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MEMBRANE TRANSPORTERS, ION CHANNELS, AND PUMPS
Departments of 1Physiology and 3Medicine, Dartmouth Medical School, Lebanon, New Hampshire; and 2Department of Neuroscience, Cell Biology and Physiology, Wright State University, Dayton, Ohio
Submitted 11 April 2006 ; accepted in final form 4 July 2006
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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hypercapnia; potassium channels; computer modeling; central chemoreceptors
We investigated the ionic basis of CO2 chemosensitivity in CO2 chemosensitive neurons in Helix aspersa, an air-breathing terrestrial pulmonate snail, and we identified at three least potassium conductances that were inhibited by hypercapnia and acidosis in isolated neurons from the subesophageal ganglia (12). Using a combination of voltage-clamp protocols and pharmacological interventions, we identified an A-type potassium channel (IKA) and a delayed-rectifier potassium channel (IKDR) for which we were able to determine activation and inactivation characteristics. We also found evidence of a calcium-activated potassium channel (IKCa) that was inhibited by hypercapnia. We identified two inward conductances: a fast sodium channel (INa) and a slower calcium channel (ICa), but these did not seem to contribute to CO2 chemosensitivity, and these channels were not studied in detail. Finally, we identified a proton conductance (IProton) that has previously been described in molluscan neurons (9). There may be additional channels in particular neurons (although we did not identify any other conductances; see Ref. 12), but these six channels were ubiquitous in H. aspersa neurons (12).
None of the electrophysiological or pharmacological isolation methods that we used to study these channels provided perfect separation of these conductances; therefore, it was difficult to know the exact role of each channel in CO2 chemosensory function. To gain more insight into the chemosensory function of these channels, we constructed a single-compartment computer model using data from our previous work (12) and previously published information about these channels in invertebrates. The model incorporated six ionic conductances (IKA, IKDR, IKCa, INa, ICa, and IProton), pHi buffering characteristics and the pH regulatory processes typical of CO2 chemosensory neurons in the snail (20), which are also typical of mammalian CO2 chemosensory neurons (31, 38). This represents a minimal configuration for CO2 chemosensitivity, but we were able to construct a model neuron that demonstrated CO2 chemosensitivity. Within the model, we tried to address the following five issues: 1) we determined the optimal activation and inactivation characteristics of each channel to support chemosensory function; 2) we determined the role of each channel in the frequency response of the action potential (AP) during hypercapnic stimulation; 3) we assessed the role of the proton conductance in the electrophysiological and pH responses of each of the neurons; 4) we compared the chemosensory responses to changes in extracellular pH (pHe) or pHi alone to simultaneous changes in pHe and pHi; and 5) we assessed the role of acid-base regulation in modulating activity of the chemosensory cell.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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We did not measure the rate constant of activation in our previous studies but adopted the voltage-dependent rate constant found in a similar delayed-rectifier channel described by Buchholtz et al. (7):
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Mathematical description of IKCa.
The calcium-activated potassium channel was also adapted from Buchholtz et al. (7) and described by the following equation:
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We did not include any calcium-dependent inactivation of this channel in our model. The formulation of the activation characteristics of the IKCa reflects the existence of two calcium-binding sites with different voltage dependencies characterized by different half-maximal voltages (Va01 and Va02) and different step widths (Sao1 and Sao2). The activation curve, which is a function of voltage and intracellular calcium concentration, was described as follows:
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The value, f, is a slope factor that shifts the half-maximal voltage of the activation curves as a function of the intracellular calcium concentration (21, 27), and c1 is the half-maximal value for the intracellular calcium concentration dependence of activation. The calcium concentration inside the cell was modeled as a function of the calcium current as follows (40, 41):
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is the time constant for the calcium pump. The probability of intracellular calcium buffering was, in turn, derived from:
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Mathematical description of INa and ICa.
The fast INa was adapted from the crab model developed by Buchholtz et al. (7).
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Mathematical description of IProton.
