Regional acidosis locally inhibits but remotely stimulates Ca2+ waves in ventricular myocytes

Abstract Aims Spontaneous Ca2+ waves in cardiomyocytes are potentially arrhythmogenic. A powerful controller of Ca2+ waves is the cytoplasmic H+ concentration ([H+]i), which fluctuates spatially and temporally in conditions such as myocardial ischaemia/reperfusion. H+-control of Ca2+ waves is poorly understood. We have therefore investigated how [H+]i co-ordinates their initiation and frequency. Methods and results Spontaneous Ca2+ waves were imaged (fluo-3) in rat isolated ventricular myocytes, subjected to modest Ca2+-overload. Whole-cell intracellular acidosis (induced by acetate-superfusion) stimulated wave frequency. Pharmacologically blocking sarcolemmal Na+/H+ exchange (NHE1) prevented this stimulation, unveiling inhibition by H+. Acidosis also increased Ca2+ wave velocity. Restricting acidosis to one end of a myocyte, using a microfluidic device, inhibited Ca2+ waves in the acidic zone (consistent with ryanodine receptor inhibition), but stimulated wave emergence elsewhere in the cell. This remote stimulation was absent when NHE1 was selectively inhibited in the acidic zone. Remote stimulation depended on a locally evoked, NHE1-driven rise of [Na+]i that spread rapidly downstream. Conclusion Acidosis influences Ca2+ waves via inhibitory Hi+ and stimulatory Nai+ signals (the latter facilitating intracellular Ca2+-loading through modulation of sarcolemmal Na+/Ca2+ exchange activity). During spatial [H+]i-heterogeneity, Hi+-inhibition dominates in acidic regions, while rapid Nai+ diffusion stimulates waves in downstream, non-acidic regions. Local acidosis thus simultaneously inhibits and stimulates arrhythmogenic Ca2+-signalling in the same myocyte. If the principle of remote H+-stimulation of Ca2+ waves also applies in multicellular myocardium, it raises the possibility of electrical disturbances being driven remotely by adjacent ischaemic areas, which are known to be intensely acidic.


Introduction
An aberrant form of Ca 2þ signalling is the Ca 2þ wave, commonly observed in ventricular myocytes during periods of Ca 2þ -overload. 1 Ca 2þ waves can occur spontaneously, initiated by a localised SR Ca 2þ release that propagates spatially, via a 'fire-diffuse-fire' form of Ca 2þinduced Ca 2þ release from the SR 2 . Ca 2þ waves are believed to facilitate triggered arrhythmias, by driving delayed after-depolarizations (DADs) that may transition to ectopic action potentials. 3,4 Spontaneous Ca 2þ waves are common events during clinical conditions such as myocardial ischaemia. One factor that may trigger Ca 2þ waves is a fall of pH i , although wave initiation has been variously reported to be stimulated or inhibited by acidosis. 5,6 Ca 2þ waves are also promoted by other factors, in particular by elevations of [Na þ ] i that occur when the Na þ /K þ pump is inhibited. 7 It is notable, therefore, that a significant [Na þ ] i rise occurs when the sarcolemmal Na þ /H þ exchanger (NHE1) is stimulated by acidosis. 8 In the present work, we have investigated the mechanisms coupling Ca 2þ waves to changes of pH i .
Intracellular H þ ions are powerful modulators of cell function. In ventricular myocytes they are generated metabolically, but maintained at low cytoplasmic levels ([H þ ] i $60 nM, equivalent to pH i 7.2), most commonly via H þ i extrusion on NHE1. 9 Despite regulation, reversible increases of [H þ ] i of about 30 nM occur physiologically (equivalent to a fall of $0.15 pH units), while much larger increases of about 400 nM (equivalent to a fall of $0.6 pH units) occur during myocardial ischaemia. 10 These [H þ ] i elevations represent a form of intracellular H þ signalling. Prominent among the targets for such signalling are Ca 2þ handling proteins, namely the ryanodine receptor (RyR), [11][12][13] the sarco/endoplasmic reticulum Ca 2þ ATPase (SERCA), 14,15 Na þ /Ca 2þ exchanger (NCX), 16 and the L-type calcium channel. 17 Although direct H þ interaction with these proteins is predominantly inhibitory, an elevation of [H þ ] i can enhance the electrically evoked calcium transient (CaT), 18 an effect that helps to protect contractility during acidosis. As mentioned above, this latter stimulation occurs indirectly through H þ activation of NHE1. The resulting rise of [Na þ ] i slows Ca 2þ efflux on sarcolemmal NCX, which boosts sarcoplasmic reticulum (SR) Ca 2þ loading via SERCA, thereby increasing CaT amplitude. 18,19 Quite how the balance between inhibitory and excitatory effects of H þ i on Ca 2þ signalling impacts on the generation of arrhythmogenic Ca 2þ waves has yet to be examined.
The importance of spatial interactions among [H þ ] i , [Na þ ] i and [Ca 2þ ] i in ventricular myocytes has been highlighted in recent work. 18 Because of high intracellular buffering, cytoplasmic H þ mobility is low, 20 so that localised [H þ ] i microdomains can form. 21 A microdomain of elevated [H þ ] i , by locally stimulating NHE1, elevates Na þ i , which increases the CaT amplitude. But because Na þ diffuses rapidly in cytoplasm, 18,22 it can enhance the CaT globally within the cell, including in regions not experiencing acidosis. In the present work we investigate if spontaneous Ca 2þ waves are similarly controlled through interacting spatial H þ i and Na þ i signals.
In order to investigate the coupling of Ca 2þ waves to pH i , we have manipulated intracellular pH, Na þ , and Ca 2þ in rat ventricular myocytes. Our data indicate that H þ ions exert direct inhibitory and indirect excitatory effects on Ca 2þ waves. The excitatory effect is mediated via intracellular Na þ . When excitation is induced by a localised acidic microdomain, it is typically expressed remotely in non-acidic regions of the cell, driven by fast Na þ i diffusion. Our data provide evidence that acidosis, and its spatial heterogeneity, is a powerful substrate for the initiation and spatial organisation of pro-arrhythmic Ca 2þ waves.

