JN Fuel your research with LabChart
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
 QUICK SEARCH:   [advanced]


     


J Neurophysiol 95: 3686-3697, 2006. First published April 12, 2006; doi:10.1152/jn.01312.2005
0022-3077/06 $8.00
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
95/6/3686    most recent
01312.2005v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via ISI Web of Science (3)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Tong, C.-K.
Right arrow Articles by Chesler, M.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Tong, C.-K.
Right arrow Articles by Chesler, M.

Kinetics of Activity-Evoked pH Transients and Extracellular pH Buffering in Rat Hippocampal Slices

Chi-Kun Tong1, Kevin Chen2 and Mitchell Chesler1

1Department of Physiology and Neuroscience and Department of Neurosurgery, New York University School of Medicine, New York, New York; and 2Department of Chemical and Biomedical Engineering, Florida State University, Tallahassee, Florida

Submitted 14 December 2005; accepted in final form 27 February 2006


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
The kinetics of activity-dependent, extracellular alkaline transients, and the buffering of extracellular pH (pHe), were studied in rat hippocampal slices using a fluorescein-dextran probe. Orthodromic stimuli generated alkaline transients ≤0.05 pH units that peaked in 273 ± 26 ms and decayed with a half-time of 508 ± 43 ms. Inhibition of extracellular carbonic anhydrase (ECA) with benzolamide increased the rate of rise by 25%, doubled peak amplitude, and prolonged the decay three- to fourfold. The slow decay in benzolamide allowed marked temporal summation, resulting in a severalfold increase in amplitude during long stimulus trains. Addition of exogenous carbonic anhydrase reduced the rate of rise, halved the peak amplitude, but had no effect on the normalized decay. A simulation of extracellular buffering kinetics generated recoveries from a base load consistent with the observed decay of the alkaline transient in the presence of benzolamide. Under control conditions, the model approximated the observed decays with an acceleration of the CO2 hydration–dehydration reactions by a factor of 2.5. These data suggest low endogenous ECA activity, insufficient to maintain equilibrium during the alkaline transients. Disequilibrium implies a time-dependent buffering capacity, with a CO2/HCO3 contribution that is small shortly after a base load. It is suggested that within 100 ms, extracellular buffering capacity is about 1% of the value at equilibrium and is provided mainly by phosphate. Accordingly, in the time frame of synaptic transmission, small base loads would generate relatively large changes in interstitial pH.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Neural activity generates a variety of changes in the extracellular pH (pHe) of the brain (Chesler 2003Go). Alkaline transients have received particular attention because a rise in pHe can augment N-methyl-D-aspartate (NMDA)–receptor activity (Tang et al. 1990Go; Traynelis and Cull-Candy 1990Go). In hippocampus, two kinds of alkaline transients occur with stimulation of the Schaffer collaterals. One form arises from the efflux of HCO3 across {gamma}-aminobutyric acid type A (GABAA) anion channels and is blocked by inhibitors of extracellular carbonic anhydrase (ECA) (Chen and Chesler 1992bGo; Kaila et al. 1992Go). A second form of alkaline shift, addressed in this study, is independent of HCO3 (Chesler and Chan 1988Go; Gottfried and Chesler 1994Go) and is amplified by ECA blockers such as benzolamide (Chen and Chesler 1992bGo,cGo). This alkalosis has been suggested to arise from Ca2+–H+ exchange by the plasma membrane Ca2+-ATPase (Schwiening et al. 1993Go). However, there is no direct evidence that this mechanism accounts for extracellular alkaline shifts noted in mammalian brain (Chesler 2003Go).

Benzolamide was shown to augment synaptic currents mediated by NMDA receptors (Gottfried and Chesler 1994Go), suggesting that control of these pHe shifts by ECA could play a role in the regulation or modulation of synaptic transmission. The amplification of the alkalosis by inhibitors of ECA has been attributed to slowing of the extracellular buffering reactions. A net fall in extracellular H+ or "proton sink" is buffered by the hydration of CO2 (Chen and Chesler 1992cGo). In the presence of benzolamide, buffering proceeds by the uncatalyzed, reversible reaction

Formula 1(1)
The forward hydration step is an extremely slow reaction with a time constant of nearly 12 s at 32°. In brain, the formation of HCO3 is catalyzed by ECA, which exists as the carbonic anhydrase (CA) type IV (Tong et al. 2000Go) and type XIV isoforms (Parkkila et al. 2001Go) with a probable small contribution from recently described carbonic anhydrase XV (Hilvo et al. 2005Go). The acceleration of HCO3 formation by these enzymes depends on their respective concentrations and catalytic rates (Maren 1988Go). Previous studies showed that extracellular buffering capacity (betae) was decreased by the inhibition of ECA (Chen and Chesler 1992bGo,cGo), whereas the addition of exogenous carbonic anhydrase to brain slice saline augmented buffering of the interstitial fluid (Huang et al. 1995Go). Because of the limited speed of pH microelectrodes, these prior experiments were unable to accurately discern the time course of the induced alkaline shifts or the role of ECA in shaping the kinetics of the interstitial pH changes.

Here we have used a dextran-linked, pH-sensitive, fluorescein probe to investigate at high temporal resolution the kinetics of hippocampal alkaline transients and their dependency on ECA. Our data show that the amplitude of rapid responses is curtailed nearly 50% by the endogenous ECA. In addition, the ECA causes a pronounced acceleration of the recovery from alkalosis, and thereby severely limits the extent to which these responses can temporally summate during prolonged neural activity. Thus during extended stimulus trains, a manyfold increase in amplitude can be observed after inhibition of ECA. Addition of type II carbonic anhydrase to the saline is shown to curtail the alkalosis, suggesting that the endogenous ECA activity is not sufficient to maintain equilibrium of the buffering reactions. A kinetic model of the buffer system generated pH relaxations from a base load that approximated the experimentally observed decays of the alkaline transient in the presence of benzolamide. Acceleration of the hydration and dehydration reactions by just two- to threefold was sufficient to model the decay phase of the alkaline transient in the presence of normal ECA. These results suggest that because of limited ECA activity, the brain interstitial fluid has a time-dependent buffering capacity that is on the order of 1 mM during the rise of the alkalosis, and requires several seconds to attain equilibrium and maximum buffering.


    METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Preparation and solutions

Thin hippocampal slices (200–250 µm) were prepared from juvenile (P8–P12) Sprague–Dawley rats. Procedures were carried out with review and approval of the New York University School of Medicine Institutional Animal Care and Use Committee. Slices were placed in a submersion-style chamber mounted on a Zeiss Axiovert 100 inverted microscope. The preparation was superfused with saline (32°C) containing (in mM): 124 NaCl, 3 KCl, 26 NaHCO3, 10 glucose, 1 Na2HPO4, 3 CaCl2, and 1 MgCl2, gassed with 95% O2-5% CO2 (pH 7.4). Before the start of experiments the saline was switched to one with 0 MgCl2 and 100 µM picrotoxin. The absence of Mg2+ and use of 3 mM Ca2+ served to maximize the extracellular alkaline shifts (Chen and Chesler 1992aGo; Grichtchenko and Chesler 1996Go; Paalasmaa and Kaila 1996Go). This was necessary because of the extremely brief (20-ms) orthodromic stimulus train used to elicit rapid alkaline transients (see following text and DISCUSSION). Picrotoxin (100 µM) was included to prevent the generation of extracellular alkaline transients arising from HCO3 efflux across GABAA anion channels (Chen and Chesler 1992bGo; Kaila et al. 1992Go). Exogenous CA, added to the saline in some experiments, consisted of purified bovine type II isoform. To elicit pure antidromic responses in the absence of excitatory synaptic activity, 25 µM 6-cyano-7-nitro-nitroquinoxaline-2,3-dione (CNQX) and 50 µM D-2-amino-5-phosphonovalerate (APV) were added to the saline. Picrotoxin, CNQX, APV, and carbonic anhydrase type II were obtained from Sigma Chemical (St. Louis, MO). Benzolamide was a gift of Lederle Laboratories.

Electrical stimulation and recording

Synaptically evoked extracellular alkaline transients were activated by supramaximal stimulation of the Schaffer collateral fibers with constant-current pulses of 200-µs duration, using a pair of 50-µm, Teflon-insulated, platinum-iridium wires (Chen and Chesler 1992bGo). In a few experiments, alkaline shifts were induced by antidromic activation of the CA1 pyramidal neurons by stimulation of the alveus in the presence of picrotoxin, CNQX, and APV (Chen and Chesler 1992aGo). Methods for fabrication and calibration of the pH microelectrodes (tip diameter 4–6 µm) were the same as previously described (Chesler and Chan 1988Go), except that the reference barrel contained 150 mM NaCl, 2 mM HEPES (pH 7.3), and 0.5 µM of a 2,000-kDa (mean weight) fluorescein-dextran (FD) conjugate (Molecular Probes D-7137). The reference barrel was fitted with Teflon tubing for pressure ejection, a silver wire for recording extracellular slow and fast potentials, and was sealed with dental wax.

The pH microelectrode was lowered into the stratum radiatum or the stratum pyramidale and placed at a depth (typically about 100 µm) of maximum evoked field potential amplitude. Field potentials were recorded directly from the output of the reference head stage. The slow DC potential of the reference barrel was continuously subtracted from the potential on the pH-sensitive barrel to yield pHe traces. To conform to the direction of the fluorescence signals, the pH microelectrode responses were arranged such that alkaline shifts were upward.

Ejection of fluorophore and optical recording of pHe transients

After final placement of the double-barreled microelectrode, the FD conjugate was pressure-ejected from the reference barrel using five to ten pulses of compressed air (60 p.s.i., 100-ms duration). The excitation of FD and collection of corresponding emissions were accomplished with an epifluorescence arrangement (Fig. 1A) using a x40 dry objective (numerical aperture 0.75). Excitation was provided by a 75-W xenon lamp and 495 ± 10 nm filter through a fiber-optic coupling fitted with a Uniblitz VS25 shutter (controlled by a VMM-T1 shutter driver). A few experiments entailed excitation at the isobestic wavelength, using a 440 ± 10 nm excitation filter. Fluorescein emissions elicited by these excitation wavelengths (referred to as the F495 and F440 emissions, respectively) were collected by the objective and directed to a photomultiplier (Photon Technology International) through a high-pass (515-nm) dichroic mirror followed by a 535-nm emission filter (band-pass 25 nm). Adjustable horizontal and vertical shutters on the photomultiplier assembly restricted the measured emissions to those from an area of the slice constituting 100–200 µm2.


Figure 1
View larger version (27K):
[in this window]
[in a new window]
 
FIG. 1. Fluorescence recording of extracellular pH. A: experimental arrangement. A juvenile rat hippocampal slice was placed on a coverslip serving as the floor of a superfusion chamber. Fluorescein-conjugated dextran was pressure injected by the reference barrel of a pH microelectrode. Fluorophore was excited at 495 nm, and emissions were collected via a 535-nm dichroic mirror. B: image of an injected fluorescein-dextran bolus in a hippocampal slice. Recording window for s. radiatum is approximated by the square area entirely filled by fluorophore. C: fluorescence change in slice pHe in response to a shift in bath pH. Photomultiplier window was opened for brief periods resulting in discontinuous fluorescence trace (gray). Continuous line is the simultaneous recording of pHe by a pH microelectrode. D: data in C were plotted as absolute pHe (obtained from the pH microelectrode) vs. fractional change in fluorescence. This relationship was roughly linear over the pHe range encountered in our experiments. Line was obtained by linear regression.

 
By focusing on the tip of the microelectrode (visible through the thin translucent tissue of the P8–P12 slices) the optical depth of field was made to correspond with both the point of FD ejection and the locus of the pH microelectrode recordings. The depth of field, defined as the distance between the principal minima of the z-axis point spread function, would be roughly 2 µm for a x40 dry objective with a numerical aperture of 0.75 (Tao and Nicholson 1995Go). Because of the epifluorescence arrangement, the intensity of fluorescence excitation would be defined by a similar point spread function. Thus the fluorescence excitation, its corresponding emissions, and the intensity of light acquired by the objective were similarly constrained along the z-axis, limiting the origin of most of the evoked fluorescence to a thin section of tissue in the xy plane.

To determine whether our ejection procedure resulted in a bolus of fluorophore sufficient to fill the area of the photomultiplier aperture, images were obtained on a separate setup, using a 12-bit, cooled CCD camera (Cooke Sensicam), an upright microscope (Zeiss Axioskope), and a x40 water immersion objective (numerical aperture 0.75). Figure 1B illustrates the dimensions of an FD bolus in stratum radiatum within the focal plane of the microejection pipette tip. A red square outline with an area of 200 µm2 is superimposed to represent the dimensions of the photomultiplier window and to illustrate that the typical area of recording was readily filled by the fluorophore. The size of the imaged FD bolus changed little over the course of 1 h. This observation was consistent with negligible extracellular diffusion of the high molecular weight dextran (Nicholson and Tao 1993Go). When using the photomultiplier, however, some loss of baseline fluorescence was noted over the course of 1 h. This may have been a result of photobleaching or of diffusion of some lower molecular weight components of the dextran. In the span of roughly 1 h required for the acquisition of fluorescence data, this decline amounted to no more than 15% of the original baseline fluorescence.