We used data from Byerly et al. (9, 10) to model the proton channel. The hydrogen ion channel was assumed to be noninactivating and to have first-order activation kinetics:
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Modeling pHi, pHe, and pH regulation: pH effects on channel activity. We did not incorporate any pH-mediated changes in channel-gating characteristics even though hypercapnia shifted the V1/2 of inactivation of IKDR to more negative values of membrane voltage (Vm; see Ref. 12). The rate of inactivation of IKDR was so slow that pH modulation of inactivation did not affect the output of the model in any condition we studied. We assumed that proton block of the channel pore was the fundamental mechanism of inhibition in each case based on our previous electrophysiological studies (12). We assumed that the proton block of each channel depended on titration of weak acids and weak bases within the protein structure of the channel. Therefore, the pH dependence of inhibition was scaled by a sigmoidal pH titration curve that had a slope factor of one and a pKa value that represented the pH of half-maximal pH-dependent inhibition of each channel. We set the maximal level of inhibition at 50%; greater levels of pH-dependent inhibition disrupted the rhythmic behavior of the model neuron. This degree of inhibition was close to the maximal value that we observed experimentally (12). Greater levels of inhibition tended to unbalance the conductances, and the model ceased to generate APs.
pH-dependent inhibition of IKA.
The pH-dependent inhibition of IKA was complicated by the fact that pH-dependent inhibition was also voltage dependent (12). In some cells, pH-dependent inhibition of IKA increased as the cell was depolarized, but, in other cells, pH-dependent inhibition of IKA decreased as the cell was depolarized. The negative slope of the voltage dependence of pH inhibition (less pH-dependent inhibition as the membrane potential depolarizes) implies that proton block was at an extracellular site in some neurons (the electromotive force driving protons from outside the cell into the cell becomes less as the membrane potential becomes more positive inside the cell), but proton block was at an intracellular site in other cells (increased inhibition at more positive potentials and increased electromotive force moving intracellular protons out of the cell as the membrane becomes more positive inside the cell; see Refs. 12 and 49). To account for the voltage dependence of pH-related inhibition, gmax of each channel was multiplied by a factor 
. The value of varied inversely with the extent of pH-dependent inhibition, and incorporated a term, 
, which varied as a function of voltage and a term that captured the pH dependence of the voltage-dependent inhibition of IKA as follows:
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varied, in theory, between 1 and 0, with 0 representing complete inhibition, but, in practice, the value of varied between 0.5 and 1.0 over the pH range that we studied. The value of depended on whether the channel was inhibited by pHi or pHe. For intracellular proton block of IKA, the value of i was lowest at higher membrane potentials (the channel was most inhibited), and i increased at more negative potentials (greater channel conductance when proton block was less). For extracellular proton block, e was highest when membrane potential was positive, and e diminished at more negative potentials. These intracellular and extracellular factors were derived from our previous work (12) and defined as
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values into the model: one sensitive to pHe and the other sensitive to pHi. We adjusted the relative contribution of each channel by multiplying one IKA current by a coefficient, 
, which ranged from 0 to 1, and multiplying the other by 1 – . Thus the complete expression for IKA became
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(pHi,
i) is from Eq. 20 using i and pHi and (pHe,e) is from Eq. 20 using e and pHe. This expression captures the traditional activation and inactivation characteristics as well as the different patterns of intracellular and extracellular proton block of IKA and the distribution of these two patterns of proton block within the model neuron.
pH-dependent inhibition of IKDR.
The pH-dependent inhibition of IKDR was implemented exactly like the A-type channel. However, the IKDR was sensitive only to pHe (12). As a result, a single was used for IKDR, and was best described by a nonlinear equation
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pH-dependent inhibition of IKCa. In our model, pH sensitivity of the calcium-activated potassium channel was voltage independent and inhibited by pHe only. Therefore, we used a simple titration curve with a pKa of 7.4 and relative inhibition that ranged from 0 to 50% to modify the value of the maximum conductance of IKCa (gKCa) as a function of pHe.
Independent manipulation of pHi and pHe.
