protocols for identifiability before performing experiments, and the work on HH model identifiability by Csercsik et al. ( 2012 ) ends with several recommendations for protocol design.

A more radical approach to protocol design had previously been taken by Millonas and Hanck ( 1998b ), who measured INa currents resulting from protocols that fluctuated rapidly between a high and a low voltage and used it for model calibration. They then fit a model to currents from conventional voltage-clamp protocols, and showed that it could not predict the response to the novel protocol, showing that the rapidly fluctuating protocol had the potential to uncover new information (Millonas & Hanck, 1998b , 1998a ). A follow-up study (Kargol, Smith, & Millonas, 2002 ) investigated systematic protocol design, and showed an example where a protocol was designed to maximize the predictions from two competing models that showed a similar response to conventional protocols. One method to systematically generate (and compare) protocols, is to create them by superimposing similar waveforms, for example, sine waves of different frequencies and amplitudes, and the authors briefly discuss this before suggesting wavelets as a more suitable basis (which they further explored in Hosein-Sooklal and Kargol, 2002 Kargol, 2013 ).

A superposition of sine waves also formed the basis of a protocol introduced in Beattie et al. ( 2018 ). In this study, we measured IKr current in response to an 8 s optimized protocol, and used it to fit a four-state Markov model (equivalent to a Hodgkin–Huxley model with two independent gates). The model was then used to predict the response to an AP waveform validation protocol (i.e., not used in the fitting data), and found to outperform models published in the literature which were fitted to conventional step protocols. Notably, this study performed a sinusoidal calibration protocol, and independent validation protocols in the form of (shortened versions of) conventional voltage-clamp protocols and an APs clamp, all in the same cells. In a follow-up publication (Clerx, Beattie, et al., 2019 ), we used this data set to compare four different fitting methods (each characterizing a common group of methods found in the literature) in terms of predictive power and robustness. These methods are summarized in Figure 5. In agreement with the theoretical studies discussed above, we found that whole-trace fitting greatly outperformed fitting based on steady state and time-constant approximation, and that the novel shortened protocol performed as well as its conventional counterparts.

Automated patch-clamp platforms have recently become available, and offer a chance to perform experiments in much larger numbers than was possible before. A recent study by Lei, Clerx, Beattie, et al. ( 2019 ) adapted the information-rich protocol work by Beattie et al. ( 2018 ) for these machines, replacing the sine waves by a staircase protocol (to overcome practical limitations) and creating 124 cell-specific models in a single pass.

3.1.5 Combining data sources

An advantage of optimization-based fitting methods is that they provide a straightforward manner to incorporate data from different sources. For example, Vandenberg and Bezanilla ( 1991 ) and Irvine, Saleet Jafri, and Winslow ( 1999 ) combined measurements of whole-cell current, single-channel current, and gating-current (the microscopic current generated by charge displaced in the channels' conformational changes) in a single model. More recently, measurements from voltage-clamp fluorometry have been used in conjunction with electrophysiology data to calibrate and/or validate mathematical models of ion-channel gating (Moreno, Zhu, Mangold, Chung, & Silva, 2019 Zaydman et al., 2014 ). While combining data this way has great potential, it can also lead to problems with finding a unique solution if the different data sets suggest a different “best” answer. This could happen if the model is known and accepted to be imperfect, in which case adjusting the weighting of the different data sets could allow a modeler to “tweak” the outcome, steering it toward a model assumed to be most useful in the expected context of use. But even if we do assume the model has the capability to fit all data sets at once, we might still expect difficulties from such a multi-objective optimization problem, for example if each measurement was made on different cells or under slightly different conditions.

Finally, several authors have investigated fitting voltage-sensitive ion-channel models to data from sources other than whole-cell current recordings. For example, single-channel voltage-clamp measurements (see below), but also single-channel current clamp (Tveito, Lines, Edwards, & McCulloch, 2016 ). Several studies have investigated fitting to measurements of the AP and calcium transient (Bueno-Orovio et al., 2008 Cairns, Fenton, & Cherry, 2017 Dokos & Lovell, 2004 ), which would allow kinetics to be determined for myocytes without using channel blockers or current-separation protocols (see Section 4.3.2). Another approach to multichannel identification was introduced by Milescu, Yamanishi, Ptak, Mogri, and Smith ( 2008 ), who measured the AP in a cell and then blocked the current of interest, injected a simulated current using dynamic clamp, and adjusted the simulation parameters until the cell displayed its original behavior. This process can then be repeated by adding further blockers and models for subsequent currents.

3.2 Modulated voltage-sensitivity

The next step up in complexity from purely voltage-sensitive channels, is to study the situation where an ion current's voltage-sensitive behavior is modulated by other factors, for example, temperature or binding of ligands. This comes into play in several ways in cardiac physiology, for example, when measurements are temperature-adjusted to incorporate room-temperature data or study fever and hypothermia, when studying the effects of mutations, drugs, or signaling (e.g., through channel phosphorylation), or when modeling currents like L-type calcium which exhibit both voltage and Ca-dependent kinetics.