Methods
Detailed methods are available in the Supplementary material online.

Ventricular myocyte isolation
All procedures were performed in accordance with UK Home Office and local guidelines. Ventricular myocytes were isolated from 46 male Sprague-Dawley rats, as previously described, 23 or from neonatal rats (1 day old).

Fluorescence measurements of intracellular pH and Ca 2þ
pH i : myocytes were loaded with carboxy-seminaphthorhodofluor-1 (cSNARF-1, 10 lM) at room temperature. Cells were imaged confocally on a Leica SP5 inverted microscope. Intracellular calibration of cSNARF-1 was performed in separate experiments using nigericin. 23 Ca 2þ waves and sparks: myocytes were AM-loaded with fluo-3 (18 lM). Cells were superfused and quiescent cells were imaged in linescan (xt) mode along the cell's longitudinal axis at 400 lines per second. Ca 2þ sparks were imaged in solution containing 1 mM free Ca 2þ . Switching the superfusate to one containing raised (5 mM) free Ca 2þ induced a modest calcium overload that triggers Ca 2þ waves.

Generating intracellular pH gradient
A pH i gradient was induced using a microfluidic device consisting of a squarebore double-barrelled micropipette, which released two parallel microstreams of solution perpendicular to the cell. 24 One microstream contained Tyrode with 5 mM CaCl 2 plus 10 mM sucrose to help visualize the interstream boundary; the other microstream contained 80 mM acetate with 5 mM free Ca 2þ . The position of the microstream boundary across the cell was recorded in xy before and after each linescan experiment. The smooth pH i gradient induced is illustrated in Figure 4B.