Acquisition of fluorescence data

In a previous study in which FD was microejected into the extracellular space of hippocampal slices, it was demonstrated that the conjugated fluorescein retained its characteristic pH-dependent properties (Gottfried and Chesler 1996Go). The F495 increased in intensity with alkalinization, whereas the F440 was insensitive to pH (Tsien 1989Go). Because there were no discernible changes in the F440 during or following evoked electrical activity, ratios of the F495 and F440 were deemed unnecessary. In the present study, we similarly recorded only changes in the F495 evoked by electrical activity. During slow pHe shifts, the time course of the F495 was approximated by the pH microelectrode traces (see following text). A trigger pulse was used to begin data acquisition, open the shutter, and start the electrical stimulus protocol. Analog photomultiplier output was low-pass filtered with a 5-ms time constant. The shutter was closed after decay of the evoked alkaline transients. Final fluorescence records were presented as percentage change over baseline (100 x [{Delta}F/F]).

pH calibration

For slow fluorescence signals, the presence of the pH microelectrode served as an in situ reference for calibration. Figure 1C illustrates the correspondence between the slow, intermittently sampled extracellular fluorescence changes (in gray) and the response of a pH microelectrode, when a hippocampal slice was superfused with low-bicarbonate media of pH 6.8 followed by return to normal saline of pH 7.4. Correspondence of slow fluorescence changes and the pH electrode response was also evident during low-frequency stimulation, as can be seen in Fig. 4, A and C. Over this limited pH range there was an approximate linear dependency of {Delta}F/F on extracellular pH. This is illustrated Fig. 1D, where the {Delta}F/F from Fig. 1C was plotted against the extracellular pH measured by the pH microelectrode and fitted to a line. In similar experiments on seven hippocampal slices the mean slope of this relationship fitted by linear regression was 0.36 ± 0.03 ({Delta}F/F)/{Delta}pH (R = 0.93 ± 0.01). During low-frequency stimulation, where the pH changes had an obvious slow component, the entire fluorescence record could be calibrated on the basis of the pH electrode response. With stimulation at high frequency, however, the pH electrode response was too slow to offer a reliable calibration. For these experiments, the mean slope ({Delta}F/F per {Delta}pH) of 0.36 was used to provide an approximation of the {Delta}pHe magnitude.


Figure 4
View larger version (28K):
[in this window]
[in a new window]
 
FIG. 4. Summated alkaline shifts elicited by repetitive orthodromic stimulation. A: fluorescence trace displayed a brief rise in pHe followed by a slower decay after each stimulus (arrowheads). A saw tooth pattern with temporal summation resulted from the prolonged decay phase after each stimulus. Simultaneous pH microelectrode response (gray line) was a monotonic slow rise in pHe interrupted by small stimulus artifacts (arrows). B: expanded sweep illustrates summation of the alkalosis arising from the incomplete recovery of the preceding transient response. C: summated response to 2-Hz stimulation was 3- to 4-fold greater in the presence of benzolamide. Gray trace is the averaged pH microelectrode response. D: expansion of the initial segment of C illustrates that the increased temporal summation in benzolamide was attributed to the prolongation of the decay phase of each alkaline transient.

 
Analysis of fluorescence data

The fluorescence changes elicited by a single train of stimuli were excessively noisy, requiring averaging of the data of multiple stimulus trials from the same slice. A mean record was obtained for each slice by averaging the raw fluorescence traces aligned at the instant of the first electrical stimulus artifact. Trials of low-frequency stimulus trains were repeated at 2-min intervals and averaged over five trials. To study the onset and decay of the most rapid phases of the alkaline responses, we used a stimulus paradigm of three shocks applied to the Schaffer collaterals at 100 Hz, consisting of a stimulus train that terminated in 20 ms. To discern the pH responses evoked by this procedure, it was necessary to average the raw traces from 50 separate trains, separated by 30-s intervals. Thus when studying the effect of benzolamide or exogenous carbonic anhydrase on these responses, we obtained 50 raw control traces, followed by 50 raw traces in the test saline, requiring a total recording time of 50 min for each slice. We did not observe significant rundown of the responses over this time. The digitized averaged traces were plotted in Microsoft Excel and imported into Adobe Illustrator. For analysis, the start of each trace was taken as the instant of the initial stimulus evident from the simultaneous recording of the extracellular field potential. To compute comparative rates of rise, the control and paired benzolamide (or carbonic anhydrase) records were expanded and the baselines and start of the two traces were superimposed. The initial rate of rise of each trace was taken as the slope of a straight line fitted to the roughly linear initial 100 ms of each rising phase. Measurements of peak amplitude, time to peak, and decay half times were obtained using horizontal and vertical cursors. Comparisons were made using a paired Student's t-test. The corresponding mean values were presented with the SE.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Alkaline transients elicited by a rapid-stimulus train

To discern the kinetics of the stimulus-evoked alkaline transient, it was necessary that the stimulus be brief compared with the rising phase of the response. A single 200-µs orthodromic stimulus could sometimes elicit a sizable averaged alkalosis, although sufficiently large responses were most reliably evoked by three successive stimuli at 100 Hz. This paradigm limited the stimulus duration to 20 ms, which was a small fraction of the rise time of the ensuing alkaline transient. An example of such a response, recorded from stratum radiatum, is shown in Fig. 2A. Whereas, the stimulus train was terminated in 20 ms, the rising phase of the alkaline transient lasted for nearly 370 ms, and peaked at a {Delta}F/F of 1.7% (or an estimated {Delta}pH of roughly 0.05). The peak was followed by a slower recovery, with a half decay time of 560 ms. Mean values for the peak fluorescence change, time to peak, rate of rise, and half decay time of these orthodromic responses from 23 slices are listed in Table 1A. Notably absent in these records was any trace of an initial acid shift after the stimulus, as was described in an early study by Krishtal et al. (1987)Go.


Figure 2
View larger version (17K):
[in this window]
[in a new window]
 
FIG. 2. Stimulus-evoked, extracellular alkaline shifts recorded by the fluorescein-dextran method. A: orthodromic alkaline transient elicited by 3 stimuli to the Schaffer collaterals delivered at 100 Hz. B: antidromic alkaline transient elicited by 3 stimuli delivered to the alveus at 100 Hz. C: orthodromic stimulation (3 stimuli, 100 Hz) elicited a typical transient increase in the F495. D: orthodromic stimulation (3 stimuli, 100 Hz) produced no change in the F440. Record is from the same slice as C.