To investigate the response of neuronal activity to independent changes in pHi and pHe, we incorporated a model of pHi regulation based on work by Boron and De Weer (5). The change in pHi may be derived by solving the following differential equations simultaneously.
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is the area-to-volume ratio; PHA and PA are the membrane permeabilities of the weak acid and the conjugate base, respectively; 
equals Vm·F/(R·T); and K is the dissociation constant of the particular weak acid. is equal to the intrinsic buffering power within the cell. RH represents the proton flux across the cell membrane. The original formulation by Boron and DeWeer had a term, MH, which represented the proton flux that opposed the deviation of the intracellular proton concentration from its normal level and restored pH toward its initial value. The transport process responsible for this proton flux was not explicitly defined. In our model, RH was made of three terms:
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These two polynomials coupled together create a sigmoidal pHi regulatory curve so that, as pHi deviates more from the control condition, the rate of proton fluxes increases at an ever faster rate. One of the unusual features of pH regulation in chemosensory and nonchemosensory neurons is that pHi regulation is inhibited by acidosis when both pHe and pHi fall (20, 31, 37). To include extracellular inhibition of acid-base regulatory activity as a function of pHe, we calculated TH and then used a titration curve based on pHe with a pKa of 7.4 and percent inhibition values that varied from 0 to 95% as pHe varied from 8.4 to 6.4. We did not include any effect of pHe on pHi regulation during alkalotic conditions since we were concerned solely with hypercapnic responses.
Implementation of the model.
The model was constructed using Simulink (MathWorks, Natick, MA), and the simultaneous differential equations were solved with a variable-step trapezoidal solver designed for stiff systems. In general, we conducted simulated experiments in which different parts of the model were manipulated one at a time, and the model output was examined during a control period (pHe = 7.8 and PCO2 = 17 torr, these are typical values at 23°C in active H. aspersa; see Ref. 8). We compared these with the response of the model during a hypercapnic challenge (pHe 7.4 and PCO2 
30 torr).
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Role of each potassium channel in chemosensory responses. There are two ways to assess the contribution of each channel to CO2 chemosensitivity. One may examine the effect of dropping pH-dependent inhibition of one channel while retaining pH-dependent inhibition of the other channels (Fig. 4 middle), or one may examine the effect of pH-dependent inhibition of only one channel at a time (Fig. 4 right). The average interspike intervals, frequencies, and burst durations are summarized in Table 3. The results of this analysis are shown only for the bursting pattern of activity. The interpretation of the response of nonbursting patterns was identical, but the effect of inhibition during hypercapnia was more easily seen in the bursting cells, particularly the role of IKCa. The pHi and electrophysiological responses of the model neuron with all three potassium channels inhibited by pH are shown in Fig. 4, left. The pHi response to a square wave hypercapnic stimulus (FICO2 from 2.5 to 5%; pHe from 7.8 to 7.4) is shown above the electrophysiological response of the model. pHi regulation was included in these calculations (note the pHi recovery during hypercapnia and the alkaline overshoot when the hypercapnic stimulus was removed). Although pH regulation during hypercapnia is not typical of chemosensory cells (6, 20, 31, 38), the changing pHi within the cells as the cells regulate pH more effectively demonstrated the pH responsiveness of the ion channels within the model than the physiologically more accurate lack of pHi regulation typical of chemosensory cells. For example, the rate of AP formation slowed as pHi recovery occurred during the course of the hypercapnic response. This is not typical of neuronal responses to sustained hypercapnia, and pHi recovery during hypercapnia is not typical of chemosensory neurons (20, 31), but the model response, although not physiologically inaccurate, clearly demonstrates that the ion channels are responding to pHi. In the control condition (all 3 pH-sensitive potassium channels included), hypercapnia increased the frequency of APs from 0.5 to 8.1 Hz, but the frequency diminished dramatically as pHi recovered during hypercapnia. When the hypercapnia was removed, the alkaline overshoot was associated with a markedly reduced frequency of firing until pHi recovered toward the control value. The increase in frequency of APs during hypercapnia occurred because there were more APs within each burst of activity and the interburst interval declined. The duration of each burst was not modified much by hypercapnia (Fig. 4, bottom left).
