The effects of acidosis on cardiac electrophysiology and excitation–contraction coupling have been studied extensively. Acidosis decreases the strength of contraction and leads to altered calcium transients as a net result of complex interactions between protons and a variety of intracellular processes. The relative contributions of each of the changes under acidosis are difficult to establish experimentally, however, and significant uncertainties remain about the key mechanisms of impaired cardiac function.
In this paper, we review the experimental findings concerning the effects of acidosis on the action potential and calcium handling in the cardiac ventricular myocyte, and we present a modelling study that establishes the contribution of the different effects to altered Ca2+ transients during acidosis. These interactions are incorporated into a dynamical model of pH regulation in the myocyte to simulate respiratory acidosis in the heart.
It has long been known that acid solutions are detrimental to cardiac performance: Isaac Newton is reported to have shown that vinegar stopped the contraction of eel heart (Roos & Boron 1981), and in 1880 Gaskell reported that perfusing isolated cardiac tissue with an acid solution caused a rapid and marked decrease in the strength of contraction (Gaskell 1880). Since the work of Gaskell, the pathological importance of acidosis has been increasingly recognized. The heart becomes acid in a number of pathological conditions, most dramatically during myocardial ischaemia. It has been suggested that many of the detrimental effects of ischaemia, such as decreased strength of contraction (Katz & Hecht 1969) and the development of arrhythmias, are due to the associated acidosis (Orchard et al. 1987; Orchard & Cingolani 1994). However, the mechanisms underlying these effects of acidosis have only started to be elucidated relatively recently.
In this paper, we will (i) review the response of cardiac myocytes to acidosis; (ii) present a computational study of the effects of acidosis on intracellular Ca2+ handling; (iii) briefly review the mechanisms of pH regulation in the myocyte; and (iv) describe a dynamic mathematical model for pH regulation and acidosis in cardiac myocytes.
2. The response of cardiac muscle to acidosis
When isolated cardiac muscle—whole heart, muscle strip, or single cell—is exposed to acidosis, the force of contraction decreases. This decrease is faster in response to interventions that rapidly alter intracellular, rather than extracellular, pH, indicating that intracellular acidosis is responsible for the decrease (Vaughan-Jones et al. 1987). During prolonged exposure to acidosis a secondary recovery of developed force can also be observed (Allen & Orchard 1983; Orchard 1987).
The amplitude of the intracellular systolic Ca2+ transient, which initiates contraction, has been reported, variously, to increase, decrease, or not change, during the initial decrease of developed force. The time course of the transient is prolonged (Allen & Orchard 1983; Orchard 1987). Thus, it appears that the decrease in developed force is not due to a decrease of activating Ca2+, and it is now generally accepted that the negative inotropic effect of acidosis is due predominantly to a decrease in the sensitivity of the contractile proteins to Ca2+ (Fabiato & Fabiato 1978; Solaro et al. 1989; Orchard & Kentish 1990). The secondary recovery of developed force that occurs during acidosis is, however, accompanied by (i) an increase in diastolic Ca2+, (ii) an increase in the amplitude of the systolic Ca2+ transient, which appears to underlie the contractile recovery and (iii) recovery of the time course of the Ca2+ transient (Allen & Orchard 1983; Orchard 1987; Harrison et al. 1992; DeSantiago et al. 2004).
Acidosis also has complex electrophysiological effects, although its effect on the action potential is less dramatic than on force: near normal action potentials can be elicited at pH∼6.0, when force is completely inhibited (Vogel & Sperelakis 1977). The electrophysiological response to acidosis is varied, with prolongation and abbreviation of the action potential being reported, accompanied by changes in configuration that often include depression of the plateau and a small depolarization of the resting potential (see Orchard & Kentish 1990; Orchard & Cingolani 1994 for review).