Modifications to incorporate modulation can include changes to (a) the maximum conductance, for example, drug-induced pore block (Mirams et al., 2011 ), mutations which reduce whole-cell current (Sadrieh et al., 2014 ), or ion-concentration dependence (Fink, Noble, Virag, Varro, & Giles, 2008 ) (b) kinetic parameters, for example, for temperature changes (Li et al., 2016 ), mutations (Clancy & Rudy, 2001 ), or again ion-concentration dependence (Fink et al., 2008 Mazhari, Greenstein, Winslow, Marbán, & Nuss, 2001 ) or (c) the kinetic scheme itself, for example, to model the availability of drug-receptor sites (Starmer, Grant, & Strauss, 1984 ) or to incorporate new “modes” created by mutations (Clancy & Rudy, 2002 ) or ligand-binding (Bondarenko, 2014 ). For drug-induced changes specifically, a useful overview can be found in Brennan, Fink, and Rodriguez ( 2009 ).

The simplest case, from a modeling point of view, is when channels can be split into an altered and an unaltered group, so that we simply perform inference twice to create two independent models whose combined behavior represents the situation of interest. For example, homozygous mutations in SCN5A (where a single gene encodes for the entire alpha subunit) have been modeled by simply replacing the entire INa model (Clancy & Rudy, 1999 ). Heterozygous mutations have been modeled by assuming a certain ratio between the two inherited types (Loewe et al., 2014 ), although often the heterozygous whole-cell current is modeled as a single entity instead (Whittaker, Ni, Harchi, Hancox, & Zhang, 2017 ). For processes such as channel phosphorylation it is also common to include two independent channel models (O'Hara et al., 2011 ), but with a varying instead of a fixed ratio between the two.

An alternative representation of the same idea is to connect the two models in a single kinetic scheme, with (perhaps voltage-insensitive) rate constants allowing the channel to switch from one mode to another. This representation is common for L-type calcium models (Jafri, Rice, & Winslow, 1998 Mahajan et al., 2008 ) but has also been used to model drug effects (Brennan et al., 2009 Li et al., 2017 ).

For some modulating factors it can be more appropriate to keep the model structure fixed but modify the rate constants. This is a common strategy for temperature (Destexhe & Huguenard, 2000 ) but also for mutations (see Carbonell-Pascual, Godoy, Ferrer, Romero, & Ferrero, 2016 for a discussion of modifying rates versus model structure). Recently, Lei, Clerx, Gavaghan, et al. ( 2019 ) measured and fitted IKr-kinetics independently at several temperatures, so that plots of the kinetic rates versus temperature could be made. Note that identifiability is crucial for such an exercise, as lack of identifiability could introduce meaningless changes in the obtained parameters (in this case, good identifiability properties had previously been shown [Lei, Clerx, Beattie, et al., 2019 ]). It may be possible to extrapolate this independent-fits strategy to other areas, for example to see which rates are affected by a drug, and in this context shortened information-rich protocols could be particularly useful. Finally, if an equation for the modulating effect on the rates is known, it may also be possible to vary both voltage and modulating factors during a single experiment, and fit a single model to the results.

3.3 Ligand-gated channels

Purely ligand-gated channels have not received as much attention in the cardiac literature as their voltage-gated counterparts. A notable exception is the Ryanodine receptor (channel), which plays a crucial role in calcium handling and has been included in cardiac AP models since the work of Hilgemann and Noble ( 1987 ). In the neurological literature studies of ligand-gated channels abound, with particular interest paid to the problem of fitting Markov models to single-channel currents. For example, Colquhoun and Sigworth ( 1995 ), Horn and Lange ( 1983 ), and Bauer, Bowman, and Kenyon ( 1987 ) provide detailed early overviews of the statistical (maximum likelihood) methods involved, and Fredkin, Montal, and Rice ( 1985 ) derived an important result on rate identifiability. An overview of the early literature on this topic was compiled by Ball and Rice ( 1992 ), and a more recent assessment of maximum likelihood methods is given by Colquhoun, Hatton, and Hawkes ( 2003 ).

Several studies have addressed identifiability in this context, both analytically (Edeson, Ball, Yeo, Milne, & Davies, 1994 ) and using Bayesian sampling (MCMC) methods (Hines et al., 2014 Siekmann et al., 2012 ). The widespread use of statistical methods has also led naturally to likelihood-based methods for model selection (Hodgson & Green, 1999 Horn & Vandenberg, 1984 ) and Bayesian analysis (Epstein, Calderhead, Girolami, & Sivilotti, 2016 Hodgson, 1999 ). In an interesting parallel with whole-cell voltage-clamp work, studies such as VanDongen ( 2004 ) have compared methods that pre-analyze (“idealize”) the data before fitting, to methods that perform both steps simultaneously.

3.4 Pumps and transporters

Pumps and transporters perform key roles in cardiac myocytes, restoring the electrochemical gradients needed for passive transport through ion channels and refilling the sarcoplasmic reticulum after calcium release for contraction (Eisner, Caldwell, Kistamás, & Trafford, 2017 ). Despite this, the literature on modeling active transport in cardiomyocytes is sparse. For example, an analysis by Bueno-Orovio, Sánchez, Pueyo, and Rodriguez ( 2014 ) found that Na/K pump formulations in AP were predominantly inherited from either DiFrancesco and Noble ( 1985 ) or Luo and Rudy ( 1994 ), while Niederer, Fink, Noble, and Smith ( 2009 ) showed that in this process the connection (and fit) to the source data was occasionally lost.