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When pH sensitivity of only the IKA current was included in the model (Fig. 4, top right), CO2 sensitivity was retained; the AP frequency increased from 0.55 to 2.25 Hz. The alkaline inhibition of activity when the hypercapnia stimulus ceased was also present. In contrast, including pH sensitivity of either IKCa or IKDR as the sole pH-sensitive channel resulted in virtually no CO2 sensitivity; the AP frequency only increased from 0.45 to 1.60 Hz during hypercapnia when IKDR was inhibited by pH, and the AP frequency did not change at all when IKCa was the sole pH-sensitive channel. Without inhibition of IKA to start the depolarization, there was little opportunity for pH-dependent inhibition of IKDR and IKCa to modify the burst duration or the AP frequency. IKDR activates slowly and is mainly involved in repolarization, and IKCa requires an elevation of intracellular calcium, which accumulates only after multiple APs. Thus, modifying these later events in the process of AP formation, repolarization and the accumulation of intracellular calcium was the main way in which these channels enhanced AP frequency during hypercapnia.
Chemosensory responses to changes in pHe or pHi alone. IKA was inhibited by both pHi and pHe in the foregoing analysis. We separated the role of pHi- and pHe-dependent inhibition of IKA by varying the contribution of each type of IKA in the model (see Fig. 5). When pHi was the sole source of inhibition, the AP frequency in the bursting model increased from 0.45 Hz during normocapnia to 5.9 Hz during hypercapnia. In contrast, AP frequency increased from 0.45 to 8.55 Hz when pHe mediated the inhibition of IKA. One should not read too much into the differences between pHi- and pHe-mediated inhibition of IKA. The relative inhibition of IKA was similar in each case, but the fall in pHe was greater than the fall in pHi because the extracellular space was less well buffered and pHe was not regulated by any transport processes. For similar reasons, only pHi-mediated inhibition of IKA was affected by the alkaline overshoot following removal of hypercapnia. These results demonstrate that either a pHe or pHi sensor may be effective, but the relative magnitude of the pH-dependent inhibition of channel function will depend on the details of pH regulation and the voltage-dependent and pH-dependent properties on the intracellular and extracellular surfaces of each channel in the model. Experimental data support a prominent role for pHi rather than pHe in neuronal responses to hypercapnia (14, 17, 45), but the model indicates that pHe may still make a significant contribution.
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40% of the current flux through the delayed rectifier (10).
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DISCUSSION |
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Our computational analysis is a single-compartment model, and it raises a number of issues relevant to the definition of a chemosensory cell. At the single cell level, we have defined a CO2 chemosensitive cell as any cell in which the AP frequency is significantly increased or decreased from the control normocapnic value. However, to be called a respiratory chemosensory cell, we require that the activity of the chemosensory cell modify the respiratory response of the animal. This definition has only been fulfilled in invertebrates, so far as we know (15). The problem is complicated by the fact that synaptic drive may raise or lower the resting membrane potential, the activity of intrinsically CO2-sensitive neurons may be amplified or suppressed by synaptic inputs, and the in situ CO2 sensitivity of a cell may be quite different from its CO2 sensitivity when isolated from synaptic input. For these reasons, identification of CO2 sensitivity in synaptically isolated cells is only a first step in identifying respiratory CO2 chemosensory cells. Our model is an analysis of the factors determining neuronal CO2 sensitivity, not respiratory CO2 chemosensitivity.
