We created a single-compartment computer model of a CO2 chemosensory neuron using differential equations adapted from the Hodgkin-Huxley model and measurements of currents in CO2 chemosensory neurons from Helix aspersa. We incorporated into the model two inward currents, a sodium current and a calcium current, three outward potassium currents, an A-type current (IKA), a delayed rectifier current (IKDR), a calcium-activated potassium current (IKCa), and a proton conductance found in invertebrate cells. All of the potassium channels were inhibited by reduced pH. We also included the pH regulatory process to mimic the effect of the sodium-hydrogen exchanger (NHE) described in these cells during hypercapnic stimulation. The model displayed chemosensory behavior (increased spike frequency during acid stimulation), and all three potassium channels participated in the chemosensory response and shaped the temporal characteristics of the response to acid stimulation. pH-dependent inhibition of IKA initiated the response to CO2, but hypercapnic inhibition of IKDR and IKCa affected the duration of the excitatory response to hypercapnia. The presence or absence of NHE activity altered the chemosensory response over time and demonstrated the inadvisability of effective intracellular pH (pHi) regulation in cells designed to act as chemostats for acid-base regulation. The results of the model indicate that multiple channels contribute to CO2 chemosensitivity, but the primary sensor is probably IKA. pHi may be a sufficient chemosensory stimulus, but it may not be a necessary stimulus: either pHi or extracellular pH can be an effective stimuli if chemosensory neurons express appropriate pH-sensitive channels. The lack of pHi regulation is a key feature determining the neuronal activity of chemosensory cells over time, and the balanced lack of pHi regulation during hypercapnia probably depends on intracellular activation of pHi regulation but extracellular inhibition of pHi regulation. These general principles are applicable to all CO2 chemosensory cells in vertebrate and invertebrate neurons.
- potassium channels
- computer modeling
- central chemoreceptors
three themes have emerged in recent studies of the mechanism of respiratory CO2 chemosensitivity. A growing number of studies indicate that intracellular pH (pHi) is a sufficient stimulus of chemosensory cells (14, 17, 45), but these studies have not shown that pHi is the necessary stimulus. In addition, CO2 chemosensory neurons seem to lack the potent pH regulatory mechanisms that are operative in other cells (20, 37, 38). At least in neurons, the lack of effective pHi regulatory function may not be unique to CO2 chemosensory cells (6), and many nonchemosensory neurons seem to lose the ability to regulate pHi during acidic stress as development progresses (31). Therefore, neuronal pHi regulation is surprisingly poor during exposure to hypercapnia in adult animals even in nonchemosensory regions of the brain (29, 30). The final theme has been the recognition that inhibition of outward currents, usually potassium channels, is probably the fundamental sensory process in CO2 chemoreception. However, different potassium channels have been identified in different chemosensory regions of the mammalian brain stem. For example, a potassium channel inhibited by 4-aminopyridine, probably an A-type current, seemed to be responsible for CO2 chemosensitivity in the nucleus tractus solitarius (11), and inhibition of an inward rectifier potassium channel (34) or possibly two potassium channels (a TEA-sensitive channel and a TASK channel; see Ref. 18) seemed to mediate CO2 chemosensitivity in neurons in the locus coeruleus.
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.
The elements of the model are shown in Fig. 1. The model contained six voltage-gated ion channels, a calcium pump, a source of intracellular protons (reflecting either metabolic proton production or HCO3− efflux from the cell), and a pH regulatory mechanism resembling a sodium-hydrogen exchanger (NHE) in the acidic range and chloride-HCO3− exchange in the alkaline range. Hypercapnia was imposed on this model as a stimulus to assess the response of each of the elements to CO2. Neuronal activity was described using a single compartment model in which the instantaneous change in membrane potential was computed by summing the individual contributions of each channel and dividing by the membrane capacitance (Cmem; see Ref. 22): (1) where i is the current due to the nth channel. The current associated with each channel is given by: (2) gmax is the maximum conductance, and a and b are normalized activation and inactivation factors, which were each raised to an integer power (p and q, respectively) that may vary between zero and four. Erev is the reversal potential for the particular ion that the channel conducts (22). The steady-state activation curves were expressed as a function of membrane potential using a Boltzmann function: (3) where VH is the voltage at which activation is at half its maximum value, and sa is a factor determining the slope or step-width of the curve. The state of activation at any point in time was computed by integration of the equation: (4) where the rate at which activation (a) approaches the steady-state value (ainf) is determined by the rate constant (ka). The initial value of a was set to zero for all ion channels. The value of ka was either voltage dependent or a constant value depending on the particular channel. Equations 3 and 4 apply to inactivation as well, and, when inactivation was incorporated into particular channels, the initial value of b was set to one.