Data analysis
Data are expressed as mean ± SE. Statistical significance was tested using paired Student's t-test or nested ANOVA, depending on the experimental protocol. Where relevant, the Holm correction for multiple testing was applied. Significance is denoted as * for P < 0.05, ** for P < 0.01, *** for P < 0.001.
Wave propagation velocity was calculated from linescan images using the angle of incidence of the wavefront, relative to the longitudinal axis of the cell.
Linescan recordings of Ca 2þ sparks were normalized using a custom-built Matlab macro, followed by spark frequency analysis using an algorithm developed by Kong et al. 25 Results Acidosis affects Ca 2þ waves via H þ i and Na þ i signals We explored the H þ i -sensitivity of Ca 2þ waves, by first imposing wholecell changes of pH i, at constant pH o . Individual ventricular myocytes, when subjected to modest Ca 2þ overload (5 mM Ca 2þ o ), displayed spontaneous Ca 2þ waves (Figure 1Ai), with a frequency of 18.7 ± 2.5 min -1 . At times these waves converted into whole-cell CaTs (Supplementary material online, Figure S1), induced by the Ca 2þ -driven transient inward current (I ti ) triggering an action potential. 3,4 Cells displaying wave-triggered CaTs were not included in the analysis, because of their confounding effects on wave properties. Intracellular acidification (from pH i 7.3 to 6.6), induced by superfusion of 80 mM acetate, initially reduced wave frequency ( Figure 1Aii). After 30 s, wave frequency then progressively increased above control levels ( Figure 1Ai, ii, Supplementary material online, Figure S2A). The increase could be graded by varying the magnitude of intracellular acidosis (superfusion with 20, 40, or 80 mM acetate; Figure 1Aiv). The increase was attributable to an H þ i -dependent stimulation of NHE1 activity, as it was abolished in the presence of 5-(N,N-dimethyl) amiloride (DMA, 30 lM), a high-affinity NHE1 inhibitor. Under these conditions, reducing pH i from 7.3 to 6.6 now produced a decrease in Ca 2þ waves (Figure 1Bi, ii, Supplementary material online, Figure S2B), which was also graded with the severity of acidosis (Figure 1Biv; note that, in these latter experiments, extreme alkalosis, produced by 20 mM trimethylamine superfusion, also reduced wave frequency). Abolition of H þ i -evoked Ca 2þ waves was confirmed with a structurally different NHE1 inhibitor, cariporide, which targets NHE1 more specifically among NHE isoforms than DMA 26 ; Supplementary material online, Figure S2C, D. Thus, for the pH i range from 7.3 to 6.6, raising [H þ ] i exerts opposing effects on Ca 2þ wave frequency; an NHE1-independent inhibition, and a delayed, NHE1-dependent stimulation.  Figure S6). For clarity, [Na þ ] i data have been replotted in Figures 1Aiii and 1Biii. The data emphasize that preventing the H þ -evoked rise of [Na þ ] i with DMA, prevents wave stimulation. Stimulation is thus dependent on the rise of [Na þ ] i , while acid-induced wave inhibition, observed in the presence of an NHE1 inhibitor, is attributable directly to the rise of [H þ ] i . N.B. since the rise of [Na þ ] i is completely prevented by inhibiting NHE, we do not anticipate a role for H þ -induced inhibition of the Na þ /K þ pump under these conditions. Ca 2þ wave stimulation has been quantified in Figure 2Ai, which plots, on logarithmic axes, wave frequency vs. [Na þ ] i (data amalgamated from Figure 1Aii, Aiii). Wave frequency rises steeply with [Na þ ] i (to a first approximation, wave frequency / [Na þ ] i 4 ). In contrast, wave frequency in the absence of NHE1 activity decreased with a rise of [H þ ] i , displaying a more shallow H þ -dependence ( Figure 2Aii). The net result for whole-cell acidosis on wave frequency will be a combination of these stimulatory and inhibitory components. At steady-state, the combination is net stimulatory (Figure 1Aii, iv), reflecting the steep positive dependence of wave frequency on [Na þ ] i .

Mitochondrial NCX does not promote Ca 2þ waves during acidosis
Although sarcolemmal NCX is likely to mediate the [Na þ ] i -dependence of Ca 2þ wave frequency, this does not exclude an additional role for mitochondrial NCX (mNCX). Elevating [Na þ ] i has been proposed to promote mitochondrial Ca 2þ efflux on mNCX, 27 in addition to slowing the forward mode of sarcolemmal NCX. Promoting mitochondrial Ca 2þ efflux may therefore supplement the domain of cytoplasmic Ca 2þ that eventually enhances Ca 2þ wave frequency. To test this hypothesis, myocytes were first subjected to intracellular acidosis in the presence of the sarcolemmal NCX inhibitor, SN-6. The drug fully inhibited the H þ -evoked stimulation of Ca 2þ wave frequency ( Figure 2C), indicating a necessary role for the sarcolemmal exchanger. In contrast, selective inhibition of mNCX with CGP-37157 had no effect on H þ -evoked waves ( Figure 2C), indicating that mNCX is unlikely to be supplementing Ca 2þ wave stimulation. Indeed, it is more likely that mitochondria attenuate Ca 2þ waves. This is supported by the observation that when the mitochondrial uniporter (MCU), which mediates Ca 2þ uptake, was blocked by pre-incubation with ruthenium-360 (Ru360), followed by inhibition of mNCX with CGP-37157, then H þ -induced Ca 2þ wave frequency was enhanced by 70% ( Figure 2C). The result suggests that mitochondrial Ca 2þ uptake normally plays a protective role during intracellular acidosis, by sequestering some of the intracellular Ca 2þ -overload.