Multiple pH-sensitive channels. We found that three potassium channels contribute to CO2 sensitivity in H. aspersa. The model reveals that IKA acts as the primary pH sensor, but pH-dependent inhibition of IKDR and IKCa amplifies the hypercapnic response by prolonging bursts of APs. Previous investigators have found a variety of other channels, mainly potassium channels, that may contribute to CO2 sensitivity, and they have focused, with rare exceptions, on only one channel as the CO2 sensor (24, 28, 34, 46). We think that multiple channels must be involved to explain all of the changes in AP morphology and firing patterns seen in native cells, and, recently, others have also suggested that more than a single channel is involved (18). There is disagreement among investigators about which channels play a role and which channels are active in which particular sites. We did not investigate all of the proposed ionic mechanisms whereby CO2 sensitivity might be achieved; we did not, for example, incorporate either inward-rectifying channels or TASK channels in our model since they were not present in CO2-sensitive snail neurons (12) even though they may play some role in CO2 chemosensory processes in mammals (28, 34). Among the putative chemosensory neurons, our model calculations do not support a prominent role of IKCa or IKDR as primary acid sensors, although it has been suggested that IKCa might act as a chemosensor (48). Both IKCa and IKDR seemed to modulate rather than initiate the chemosensory response to CO2 in our model. The delayed pattern of activation of IKDR and the requirement that intracellular calcium rise to activate IKCa precluded any role for either channel as the primary sensor, since some other pH-dependent process(es) had to trigger depolarization to activate IKDR and induce a rise in intracellular calcium to activate IKCa.
Rather than speculate about which channels are active in which cell types and which chemosensitive sites within the brain stem, it is probably more useful to emphasize the coordinated way in which inhibition of multiple channels within single neurons regulated neuronal behavior. We believe that IKA is the fundamental sensor in the snail chemosensory neurons. The key features of a chemosensory channel are that it be inhibitable at resting membrane potential in a physiologically relevant pH range. The window current of IKA, the voltage region where inactivation and activation overlap, encompassed the upper limit of the resting membrane potential. Therefore, pH-dependent inhibition of IKA is well-suited to initiate neural chemosensory activity. Activation of IKA tended to short circuit the AP, and pH-dependent inhibition of IKA increased the rate at which the membrane potential rose to the threshold of AP firing. Moreover, the lack of pH-dependent inhibition of IKA in the posthypercapnic period, when pHi was alkaline, led to an increased short-circuiting potassium current, which prevented AP formation. Note that inhibition of IKDR and IKCa either alone or in combination could not reproduce this alkaline inhibition of neuronal activity (Fig. 4). IKDR was only slowly activated as the cell depolarized, and, after multiple rapid APs, the activity of IKDR tended to suppress AP formation. Thus, when IKDR was inhibited by a fall in pH, the average membrane potential between APs was more depolarized, and the duration of each burst of APs was prolonged. Much like IKDR, IKCa was activated only as calcium accumulated inside the cell, which required multiple APs in rapid succession, and activation of IKCa, when it finally occurred, limited the duration of each burst. Thus hypercapnic inhibition of IKCa tended to prolong the duration of each burst. The relatively delayed patterns of activation of IKDR and IKCa make them ill-suited to act alone as a pHi or pHe sentinel, even though pH-dependent inhibition of IKDR and IKCa did support a hypercapnic response without any pH-dependent modulation of IKA (Fig. 7). On the other hand, only pH-dependent inhibition of IKA, acting alone, generated a significant chemosensory response.
Although pH-dependent inhibition of one or more of the potassium channels may suffice to preserve CO2 chemosensitivity, inhibition of no single channel or combination of two channels exactly replicated the effect of inhibition of all three channels. Inhibition of all three channels best duplicated our findings in actual neurons (12). The pH-dependent inhibition of all three channels optimized the generation, sustained formation of APs, and increased AP frequency in a way that inhibition of each single channel did not. The pH response of each channel is not all that surprising, but the coordination resulting from simultaneous inhibition is quite elegant. Finally, it is worth reiterating that the activation/inactivation characteristics of these channels are not particularly unusual. Many cells possess potassium channels with these characteristics, and, as a consequence, intrinsic CO2 sensitivity may be quite common, even in neurons without any respiratory function. Thus intrinsic neuronal CO2 sensitivity is a necessary, but not a sufficient, criterion for functional respiratory chemosensitivity. Functional respiratory CO2 chemosensitivity requires intrinsic CO2 sensitivity at the cellular level, but also requires appropriate synaptic connectivity to modulate respiratory activity.