A very systematic approach to creating a model of the Na/K pump was taken by Smith and Crampin ( 2004 ). Starting from a detailed (but hard to parameterize) 15-state kinetic scheme (the Post-Albers model), they exploited the large differences in the model's (estimated) reaction rates to perform significant model reduction, leading to a simplified four-state model with 14 parameters. Initial guesses for each parameter were made using a variety of published experimental results, after which optimization was used to fit the model to a published study of cycle rates versus voltage. Interestingly, some of the final rates shown in the article are equal to the initial values, which may indicate identifiability issues if the quality of fit was not found to vary when changing these parameters. A refinement of the model was made in Terkildsen, Crampin, and Smith ( 2007 ) using the same approach but fitting to an extended experimental data set. The same group then created a model of the SERCA pump, this time reducing a 12-state kinetic scheme down to a 3-state model, and again fitting to a combined data set from several sources (Tran, Smith, Loiselle, & Crampin, 2009 ). A recent publication by Pan, Gawthrop, Tran, Cursons, and Crampin ( 2019 ) introduces an extension of this approach, which uses bond graphs to derive reduced models that automatically obey laws of thermodynamics, this makes them more likely to give realistic predictions when extrapolating (see Section 2.2).

While current recordings from (human) cardiac pumps (especially at physiological temperatures) are rare, crystal structure data is available. A review by Gadsby ( 2009 ) uses these to argue that the principles behind active transport are more similar to passive ion-channel transport than previously thought. If so, techniques used in the analysis of ligand-gated channels may be applicable: while the current through a single pump is too small to be measured in isolation, studies have investigated extending single-channel analysis methods to fitting to macroscopic data (Celentano & Hawkes, 2004 Milescu, Akk, & Sachs, 2005 ).


Polycondensation

5.10.2.3.2 Oxidative polymerization of aniline compounds

Polyaniline (PANI) has been known over a century. Currently, PANI is one of the most popular conducting polymers because of its stability and good electrical and optical properties, which are attractive for technological applications in lightweight batteries, microelectronics, electrochromic displays, light-emitting diodes, electromagnetic shielding , sensors, and so forth. The well-known methods for the synthesis of PANI are either chemical or electrochemical oxidation polymerization of aniline monomer. However, the reaction conditions are harsh involving extreme pH, high temperature, strong oxidants, and highly toxic solvents.

On the contrary, enzymatic polymerization of aniline, its derivatives, and other aromatic compounds provides an alternative method of a ‘green process’ toward the formation of soluble and processable conducting polymers. These reactions are usually carried out at room temperature and in aqueous organic solvents at neutral pH. The reaction condition is greatly improved and the purification process of the final products is simplified when compared to traditional methods ( Scheme 28 ). 54

Scheme 28 . HRP-catalyzed oxidative polymerization of aniline.

Water-soluble conducting PANI was obtained by HRP-catalyzed polymerization of aniline using H2O2 oxidant, in the presence of sulfonated polystyrene (SPS), which acted as a polyanionic template. The resulting polymer was complexed to the SPS and exhibited electroactivity. The conductivity of the PANI/SPS complex was measured to be 0.005 S cm −1 . The values increased to 0.15 S cm −1 after HCl doping and could be increased further with an increase in the aniline to SPS molar ratio. The enzymatic approach is claimed to offer unsurpassed ease of synthesis, processability, stability (electrical and chemical), and environmental compatibility. 55

Enzymatic polymerization of aniline in the presence of a template like SPS produced PANI having a linear structure, due to the electrostatic alignment of the monomer and SPS to promote a para-directed coupling. Without the template, the PANI structure became branched, which is not a desirable property of conducting materials. 56 Enzymatically synthesized PANI is normally in the protonated form, which can be converted to the unprotonated base form by treatment with aqueous ammonia solution or other suitable bases. The unprotonated base form of PANI consists of reduced base units ‘A’ and oxidized base units ‘B’ as repeat units, where the oxidation state of the polymer increases with decreasing values of y (0 ≤ y ≤ 1). The three extreme possibilities for values of y are 1, 0.5, and 0, corresponding to fully reduced PANI (leucoemeraldine), the half-oxidized PANI (emeraldine), and fully oxidized PANI (pernigraniline), respectively ( Scheme 29 ). 57

Scheme 29 . Three extreme possibilities of the oxidation state of polyaniline.

PANI colloid particles were prepared by HRP- or SBP-catalyzed oxidative polymerization of aniline in a dispersed medium together with toluenesulfonic acid using poly(vinyl alcohol), poly(N-isopropylacrylamide), or chitosan as the steric stabilizer. The colloidal particles are pH- and thermosensitive, and are claimed to have potential applications in smart devices such as thermochromic windows, temperature-responsive electrorheological fluids, actuators, and colloids for separation technologies. 58


Introduction

Interstitial cells of Cajal (ICCs), identified using c-Kit immunoreactivity, are distributed throughout the gastrointestinal (GI) tracts. These cells are believed to play an essential role in GI motility, such as pacemaking (e.g. Thuneberg, 1982 Suzuki, 2000 Hirst and Ward, 2003 Takaki, 2003). There is now an accumulating body of evidence that some gastroenteropathies involve impairment of ICCs. For instance, it has been shown that the number of ICCs decreases in patients with diabetes mellitus, which is frequently complicated by impaired motility of the GI, and consequently making it more difficult to control the postprandial blood-glucose concentration (Koch, 2001 Camilleri, 2002).

Pacemaker potentials underlie spontaneous mechanical activity in the GI tract. There are several studies reporting that Ca 2+ -dependent plasmalemmal ion channels are periodically activated in ICCs (Tokutomi et al., 1995 Huizinga et al., 2002 Walker et al., 2002). It is therefore deduced that oscillations of the intracellular (cytosolic) Ca 2+ concentration ([Ca 2+ ]i) in these cells are the primary mechanism generating pacemaker potentials. Indeed, we have previously demonstrated that spontaneous electrical activity occurs in synchrony with [Ca 2+ ]i oscillations in c-Kit-immunopositive-cell-rich regions (Torihashi et al., 2002).