Acidosis affects multiple properties of Ca 2þ waves
In addition to Ca 2þ wave frequency, we investigated whether raising [H þ ] i influenced other features, notably, Ca 2þ wave propagation velocity (v prop ), amplitude, and time-course. Raising [H þ ] i increased wave velocity, both in the presence and absence of NHE1 activity ( Figure 3A, B). As shown in Figure 3C, velocity rose with a fall of pH i from 7.7 to 6.65 (equivalent to a 250 nM rise in [H þ ] i ), increasing by $40% over the range. According to a recent model of Ca 2þ wave propagation, 28 a plausible explanation for the velocity increase is an H þ -dependent reduction in cytoplasmic Ca 2þ buffering, for example, by troponin C and other proteins, as well as by cytoplasmic histidyl-dipeptides. 24 Decreased Ca 2þ buffering may reflect a reduction in the Ca 2þ binding constant (k on ), or an increase in the unbinding constant (k off ). Increasing [H þ ] i also increased resting [Ca 2þ ] i (as reported previously 24 ) and peak F/F 0 fluorescence, and slowed Ca 2þ wave relaxation (Suuplementary material online, Figure S3).

Local acidosis stimulates downstream Ca 2þ waves in remote regions of the myocyte
Acidosis was imposed locally at one end of an isolated myocyte using a dual micro-superfusion device positioned at right-angles to the cell (see Methods). One microstream contained 80 mM acetate while the other contained acetate-free Tyrode ( Figure 4A). This generated a stable endto-end pH i gradient of $0.6 units ( Figure 4B).
Under control conditions (before imposing the pH i gradient), no significant difference was observed in Ca 2þ wave frequency between ROIs positioned at opposite ends of the cell (P = 0.23; these regions were defined as segments along the line-scan at either end of the myocyte, of length equal to one third of total cell length). In contrast, after imposing the pH i gradient, Ca 2þ waves were initiated, and became clustered in the non-acidic end of the cell, even though this region was many sarcomerelengths away from the acidic zone. Thus, over the first 2 min of an imposed pH i gradient, Ca 2þ waves were rarely initiated in the acidic zone, but their frequency increased up to five-fold in the non-acidic zone (Figure 4Ci, D). Selective pharmacological inhibition (DMA) of NHE1 activity in the non-acidic zone did not prevent the local increase in Ca 2þ wave frequency (P = 0.01, n = 6), indicating that the relevant NHE1 activity driving wave initiation was in the acidic zone. This was tested further by selectively superfusing DMA over the acidic end of the myocyte. Although the pH i gradient itself was unaffected by this manoeuvre, the stimulation of Ca 2þ waves in the non-acidic zone was now greatly attenuated ( Figure 4D cf. 4E). Thus, locally enhancing NHE1 activity remotely stimulates Ca 2þ waves.
In summary, during uniform acidosis, all regions of a myocyte are equally likely to support a Ca 2þ wave, driven by NHE1 activity. However, when NHE1 is stimulated locally (by inducing a localised acidosis within the cell) there is selective stimulation and clustering of Ca 2þ waves in downstream non-acidic zones.

Local acidosis inhibits local Ca 2þ sparks
Since H þ ions affect multiple proteins involved in Ca 2þ signalling, the mechanism by which Ca 2þ waves are inhibited in the acidic microdomain, but remotely stimulated in the non-acidic microdomain, is not immediately obvious. One possibility is that H þ ions locally decrease RyR open probability (P o ), which could account for inhibition of wave

initiation.
A decreased P o may also enhance SR Ca 2þ retention. 29 This could contribute to remote wave stimulation if the locally elevated SR Ca 2þ load then diffused rapidly into non-acidic regions of the SR lumen.
To explore whether the spatial effects of acidosis on wave frequency are all due to RyR inhibition, Ca 2þ spark frequency was measured.
Under resting conditions, spark frequency at either end of the myocyte was not different (P = 0.33, n = 9). However, when a pH i gradient was imposed, Ca 2þ spark frequency in the acidic microdomain decreased by 72 ± 11% (P = 0.0002, n = 9), while that in the non-acidic microdomain was not significantly altered ( Figure 5A, P = 0.24, n = 9). This phenomenon In order to compress the results, the timecourse for the line-scans has been broken into three parallel columns. Note that, during control conditions, Ca 2þ waves initiate randomly along the length of the myocyte, whereas, during imposition of the pH i gradient, waves initiate almost exclusively in the non-acidic microdomain (represented by the blue bar above each column of line-scans), and their frequency increases. The acidic zone is represented by the red bar above each column of linescans. (Cii) Exemplar linescans recorded from 2 cells under equivalent conditions, but with 30 mM DMA included in the regional acetate superfusion (to inhibit NHE activity). During imposition of the pH i gradient, wave initiations remain restricted to the non-acidic microdomain, but now their overall frequency does not change compared with control. (D) Ca 2þ wave initiation was inhibited in the acidic (acetate, A) microdomain and remotely stimulated in the non-acidic (control, C) microdomain (n = 6 cells/3 animals). (E) Ca 2þ wave initiation was attenuated in the acidic microdomain, but absence of NHE1 activity prevented the remote stimulation of Ca 2þ waves in the non-acidic microdomain (n = 5 cells/2 animals). Paired t-tests.
was insensitive to NHE1 inhibition (Figure 5Aii). The results argue for local H þ inhibition of RyRs, but also indicate that any resulting local rise in luminal SR [Ca 2þ ] does not affect the P o of remote RyRs.
To verify the effect on Ca 2þ waves of regional RyR inhibition, tetracaine (an RyR antagonist) was applied to one half of a myocyte to simulate the inhibitory effect of H þ ions, while maintaining pH i uniformly at resting levels throughout the cell. Figure 5B shows that Ca 2þ wave initiation frequency observed with locally applied tetracaine was very similar to that observed with local acidosis and NHE1 inhibition (cf. Figure 4E). In both cases, Ca 2þ wave frequency was suppressed in the tetracaine/ acetate-exposed region of the cell, and did not significantly change in the downstream (unexposed) region. These findings confirm that, while local RyR blockade by H þ ions or tetracaine can explain local (upstream) inhibition of Ca 2þ waves, it cannot explain wave stimulation in downstream regions. This latter effect requires the local, upstream activity of NHE1.