An intracellular or extracellular site of the sensor. There has been a long-standing debate about the intracellular vs. extracellular site of the central CO2 chemosensor (13, 14, 17, 19, 33, 45). In general, as the ability of investigators to measure pH has moved from the arterial blood to ever smaller and more discrete locations within the brain, the site of the sensor has moved from something that sampled arterialized blood (4) to a sensor at a virtual interstitial location (33) to pHi (14, 17, 45). Sensors that detect the pHe-pHi difference have been proposed (50), but the pHe-pHi gradient does not consistently change during acid-base disturbances in ways that are correlated with ventilation (14). Our model calculations and patch-clamp studies (12) demonstrate the capacity of either pHe or pHi, acting as independent stimuli, to contribute to CO2/pH chemosensitivity without resolving whether pHi or pHe is the stimulus at any particular location in the brain. Our recent studies of lactate transport in the retrotrapezoid nucleus in rats strongly suggest that pHe may act as an independent chemosensory stimulus to ventilation (26). There is also ample evidence that pHi alone is a sufficient chemosensory stimulus (14, 17, 45). There is not actually much patch-clamp data in mammalian systems to resolve this issue. Thus the role of pHe and pHi as separate and independent modulators of particular ion channels in chemosensory cells remains to be studied. The essential result of the model calculations is that either an extracellular or intracellular site of potassium channel inhibition can be effective, but the relative importance of these sites will depend on the pKa of the sensor, the inhibitory potency of the site, and the buffer capacity and pH regulatory function in the region of each particular pH sensor.
pH regulation and chemosensitivity.
The ventilatory response to CO2 is sustained over minutes to hours with little evidence of accommodation. The respiratory system behaves as if the chemosensory stimulus is also sustained and relatively stable. Measurements of average brain pH in intact animals support the idea that brain pH is not regulated in the early hours of CO2 exposure (29, 30), particularly in the brain stem. This makes good sense in terms of sensor design, that is, the sensor should not modify the stimulus. The inadvisability of regulating pHi in chemosensory neurons is shown in Figs. 3 and 4. As pHi was regulated toward the control value during hypercapnia, the frequency of APs declined, and, in the immediate posthypercapnic period, the frequency of APs was completely suppressed. Such a loss of chemosensory drive would result in apneas and respiratory instability. Thus the lack of pHi regulation promotes a stable chemosensory output during and after hypercapnia. On the other hand, it seems a little surprising that so many nonchemosensory neurons should express multiple pH-regulatory proteins only to suppress their function when the acidic stress is greatest: when both pHe and pHi fall (20, 31, 37). The other surprising finding, which comes out of the model, is that, to achieve this "perfect" lack of pHi regulation during hypercapnia, the extent of activation of pH regulatory processes by pHi must be exactly balanced by extracellular pH-mediated inhibition of these same processes. NHE seems to be the main process regulating pH during acidosis in chemosensory regions (20, 31, 37), and the activation and inhibition of NHE are clearly independent, since NHE is activated when only pHi is reduced and pHe is held constant (20, 37). pHi activates NHE1, the best studied of the mammalian NHE isoforms, by allosteric modulation of the protein, which may involve more than one proton-binding site (36). Inhibition of NHE activity by extracellular protons is, on the other hand, thought to involve simple competition by protons for the extracellular sodium-binding site. To achieve exactly matching intracellular activation and extracellular inhibition, the activation/inhibition sites would require identical pH response profiles, but pKa values shifted by 0.4 pH units to allow intracellular activation at a control pHi of 7.4 and extracellular inhibition at a control pHe of 7.8. Such a regulatory scheme seems very unlikely, and it is not obvious how it might be achieved when the intracellular and extracellular proton regulatory processes are so different. It is not enough simply to have inhibition of NHE by pHe exceed activation of NHE by pHi; NHE activity cannot be completely suppressed during hypercapnia. The presence of metabolic processes that steadily produce protons in snail neurons (20) means that, even when pHe declines, some small level of NHE activation must persist to hold pHi stable during hypercapnia. It may be that there is coordinated regulation of multiple processes so that no single process of activation is exactly matched by inhibition, but, in the aggregate, the activation and inhibition are matched.