(a) Consequences for heart function
The changes in the action potential, intracellular Ca2+ and developed force induced by acidosis have important consequences for the heart. The decrease in force is obviously detrimental to the ability of the heart to pump blood, although this is offset to some extent by the secondary recovery of intracellular Ca2+ and hence developed force. However, increasing intracellular Ca2+ may also have detrimental effects: first, because it increases gap junction resistance (Noma & Tsuboi 1987), which can slow propagation of the action potential, and may lead to re-entry in the intact heart. Second, because it may cause spontaneous Ca2+ release from the sarcoplasmic reticulum (SR); this can activate inward currents which, if large enough, can trigger arrhythmias (Orchard et al. 1987). Brief exposure to acidosis inhibits spontaneous Ca2+ release, as a result of its inhibitory effect on SR Ca2+ release channels (ryanodine receptors, RyRs: Orchard et al. 1987; Xu et al. 1996; Balnave & Vaughan-Jones 2000). During prolonged exposure, however, spontaneous release increases, probably a result of increased SR Ca2+ content, and can produce extrasystoles (Orchard & Kentish 1990). If it occurs between two stimulated contractions, spontaneous Ca2+ release may also decrease force in the subsequent contraction. Perhaps more importantly, on returning to control pH, the inhibitory effects of acidosis on the (Ca2+ loaded) SR are rapidly removed, so that a marked increase in spontaneous Ca2+ release may occur (reviewed in Orchard & Cingolani 1994). Finally, the changes in SR function during acidosis have also been implicated in the development of alternans of the Ca2+ transient and action potential that can occur during acidosis (Orchard et al. 1991), which may also be arrhythmogenic.
The changes in the resting potential and action potential may also be detrimental: the decreased resting potential observed during acidosis may contribute to the T-Q segment depression that can occur in the ECG during ischaemia (reviewed in Orchard & Cingolani 1994). More importantly, re-entrant arrhythmias may develop. Localized acidosis, by causing local changes in the configuration of the action potential, will change action potential dispersion, so that cells that have repolarized may be excited by their still depolarized neighbours, generating arrhythmias. Homogeneous acidosis may also change action potential dispersion because of regional differences in channel expression. For example, Antzelevitch et al. (1991) reported that simulated ischaemia, which included acidosis, caused a marked depression of the sub-epicardial action potential, which could be reversed by 4-AP, an inhibitor of , but had little effect on the sub-endocardial action potential. These changes may therefore be due to acidosis-induced changes of (Hulme & Orchard 2000), which is found in the sub-epicardium but not the sub-endocardium, which will alter the pattern of repolarization in the heart and may produce arrhythmias.
It is clear from the preceding sections that acidosis has marked effects on the heart, which are detrimental to cardiac function. Understanding the mechanisms that underlie these changes is, therefore, an important goal.
The systolic Ca2+ transient is initiated by Ca2+ influx across the cell membrane via the L-type Ca2+ current (); this Ca2+ influx stimulates Ca2+ release channels (RyRs) in adjacent SR, causing the release of a larger amount of Ca2+. Intracellular Ca2+ is subsequently reduced to its resting level by Ca2+ extrusion across the cell membrane, predominantly via Na+/Ca2+ exchange (NCX), and by uptake into the SR via a Ca2+-ATPase (SERCA). All these pathways are inhibited by acidosis, which might be expected to reduce Ca2+ transient amplitude. However, the decrease in Ca2+ binding to troponin, which underlies the acidosis-induced decrease in myofilament Ca2+ sensitivity, will tend to increase Ca2+ transient amplitude. It is likely that the variability of the initial response of the Ca2+ transient to acidosis is due to differences in which of these effects dominates in particular experimental models (Orchard 1987).