Properties of the Ca 2þ wave map onto pH i gradients
To investigate whether properties of Ca 2þ waves, other than initiation frequency, also map onto pH i heterogeneity, Ca 2þ wave velocity (v prop ), amplitude and time-course were measured in the acidic and non-acidic microdomains. For the few Ca 2þ waves that successfully propagated from the non-acidic to the acidic zones of the cell, their velocity increased in the acidic zone (Figure 6Aii, 40 ± 7% faster, P = 0.0002, n = 8). A similar trend was observed when DMA was superfused over the acidic end of the cell, indicating that the faster propagation was independent of NHE1 activity (Figure 6Aii, 40 ± 6% faster v prop than non-acidic microdomain, P = 0.0002, n = 5).
The peak F/F 0 of the Ca 2þ wave was also significantly higher in the acidic microdomain compared with the non-acidic microdomain (Supplementary material online, Figure S4), while wave relaxation was significantly slower in the acidic microdomain (Supplementary material online, Figure S4). It was also noted that Ca 2þ waves frequently failed to propagate within the acidic microdomain (irrespective of the initiation site), unlike the negligible failure rate observed under control conditions ( Figure 6B, C). Taken together, our results show that multiple properties of the Ca 2þ wave (velocity, propagation-failure, amplitude, and relaxation rate, in addition to initiation frequency) are all subservient to the local pH i . Spatial non-uniformity of pH i thus induces dramatic heterogeneity of Ca 2þ waves.

pH i gradients across confluent monolayers of myocytes induce [Na þ ] i gradients
To explore whether spatial pH i gradients can be established in multicellular cardiac structures, as well as in isolated cells, dual microperfusion was used to deliver a microstream containing 40 mM lactate in parallel to a lactate-free microstream over a confluent monolayer of neonatal rat ventricular myocytes. Under control conditions (i.e. uniform exposure to lactate-free solution), no pH i heterogeneity was observed when imaging the cSNARF-1 fluorescence ratio (Figure 7Ai). However, when the monolayer was regionally superfused with 40 mM lactate (to represent the metabolic acidosis seen during myocardial ischaemia), a stable pH i gradient of $0.3 units formed in the region of the solution boundary, of width $100 mm, equivalent to several neonatal cell-lengths ( Figure  7Aii; cell-length is typically 20-40 mm). Cytoplasmic acidification in lactate-exposed cells activates NHE1 locally, which produces a rise in [Na þ ] i , detected using SBFI fluorescence. 30 In the monolayers analysed in Figure 7, cytoplasmic diffusion and gap junctional permeation of Na þ ions then resulted in a smooth gradient of elevated [Na þ ] i , $2.5 mM in magnitude, co-located with the pH i gradient but extending up to 100 mm beyond the acidic zone. Note that, although SBFI fluorescence is modestly pH-sensitive, 31 the ensuing SBFI response cannot be explained as an artefact generated by the underlying pH i gradient, because the shapes of the pH i and Na þ i profiles are not superimposable. The observations in monolayers are thus consistent with those made in isolated ventricular myocytes, showing that intracellular Na þ signalling can be stimulated downstream of a localised acidic domain.