Limitations of the model. Before extolling the virtues of computer modeling in general and the results of our model in particular, it is worth confronting the very real limitations of our model. First, we included only a minimum set of channels. There are likely to be additional channels that may modulate the behavior of chemosensory neurons; for example, two-pore domain potassium channels and the inwardly rectifying potassium channel have been identified in chemosensory regions of the medulla in vertebrates (34, 43). Furthermore, we used formulations for different channels derived from a variety of sources, and the characteristics of individual channels may not match the particular channels in H. aspersa. However, the key elements in the model, the potassium channels and estimates of pH regulatory mechanisms, were taken from our own experimental studies in H. aspersa (12). Moreover, the nonmolluscan parts of the model do not detract from the relevance of the model to CO2 chemosensitivity, since none of the nonmolluscan parts of the model were modified during the experiments meant to elucidate the general principles that may govern the design and function of chemosensory cells.
It is worth pointing out what is not in the model. There is no potassium current activated by hyperpolarization, no inward-rectifying potassium current, and no TASK channel. These channels may participate in CO2 chemosensory responses in mammalian neurons in certain locations (28, 34, 42, 47), but we never saw evidence of these channels in molluscan neurons. In addition, we did not include any inhibition of INa or ICa, although protons probably inhibit both channels (23, 35, 44). IProton was inhibited by hypercapnia (12), but IProton was such a small fraction of the total conductances in the cell that we left the pH-dependent inhibition of IProton out of the model.
The details of the ion conductances that we included in the model must be viewed as a first approximation. To obtain model output that approximated the physiological output of neurons, we had to balance the conductances of the various channels. We have no effective way of confirming that the particular weighting of different conductances that we selected actually match typical neurons. Our experimental data were derived from isolated cells that lack the full compliment of dendritic and axonal arborization and therefore may lack full representation of all channels in the membrane. Furthermore, we assumed that the channels were homogenously distributed in our model neuron. We did not include any cable properties of chemosensory neurons and made no attempt to model the geometry of identified chemosensory cells. In real neurons, the channel types may segregate to particular locations in the cell, and the heterogeneous distribution of channels will certainly affect the electrophysiological behavior of the cell. We did not study the effect of distributing the pH stimulus to different locations within the cell, which may be important (39). Finally, we did not include any intercellular communication between adjacent chemosensory cells either by gap junctions or synaptic events (16). Any of these factors may amplify or reduce the CO2 sensitivity of a given cell, and we are currently revising our model to integrate these additional factors into our analysis.
In respect to pH regulation, we have mainly qualitative data; we know which processes are present and active. However, we do not have detailed information in respect to the quantitative relationships among the activity of pH regulatory proteins, pHi and pHe from chemosensory cells. We used as our guide data from cardiac myocytes (25). However, neurons regulate pHi poorly during hypercapnia, whereas myocytes regulate pHi effectively during hypercapnia. Even when neurons regulate pHi (for example, when only pHi declines), the rate of pHi regulation is small compared with cardiac myocytes (20, 25, 31, 37). Thus more detailed and chemosensory-specific information about pHi regulation would be helpful.
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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REFERENCES |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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). ENa, EK, and ECa, equilibrium potential for sodium, potassium, and calcium, respectively; R, gas constant; T, temperature; F, Faraday constant; [Ca]e, extracellular calcium concentration; [Ca]shell, intracellular Ca2+ concentration just inside the cell membrane; V, voltage; [Ca2+], calcium concentration; INa, sodium channel; ICa; calcium channel; IPR, proton conductance; JCa++, flux of Ca2+ ions; JH+, flux of protons.
