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REPORT
Department of Cellular and Molecular Physiology, Yale University School of Medicine, New Haven, Connecticut 06520-8026
Address for reprint requests and other correspondence: W. F. Boron, Dept. of Cellular and Molecular Physiology, Yale Univ. School of Medicine, 333 Cedar St., New Haven, CT 06520 (E-mail: walter.boron{at}yale.edu)
Abstract
The approach that most animal cells employ to regulate intracellular pH (pHi) is not too different conceptually from the way a sophisticated system might regulate the temperature of a house. Just as the heat capacity (C) of a house minimizes sudden temperature (T) shifts caused by acute cold and heat loads, the buffering power (ß) of a cell minimizes sudden pHi shifts caused by acute acid and alkali loads. However, increasing C (or ß) only minimizes T (or pHi) changes; it does not eliminate the changes, return T (or pHi) to normal, or shift steady-state T (or pHi). Whereas a house may have a furnace to raise T, a cell generally has more than one acid-extruding transporter (which exports acid and/or imports alkali) to raise pHi. Whereas an air conditioner lowers T, a cell generally has more than one acid-loading transporter to lower pHi. Just as a house might respond to graded decreases (or increases) in T by producing graded increases in heat (or cold) output, cells respond to graded decreases (or increases) in pHi with graded increases (or decreases) in acid-extrusion (or acid-loading) rate. Steady-state T (or pHi) can change only in response to a change in chronic cold (or acid) loading or chronic heat (or alkali) loading as produced, for example, by a change in environmental T (or pH) or a change in the kinetics of the furnace (or acid extrudes) or air conditioner (or acid loaders). Finally, just as a temperature-control system might benefit from environmental sensors that provide clues about cold and heat loading, at least some cells seem to have extracellular CO2 or extracellular HCO3– sensors that modulate acid-base transport.
Key words: hydrogen ions; bicarbonate; exchanger; cotransporter
INTRACELLULAR pH (pHi), which for our purposes we will regard as the pH of the aqueous cytosolic solution, is a parameter that is of interest to most biologists. The reason for this interest is that changes in pHi affect the ionization state of all weak acids and weak bases–a bewildering array of cellular molecules that includes all peptides and proteins–and thus may potentially affect a wide array of biological processes. Not surprisingly, all animal cells that have been examined, aside from non-nucleated erythrocytes, vigorously regulate their pHi (36). They do this by sensing changes in pHi and then appropriately speeding up or slowing down various transporters that move acids and/or bases across the plasma membrane.
Many nonspecialists find it difficult to think about pHi and pHi regulation. After all, the pH scale is upside down (increases in pHi correspond to decreases in [H+]), and protons have the disconcerting habit of binding to molecules (at any time, more than 99.99% of available protons are bound to "buffers"). Moreover, if a proton dissociates from a buffer and collides with a water molecule, this proton may become part of a perfectly respectable H2O molecule, but simultaneously cause a completely different proton to pop off from another H2O molecule some distance away—an example of the effects of a proton wire.
Sound complicated? It is and it isn’t. "It is" in the sense that any biological process is complex when one considers it at the molecular level. However, my PhD mentor, the venerable Albert Roos, now retired from Washington University School of Medicine and approaching his 90th birthday, used to tell me that if a scientist really understands his or her work, the scientist should be able to explain the essence of that work to the average person on the street. Thus my job in this review should be rather easy: I must only explain pHi regulation to the physiologist on the street.
As it happens, the way cells approach the problem of pHi regulation is not so different–conceptually, at least–from the way we might approach the problem of regulating the temperature in a house. Just as a furnace makes the temperature go up, transporters called "acid extruders" (which move H+ out of the cell and/or move bases such as HCO3– into the cell) make pHi go up. Similarly, just as an air conditioner makes the temperature go down, transporters called "acid loaders" (which move H+ into the cell and/or move bases such as HCO3– out of the cell) make pHi go down. In this review, we will develop a model of temperature regulation that we will subsequently apply to pHi regulation. Every hypothetical example of a rise or fall in temperature corresponds to an analogous real-life instance of a rise or fall in pHi.
The reader is directed to a website (http://www.the-aps.org/education/refresher/CellRefresherCourse.htm) that includes the PowerPoint slideshow that I presented during my oral presentation at Experimental Biology 2004, on April 17, 2004.
Temperature Regulation in a House
Heat capacity.
Imagine that our house has an initial temperature (T) of 22°C. Imagine also that our house has a heat capacity (C) of 50 x 106 cal/°C. This value is equivalent to that of 50,000 kg of H2O (a 50-m3 pool of water).