Discussion
We have demonstrated that acidosis powerfully stimulates arrhythmogenic Ca 2þ waves. While this is consistent with earlier phenomenological descriptions, 5 we have now quantified the relationship among [H þ ] i , [Na þ ] i , and Ca 2þ waves, and demonstrated antagonistic control by H þ i and Na þ i . Furthermore, since H þ and Na þ diffuse at different rates in myocyte cytoplasm, the control of Ca 2þ wave generation becomes a complex spatio-temporal process. A key finding is that a localised source of intracellular acid inhibits Ca 2þ waves in the immediate   32 A previous report concluded that intracellular acidosis caused only Ca 2þ wave suppression, 6 in contrast to our findings. This apparent discrepancy can be explained partly by the lower experimental temperature in the earlier study, which would decrease NHE1 activity, 33 and by the briefer exposure to weak acid, which would limit any rise of [Na þ ] i .
In our own work, we have clearly identified both Na þ i -dependent stimulation and H þ -dependent inhibition of Ca 2þ waves.
We further demonstrate that increased [Na þ ] i couples to Ca 2þ waves via the modulation of sarcolemmal NCX, since the increase in wave frequency was prevented by pharmacological inhibition of this transporter. In principle, mitochondrial NCX could also make a contribution, however inhibiting mNCX provided no evidence for this. Instead, we confirm a cardioprotective role for mitochondria in buffering excess cytoplasmic Ca 2þ . 34 Rapidly diffusing Na þ ions couple local acidosis to remote Ca 2þ wave stimulation Microdomains of pH i are intuitively expected to affect local Ca 2þ signals, under conditions such as vascular perfusion heterogeneity. The unexpected finding from our study is that an acidic microdomain can affect more than just local signalling; it drives downstream Ca 2þ waves remotely, a phenomenon that depends on NHE1 activity in the acidic zone. For clarity, our results supporting this stimulatory mechanism have been amalgamated in Figure 8A.
One explanation for remote Ca 2þ wave triggering is that the NHE1-driven increase in [Na þ ] i raises luminal SR Ca 2þ within the acidic zone (via Na þ i -slowing of sarcolemmal Ca 2þ efflux on NCX, and subsequent Ca 2þ -sequestration into the SR by SERCA). Elevated luminal Ca 2þ might then diffuse throughout the whole SR, enhancing P o for RyRs in non-acidic regions, 35 thereby facilitating downstream Ca 2þ wave generation. Measurements of SR Ca 2þ diffusivity, however, are in the range of 9 to 60 mm 2 /s, 36,37 values that predict a luminal transit time of about 6 and 1 min, respectively over a distance of 80 mm (mean distance between mid-point of microdomain ROIs within a single myocyte). Since the remote stimulatory effects on Ca 2þ waves are already well established within 1 min of imposing a local acidosis, the contribution from diffusive re-distribution of luminal SR Ca 2þ can, at best, only partially account for our observed results. Additionally, the re-balancing of flux between SERCA activity and passive leak would tend to return SR Ca 2þ to physiological levels in regions away from the acidic source.
An alternative explanation is that rapid downstream diffusion of cytoplasmic Na þ ions, initially imported by NHE1 into the acidic microdomain, is the signal that raises SR [Ca 2þ ] throughout the cell. This global stimulation by Na þ is then superimposed with local inhibitory effects of H þ in the acidic microdomain, leading to Ca 2þ wave suppression in acidic zones, but wave initiation and clustering in downstream, nonacidic zones. Our recent measurements of high cytoplasmic Na þ diffusivity ($680 lm 2 /s) 18 are consistent with the time-frame of our Ca 2þ wave responses.
To test the quantitative feasibility of the above hypothesis, a simple model was constructed (see Figure 8), based on the [Na þ ] i -and [H þ ] i - ] i and SBFI ratio during regional superfusion with 40 mM lactate, normalized to starting levels. (C) SBFI ratio normalised to control conditions, absolute [Na þ ] i (uniform exposure to lactate-free solution), and the change in pH i (calculated from cSNARF-1 ratio) plotted across an axis perpendicular to the boundary between microstreams recorded at three different time-points during dual microperfusion. Measurements obtained from four monolayers. The rise in [Na þ ] i in cells under the lactate-containing microstream is due to Na þ entry via NHE1, stimulated by the ensuing intracellular acidosis. The pH i gradient across the inter-stream boundary is sharp due to slow H þ ion diffusion and rapid transmembrane H þ -equivalent fluxes (lactate-H þ transport by MCT). The [Na þ ] i gradient, in contrast, is shallower due to fast Na þ permeation through gap junctions and diffusion within the cytoplasm.