Mathematical description of IKA.
The current associated with IKA is given by: (5) where gA is the maximal conductance of IKA. The parameters for each of the terms in Eq. 5 are summarized in Table 1 (along with the parameters for all other conductances in the model). We used activation (a) and inactivation (b) equations derived from measurements that we made previously in H. aspersa neurons (12). We did not assess the time constants of activation and inactivation in our previous study; therefore, we used two of the three time constants described by Bal et al. (1) in the same species. The time constants for IKA vary as a function of voltage, and the time constants described by Bal et al. were fitted piecewise as two linear functions and converted to rate constants (1/time constant). We did not include the time constant of the fast inactivation component described by Bal et al., which was small in any event. (6) (7)
The characteristics of Eqs. 3–7 are shown graphically in Fig. 2. The activation and inactivation curves, the fitted rate constants, and the response of the model IKA channel to a simulated voltage-clamp protocol are shown in Fig. 2.
Mathematical description of IKDR.
The activation characteristics of IKDR were taken from our previous studies (12) using data shown in Table 1. The delayed rectifier in H. aspersa takes a very long time to inactivate (>2 s); therefore, IKDR was treated as a noninactivating channel in the model, as shown in Eq. 8. (8)
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): (9)
Mathematical description of IKCa.
The calcium-activated potassium channel was also adapted from Buchholtz et al. (7) and described by the following equation: (10)
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: (11)
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): (12) where ICa is the calcium current entering the membrane represented as a thin shell with a volume v, and F is Faraday’s constant. The calcium concentration within the cell is not homogeneous, but the calcium concentration just inside the cell membrane will determine the membrane effects of calcium. For this reason, the estimated calcium concentration within this thin shell beneath the cell membrane was used in our model to assess the membrane-related effects of intracellular calcium. PB is the probability of intracellular calcium buffering, [Ca]0 is the initial intracellular Ca2+ at time 0, and τ is the time constant for the calcium pump. The probability of intracellular calcium buffering was, in turn, derived from: (13) where K is the equilibrium constant for the second-order calcium buffering reaction, and [B]total is the total concentration of the buffer. In our model, the volume of distribution of intracellular calcium was equal to 2.5 × 10−4 nl, which is the volume of a thin shell of the intracellular space just within the cell membrane. We calculated thevolume of this shell assuming a cell diameter of 20–30 μm, a cell surface area of 0.0025 mm2, and a shell thickness just below the cell surface of 0.1 μm (51).
Mathematical description of INa and ICa.
The fast INa was adapted from the crab model developed by Buchholtz et al. (7). (14) The activation and inactivation rate constants were voltage independent and are given in Table 1 along with the other parameters (peak conductance and equilibrium potential for sodium). The ICa was taken from a model of neurons in Helix pomatia developed by Berezetskaya et al. (3) as a noninactivating channel. The calcium current was described as follows: (15) The parameters describing peak conductance, activation, and the rate constant of activation are given in Table 1. The equilibrium potential of calcium (ECa) was calculated from the Nernst equation as follows: ECa = (2.303·RT/2F)log([Ca2+]e/[Ca2+]i) where R is the universal gas constant, T is the temperature, and [Ca2+]e and [Ca2+]i are extracellular and intracellular calcium concentrations, respectively.
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: (16) The equilibrium potential (EH) for protons is not constant, but varies as a function of the pH gradient (pHe − pHi) across the cell membrane: (17) The rate constant of activation of IProton varies as a function of voltage. Data given by Byerly et al. (9, 10) were fitted to a Boltzmann curve, and the pH dependence of the rate constant, which was relatively modest, was ignored: (18) VH is also dependent on pHi: (19) In our previous experiments, the proton conductance started to activate at approximately −10 mV (12). Using our own electrophysiological measurements of activation characteristics and rate constants derived from the data presented by Byerly et al., we obtained current traces from a simulated voltage-clamp experiment that were similar to those obtained experimentally in our own laboratory (12) and by others (9, 10).