We will now suddenly inject into our house 50 x 106 calories of heat; this is roughly the amount that would be given off by a 1,000-W electrical heater over a period of 2.4 days. If we wait long enough for the injected heat to equilibrate with the mass of the house—and if no other processes add or withdraw heat—the temperature will increase by precisely 1°C:
 | (1) |
In other words, the temperature of our house will rise from 22°C to 23°C.
If we introduce a 50-m3 indoor swimming pool into our house, the heat capacity will double to 100 x 106 cal/°C. Thus a heat load of 50 x 106 calories will cause the temperature to increase by only 0.5°C
 | (2) |
Because the magnitude of the temperature change is inversely proportional to the heat capacity, raising the heat capacity of the house increases the ability to resist temperature fluctuations. In other words, heat capacity represents the ability to "buffer" loads of heat or cold, just as buffering power (ß) in a cell represents the ability to resist pHi fluctuations in the face of loads of alkali or acid. However, raising the heat capacity (or ß) does not eliminate temperature (or pHi) fluctuations, it only reduces their magnitude. Moreover, once we have imposed a heat/cold load (or alkali/acid load) and observed the resulting increase/decrease in temperature (or pHi), subsequently raising the heat capacity (or ß) does not return the temperature (or pHi) to its initial value, which would be 22°C in our temperature example.
The last statement in the previous paragraph is worthy of some clarification. Consider our example in Eq. 1, in which C is 50 x 106 cal/°C. Imposing a heat load of 50 x 106 calories will cause the temperature to rise from 22 to 23°C. If we now double the heat capacity by adding 50,000 kg of water with a temperature of 23°C, the temperature of the house (and that of the water that we just added) will remain at 23°C. If we had instead added 50,000 kg of water with a temperature of 22°C, the temperature of the house would fall by 0.5°C, and that of the water would rise by the same amount. However, this maneuver of adding 22°C water to the 23°C house simultaneously did two things: 1) it raised the heat capacity and 2) it injected a "cold" load. In analyzing the effects of various maneuvers—both in our temperature-regulation model and in pHi regulation—we must constantly be vigilant to identify such dual effects.
Perturbations: Acute and Chronic Heat/Cold Loads
Acute heat loads.
In a house, appliances can impose a heat load: hot plates, toasters, ovens, clothes dryers, irons, and water heaters, to name a few. On a hot day, opening an exterior door imposes a heat load on an air-conditioned house. These heat loads I will define as "acute," acute as opposed to "chronic," which we will discuss later. The most critical attributes of acute heat loads is that they exert their effects over a limited period of time that is—from the perspective of our observations—relatively brief. Thus we can easily describe the absolute magnitude of the heat load. For example, if one turns on a 1,000-W hair drier for 2 min, the imposed heat load is
 | (3) |
Moreover, we can predict that this acute heat load will raise the temperature of our house (the one without the swimming pool) by 0.000, 57°C:
 | (4) |
Later, we will see that acutely loading a cell with a known amount of alkali will produce a pHi increase, the magnitude of which we can predict-using an equation analogous to Equation 4-if we know the buffering power.
Chronic heat loads.
Unlike the heat sources discussed above, those that impose a chronic heat load exert their effects over an indefinite period of time that—from the perspective of our observations—is relatively long. For example, on a sunny summer day, the heat introduced from the environment by radiation, conduction, and convection may impose a heat load for many hours. Chronic heat loaders are best described in terms of the rate at which they impose a heat load, inasmuch as it is impossible to predict the total heat load.
In our temperature-regulation model, the distinction between acute and chronic heat loads is somewhat artificial. For example, if we inadvertently left an iron "on" indefinitely, the iron would become a chronic heat loader. In moderate climates, the heat load imposed by sun has a predictably limited duration (i.e., daylight hours); does the sun then become an acute heat loader? Nevertheless, when we turn to pHi regulation, we will see that alkali loads to a cell usually segregate rather neatly into those with either a limited duration (and thus magnitude), such as exposing a cell to a permeant weak base, or an indefinite duration (and thus magnitude), such as stimulating a transporter that continually imports HCO3– into the cell.
Acute cold loads.
Our house might also have a few mechanisms for imposing acute cold loads, such as frozen food left to thaw on the kitchen counter, or a refrigerator with an open door. On a cold winter day, we could impose a more substantial acute cold load by temporarily opening an exterior door. Each of these mechanisms exerts its effects over a limited and relatively short period of time, and thus withdraws a limited amount of energy from our house. The counterpart in pHi regulation might be the acute acid load imposed by exposing a cell to a permeant weak acid.
Chronic cold loads.