 

View this table:
[in this window]
[in a new window]
 
TABLE 1. Characteristics of stimulus-evoked alkaline transients

 
Antidromic stimulation of the CA1 pyramidal neurons can also elicit an extracellular alkaline transient (Chen and Chesler 1992aGo). In the presence of 25 µM CNQX and 50 µM APV (in addition to 100 µM picrotoxin) a train of three antidromic stimuli at 100 Hz generated a rapid alkaline transient in stratum pyramidale (Fig. 2B). The mean amplitude and rate of rise of the antidromic transient were roughly half that of orthodromic responses evoked by the same three-shock paradigm (P < 0.05). However, the time to peak and half decay time did not differ significantly from the corresponding orthodromic parameters (Table 1A). In an earlier study using conventional pH microelectrodes in this preparation, it was also noted that the orthodromic alkaline shifts were larger than the antidromic responses, when elicited by identical stimulus trains (Chen and Chesler 1992aGo).

Neural activity has been associated with short-latancy increases in the autofluorescence of flavoproteins (Reinert et al. 2004Go; Shibuki et al. 2003Go). If sufficiently large (in relation to the FD emissions), these endogenous signals could contaminate the pHe traces. Excitation at 440 nm would be expected to elicit optimal flavoprotein emissions between 515 and 570 nm (Reinert et al. 2004Go). It is convenient that 440 nm is also the isobestic (pH-insensitive) excitation wavelength of the fluorescein dextran (Gottfried and Chesler 1996Go). Observation of the F440 during electrical stimulation therefore provides a good test for contamination of the FD signal by endogenous flavoprotein emissions. Alternate F495 and F440 fluorescence records obtained from the same hippocampal slice are shown in Fig. 2, C and D, respectively. Whereas the F495 trace of Fig. 2C shows a typical orthodromic response (similar to the record in Fig. 2A), there was no stimulus-evoked change in the F440 signal, as shown in Fig. 2D. The F440 was also found to be unchanged during stimulation of hippocampal slices in an earlier study from this laboratory (Gottfried and Chesler 1996Go). Thus against the background fluorescence of the FD, there were no observable, stimulus-evoked flavoprotein emissions.

Effect of benzolamide during a rapid-stimulus train

Numerous brain slice studies with pH microelectrodes have reported that alkaline transients evoked by stimulus trains are amplified by benzolamide (Chesler 2003Go). To discern the kinetic basis of this enhancement, we studied the effect of benzolamide on the rapid alkaline transient evoked by a 20-ms, 100-Hz orthodromic train of three stimuli. The control record of Fig. 3A (black trace) shows a rapid alkaline transient that peaked in 140 ms. After superfusion of 10 µM benzolamide the response (gray trace) displayed more than a doubling of the time to peak (340 ms), and a 70% increase in peak amplitude. Expansion of the onset of the traces (Fig. 3B) indicated that inhibition of ECA by benzolamide caused a modest increase in the initial slope of the response. The most pronounced effect of benzolamide was a prolongation of the falling phase. This is evident in Fig. 3C, where the decay phase of the control and benzolamide traces were normalized. In this experiment, the time to half decay increased from 470 ms in the control response to 1,720 ms in the presence of 10 µM benzolamide.


Figure 3
View larger version (27K):
[in this window]
[in a new window]
 
FIG. 3. Effects of benzolamide and exogenous carbonic anhydrase. A: alkaline response in 10 µM benzolamide (gray traces) had a larger and later peak amplitude, and a slower rate of decay. B: expanded sweep illustrates that the larger amplitude of the benzolamide response was partly the result of a faster rate of rise. C: comparison of the normalized decay of the alkaline transient in the presence and absence of benzolamide. D: after superfusion of 300 nM carbonic anhydrase II (gray traces) the alkaline shift was decreased to roughly one half the control amplitude. E: expanded sweep illustrates that the smaller response in exogenous carbonic anhydrase was the result of a decreased rate of rise. F: normalized alkaline transient decays (from A) in the control condition and after addition of exogenous carbonic anhydrase. Exogenous enzyme had no effect on the normalized decay of the response.

 
Similar results, obtained from 10 hippocampal slices, showed that benzolamide caused a significant increase in the peak response, time to peak, rate of rise, and half time of decay (Table 1B). Percentage changes in the mean values amounted to respective increases of 91, 74, 25, and 185 percent.

If it is assumed that the magnitude and time course of the base loads to the extracellular space were comparable in control versus benzolamide trials, then the ratio of the betae values during the rising phase would be given by the inverse ratio of the rates of rise, i.e., [dpH/dt]0/[dpH/dt]1 = betae1/betae0, where the subscripts 1 and 0 refer to control versus benzolamide trials, respectively. Given that benzolamide increased the mean rate of rise from 9.33 to 11.7 {Delta}F% s–1 (Table 1B), the activity of the endogenous ECA activity appeared to augment betae by just 25%.

Effect of exogenous carbonic anhydrase on the rise and decay of the alkaline shift

Adding exogenous carbonic anhydrase to brain slice saline has been shown to augment the buffering of slow extracellular alkaline shifts recorded with conventional pH microelectrodes (Huang et al. 1995Go). This result suggested that the amount of endogenous ECA activity was insufficient for full manifestation of CO2–HCO3-mediated buffering. To better discern the basis for this phenomenon, we examined the effect of exogenous carbonic anhydrase on the alkaline transient evoked by a three-shock, 20-ms, 100-Hz, orthodromic stimulus train. Results from these experiments are summarized in Table 1C.

Addition of carbonic anhydrase type II (300 nM) caused a marked decrease in the amplitude of the alkaline transient (Fig. 3D) from a {Delta}F/F% of 1.48 ± 0.14 to 0.72 ± 0.07 (n = 13, P < 0.001), or roughly half the control value. The decreased amplitude was not accompanied by a noticeable change in the evoked field potentials, indicating that the diminished pH response did not result from a general fall in excitability. With expansion of the traces (Fig. 3E) it was evident that the addition of the exogenous enzyme was associated with a marked slowing of the rising phase (from 7.65 ± 0.76 to 4.82 ± 0.67 {Delta}F/F% s–1, n = 13, P < 0.001) and an earlier time to peak (348 ± 29 in control vs. 239 ± 27 ms with exogenous carbonic anhydrase; n = 13, P < 0.001).