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 θ. The value of θ varied inversely with the extent of pH-dependent inhibition, and θ incorporated a term, φ, which varied as a function of voltage and a term that captured the pH dependence of the voltage-dependent inhibition of IKA as follows: (20) The pKa of the inhibitory titration curve was set equal to 7.4. The value θ varied, in theory, between 1 and 0, with 0 representing complete inhibition, but, in practice, the value of θ varied between 0.5 and 1.0 over the pH range that we studied. The value of φ depended on whether the channel was inhibited by pHi or pHe. For intracellular proton block of IKA, the value of φi was lowest at higher membrane potentials (the channel was most inhibited), and φi increased at more negative potentials (greater channel conductance when proton block was less). For extracellular proton block, φe was highest when membrane potential was positive, and φe diminished at more negative potentials. These intracellular and extracellular φ factors were derived from our previous work (12) and defined as (21) (22) Finally, we included two IKA currents with identical gating properties but different φ 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, β, which ranged from 0 to 1, and multiplying the other by 1 − β. Thus the complete expression for IKA became (23) where θ(pHi,Φi) is from Eq. 20 using Φi and pHi and θ(pHe,Φe) is from Eq. 20 using Φe 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 θ was used for IKDR, and φ was best described by a nonlinear equation (24) The pKa of inhibition of IKDR was also set to pH = 7.4.
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. (25) (26) where HA is the concentration of the protonated form of the weak acid (in our case this is the dissolved CO2 from the Henderson-Hasselach equation) and A is the conjugate weak base − HCO3−. We changed pHe, and thereby changed pHi, by varying the partial pressure of CO2. The variable [TA]i is the intracellular concentration of the acid ([HA]i + [A]i) inside the cell; ρ is the area-to-volume ratio; PHA and PA are the membrane permeabilities of the weak acid and the conjugate base, respectively; ε equals Vm·F/(R·T); and K is the dissociation constant of the particular weak acid. β 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: (27) where CIProton represents the proton flux through the proton channel present in snail neurons (9, 12), and MProton represents a small and constant source of metabolically produced protons (20). We cannot actually distinguish metabolic production of protons from an outward HCO3− flux, but these processes are equivalent in this part of the model. TH is analogous, in principle, to the MH term in the Boron and DeWeer model (5) save that we used a different mathematical formulation that more accurately reflects the transport processes described in snail and mammalian neurons (described below). These flux rates were multiplied by the intrinsic buffer capacity and the cell volume and integrated to determine the actual proton concentrations in the model. TH was set equal to zero in the model unless we were explicitly examining the effects of pH regulation on chemosensory function. The values for all the constants are given in Table 2.
Modeling pHi regulation.
NHE is the dominant pH regulatory process in chemosensory areas in neurons during hypercapnia in H. aspersa (20) and in mammals (31, 38). The activity of NHE is increased when pHi falls but inhibited by reductions in pHe (32, 52). In the alkaline pH range, we simply included a chloride-HCO3− anion exchanger. We created two polynomial equations that define proton flux (TH in mol·cm−2·ms−1) as a function of pHi. The first term describes the activity of NHE when acidic pHi values are present, and the other term pools the pHi regulatory processes present during alkalosis into a single equation that mimics chloride-HCO3− exchange. Both equations were derived from data provided by Leem et al. (25). (28) (29)
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).
Performance of the model.