It has been extensively shown in numerous regions of the GI tract that spontaneous mechanical and electrical activities are highly temperature-dependent and sensitive to metabolic inhibitors (e.g. Tomita, 1981 Conner et al., 1974 Nakayama et al., 1997). If pacemaker [Ca 2+ ]i oscillations in ICCs are generated through mechanisms involving and/or affected by energy-level-relating signals, such mechanisms could be responsible for these characteristic spontaneous rhythmicity of the gut.

From the muscle layers of the gastrointestinal tract, we have recently developed a cultured cell cluster preparation containing essential minimum cell members to investigate gastrointestinal motility: smooth muscle, enteric neurons and ICCs (c-Kit-immunopositive interstitial cells). This preparation shows spontaneous contractions, and preserves several characteristic features seen in tissue-level experiments (Nakayama and Torihashi, 2002 Torihashi et al., 2002). It is hypothesized that the link between gut pacemaker activity and energy metabolism could be mediated by KATP channels and sulphonylurea receptors (SURs). In the present study, we thus examined the effects of KATP channel openers on pacemaker [Ca 2+ ]i oscillations in ICCs and smooth muscle contractions, using cell cluster preparations from the mouse ileum. We also carried our RT-PCR and immunostaining examinations, and found that SUR2 occurs in smooth muscle cells, while surprisingly, SUR1 is predominant in ICCs. Accordingly, we observed modulations of pacemaker [Ca 2+ ]i activity and contraction, reflecting these distinct SUR isoforms in ICCs and smooth muscle. Our findings may provide a new insight into the mechanisms of blood glucose control, and also a link between gastrointestinal motility and metabolic diseases.


Membrane Resonance

Subthreshold membrane potential oscillations in neurons are often associated with membrane resonance—the ability to amplify input at a specific frequency. In general, membrane potential oscillations and membrane resonances in neurons are similar in mechanism (Lampl and Yarom 1997 Moca et al. 2014 Tseng and Nadim 2010 Wu et al. 2001), suggesting that the combination of CaV1, CaV2.2, and CaCCs could account for the membrane resonance in LTS interneurons.

Voltage-gated calcium channels are necessary for membrane resonance.

Membrane resonance was measured using a chirp stimulus in voltage clamp (see materials and methods ). Like the membrane potential oscillation (Fig. 6A), the membrane resonance was voltage dependent (Fig. 6B) and was blocked by 400 μM cadmium (Fig. 6C). Resonance is measured as a frequency-dependent reduction in the amplitude of the current generated by the cell during the constant-amplitude voltage command. In addition to its effect on resonance, cadmium increased the holding current necessary to maintain the membrane potential at −30 mV (from 9.0 ± 5.4 pA in TTX to 41.2 ± 6.2 pA in cadmium t = −5.62, df = 8, P < 0.001 Fig. 6D). This reflects the negative membrane potential shift caused by cadmium in current clamp (Fig. 2D). The input resistance (measured from a voltage step) did not change with the application of cadmium (TTX = 217 ± 58 MΩ vs. Cd 2+ = 215 ± 24 MΩ), as shown in Fig. 6E, zero-frequency impedance.

Fig. 6.Membrane resonance in LTS interneurons requires calcium currents. Comparison of the voltage sensitivity of the membrane potential oscillation (A) with the membrane resonance (B). The impedance curves show relative impedance, normalized by the input resistance measured at each holding potential. C: an example of the membrane response to a chirp protocol shown before and after the application of 400 μM cadmium. D: the holding current to maintain the membrane potential at −30 mV was significantly increased after cadmium application. E: the sample data depict the change in the impedance curves when voltage-gated calcium channels were blocked. The 0-frequency impedance indicates the input resistance. F: the phase of the membrane response lost the positive phase shift after cadmium application. Error bars are SE ***P < 0.005.

Cadmium completely blocked the membrane resonance. The average membrane impedance curves for the sample before and after the application of cadmium are shown in Fig. 6E. There was statistically significant reduction in impedance between 1 and 5 Hz, as measured by a mixed-design ANOVA (F = 11.8, df = 1, 17, P < 0.005).

Changes in the phase of the membrane response were consistent with the abolition of resonance (Fig. 6F). Resonances are associated with positive phases (voltage leading the current) below the resonance frequency, and these were lost after the application of cadmium.

The role of specific voltage-gated calcium channels in membrane resonance.

Like the membrane potential oscillation, resonance was unaffected by blockade of CaV2.1 currents with 100 nM ω-agatoxin (Fig. 7A1). There were likewise no changes in the holding current (TTX = 34.2 ± 5.1, ω-agatoxin = 39.6 ± 5.4 Fig. 7A2) or input resistances (TTX = 166 ± 24 MΩ, ω-agatoxin = 172 ± 28 MΩ Fig. 7A1, 0-frequency impedance). Likewise, the phase of the membrane response with regard to the input frequency was unaffected by ω-agatoxin application (Fig. 7A2).

Fig. 7.L-Type currents, not P/Q-type currents, are necessary for membrane resonance. A1: the sample impedance curves and the input resistance showed no effect of blocking P/Q-type currents. The 0-frequency impedance indicates the input resistance. A2: the phase of the membrane response was also unaffected by ω-agatoxin inset: the holding current (H. Current) was not changed by ω-agatoxin (A) application. T, TTX. B1: in contrast, application of 5 μM isradipine significantly reduced the impedance at all frequencies but did not significantly change the input resistance. B2: the positive phase shift in the membrane response was reduced after isradipine application inset: isradipine (I) significantly increased the required holding current. Error bars are SE *P < 0.05.