If it is assumed that the magnitude and time course of the base loads to the extracellular space were comparable in control versus exogenous carbonic anhydrase trials, then the ratio of the betae values during the rising phase would be given by the inverse ratio of the rates of rise, i.e., [dpH/dt]1/[dpH/dt]2 = betae2/betae1, where the subscripts 1 and 2 refer to control versus exogenous enzyme trials, respectively. Thus the effective betae was apparently increased by a factor of 1.6 with the addition of 300 nM carbonic anhydrase II to the saline.

Although the addition of exogenous carbonic anhydrase had an obvious effect on the rate of rise, time to peak, and peak amplitude of the alkaline transient, the time to half decay was not significantly altered, averaging 538 ± 31 versus 528 ± 51 ms for control and added enzyme trials, respectively (n = 13, P ≥ 0.05). As shown in Fig. 3F, the normalized decays before and after addition of exogenous carbonic anhydrase were virtually identical. Similar overlap of the normalized decay phases was noted in all 13 slices in which addition of the exogenous enzyme was tested.

Alkaline shifts elicited by a prolonged, low-frequency–stimulus train

The rapid rise and comparatively slow decay of the alkaline transients suggested that these responses would undergo marked temporal summation during a prolonged stimulus train. An extracellular alkaline response evoked by 2-Hz stimulation of the Schaffer collaterals is shown in Fig. 4A. The first stimulus generated a rapid pH rise of 0.05 pH units, which peaked after 120 ms. This was followed by a slower recovery with a half decay time of roughly 400 ms. During repeated stimulation at 2 Hz, the fluorescence record displayed a sawtooth pattern with marked temporal summation. The accrual of amplitude that occurred with each new stimulus was clearly a result of the incomplete decay of the prior response, as is evident in the expansion of the first two responses in Fig. 4B.

This particular experiment provided a revealing comparison of the response time of the fluorescence probe versus the pH microelectrode during a stimulus train. Whereas the fluorophore responded to a single shock with a rapid alkaline shift and slow decay, the pH microelectrode recorded only a brief electrical stimulus artifact (Fig. 4A, arrows) followed by a slow, attenuated pH increase. Thus the sawtooth pattern generated by the whole stimulus train could not be resolved by the pH electrode, which instead recorded only a slow monotonic rise in pHe, interrupted by small stimulus artifacts (gray trace). Yet, after several stimuli, it was apparent that the time course of the pH microelectrode record approximated the bottom envelope of the fluorescence trace. Thus conventional pH microelectrodes appear to be accurate in recording the slow, summated alkalinization during a long-stimulus train, but miss the high-frequency components that give rise to the response.

In pH microelectrode studies, the alkaline shifts generated by a prolonged-stimulus train were often amplified four- or fivefold after addition of benzolamide (Grichtchenko and Chesler 1996Go; Taira et al. 1995Go). Yet, the more rapid alkaline transients recorded optically in response to brief stimulation, although amplified, were only doubled by benzolamide (Fig. 3A and Table 1B). The greater effect of the drug during a long-stimulus train can now be attributed to the pronounced slowing of the recovery after each single stimulus, as demonstrated in Fig. 4, C and D. In this example, the summed response to the train was fourfold greater in amplitude after superfusion of 10 µM benzolamide (Fig. 4C). Expansion of the initial part of the record (Fig. 4D) illustrates that the degree of summation was greatly influenced by the time course of the decay phase after each stimulus. In the presence of benzolamide, the prolonged decays led to enhanced temporal summation. By inference, one of the principal effects of ECA would appear to be the suppression of alkaline summation during synchronous, sustained neural activity.

Magnitude and time course of passive pH buffering

When considering the decay of the alkaline transient, it is useful to compare the observed results with the expected time course of uncatalyzed buffering. To this end, we simulated an instantaneous alkaline load applied to extracellular fluid and numerically solved the kinetic equations for the subsequent relaxation of the buffer system.

The relevant buffering of hydrogen ions is provided by the equilibria of the carbonic acid–derived species (CO2, H2CO3, HCO3, CO32–) and phosphate (H2PO4, HPO42–), as shown in Fig. 5A. The contributions of proteins to interstitial buffering are not known and for this simulation were assumed to be negligible. The instantaneous response of the buffer system to a given injection of OH was solved by solution of the simultaneous linear equations governing the fast reactions (encompassed by the square in Fig. 5A). This provided initial conditions used to numerically solve the subsequent relaxation of the entire system, as detailed in the APPENDIX.


Figure 5
View larger version (19K):
[in this window]
[in a new window]
 
FIG. 5. Kinetic model of passive buffering. A: modeled buffering system of the interstitial compartment. Rapid reactions, with equilibrium constants K2K4 are encompassed by the gray square. Injection of NaOH was assumed to produce an instantaneous adjustment of the rapid reactions, followed by a slow relaxation toward equilibrium, governed by the rate constants k1 and k1. Model assumed a temperature of 32° and a brain slice CO2 concentration of 2.07 mM (Chesler et al. 1994). Kinetic and equilibrium constants used in the simulation are provided in Table A1. Assumed concentrations are given in Table A2. B: normalized modeled relaxations following simulated addition of NaOH sufficient to cause instantaneous alkalizations of 0.01 (gray trace) and 0.05 (black trace). Simulated time course of recovery was virtually identical for alkaline shifts of 0.01 and 0.05. C: comparison of modeled vs. experimental decays. Gray experimental trace (top) is the normalized and averaged decay from 10 slices in the presence of benzolamide. Accompanying solid, smooth gray line is the modeled decay for the simulated buffering system with no acceleration of the hydration and dehydration reactions (a = 1.0). Normalized, averaged decay under control conditions (black experimental trace) was approximated by a simulation (black smooth trace) in which the hydration and dehydration rate constants were increased 2.5-fold. Experimental records were obtained from alkaline responses recorded in 10 slices. Alkaline decays were aligned at their peaks, normalized and averaged. Details of the buffering simulation are provided in the APPENDIX.

 
Solutions for the uncatalyzed time course of buffering are shown as normalized curves of pH recovery after initial alkaline shifts 0.01 or 0.05 pH units (gray and black traces, respectively, in Fig. 5B). It is evident that the decays lasted several seconds and were nearly identical. Thus within the range of experimentally observed alkaline transients, the normalized time course of uncatalyzed buffering was not critically dependent on the magnitude of the initial alkalosis chosen for the simulation.

Figure 5C compares the modeled relaxation for a typical alkalosis (using a base load of 25 µM NaOH that produced an instantaneous {Delta}pH of 0.036) with a composite decay obtained by averaging normalized experimental records from 10 slices in the presence of 10 µM benzolamide. The computed passive relaxation of the buffer system (solid gray line) had a time course that approximated the experimental data, with increased deviation from the passive model at later times. This result indicated that the decay of the recorded alkaline transients in the presence of the carbonic anhydrase inhibitor was largely consistent with simple, uncatalyzed relaxation of the buffering system.