dependencies of Ca 2þ wave frequency (Figure 2Ai, Aii). This was then used to predict the frequency of Ca 2þ waves during imposition of a local acid load ( Figure 8B). In the simulation, if [Na þ ] i is restrained at resting levels of $8 mM (analogous to NHE1 inhibition), the model predicts that wave frequency is unchanged in areas of normal pH i , but inhibited in the acidic microdomain. If [Na þ ] i is allowed to rise uniformly to around 20 mM, comparable to that observed under whole-cell acidosis (cf. Figure 1Aiii), the model predicts Ca 2þ wave stimulation globally. Thus, regardless of the pH i gradient, a significant Na þ i overload now promotes stimulation of waves in all cellular regions. However, the model prediction is radically different for an intermediate [Na þ ] i -rise to 12 mM. This rise is comparable to that measured experimentally during imposition of the pH i gradient 18 (note that, because of rapid diffusion, this [Na þ ] i -rise is near-uniform throughout the cell 18 ). Under these conditions, the model predicts an inhibition of Ca 2þ waves in the acidic microdomain and stimulation in the more alkaline microdomain ( Figure 8B). Quantitative analysis therefore supports the mechanistic interpretation of our data.
We conclude that rapid spread of cytoplasmic Na þ ions, resulting in a modest, global rise of [Na þ ] i , is responsible for remote triggering of Ca 2þ waves in regions where the pH i is normal. Although [Na þ ] i will also be raised at the source of acid, the superimposed inhibitory effects of H þ ions will dominate in that region. Our data suggest that local Ca 2þ wave suppression is, at least in part, a result of RyR inhibition by H þ ions, on the basis that, in separate experiments, regional acidosis also suppresses local spark frequency.
Ca 2þ waves organized by spatial H þ and Na þ signals: cellular consequences The above data and modelling indicate that spatial domains for H þ and Na þ will control both the site and frequency of spontaneous Ca 2þ waves within a ventricular myocyte. Spatial pH i non-uniformity will also grade wave propagation velocity, which will grade the magnitude of any consequent DAD. 38 Because of low H þ i mobility, myocytes readily develop non-uniformity of pH i during enhanced sarcolemmal H þ flux, compounded by the spatial distribution of H þ -transporters, with NHE1 predominantly located at the lateral sarcolemma and intercalated discs. 21 As a result, NHE1 activation results transiently in both longitudinal and radial pH i gradients. 21,39 Under conditions of Ca 2þ overload, this pH i pattern predicts preferential Ca 2þ wave emergence in less acidic subsarcolemmal regions. This will influence the spatial distribution of excitation-contraction coupling within the cell, and may also modulate the gating of connexin channels at gap junctions. 9 At present, in an  Figure 4B) was used in the model. Bottom: Results of a simulation based on the numerical relationships described in Supplementary material online, Figures 1 and 2. The model was used to predict wave initiation frequency (color-coded: red = wave inhibition, white = no change, blue-= wave stimulation) during a pH i gradient, for a range of [Na þ ] i (y-axis, with representative values indicated). The simulation predicts (i) for resting [Na þ ] i (8 mM, bottom white dashed line, i.e. when NHE is inhibited with DMA), waves are inhibited in the acidic region and remain at control frequency in the non-acidic region; (ii) for a rise in [Na þ ] i comparable to the load during whole-cell acidosis 18 (20 mM, top white dashed line), wave frequency is stimulated throughout the cell; (iii) for a modest rise in [Na þ ] i (12 mM, middle white dashed line), as seen during an imposed pH i gradient 18 , waves are inhibited in the acidic zone and stimulated downstream in non-acidic regions. d.m. = dual microperfusion. (C) Schematic of differential effects of pH i non-uniformity on Ca 2þ wave frequency. Local intracellular acidosis (represented in bottom part of schematic; x-axis is distance along cell) activates NHE1, leading to a rapid and global rise in [Na þ ] i (fast diffusion-yellow arrow). This loads the SR throughout the cell, but waves preferentially emerge in the non-acidic microdomain due to the absence of H þ inhibition of RyRs.
Acidosis remotely stimulates Ca 2þ waves isolated cell, it would be experimentally challenging to map Ca 2þ waves to such dynamic pH i gradients, but our current observations with larger, stable pH i gradients show clear spatial wave initiation and clustering at the alkaline border of an acidic zone.