CaV1 antagonism with 5 μM isradipine was effective in blocking the membrane resonance (Fig. 7B1). Because isradipine acts slowly, we did not compare data from individual cells before and during application of isradipine, but instead, slices were incubated in isradipine throughout the experiment, and separate groups of cells were used for control and drug treatments. Isradipine significantly increased the current needed to hold the neurons at −30 mV after the application of isradipine (TTX = 28.5 ± 7.0 pA, isradipine = 53.5 ± 6.9 pA, t = −2.28, df = 7, P < 0.05, unpaired t-test). The holding current in isradipine was similar to that seen in cadmium (compare Figs. 7B2 with 6C, respectively). There was no significant change in steady-state input resistance (TTX = 196 ± 21 MΩ, isradipine = 171 ± 14 MΩ), as shown in Fig. 7B1, zero-frequency impedance.

Isradipine significantly reduced the impedance measured in LTS interneurons (F = 4.14, df = 1, 37, P < 0.05 Fig. 7B1). Antagonism of Cav1 channels also resulted in a reduction in size of the membrane resonance, measured as a difference in the slopes of the frequency-impedance curve between 1 and 5 Hz (F = 3.07, df = 9, 342, P < 0.005), but a residual membrane resonance persisted (F = 4.16, df = 9, 342, P < 0.05). The effect of Cav1 channel antagonism on the phase of the membrane response is seen in Fig. 7B2. The positive phase shift in the membrane response at low frequencies was greatly reduced after isradipine application, consistent with the reduction in membrane resonance size.

Blockade of CaV2.2 also greatly altered the neurons' membrane resonance. Application of 1 μM ω-conotoxin GVIA abolished the membrane resonance (F = 3.93, df = 8, 162, P < 0.005 Fig. 8A1). The impedance was increased at low frequencies, including a significant increase in the steady-state input resistance from 206 ± 29 to 313 ± 59 MΩ (t = −2.67, df = 8, P < 0.05 Fig. 8A1, 0-frequency impedance). Unlike isradipine, ω-conotoxin GVIA did not change the holding current required at these voltages (Fig. 8A2). Consistent with its effect on membrane resonance, ω-conotoxin GVIA shifted the phase of the impedance from a lead to lag at low frequencies (Fig. 8A2).

Fig. 8.N-Type calcium currents and calcium-activated chloride channels are necessary for membrane resonance. A1: the sample impedance curve shows a blockade of membrane resonance after the application 1 μM ω-conotoxin GVIA. The input resistance (0-frequency impedance) significantly increased. A2: the phase advance in the membrane response was prevented after application of ω-conotoxin GVIA inset: the holding current did not change after blocking N-type calcium currents (C). B1: the blocking of CaCCs with 100 μM niflumic acid prevented expression of membrane resonance, reducing the peak in the impedance profile. The input resistance (0-frequency impedance) did not change after the application of niflumic acid. B1: niflumic acid prevented the phase advance in the membrane response inset: the holding current was not significantly altered after niflumic acid (N) application. Error bars are SE.

Both isradipine and ω-conotoxin GVIA inhibited the membrane resonance but did so in different ways. The effects of isradipine on the membrane resonance and holding current were similar to the effects of cadmium. Isradipine and cadmium both blocked resonance by reducing the impedance over a wide range of frequencies while leaving the input resistance unaffected. In contrast, ω-conotoxin GVIA increased the impedance at low frequencies and input resistance to levels near the peak impedance measurements in TTX.

CaCCs are necessary for the membrane resonance.

Blockade of CaCCs with 100 μM NFA abolished membrane resonance (Fig. 8B1). There was no significant change in holding current (Fig. 8B2) or input resistance (Fig. 8B1, 0-frequency impedance). The change in the impedance curves resembles the effect of cadmium or isradipine application. After blocking CaCCs, membrane resonance was significantly reduced (F = 4.42, df = 13, 208, P < 0.005), although there was still a small peak in the impedance curve (F = 8.05, df = 13, 208, P < 0.01). The phase of the membrane response changed from a phase advance below the resonance frequency to no phase advance after NFA application (Fig. 8B2).


Abstract : Interaction between a membrane oscillator generated by voltage-dependent ion channels and an intracellular calcium signal oscillator was present in the earliest models (1984 to 1985) using representations of the sarcoplasmic reticulum. Oscillatory release of calcium is inherent in the calcium-induced calcium release process. Those historical results fully support the synthesis proposed in the articles in this review series. The oscillator mechanisms do not primarily compete with each they entrain each other. However, there is some asymmetry: the membrane oscillator can continue indefinitely in the absence of the calcium oscillator. The reverse seems to be true only in pathological conditions. Studies from tissue-level work and on the development of the heart also provide valuable insights into the integrative action of the cardiac pacemaker.

The earliest models of cardiac rhythm, beginning with that of Noble, 1 were restricted to interactions between surface membrane ion channels. The first cardiac cell model to incorporate the intracellular calcium signaling system involved in excitation-contraction coupling was that of DiFrancesco and Noble. 2 That model was developed for sheep Purkinje fibers, and it was the first to predict a large role for sodium/calcium exchange current during the action potential. In fact it identified the slower components of inward current that had previously been attributed to calcium channel current as being attributable instead to the exchanger. Pacemaker activity in that model was attributed almost entirely to the slow onset of the nonspecific cation current, if, activated by hyperpolarization. The exchange current was not predicted to play any role in pacemaker rhythm in that case.