To determine whether the control decay in the presence of endogenous ECA was consistent with catalyzed, passive buffering, the forward and backward rate constants (k1 and k1) were increased by an acceleration coefficient (a) and the model predictions were compared with the normalized control responses averaged from ten slices. An approximate fit to the experimental decay could be obtained using an acceleration coefficient of only 2.5 (Fig. 5C, smooth black trace). Thus as noted for the rising phase of the response, the effects of endogenous ECA on the alkaline transient appear consistent with very little interstitial enzyme activity.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Comparison with previous optical studies

Most studies of activity-dependent pHe shifts have been conducted using conventional pH microelectrodes. Krishtal and colleagues (1987)Go performed an early investigation of these phenomena using hippocampal slices and an optical method based on the indicator phenol red. After a stimulus to the Schaffer collaterals, these authors reported an early acid response of about 20-ms duration that preceded an alkaline transient and a later, slow acidosis. Their initial apparent acid phase would be within the filter pass band of our detection system, yet was not noted in this study, nor was it observed in an earlier investigation using the same FD indicator (Gottfried and Chesler 1996Go). Rather, brief stimulation of the Schaffer collaterals caused only a rapid alkaline transient.

In the earlier phenol red study, the apparent early acid shift was speculated to arise from the release of the acidic contents of synaptic vesicles. Such an acid response should be enhanced by an inhibitor of ECA (Grichtchenko and Chesler 1994Go), however, the putative acid transient was unaffected by a high concentration of acetazolamide (Krishtal et al. 1987Go). By contrast, in the present report, the optical traces were confirmed to be pHe traces by manipulation of betae, using benzolamide as well as exogenous carbonic anhydrase II. In addition, the absence of a stimulus-evoked change of the F440 indicated that the pH signals were not contaminated by an observable component arising from flavoprotein fluorescence.

The present data therefore demonstrate that in response to Schaffer collateral activation, the first pH shift detectable in the sampled interstitial space is an alkalinization. This pH response is well established within 100 ms and therefore appears sufficiently rapid to influence NMDA-receptor–mediated currents, as was suggested by previous electrophysiological data (Gottfried and Chesler 1994Go). By contrast, the presynaptic release of acidic vesicular contents appears to be undetectable in the broad interstitial space. This is most likely explained by the rapid diffusion of the vesicular contents and their dilution in the vastly larger extracellular volume. The present observations do not preclude the existence of a very rapid acid transient in microdomains near postsynaptic membranes. Indeed, in specialized ribbon synapses of the retina, where the local geometry restricts diffusion, there is strong, albeit indirect evidence for sizable acid shifts that result from the emptying of vesicular contents (DeVries 2001Go; Palmer et al. 2003Go).

In the present study, the experimental saline contained picrotoxin to prevent alkaline shifts evoked by GABAA receptors. This was necessary because the bicarbonate-dependent, GABAergic alkalosis requires ECA (Chen and Chesler 1992bGo; Kaila et al. 1992Go). A GABAergic component of the alkalinization would have been blocked by benzolamide (and perhaps increased by exogenous CA II), thereby confounding the analysis of buffering. In addition, Mg2+ was omitted from the saline and extra Ca2+ was added to maximize the alkalosis. This modified Ringer solution was used because of a specific limitation of the fluorescence method. The trade-off in recording at increased temporal resolution is a high baseline noise level. To study the response kinetics, it was necessary for the alkaline transients to manifest after a stimulus that was sufficiently brief (so as not to distort the ensuing pH waveform), yet capable of eliciting a response well above the noise. Use of these technical adjustments should not be interpreted to indicate that the generation of these pH shifts requires such modified solutions. It is well established that in more typical brain slice saline, in the absence of picrotoxin, repetitive stimulation of the Schaffer collaterals can give rise to summated responses on the order of 0.10–0.20 unit pH (Carlini and Ransom 1986Go; Chen and Chesler 1992bGo; Taira et al. 1995Go). It should also be noted that in the absence of picrotoxin, responses to long-stimulus trains appear to be primarily a result of the non-GABAergic, bicarbonate-independent mechanism that was the focus of this study (Taira et al. 1995Go).

It is useful to consider whether the summated alkaline responses elicited by repetitive stimulation in a slice preparation might occur in vivo in response to intrinsic patterns of activation. Seizure activity is of course defined by sustained synchronous discharge and has been shown to give rise to large summated alkaline shifts on the order of 0.10–0.20 unit pH (de Curtis et al. 1998Go). Synchronous discharge, however, is also a fundamental property of normal brain function. Indeed, it is the synchronous firing of millions of neurons that gives rise to the well-known electroencephalographic patterns such as the 5- to 10-Hz theta rhythm of the hippocampus (Buzsáki 2002Go). Activation of CA1 pyramidal neurons at similar frequencies has produced summated alkaline shifts on the order of 0.10–0.20 unit pH (Carlini and Ransom 1986Go; Chen and Chesler 1992bGo; Taira et al. 1995Go). The results of this study suggest that the summation of such responses is chiefly dependent on the activity of ECA, as noted below.

Effect of benzolamide on the alkaline transient

After a brief stimulus, the peak alkalosis was doubled by benzolamide. This increase in peak amplitude resulted from a modest acceleration and prolongation of the rising phase. Based on the respective rates of rise in the presence and absence of benzolamide, it appeared that the endogenous ECA increased betae by just 25% compared with the uncatalyzed condition. As noted further below, a 25% increase in betae by ECA is consistent with a model in which the hydration and dehydration reactions in the broad interstitial space were accelerated just two- to threefold by the enzyme.

The major effect of benzolamide was a significant slowing of the recovery phase of the alkalosis when elicited by a brief stimulus. This prolongation allowed for marked temporal summation with repetitive stimulation. This appears to account for the manyfold amplification of alkaline transients elicited by long-stimulus trains when benzolamide was used with conventional pH microelectrodes (e.g., Grichtchenko and Chesler 1996Go; Taira et al. 1995Go).

In the presence of benzolamide, the decay of the alkaline shift was consistent with a simple relaxation of the buffering system, rate limited by the CO2 hydration and H2CO3 dehydration reactions. Passive buffering also provided a good approximation of the recovery under control conditions, when the CO2 reactions were accelerated by a factor of just 2.5. This extremely small acceleration coefficient is consistent with low endogenous ECA activity in the broad interstitial space.