We assessed the model piecemeal, and our first goal was to assess the responses of the ion channels to acid stimulation. Therefore, we deleted active pH regulation (TH in Eq. 27), and the first set of model responses represents neural activity in cells with only passive, physical-chemical buffering and the ion channel activation and inactivation characteristics that closely match the actual values measured in snail neurons (12). In the initial studies, we assumed that pH-dependent inhibition of IKA was evenly split between pHi and pHe. We do not have detailed knowledge of the absolute or relative gmax for the ion channels we studied, and it was necessary to balance the conductances in the model. In the process of doing this, we obtained two patterns of neuronal behavior: single regularly spaced APs and phasic bursting behavior. We observed similar bursting and nonbursting behaviors and similar AP frequencies in neurons studied in the subesophageal ganglia in semi-intact preparations (15). Examples of these patterns of behavior and the response of each pattern to hypercapnic stimulation are shown in Fig. 3. The only change in the model necessary to elicit bursting behavior was to decrease the peak conductance of the calcium current (Table 1). Reducing the peak calcium conductance decreased the inward calcium current but also decreased the role of the IKCa in terminating runs of APs so that sustained bursts of APs were enhanced. Both bursting and nonbursting neurons responded to hypercapnic acidosis, as shown in Fig. 3. The frequency of APs increased from a normocapnic frequency of 0.15–0.65 Hz during hypercapnia when the model was in the nonbursting mode and from 0.5 to 8.4 Hz in the bursting mode. The intracellular potassium and calcium values in the shell beneath the cell membrane are also shown in Fig. 3 during the two patterns of neuronal activity. The intracellular calcium levels increased in both types of neurons during hypercapnia, but the total potassium conductance during each AP changed only modestly. Hypercapnia induced an increase in [Ca2+]i in both bursting and nonbursting cells, but, in the nonbursting cells, [Ca2+]i rose to high levels because the calcium current was substantially larger than in the bursting model. These relatively high concentrations are, however, restricted to the small submembranous shell in our model.
Evaluation of activation and inactivation characteristics.
The activation/inactivation characteristics of the pH-sensitive potassium channels included in the model may alter the CO2-dependent behavior of the model neuron. We performed a sensitivity analysis to assess the impact of changing VH and the slope factor (s) on the model behavior. We did not study the effect of changing the rate constants of activation and inactivation on pH sensitivity of the model neuron since we did not investigate this aspect of channel function in our previous study (12). Each test of the channel parameters was assessed during normocapnia (pHe = 7.8, FiCO2 = 2.5%) and during hypercapnia (pHe=7.4; FiCO2 = 5.0%), and the ratio of neuronal activity in these conditions was used to determine which value of VH maximally enhanced CO2 sensitivity. We studied IKA first (both activation and inactivation) while holding other aspects of the model constant, and we performed a similar analysis of the VH and “s” of activation of IKDR. Once the choice of VH and s was restricted to values that produced stable AP formation, CO2 sensitivity did not vary much as a function of the particular values of VH or s for either IKA or IKDR, and the measured values in native cells are close to those values that produce stable firing patterns and maximal CO2 responsiveness.
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).
Removing the pH-dependent inhibition of IKA, while leaving pH-dependent inhibition of IKDR and IKCa, still resulted in a small increase in AP frequency during hypercapnia; the AP frequency increased from 0.45 to 2.0 Hz. The rate of AP formation was not markedly increased, but, when APs formed, the bursts of activity lasted slightly longer. The inhibition of activity by alkaline pH was completely lost when pH-dependent inhibition of IKA was absent from the model. Removing inhibition of IKDR did not prevent a hypercapnic response, but the CO2 sensitivity was reduced (the AP frequency increased from 0.55 to 2.25 Hz). The bursts of APs lasted slightly longer, and the interburst interval was shortened, but the lack of pH-dependent inhibition if IKDR resulted in a persistent hyperpolarizing effect during hypercapnia that slowed the overall AP frequency. When pH-dependent inhibition of IKCa was dropped from the model, hypercapnic sensitivity persisted, but CO2 sensitivity was reduced relative to the control condition in that the AP frequency increased from 0.5 Hz to only 3.2 Hz during hypercapnia. The burst duration was only slightly prolonged, and the interburst interval was shortened during hypercapnia.
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.
Effect of IProton in the electrophysiological and pH responses.