However, the DiFrancesco-Noble Purkinje fiber model was almost immediately developed to create the first mathematical model to reproduce voltage waveforms similar to those observed in rabbit sinoatrial node (SAN) cells. 3 It was also developed later to create the first models of rabbit atrial cells. 4,5 For the intracellular calcium signaling mechanisms, the 1980s models were based on the work of Fabiato on calcium-induced calcium release. 6

The experimental basis of the SAN model was the work of Brown et al, 7,8 which revealed the presence of very slow components of inward current similar to that predicted for the sodium/calcium exchange current during the action potential. In fact, the modeling gave confidence that these experimental recordings were not voltage-clamp artifacts.

One of the collaborators in that experimental work, Junko Kimura, later collaborated with Akinori Noma to measure the voltage and ion concentration dependence of the sodium/calcium exchange current under highly controlled conditions. 9,10 The results were in remarkable agreement with the equations used in the models. All subsequent developments of models of calcium signaling and of sodium/calcium exchange in the heart can be seen to derive from the models of the 1980s.

Among the experimental results on the rabbit SAN, there were 2 important findings that relate to the present controversies. The first was that, when investigating inward currents during voltage-clamp depolarizations, 2 clear components were often observed. Based on the modeling work, the first of these was attributed to activation of the L-type calcium current (called Isi in early work), whereas the second, much slower, component was attributed to activation of sodium/calcium exchange during calcium release following the onset of the action potential.

The computer model correctly reproduced these 2 components (see Figure 9 in Brown et al 8 ). Those original computations were done using OXSOFT HEART. We have repeated the computations for this article using the publicly available software COR (www.cor.physiol.ox.ac.uk) and the CellML encoded version of the model downloaded from the CellML model repository (www.cellml.org). The results are shown in Figure 1. They are very similar to the original figure but extend it by revealing the separate contributions of ICaL and INaCa. Later experimental work 11 fully confirmed the predictions of the models regarding sodium/calcium exchange current during the action potential.

Figure 1. Sodium/calcium exchange currents in the DiFrancesco-Noble (1985) model. 2 Top (A), Experimental results obtained by Kimura et al 1987 using guinea pig ventricular cells. 10 Exchange current in the inward mode (corresponding to sodium influx and calcium efflux) as a function of membrane potential at different concentrations of extracellular sodium ions. Top (B), Corresponding curves computed from the equations used for sodium/calcium exchange current in the model (note that these results were obtained before the experimental ones). Bottom, Variations of ionic currents (IK, ICa,f [now ICaL], If, and INaCa) during computed action and pacemaker potentials. Note the substantial inward exchange current predicted during the plateau of the action potential. This computation was performed for this article using COR and is exactly the same as that published in 1985.

Having established the performance of those models so far as the action potential is concerned, we now turn to the pacemaker depolarization. This is the critical question. During voltage-clamp depolarizations the sodium/calcium exchange current, reflecting the time course of the intracellular calcium transient invariably followed the onset and inactivation of the calcium channel current. By contrast, this time relationship was often reversed during the pacemaker depolarization. Figure 2 shows the experimental protocol used to reveal this in the 1984 work. The natural pacemaker depolarization was interrupted at various times by clamping the voltage to that achieved at the time of onset of the clamp. If this time was late enough (roughly, during the last third of the pacemaker depolarization), a slow inward current was recorded whose time course resembled the slow component recorded during standard voltage-clamp depolarizations. However, there was no visible preceding activation of the calcium current. This was interpreted to indicate the possibility that calcium release during sinus node pacemaker activity could precede activation of the calcium current, as observed by Lakatta et al. 12 Figure 2 shows new computations of this phenomenon using COR and the downloaded CellML file for the 1984 SAN model.

Figure 2. Calcium release preceding activation of ICaL. Top left, One of the experimental recordings made on rabbit sinoatrial node by Brown et al (Figure 9 in the article, 8 trace at −44 mV). The membrane potential was allowed to change spontaneously during an action potential and for most of the subsequent pacemaker depolarization. Near the end of this depolarization, but clearly before the upstroke of the action potential, the membrane potential was clamped at the potential reached. A slow transient inward current was recorded, the onset of which is much slower than that of the L-type calcium current. It requires ≈100 ms to reach its peak. Bottom left, Voltage protocol used to repeat the 1984 simulation of these results using the SAN model developed from the DiFrancesco-Noble model. Vertical scale is in millivolts. Horizontal scale is in seconds. Top right, Computed net ionic currents corresponding to the three levels of the clamp potential in the bottom left protocol. Clamping at the middle of the pacemaker depolarization simply generates a smooth development of net inward current corresponding to decay of IK and onset of If. The middle curve (interrupted) generates a slow transient inward current similar to that in the experimental trace (top left). The dotted curve generates a double peak as the L-type calcium current starts to be activated. Vertical scale is in nA horizontal scale in seconds. Bottom right, Computed variations in the sodium/calcium exchange current during the three voltage protocols.

The essence of the Lakatta hypothesis was therefore present in the very earliest simulations of calcium signaling in cardiac cells.

Why did Brown et al not attribute the pacemaker depolarization itself to this mechanism? The main reason was that, although slow inward ionic currents of this kind were often recorded in the experiments, they nearly always died out after 1 or 2 oscillations. The maintenance of the calcium signal oscillator was not therefore independent of the voltage-dependent ionic current oscillator.