At least three mechanisms affecting intracellular Ca2+ appear to increase SR Ca2+ content: (i) desensitization of RyRs to trigger Ca2+, which will decrease SR Ca2+ release, with a direct effect on Ca2+ transient amplitude. (However, this increases , and decreases Ca2+ efflux via NCX.) In the absence of other changes, this increases cellular, particularly SR, Ca2+ content and hence Ca2+ release until the amplitude of the Ca2+ transient recovers to control levels (Choi et al. 2000). This is achieved at a higher than normal SR Ca2+ content, where, at a smaller fractional release, Ca2+ influx and efflux across the cell membrane are again equal. (ii) Intracellular acidosis stimulates acid extrusion via Na+/H+ exchange (NHE) and (bicarbonate) cotransport (NBC), which increases intracellular Na+ and hence, via NCX, intracellular Ca2+, SR Ca2+ content and the amplitude of the Ca2+ transient (Bountra & Vaughan-Jones 1989; Harrison et al. 1992; although it has recently been suggested that NHE may be inhibited in ischaemia, Allen & Xiao 2003). (iii) Although the SERCA is directly inhibited, acidosis also causes Ca2+-dependent phosphorylation of the regulatory protein phospholamban (PLB: Hulme et al. 1997; DeSantiago et al. 2004), which will increase Ca2+ uptake by the SERCA, thus increasing SR Ca2+ content and increasing and abbreviating the Ca2+ transient. The net effect of these changes is an increase in Ca2+ transient amplitude due to increased SR Ca2+ content, even though fractional release is decreased (Hulme & Orchard 1998).
The mechanisms underlying the changes in the action potential are incompletely understood, although acidosis affects most of the currents that underlie the resting potential and action potential. In particular, acidosis inhibits the depolarizing currents , and (although this may depend on the recording configuration used; Komukai et al. 2002; see Orchard & Cingolani 1994 for a review), which may account for the abbreviation of the action potential and depression of the plateau observed in some studies, and may also contribute to changes in Ca2+ handling during acidosis. The repolarizing K+ currents , and are also inhibited by acidosis (see Orchard & Cingolani 1994 for a review). In contrast, acidosis can increase by causing a rightward shift in the inactivation curve and increases inwardly rectifying Cl− current, which will prolong the action potential (Komukai et al. 2001); although its small amplitude at depolarized potentials suggests that its contribution to the action potential will be small, it could account for the acidosis-induced depolarization of the resting membrane potential (Komukai et al. 2002). Since the action potential represents a delicate balance between inward and outward currents, most of which are altered by acidosis, the variability in its response to acidosis probably represents the different methods and degrees of acidosis used in different studies, and the different pH sensitivities of different currents, and the recording conditions used.
The inter-relationship between the action potential and Ca2+ transient is, however, complicated, because changes in the action potential may be both a cause and a consequence of changes in the Ca2+ transient. Increasing intracellular Ca2+ will alter Ca2+-dependent currents, such as and , in addition to the direct inhibitory effect of acidosis on these currents, and increasing action potential duration will increase intracellular Ca2+. Thus, although acidosis has important effects on cardiac muscle, its effects are complex and interconnected, even in a single cell. In multicellular preparations, in which cell–cell interactions and conduction pathways may also be altered, the effects may be even more complex. They are, therefore, difficult to explore experimentally. Computer models offer the possibility to investigate these inter-relationships and the key control points in the response to acidosis.
3. Modelling the effects of acidosis on action potential shape and Ca2+ transient
We designed a modelling study to investigate the relative changes to the action potential shape and Ca2+ transient produced by three major effects of acidosis: increased intracellular Na+ concentration, reduced sensitivity of the RyR receptor to intracellular Ca2+ concentration and decreased Ca2+ binding to troponin-C.
(a) Cardiac cell model
We based our simulations on the single cell model of the rat ventricular myocyte published by Pandit et al. (2001). This model was chosen, as the most detailed characterizations of changes to action potential configuration in acidosis that have been made are on rat myocytes (Komukai et al. 2002). The model was implemented as described in the paper, with modifications shown in appendix A. The differential equations were solved using a forward Euler method with a time-step of 0.1 μs. Figure 1 shows examples of action potentials and Ca2+ transients resulting from steady pacing at 4 Hz.
When the model was paced for a prolonged period, we found a monotonic increase in intracellular Ca2+ concentration, [Ca2+]i, that was associated with a fall in action potential amplitude. This is illustrated in figure 2a. Clamping intracellular Na+ to a fixed value of 11 mM resolved this problem, illustrated in figure 2b.