IProton does not play a major role in mammalian neuronal function, but it is active in invertebrate systems. We removed the pH-dependent inhibition of potassium channels from the model to isolate the ionic fluxes due to IProton during imposed pH changes. We changed the conductance of IProton within the model from small to quite large values. At peak conductance values (gmax-IProton) <0.01 μS, IProton had little detectable effect on cellular responses. At gmax-IProton values >10.0 μS, IProton began to alter pHi values significantly. We selected a gmax-IProton of 0.01 μS for further study because it had, to us, a surprising effect on CO2 sensitivity without significantly altering pHi (Fig. 6). IProton activated at membrane potentials more positive than approximately −20 mV, and the net flux of protons was generally outward. However, the flux of protons depended on EH, which was not fixed or immutable. During hypercapnic exposure, EH declined; the fall in pHe was greater than the fall in pHi, and the difference between these values was attenuated further during hypercapnia by the pH-regulatory processes included in the model. Therefore, the net outward flux of protons was reduced during hypercapnia, and, to the extent protons flowed into the cell, there was net depolarization of the membrane potential and increased AP formation. Thus, in the absence of any pH-dependent inhibition of potassium channels, the activity of IProton was still sufficient to increase APs during hypercapnia (Fig. 6, top left). If we restricted the fall in pH to the extracellular space, mimicking the early stage of a metabolic acidosis with a relatively impermeant acid, the EH was increased to zero, at which point the flux of protons depended solely on the membrane potential. In this setting as well, the increased inward proton current depolarized Vm and increased APs during the acidosis. Because the potassium channels were not inhibited by pH and IProton activated only at relatively high membrane potentials, the effect of elevating EH was only seen when spontaneous APs occurred and revealed the activity of IProton. IProton acting alone was not able to act as a pH sensor; it was only able to modify the frequency of APs once they had been initiated by other ion currents. If the acidosis was restricted to the intracellular space (Fig. 6, bottom), then EH was more negative, the inward flux of protons was reduced, and the bursting activity of the model neuron was actually inhibited. Thus IProton may enhance or inhibit responses to acid stresses depending on the relative change in EH. The effect of IProton is relatively modest compared with the effects of pH-dependent inhibition of potassium channels, and the current flux through IProton is only ∼40% of the current flux through the delayed rectifier (10).
Effect of acid-base regulation on chemosensory responses.
Chemosensory and nonchemosensory neurons in the brain stem demonstrate remarkably poor regulation of pHi when subjected to any acid stress that reduces both pHi and pHe (20, 31, 38). Acid-base regulatory proteins are present and activated by reduced pHi (20, 31, 37), but these same processes seem to be inhibited when pHe also declines. The inhibition is, on average, perfect; there is typically no pHi regulation during hypercapnia (both pHi and pHe fall and there is no apparent change in pHi over at least the first 20 min of hypercapnic exposure) and no alkaline overshoot when the hypercapnic stimulus is removed. The mathematical solution to this issue is simply to inhibit pHi regulation as a function of pHe in exact proportion to the extent to which pH regulation is activated by pHi. As shown in Fig. 7, anything less than “balanced” inhibition by pHe of the pHi-mediated activation of pH regulation leads to patterns of AP activity that do not reflect the observed changed in pHi and AP frequencies during hypercapnia (17, 20, 31, 38, 45). Thus the mathematical solution to balance pHi activation by pHe-mediated inhibition must also be the biological solution. The system behaves during hypercapnia as if a titration curve based on pHi activated pH regulation, and an exactly matching titration curve of opposite sign based on pHe inhibited those same pH regulatory processes.
The model we developed represents a minimal configuration of a CO2 chemosensory cell in H. aspersa and probably deviates significantly from actual chemosensory cells. Moreover, some features of the model may pertain only to invertebrates. Nonetheless, three general findings emerge from this relatively simple, single-compartment model that are applicable to all CO2 chemosensory cells studied to date in invertebrates and vertebrates. First, multiple channels contribute to the electrophysiological characteristics of the chemosensory response in H. aspersa and probably mammalian chemosensory neurons as well (18). CO2 chemosensitivity is robust and does not require all three channels, but each channel does contribute to the overall characteristics of the response. Second, the site of the sensor (intracellular vs. extracellular) may not be all that important in responses to CO2 since pH regulation in chemosensory cells is poor and pHi and pHe bear a relatively fixed relation to each other during hypercapnic stimuli. Finally, ion conductances and pH transport mechanisms must be carefully balanced to mimic “poor” pH regulation typical of CO2 chemosensory cells, but this poor pHi regulation is not an uncontrolled or accidental development; it requires active regulation by intracellular and extracellular pH and active regulation of transporter expression. Our model does not indicate how this balancing is achieved at the molecular level, only the necessity that it be achieved in order that the model replicates the electrophysiological and pH behavior of actual CO2-sensitive neurons and the ideals of appropriate chemosensor design.
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.
This work was supported by National Heart, Lung, and Blood Institute Grants HL-07449, HL-51238, HL-71001, and HL-56683.
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- Copyright © 2007 the American Physiological Society