In our previous study, regional acidosis was found to influence globally the amplitude of the CaT within a ventricular myocyte, via rapidly diffusing Na þ i , which co-ordinates the magnitude of electrically evoked SR Ca 2þ release throughout the cell. This response suggested a mechanism for spatially unifying the contractile signal in the face of pH i heterogeneity. 18 In the present work, however, we find that the inhibitory and stimulatory effects of a local acidosis on Ca 2þ wave frequency remain spatially separated. While this is reminiscent of the effect of local acidosis on diastolic [Ca 2þ ], 24 the mechanisms are dissimilar, since the diastolic effects are independent of changes in Na þ , whereas remote wave stimulation is entirely dependent on the H þ -driven rise in Na þ i . The apparent paradox in the difference in spatial behaviour between Ca 2þ waves and CaTs can be explained by considering the difference in nature of the events. CaT amplitude is a graded, continuous variable, and so we see a graded influence of [Na þ ] i and [H þ ] i . In contrast, Ca 2þ wave initiation is an all-or-none event. Although waves are, again, H þ -and Na þ -sensitive, we see a binary effect, dependent on the balance between the two probability distributions of H þ -dependent inhibition and Na þ -dependent stimulation. This difference between CaTs and Ca 2þ waves means that, when pH i is spatially heterogeneous, CaT amplitude can be fine-tuned in different regions of the cell, but the pH-dependent thresholding of wave initiation can result in spatially separated effects with wave suppression in acidic zones and wave triggering in non-acidic zones.
Ca 2þ waves organized by spatial H þ and Na þ signals: role in ischaemic myocardium?
Accumulation of metabolic weak acids such as CO 2 and lactate is well documented within regionally ischaemic areas of myocardium, [40][41][42] and this accumulation is expected to generate large and stable pH i gradients across borderzones. In experimental models, gradients of extracellular myocardial pH can be as steep as 0.8 units, expressed over a few myocyte lengths. 42 Indeed, here we have shown that a multicellular neonatal preparation can sustain a steep pH i gradient across several cell-lengths, and that this induces an intercellular Na þ i gradient (Figure 7). The question is whether myocardial pH i gradients will remotely trigger Ca 2þ wave initiation in a way comparable to that observed in single myocytes. In the electrically coupled myocardium, because H þ i and Na þ i diffusivities differ substantially (100 lm 2 /s 20 vs. 680 lm 2 /s 18 ), the resulting myocardial spread of H þ i will be more restricted than that for Na þ i . Consequently, any Hdependent inhibition of aberrant Ca þ -signalling within the ischaemic zone should also be spatially restricted, coupled with a wider spatial stimulation by Na þ ions, as illustrated schematically in Figure 8C. Propagation of Ca 2þ waves through myocardial gap junctions has a high failure rate, 43,44 while junctional H þ permeation is slow and requires chaperoning by carrier-molecules. 20 In contrast, Na þ ions readily permeate gap junctions, 45 which remain open even at relatively acidic pH i . 46 Thus, in a regionally ischaemic myocardium, there is potential for a spatially defined borderzone of vulnerability, characterized by only modest acidosis, but an elevated [Na þ ] i that is fuelled by Na þ diffusion from more acidic (ischaemic) zones ( Figure 8C). The elevated [Na þ ] i may contribute to the Ca 2þ waves and arrhythmias that have been observed consistently at borderzones. 47,48 Recent studies 47,49-51 demonstrate that Ca 2þ waves are most likely to be arrhythmogenic under conditions of local heterogeneity 50 that favour the synchronous emergence of waves within a specific area of tissue. It is therefore tempting to suggest that pH i non-uniformity in the myocardium 52 may provide an important substrate for such synchronous Ca 2þ waves. The arrhythmogenic risk will also be increased by the enhanced wave propagation velocity induced by acidosis. While many factors, other than H þ ions, also contribute to arrhythmogenic activity in ischaemia, 53 the principle of remote H þ -stimulation of Ca 2þ waves, established here in our single cell studies, now merits experimental evaluation in the regionally ischaemic myocardium.

Conclusions
We have shown that, in ventricular myocytes, H þ ions inhibit Ca 2þ waves, via inhibition of Ca 2þ -handling proteins such as RyRs, but they also stimulate waves by activating Na þ influx on NHE1. The steep dependence of Ca 2þ wave initiation on [Na þ ] i often results in overall stimulation. When spatial pH i heterogeneity is introduced into a myocyte, we find that acidic zones remotely trigger Ca 2þ waves in non-acidic zones. This is explained by the different-sized spatial domains for elevated inhibitory [H þ ] and stimulatory [Na þ ], predicted by their different ionic diffusivities. As well as providing a stimulus for aberrant Ca 2þ signalling in acidic myocytes, such spatial signalling may also have relevance in regional myocardial ischaemia, where the formation of pH i gradients across groups of myocytes is likely. Remote H þ -triggering of Ca 2þ waves emphasizes the importance of Na þ as a spatial messenger in the heart.

Supplementary material
Supplementary material is available at Cardiovascular Research online.