Although our data suggest a simple relaxation of the buffering system, it should be borne in mind that other factors could contribute to the recovery phase of an extracellular alkaline shift. Indeed, the time course and direction of activity-dependent pHe transients can vary considerably in different regions of the CNS (Chesler 1990Go). In this respect, the model of passive buffer relaxation is perhaps best considered a benchmark for evaluation of a given alkaline transient. If an observed decay were longer than the anticipated time course of buffering, this could indicate that the time course of the base source extended into the recovery phase. On the other hand, a relaxation that was significantly faster than the expected time course of passive buffering could suggest that an alkalosis was terminated in part by active transport.

Indeed, it has been suggested that a glial electrogenic sodium-bicarbonate cotransporter (NBCe) takes up base from the extracellular space in response to neural activity, and thereby mitigates or "muffles" activity-dependent alkaline transients (Chesler 1990Go; Deitmer and Rose 1996Go; Ransom 1992Go). In the leech, there is direct evidence that glial NBCe curtails a stimulus-evoked alkalosis (Rose and Deitmer 1994Go). NBCe has been suggested to serve a like role in mammalian brain, but this has not been similarly substantiated (reviewed by Deitmer and Rose 1996Go). Because a rapid rise in [K+]e resulting from neural activity is thought to depolarize glia and drive this transporter, the muffling of a brief alkaline transient may be expected to occur during the rising phase of the alkalosis. This speculated function of NBCe might be facilitated by its binding to surface CA type IV (Alvarez et al., 2003Go), which appears to be the major isoform of the enzyme on cortical and hippocampal astrocytes (Svichar et al. 2006Go). If NBCe functioned in such a way in the hippocampus, then the effect of benzolamide on the alkalosis could be attributable in part to a decrease in the effectiveness of this transporter.

Effect of exogenous carbonic anhydrase on the alkaline transient

Addition of exogenous carbonic anhydrase II decreased both the rate of rise of the alkalosis and the peak amplitude, and thereby provided evidence that the endogenous ECA activity was insufficient to maintain equilibrium. It is unlikely that the effects of exogenous enzyme resulted from diminished excitability because the evoked field potentials were unchanged. Moreover, addition of this enzyme to brain slice saline was previously shown to diminish extracellular alkaline shifts elicited by the local iontophoresis of OH (Huang and Chesler 1995Go), indicating that the exogenous enzyme does increase interstitial buffering capacity.

Although addition of the enzyme clearly diminished the alkaline transient, other aspects of these experiments are not readily understood. First, the decay phase of the alkaline transients was unaltered in time course by the added enzyme. In addition, the effective betae appeared to be just twofold greater. Given that 300 nM carbonic anhydrase II would be expected to increase the rate of CO2 hydration >100-fold in free solution (Maren 1988Go), these small or absent effects are puzzling. Similar observations were noted in an earlier study that used iontophoresis of OH to elicit alkaline transients. As in this study, addition of 300 nM exogenous enzyme raised the extracellular buffering capacity just two- to threefold, and increasing the enzyme concentration to 3 µM caused no additional impact on buffering (Huang and Chesler 1995Go).

The limited effects of exogenous CA may indicate that particular assumptions are incorrect. First, it is possible that the exogenous enzyme could not fully penetrate the interstitial space. This might occur as a result of the molecular clumping of the protein, cellular uptake, or its degradation by endogenous proteases. It is also plausible that a prolonged base load contributed to the time course of decay. Prolongation of the base load into the recovery phase might render a small effect of exogenous CA undetectable. The time course could also be influenced by active uptake of base, by NBCe, for example. A transporter with membrane-bound ECA already in a specific conformational relationship (Alvarez et al. 2003Go; McMurtrie et al. 2004Go) might not be facilitated by the addition of free, exogenous CA to the interstitial compartment.

Although one or more of these caveats would add to the complexity of the model, the overall curtailment of the peak alkalosis by exogenous CA remains a striking effect. Whether modified by active transport or a prolonged base source, the net base load appeared to be incompletely buffered, suggesting an endogenous ECA activity that was insufficient to maintain equilibrium. A low ECA activity would be consistent with previous studies in which CA XIV immunostaining was localized solely to neurons (Parkkila et al. 2001Go), and cell surface staining of glia or neurons for CA IV was not apparent (Ghandour et al. 1992Go), very slight (Nogradi et al. 2003Go), or scattered (Wang et al. 2002Go). Similarly, total CA IV obtained from brain slices treated with phospholipase C had a very low activity and was detectable on Western blots only after the product of multiple slices was pooled and concentrated (Tong et al. 2000Go). These experimental observations appear consistent with the theoretical treatment below, which suggests that over a short time frame, disequilibrium of the buffering system can be anticipated for a range of ECA activities.

Time dependency of the extracellular buffering capacity

The buffering capacity of an aqueous solution is classically defined as the concentration of an imposed base load divided by the resulting pH change (Roos and Boron 1980Go). If disequilibrium prevailed during a rapid base challenge, then the apparent magnitude of betae would depend on when the amplitude of the resulting pHe shift was measured. As the perturbation was slowly buffered and the system approached equilibrium, the apparent betae would become larger. This time dependency can be quantified for the modeled interstitial buffering reactions by plotting betae versus time for the simulated pHe relaxation of Fig. 5C, in which the CO2 reactions were accelerated by a factor of either 2.5 or 1.0. The resulting plots, shown Fig. 6A, have a sigmoid shape. With an acceleration coefficient of 2.5, the theoretical equilibrium buffering capacity of 59.8 mM would not be realized for 5 s.


Figure 6
View larger version (11K):
[in this window]
[in a new window]
 
FIG. 6. Time dependency of extracellular buffering. A: apparent extracellular buffering capacity (betae) is plotted vs. time after an instantaneous alkaline load, for acceleration coefficients of 1.0, 2.5, and 50. B: expansions of the traces in A (for a = 1.0 and a = 2.5) illustrate that the buffering capacity within 250 ms is expected to be <1 mM and dominated by buffering contribution of phosphate.

 
Expansion of the plots (Fig. 6B) indicates that in 250 ms, which is roughly the time for the rise of an alkaline transient, the effective betae would be <1 mM. At 250 ms, betae was computed to be 940 µM for an acceleration coefficient of 2.5 and 744 µM for the uncatalyzed reaction (a = 1). The corresponding increase in betae attributed to ECA would therefore be about 25%. This agrees remarkably with the 25% increase in buffering capacity attributed to ECA based on the mean rates of rise of the alkaline transient in the presence and absence of benzolamide.