(b) Simulation of acidosis-induced changes
Our aim is to simulate the effects of a reduction of intracellular pH by around 0.3 pH units, which is a significant, but not severe acidosis, and is typical of the degree of acidosis commonly imposed on cells experimentally. The effect on individual Ca2+ handling pathways was simulated as follows: (i) intracellular sodium, [Na+]i, was increased from 11 to 15 mM by increasing background Na+ conductance, consistent with data from Harrison et al. (1992, fig. 6A) who recorded [Na+]i during acidosis with 15% CO2 in rat ventricular myocytes; (ii) the sensitivity of the RyR to trigger Ca2+ was decreased by reducing the rate constant for channel opening by a factor of 0.25, estimated from Xu et al. (1996, fig. 7), who measured the effect of pH on single channel activity using preparations isolated from canine myocytes; (iii) Ca2+ binding to troponin-C was reduced by increasing the off-rate of Ca2+ binding to troponin by a factor of 4.0 (Bers 2001). The model was run for 30 s before each change, and the change in each parameter was made over 20 s to simulate the slow change of intracellular pH that occurs physiologically. The change was maintained for 80 s, before being returned to baseline over 20 s, followed by 30 s post-control.
Figure 3 shows the individual and collective effects of each component of acidosis on the intracellular Ca2+ for simulations in which intracellular Na+ was clamped. In each case, there were some short-lived effects on the Ca2+ transient amplitude before a stable configuration was reached. Increasing intracellular Na+ concentration resulted in a positive displacement of the Ca2+ transient by about 0.7 μM (figure 3a), with little effect on the transient shape. Reducing RyR receptor sensitivity decreased the amplitude of the Ca2+ transient slightly (figure 3b), and decreasing the affinity of Ca2+ for troponin-C prolonged the Ca2+ transient slightly (figure 3c). When all three changes were applied (figure 3d), the overall effect was displacement of the Ca2+ transient to higher [Ca2+]i by about 0.7 μM and a small prolongation of the Ca2+ transient.
The three interventions described earlier had very minor effects on the action potential. When all three interventions were combined, the effect was to slightly shorten the action potential, as shown in figure 4.
These simulation experiments were repeated as described earlier without clamping intracellular Na+. In this case, the time course of the changes to the intracellular Ca2+ transient was broadly similar, but there was a superimposed monotonic increase in intracellular Ca2+ similar to that shown in figure 2a.
4. Mechanisms which regulate pH in cardiac myocytes
Given these strong effects of physiological changes in pH on Ca2+ handling, as well as on many other cellular processes, it is not surprising to find that the cell has a dedicated set of mechanisms that regulate the flux of protons across the cell membrane. The regulation of intra- and extracellular pH is achieved by the transport of protons, bicarbonate and hydroxide ions across the cell membrane. The integrated control of this process is achieved by the balance of four separate transport proteins, each of which is specialized to a specific exchange cycle (Sun et al. 1996). Two acid extruders, NBC and NHE, use the Na+ gradient favouring Na+ entry into the cell to extrude H+ (in the case of NHE) or co-transport (for NBC) into the cell. Acid loading is facilitated by Cl−/OH− exchange (CHE) and the anion exchanger (AE), which couple influx of Cl− down its concentration gradient to the transport of hydroxide and bicarbonate out of the cell, respectively.
The concentration of free protons is strongly buffered in cardiac myocytes, which minimizes pH changes in response to net proton production or removal. To convert this change in pH to a direct flux requires intracellular buffering to be quantified. Both CO2 dependent and intrinsic (CO2 independent) buffers have been identified in the myocyte which contribute approximately equally to the total buffering power of the cell at equilibrium (Vaughan-Jones & Wu 1990; Lagadic-Gossmann et al. 1992).