Table 2. Non-standard Abbreviations and Acronyms

How Do the Different Oscillators Interact?

To investigate the contribution of the various ion currents, we compared the simulation results of the 6 mathematical models of SAN cells available in the CellML repository: Demir et al, 12a Dokos et al, 12b Kurata et al, 12c Maltsev and Lakatta, 12d Noble and Noble, 12e and Zhang et al. 12f For clarity of the figures, we show only the results of the latest 4 models in the figures but include the results of all models in the text.

Figure 3 shows the membrane potential, the intracellular calcium concentration and the inward currents the models have in common: Ca 2+ L-type current (ICaL), Na + /Ca 2+ exchanger (INaCa), funny current (If), and background sodium current (IbNa).

Figure 3. Overview of models, oscillations, and underlying currents. Note that If(solid line in bottom graphs) is always the smallest of the inward currents (ICaL, INaCa, IbNa, and If).

The ICaL shows the largest amplitude of the currents in all the models, and the maximum INaCa current is larger than If and IbNa, except in the Zhang model, which has a constant intracellular calcium concentration for model simplification. If is in all models smaller than the IbNa.

When we now block the various currents, one at a time (see Figure 4), what happens to the membrane potential (and calcium) oscillations in the SAN cell models? All the models (Demir, Zhang, Maltsev, Dokos, Noble, Kurata) agree on the importance of ICaL: without activation of this calcium current, the SAN oscillations do not occur. The models are in accord with the experimental observation that without calcium uptake or release from the sarcoplasmic reticulum (SR) the oscillations do not stop (and a 2% increase in background sodium current leads to no missing beats in the Maltsev model). In addition, complete block of If does not stop the oscillations in any of the models.

Figure 4. The voltage traces when one or several model currents are fully blocked at t=2 seconds. The rows denote block of ICaL and ICaT, of INaCa, of background currents (see below), of If, and of Iup. The missing beats in the Maltsev model at block of SERCA disappear when IbNa is increased by 2%. “Background currents” blocked in respective models: Maltsev (IbCa and IbNa), Kurata (IbNa and IstNa), Zhang (IbCa and IbNa), Dokos (IbNa and INa).

So, is only ICaL necessary for the oscillations? What is actually causing the oscillations in the models? In all models, there exist a number of background or sustained inward currents (IbNa, IbCa, Ist), and setting them to zero abolishes or diminishes the oscillations in 4 of the models (Kurata, Maltsev, Noble, Demir) does that mean that the background currents might be more important than If and intracellular Ca 2+ cycling? Clearly, we are dealing here with a multifactorial system in which even ionic currents that show no intrinsic dynamic properties (which is the definition of a “background” current) or currents that have yet to be characterized completely (such as Ist) play an important quantitative role. Ist has been first characterized by Guo et al (1995) as sustained Na + inward current, which is active during the depolarization phase, but because of unavailability of a specific blocker, it has been impossible to investigate the importance of this current in whole SAN cells.

The removal of INaCa abolishes the oscillations as well (in all models but the Zhang model which has fixed ion concentrations). INaCa is most of the time an inward current extruding Ca 2+ from the cell (see Figure 4). When additionally setting the SR Ca 2+ concentration to constant the block of INaCa does only change the frequency, but does not abolish the oscillations completely. Therefore, it is the resulting Ca 2+ overload with full INaCa block that leads to the termination of the oscillations. As there exist also other pumps and exchangers in SAN cells to extrude Ca 2+ from the cell (avoiding Ca 2+ overload), which are not present in the mathematical models it is unclear whether complete block of INaCa would abolish the oscillations in real cells.

Sensitivity analysis of the SAN period with respect to block of ion currents and pumps was performed at steady state of the model (300 seconds after the change). The Table shows that the models consistently show an increase in period of 0.7 to 1.87%, 0.77 to 4.82%, 0.14 to 0.83%, and 0.83 to 1.34% with a 10% block of ICaT, IbNa, If, and Ist, respectively. Currents and pumps related to the intracellular calcium system show rather diverse results for the different models (block of ICaL, INaCa, and Iup led to a decrease in period in Demir versus and increase in Maltsev). We assume that this lack of consistency is attributable to the differences in calcium handling in the models.

Table 1. Sensitivity Analysis of the SAN Period

In general, the largest sensitivities can be observed for IbNa/Ist and second comes ICaT (ignoring the inconsistent values for ICaL). The Maltsev model provides an exception, with Iup inducing the largest change in period (followed by IbNa and ICaT).

A bifurcation analysis would be able to provide further information on the dynamic behavior of the models but would be beyond the scope of this article. Note also that all detailed results have to be interpreted with caution because the models have not been tuned and built for these kind of investigations, ie, the analysis could be out of the predictive range of the models.

The models would suggest 3 important features of concerted action leading to and maintaining the oscillations in the SAN cells: the slow depolarization phase via inward currents (If, Ist, [IbNa]), activation of the inward calcium currents (ICaL, ICaT), extrusion of calcium (INaCa, IpCa?). The importance of SR release could lie in the stabilization of the oscillations across frequencies as indicated by Maltsev and Lakatta, 12d but in their article, they also show that the SR release is not actually driving the oscillations (see Figure 5C in their article).