It is useful to consider the time dependency of betae when the acceleration coefficient is increased because this might pertain to microdomains where ECA is more concentrated. Figure 6A shows how betae would rise with time for an acceleration coefficient of 50. It is notable that a few hundred milliseconds would still be required to attain equilibrium. If the acceleration coefficient were as high as several hundred (not shown), equilibrium would be obtained in tens of milliseconds. Thus within a time frame relevant to synaptic transmission, buffering can be expected to be time dependent and considerably lower than the equilibrium value over a very wide range of local ECA activities. Accordingly, small acid or base loads would be expected to produce relatively large local changes in pHe, providing they occurred with sufficient speed. Thus in retina, the modulatory effect that the acidic contents of synaptic vesicles appear to have on photoreceptor calcium channels (DeVries 2001Go; Palmer et al. 2003Go) may be a function of both the geometry of the specialized ribbon synapses, and a very low buffering capacity within milliseconds of transmitter release.

It is similarly plausible that rapid alkaline transients act to modulate the function of NMDA receptors, as a result of limited, time-dependent, extracellular buffering. Although such modulation has not been demonstrated to occur during an unmodified, endogenous alkalosis, these pH transients can augment NMDA-receptor–mediated excitatory postsynaptic currents after they are amplified by benzolamide (Gottfried and Chesler 1994Go). Thus from a regulatory perspective, it would seem that the catalysis of buffering by ECA, albeit limited, is sufficient to restrict the size of an alkaline transient, and thereby influence the time course of a synaptic current. In this sense, changes in ECA expression might impact the integrative properties of local circuits.

The notion of low buffering capacity at early times also has implications for the process that gives rise to the alkaline transient. In snail neurons alkaline shifts on the membrane surface were shown to arise from activity of the plasmalemmal Ca2+-ATPase, which exchanges intracellular Ca2+ for extracellular H+. Based on this finding, it was suggested that activity-dependent alkaline transients in the mammalian brain might be similarly generated (Schwiening et al. 1993Go). The dependency of the mammalian alkaline shifts on an influx of extracellular Ca2+ supported this hypothesis (Paalasmaa et al. 1994Go; Smith et al. 1994Go). However, it was calculated that the H+ flux associated with this mechanism could give rise to the observed alkaline shifts only if the extracellular buffering capacity was very low (Chesler 2003Go). The experimental and theoretical observations of this report suggest that this is indeed the case.


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
The acid–base buffering system considered by the model is depicted in Fig. 5A, with the k1 and k1 being the forward and backward rate constants, respectively. At equilibrium

Formula A1(A1)

Formula A2(A2)

Formula A3(A3)

Formula A4(A4)
Values for kinetic and equilibrium constants used in the simulation are given in Table A1. The starting molar concentrations of all species are shown in Table A2. The total phosphate concentration, [P]t = [H2PO4] + [HPO42–], remained constant and was set to 1 mM. The variable [SID+] represents the initial concentration of the "strong ion difference" (Stewart 1978Go) and is determined by charge electroneutrality as

Formula A5(A5)
In a submerged hippocampal slice, the [CO2] is elevated with respect to the overlying saline and accounts for all of the baseline interstitial acidosis (Chesler et al. 1994Go). Based on an extracellular pH of 7.25 (Gottfried and Chesler 1994Go) the [CO2] was calculated to be 2.07 mM. Because the stimulus duration was very brief, and no late acid transients were noted in these experiments, the metabolic generation of CO2 was not considered relevant (Voipio and Kaila 1993Go), and thus the [CO2] was held constant throughout the simulation.


View this table:
[in this window]
[in a new window]
 
TABLE A1. Kinetic and equilibrium constants used in buffering simulation

 

View this table:
[in this window]
[in a new window]
 
TABLE A2. Starting values for model system constituents

 
Initial pH shifts evoked by a rapid base load

At time 0, a perturbation of the [SID+] described by f(t) is imposed such that the [SID+] at any time becomes [SID+]0 + {int}0t f(t')dt'. For simplicity, f(t) is defined as a pulse function = A{delta}(t), where {delta}(t) is the Dirac delta function and A (mM) is the bolus increase in [SID+].

H+ dynamics

The time rate of changes of the three carbonic species can be expressed by standard reaction kinetics as

Formula A6(A6)

Formula A7(A7)

Formula A8(A8)
Adding Eqs.A6A8 together yields

Formula A9(A9)
Among the four reactions depicted in Fig. 5A, the CO2 hydration is the slowest. Thus the reactions involved with K2, K3, and K4 were always assumed at equilibrium, whereas the CO2 hydration occurred at a slower pace. Using the equilibrium relations in Eqs. A1A4 yields

Formula A10(A10)
Furthermore, the assumption of charge electroneutrality at any instance ensures that

Formula A11(A11)
where Kw is the water dissociation constant of 10–14 M. Substituting Eqs. A10 and A11 back into Eq. A9 and differentiating with respect to t yields a differential equation for [H+]

Formula A12(A12)
in which both F1 and F2 are functions of [H+] only

Formula A13(A13)
and

Formula A14(A14)
Equation A14 is a first-order differential equation that was solved by the standard fourth-order Runge–Kutta method.


    GRANTS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-32123 and the Attilio and Olympia Ricciardi Fund.


    ACKNOWLEDGMENTS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
We thank Dr. Charles Nicholson and Dr. Margaret Rice for comments and advice throughout this study.

Present address of C.-K. Tong: Dept. of Physiology and Cellular Biophysics, Columbia University Medical Center, W. 168th Street, New York, NY 10032 (E-mail: ct433{at}columbia.edu).


    FOOTNOTES
 
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.

Address for reprint requests and other correspondence: M. Chesler, Dept. of Physiology and Neuroscience, NYU School of Medicine, 550 First Ave., New York, NY 10016 (E-mail: mitch.chesler{at}med.nyu.edu)


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Alvarez BV, Loiselle FB, Supuran CT, Schwartz GJ, and Casey JR. Direct extracellular interaction between carbonic anhydrase IV and the human NBC1 sodium/bicarbonate co-transporter. Biochemistry 42: 12321–12329, 2003.[CrossRef][Medline]

Buzsáki G. Theta oscillations in the hippocampus. Neuron 33: 325–340, 2002.[CrossRef][ISI][Medline]

Carlini WG and Ransom BR. Regional variation in stimulated extracellular pH transients in the mammalian CNS. Soc Neurosci Abstr 12: 452, 1986.

Chen JC and Chesler M. Extracellular alkaline shifts in rat hippocampal slice are mediated by NMDA and non-NMDA receptors. J Neurophysiol 68: 342–344, 1992a.[Abstract/Free F