5. Modelling pH regulation
The regulation of pH in excitable tissues has been studied for many decades. The processes regulating pH have been modelled in a variety of tissue and cell types in which pH regulation plays an important role, including heart (Ch'en et al. 1998; Leem et al. 1999), nerve cells (Boron & De Weer 1976) and pancreatic ductal epithelium (Sohma et al. 1996, 2000), and in subcellular compartments, including intracellular organelles which maintain an acidic interior (such as lysosome, endocytic and secretory organelles, etc.; Grabe & Oster 2001). In this section, we describe the elements of a dynamic model for pH buffering, proton transport and associated model components developed by Leem & Vaughan-Jones (1998) and Leem et al. (1999), and their integration with existing cell models to provide a simulation study of pH regulation in cardiac myocytes.
The capacity of the cell to buffer against changes in proton load is measured by buffering power (Boron & Weer 1976), , where(5.1)where is the proton flux and β is the total proton buffering power. For our model, the net flux increasing the concentration of intracellular protons is(5.2)(where OH− efflux is modelled equivalently as H+ influx). The capacity to buffer against changes in pH itself depends upon the cellular acidity. Typically, the proton buffering power in the myocyte is of the order of β=20–90 mM per pH unit. This comprises (at least) two distinct intrinsic buffers (Leem et al. 1999) where, from the Henderson–Hasselbalch equation,(5.3)i.e. intrinsic buffering power falls as pH rises. (Note that in the absence of buffers, where , the residual term in equation (5.3) merely reflects the transformation from flux of [H+] to change in pH.)
In addition to these intrinsic buffers, pH is also buffered by the CO2 hydration reaction,(5.4)for which buffering power increases with increasing pH (Leem et al. 1999). This approximately doubles buffering at normal pH. Because this reaction is relatively slow, however, rather than using an equilibrium formulation as for the intrinsic buffers, this is typically modelled by the flux(5.5)The rate constants for this reaction, measured in guinea-pig cardiac myocytes by Leem & Vaugham-Jones (1998), are given in appendix A, along with parameters for the intrinsic buffers.
(b) Acid transporters
Leem et al. (1999) have performed detailed and comprehensive measurements of transmembrane proton fluxes with varying intracellular pH under a variety of acid and base loading conditions in order to characterize the pH-dependence of the four transporter fluxes. Using a variety of pharmacological agents and ligand conditions, they were able to dissect out the contributions to net proton transport of the four individual proteins. Exploiting the chloride dependence of the acid loaders, Leem et al. (1999) used Cl−-free perfusate to isolate the acid loading fluxes, which are further separated between NBC flux, which is dependent on the presence of CO2, and NHE which is independent. Thus, by altering the cell perfusate (chloride and/or CO2 free), the time course in pH resulting from the activity of a particular transporter or transporters can be determined. Using these data, Leem et al. (1999) reconstructed the intracellular pH dependence of each transporter flux, using high-order polynomial equations to fit each transporter flux, shown in figure 5.
(c) Respiratory acidosis
In order to simulate the response of the pH-regulating mechanisms in the myocyte, we have included transport processes for bicarbonate and CO2. Following Leem & Vaughan-Jones (1998), and assuming the sarcolemma is impermeable to bicarbonate and permeable to CO2,(5.6)(5.7)where(5.8)is the diffusive flux of CO2 across the sarcolemma, i.e. the rate at which intracellular CO2 equilibrates following change in [CO2]e.
(d) Simulation of respiratory acidosis
The differential equations (5.1), (5.6) and (5.7) describing pH regulation, and the polynomial expressions for the acid-equivalent transporter fluxes from Leem et al. (1999) were incorporated into the Luo–Rudy dynamic (LRd) ventricular cell model (Faber & Rudy 2000) in order to simulate the response of the cell to respiratory acidosis. We used the LRd model for these simulations as it is able to produce steady trains of action potentials, with zero net flux of the intracellular concentration variables over each beat. We implemented the model using an equation for conservation of charge to calculate cell membrane potential (Grabe & Oster 2001; Hund et al. 2001, so-called ‘algebraic method’) and assumed that the stimulus current was carried by K+ ions. Other changes made are described in appendix A.