Insights From Tissue Studies and From Development of the Heart

The studies on which we have commented so far focus at the level of ion channels and the integration of their activity at the level of single cells. The other contributions to this issue make valuable contributions to the debate at the tissue level, particularly concerning the use of imaging with voltage- or calcium-sensitive indicators 13 and the insights that come from studying the development of pacemaker tissues. 14

These studies show that integrative physiology of pacemaker activity does not end with analysis of cellular activity. In fact, it has been evident since the first electrophysiological mapping work that the sinus node acts as more than just a few thousand cells beating in synchrony. Depending on the precise physiological conditions, the apparent origin of pacemaker activity can shift from one region of the node to another. 15–17 We refer to “apparent origin” because it would be an oversimplification to suppose that the area leading the depolarization uniquely determines what happens (see also elsewhere 18 ). Electric current flows between any two connected cells that are at different potentials, and this current must influence the leading cells (by slowing them down) as much as they influence the follower cells (by speeding them up). The earliest computations of cell-to-cell interaction in the sinus node using parallel computers showed that even very low connectivity (just a few connexin channels between each cell) could synchronize cells with inherently different rhythms. 19–21 These computations also revealed that the cells with an intrinsically rapid rhythm, located at the periphery of the node, and which would therefore ‘lead’ the depolarization in an isolated node, become the follower cells when the node is connected to the atrium. Boyett and colleagues showed experimentally and computationally 22 that isolating the sinus node alters the direction of propagation, with the leading cells shifting from the center to the periphery, and more recent work from Boyett and colleagues has further emphasized how the architecture of the node influences its function. 23 Anatomy and physiology necessarily interact at the tissue level. A valuable set of insights from the debate between Efimov and Federov versus Joung and Lin in Circulation Research 13 is that the origin of the impulse is multicentric and that single cells and the intact node react differently to drugs and to genetic changes.

Does work at the tissue level shed any light on the relative roles of membrane and calcium-generated oscillations? This is the central focus of the debate between Efimov and Federov versus Joung and Lin. In principle, using voltage-sensitive markers to search for multiple waveforms could make an important contribution. And indeed, the voltage-sensitive dyes do give results that differ from microelectrode recordings. Efimov and Federov attribute this to the fact that the dyes record from an extended region that can include cells and tissues of different types, and so necessarily give composite results. Against this, Joung and Lin point to the fact that confocal calcium imaging can sometimes show calcium changes leading voltage changes toward the end of the pacemaker depolarization, particularly in the presence of isoproterenol. Dissecting out such a complicated set of interrelationships will be difficult. We concur with the remark that future work will “require close collaboration between the mathematical modelers and experimenters to dissect the role of the individual components” 13 but would add that “dissect” already biases the analysis. In nonlinear interactive systems, attributing relative roles to different components may be misleading. It is the “integrative” function that matters. As also noted in that study, the different mechanisms work synergistically. Because of nonlinearity, this necessarily means that attribution of the quantitative contributions of individual components depends on the physiological and pathological context. This context includes the fact that information flow between the genome and the phenotype is not one way. The phenotype is not a static product of its genes (reviewed elsewhere 24,25 ). There is feedback downward from the phenotype to control gene expression. Good examples are available in this review series, including, notably, the downregulation of 2 important pacemaker currents, If and IKs, during atrial tachyarrhythmias. Activity in the atrium can therefore remodel the gene expression profile in the sinus node.

Remodeling of gene expression naturally takes us on to consider the other major contribution to this focused issue of the journal because, as Christoffels et al 14 show, the development of the heart depends on suppression of gene expression as the embryo develops into the adult. All cardiac myocytes in the early embryo show pacemaker rhythm. The change to the adult forms occurs through repression of the gene expression patterns that develop to enable adult working myocardial cells to differentiate. As a consequence, the adult pacemaker cells resemble those of the early embryo. The identification of the transcriptional repressors involved is therefore an important goal. As Christoffels et al show, this is a rapidly developing area, and it contains the promise that we will eventually know the molecular basis of embryonic development of the heart. These insights will also be important in understanding adult function because there is continuous turnover of gene expression. Variations in expression levels during the turnover of ion channels have recently been shown by Ponard et al 18 to play a role in heart rate variability using a combination of myocyte cultures and computer modeling.

Conclusions

Experimental data and the in silico modeling work show the complexity of the multifactorial system of SAN excitation. The contribution of If and its importance as a pharmaceutical target has been proven by the successful development of ivabradine and is delineated further in the review article by DiFrancesco 26 in this review series. Further currents seem to be involved in the depolarization phase (Ist, mechanosensitive currents 27 and others) whose relative contributions are still to be determined.

It appears almost obvious that also the fast upstroke at the end of the depolarization phase has a large impact on the depolarization frequency by adjustment of the activation threshold. The evidence presented by Lakatta et al 12 in this review series underlines also the influence of SR Ca 2+ release in generation of the upstroke (besides ICaT and ICaL), in the extreme showing similarities to delayed afterdepolarizations.

Already, earliest modeling and experimental work showed (consistent with current findings) that neither If nor spontaneous Ca 2+ release from the SR on its own is or can be driving the pacemaking activity there is always concerted action necessary and interplay between the various ion channels. Also, the heart rate regulation via cAMP is influenced by and influences multiple ion channels, pumps, and exchangers, thereby creating a robust and stable, but still flexible, system that maintains the billions of heart beats in a normal life.

Future work will most probably discover even further mechanisms influencing heart rate that might be even more relevant targets in specific diseases and pathologies than the currently known pathways.

Original received February 12, 2010 revision received April 27, 2010 accepted April 28, 2010.

Sources of Funding

Work in the laboratory of the authors is financed by the European Union (Framework 6, BioSim, and Framework 7, VPH-PreDiCT) and the British Heart Foundation.


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