In the model, intracellular Na+ changes dynamically as a result of NHE and NBC fluxes as pH falls during acidosis. We have included the two other effects on Ca2+ handling mechanisms, described earlier, using the simple assumption that the magnitude of the effects increase linearly with pH. Thus, the reduced open probability for RyRs is modelled by reducing the flux in proportion to the difference in pH from normal (pH 7.1), to reach 0.25 of its normal value at pH 6.8. Similarly, the apparent Km for Ca2+ binding to troponin-C was increased linearly with pH from the normal value at pH 7.1 to reach a fourfold increase at pH 6.8.
Figure 6 shows results for a simulation of respiratory acidosis. After one minute of pacing under normal conditions, extracellular CO2 was stepped from 5 to 20%, and returned to 5% after two and a half minutes. Figure 6a shows the rapid drop and slow recovery of intracellular pH during respiratory acidosis, and an overshoot to alkaline pH when the respiratory acidosis is lifted. [Na+]i increases following the drop in pH (figure 6b), but on a slower timescale, and starts to recover immediately on removal of the extracellular CO2 load. [K+]i continues to rise, however, while Na+ is removed from the cell by the Na-pump. As expected, the response of intracellular Ca2+ transients (figure 6c) is qualitatively similar to the previous results. There is a pronounced increase in peak systolic Ca2+ which continues to rise during acidosis, and slight increase in diastolic [Ca2+]i can also be observed.
In this study, we investigated the effects of acidosis in two electrophysiological models. The Pandit et al. (2001) model for the rat left ventricular myocyte was chosen for this study as the best current data characterizing the effects of acidosis on myocyte electrophysiology were measured for rat myocytes (Komukai et al. 2001). Model simulations enabled us to isolate and quantify the importance of the individual mechanisms contributing to global change in acidosis. It is apparent from figure 3a that increased sodium–calcium exchange, due to the rise in intracellular Na+, dominates changes in the intracellular Ca2+ transient, consistent with the mechanism experimentally observed by Harrison et al. (1992). Increased cycling of the exchanger to remove intracellular Na+ increases intracellular Ca2+ at both peak and resting levels, although the time course is largely unchanged. The prolongation (slowed recovery) of the Ca2+ transient, which is a consistent experimental finding, appears to be due to reduced affinity of Ca2+ for troponin-C. Thus, in acidosis, changes in Ca2+ are no longer buffered to the same extent, producing a larger Ca2+ transient amplitude, reduced resting level and slowed recovery (figure 3c). This modelling study suggests that reduced sensitivity of the RyRs to trigger Ca2+ produces a relatively small but sustained depression of the Ca2+ transient, although experimental data have shown recovery to control calcium levels following changes to the calcium-induced calcium release mechanism (Trafford et al. 2000), including inhibition of Ca2+ release during acidosis (Choi et al. 2000). Further work is required to establish the reason for this discrepancy. Consistent with experimental observations (Komukai et al. 2001), these altered Ca2+ dynamics translate into only a very small perturbation of the action potential despite the combined effects elevating and prolonging the Ca2+ transient. As such, this indicates that at the cellular level the most important implication of acidosis is for contraction, which is tightly coupled to the Ca2+ transient.
To analyse these effects further, we implemented the same electrophysiological changes in a dynamic cellular model which incorporates explicit representations of proton fluxes across the cell membrane. The comprehensive studies by Vaughan-Jones and colleagues characterizing these pH regulatory mechanisms have been carried out on guinea-pig myocytes. We used the LRd model, which has been developed using data from this species (Faber & Rudy 2000; Hund et al. 2001), which also has the advantage of providing stable trains of action potentials for an indefinite period of stimulation. Specifically, the temporal variation in currents, concentrations and membrane potential is identical from one beat to the next. Results from this dynamic framework demonstrate the same dominant effect of altered sodium–calcium exchange on the Ca2+ transient. The rise in intracellular Na+ with the onset of acidosis is due to increased NBC and NHE transport, importing Na+ into the cell. This in turn produces a rise in intracellular K+ via the sodium pump, which continues to bring K+ into the cell after removal of acidosis while Na+ remains raised above the normal level (figure 6b). As before (figure 3d), the drop in intracellular pH produces a small increase in resting Ca2+ levels (despite reduced troponin-C buffering) and a large increase in the magnitude of the Ca2+ transient. The link between the time course of peak Ca2+ and intracellular Na+ once again indicates the importance of sodium–calcium exchange in producing this effect.
The dynamic beat-to-beat properties of this model will be fundamental to the next step in this study: the development of a fully integrated dynamic model of acid regulation. In such a model, pH changes alone will drive all of the other ionic concentration changes, and thus it will be crucial that there is no ‘drift’ of concentration variables over time (as occurs in the Pandit model). It will also be necessary to construct biophysically based kinetic models for each of the acid equivalent transporters that can distinguish between allosteric regulation and mass-action effects due to, for example, increased Na+ in ischaemia. This will serve to elucidate the relative importance and implications of the two mechanisms that couple extracellular to intracellular pH. The first is that within a small range around typical resting pH values, dubbed the permissive range by Leem et al. (1999), there is small but significant flux through all four transporters (approx. 0.15 mM min−1). While there is no direct metabolic cost to this acid transporter flux, Na+ entering the cell via this basal NBC and NHE activity must ultimately be removed by the ATP-consuming Na-pump. Thus, one can hypothesize that this secondary metabolic cost is balanced by the ability of the cell to quickly respond to small intracellular acid loads, both by increasing acid efflux through NBC and NHE and by reducing AE and CHE fluxes.
A second mechanism by which this pH coupling is achieved is the allosteric regulation of transporters by protons, potentially both at intracellular and extracellular sites. Vaughan-Jones & Spitzer (2002) propose strong activation of NHE when intracellular pH is reduced (a Hill coefficient of 3) and somewhat weaker inhibition by reduced extracellular pH. Similarly, Ch'en & Vaughan-Jones (2001) report that NBC flux is much more strongly modulated by pH than by either sodium or bicarbonate ions, suggesting allosteric regulation. Evidence for regulation of AE or CHE is currently lacking, although this has not been ruled out. The allosteric regulation of transporter flux by pH on both sides of the membrane strengthens the coupling between extra- and intracellular pH, such that a fall in extracellular pH allosterically inhibits acid extrusion on NBC and NHE, may also promote acid loading on AE and CHE, and thus over time will translate into a parallel fall in intracellular pH. The high concentration of intracellular, relative to extracellular, buffer implies that this tight coupling may be a mechanism for excess protons to be transported to intracellular sites where their effects can be mitigated by the relatively large intracellular buffering power.
To investigate these and other issues in pH regulation and acidosis, the challenge for the development of an integrated cellular model, coupled to existing models of electrophysiology (Noble et al. 1998; Hund et al. 2001), is to construct detailed, biophysically based schemes for each of the model components (Crampin et al. 2004). For example, while experimental evidence indicates that the acid equivalent transporters are largely influenced by intracellular pH, justifying pHi as the sole variable required to determine these fluxes, a higher level of detail will be needed to distinguish between the response to metabolic acidosis (during ischaemia, for example), where there is increased intracellular production of protons, and the changes due to CO2 build-up in respiratory acidosis, as examined in this study.
E.J.C. acknowledges support from the New Zealand Institute for Mathematics and its Applications (NZIMA) and the Centre for Molecular Biodiscovery, University of Auckland. N.P.S. and E.J.C. are supported by The Royal Society of New Zealand Marsden Fund through grant UOA0410, and thank Professor Richard Vaughan-Jones and Drs Pawel Swietach and Blanca Rodriguez for useful discussions. C.H.O., R.H.C. and A.E.L. are grateful for funding from the British Heart Foundation through grant PG/02/158/14785.
One contribution of 13 to a Theme Issue ‘Biomathematical modelling I’.
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