During the winter, the heat loss from our house to the environment represents a chronic cold load. By analogy to chronic heat loaders, chronic cold loaders are best described in terms of the rate at which they impose a cold load. The counterpart in pHi regulation might be the chronic acid load imposed by a transporter that continually imports H+ or exports HCO3–.
Regulation: Furnaces and Air Conditioners
A "dumb" temperature-control system.
Having mastered the concepts of heat capacity and the various kinds of heat and cold loads, we are in a position to discuss temperature regulation. Like any physiological regulatory system, our temperature-regulating system must have certain key components:
In our first example (Fig. 1A), the system will work like that in a typical house. The furnace will have two speeds ("off" and "on"), and the coordinating center will turn on the furnace whenever the temperature falls below 20°C. The air conditioner also will have two speeds ("off" and "on"), and the coordinating center will turn on the air conditioner whenever the temperature rises above 24°C. If the furnace and air conditioner are sufficiently powerful, the temperature-control system will insure that the temperature does not fall far below 20°C, nor does not rise far above 24°C.
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Later, we will see that cells use acid-extruding transporters (analogous to furnaces) that raise pHi, more so as pHi falls. Moreover, cells have acid-loading transporters (analogous to air conditioners) that lower pHi, more so as pHi rises. In the steady state, these two sets of transporters continuously fight each other, consuming metabolic energy-the price that life is willing to pay for the sake of control.
Total heat and cold loading.
Another way of approaching the analysis of the sophisticated temperature-control system would be to lump the heat output of the furnace with that of all other chronic heat loaders that are not part of our temperature-control system. The result is the total chronic heat loading (Jheat). Similarly, we also could lump the heat withdrawal of the air conditioner with that of all other chronic cold loaders, arriving at the total chronic cold loading (Jcold). If these "other," non-regulatory chronic heat and cold loaders have relatively low temperature dependencies, then the temperature dependency of Jheat and Jcold in Fig. 1C would have shapes similar to the "Furnace" and "Air conditioner" curves in Fig. 1B. However, at any temperature, the curves would have higher values in Fig. 1C. Nevertheless, the steady-state temperature would still be described by the intersection of the two curves.
Later, we will see that the total chronic acid extrusion in cells reflects transporters that extrude acid (analogous to furnaces) and—under special circumstances—passive chronic alkali loading (analogous to nonregulatory chronic heat loading). Similarly, the total chronic acid loading in cells reflects transporters that load the cell with acid (analogous to air conditioners) as well as passive acid loading (analogous to nonregulatory chronic cold loading).
We should not regard the curves in Fig. 1C as immutable. For example, during the winter, the nonregulatory component of Jcold (or chronic acid loading for a cell) would be higher at night (or when extracellular pH is low) than during the warmer daytime hours (or when extracellular pH is high). Moreover, the slope of the Jcold-vs.-T relationship (or the acid loading vs. pHi relationship) would decrease if the air conditioner’s filter became clogged (or if the cell downregulated an acid loader). On the other hand, the slope would increase if a fall in outside temperature made the air conditioner more efficient (or if a change in ion gradients made an acid loader more efficient). The Jheat-vs.-T relationship would be subject to comparable changes. In other words, the curves in Fig. 1C describe the temperature dependencies of chronic heat and cold loading under a defined set of conditions that are subject to alteration.
Response to an acute cold load.
Our sophisticated temperature-control system is now ready for a challenge. Imagine that it is a frigid winter’s evening, and that the temperature of our house is at a stable 22°C. Under these starting conditions, Jheat exactly matches Jcold, as represented by the intersection of the two curves in Fig. 2A. A blast of cold air through a temporarily open door now lowers the temperature from 22°C to 4°C (step 1 in Fig. 2A). Sensing this decrease in temperature, our control system increases the heat output of the furnace and simultaneously lowers the cold output of the air conditioner (step 2 in Fig. 2A). Similarly, cells will respond to a sudden decrease in pHi by stimulating their acid extruders and inhibiting acid loaders. Returning to our temperature-regulation model, because Jheat is now far greater than Jcold, the temperature begins to rise. How fast? Consider a more general representation of Eq. 1:
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We now transform this equation by dividing both sides by the time interval 
t:
 | (6) |
In other words, the rate of temperature increase is proportional to the difference between the chronic rates of heat loading and cold loading, and the proportionality constant is the reciprocal of heat capacity. Thus, if the heat capacity were infinite, the temperature would never change, whereas if the heat capacity were very low, even small differences between Jheat and Jcold would lead to rapid temperature changes. We might regard Eq. 6 as the fundamental law of temperature regulation. As we will see in Eqs. 21 and 22, a comparable law exists for pHi regulation in cells.
Returning now to step 2 in Fig. 2A, we can appreciate that the difference Jheat – Jcold, and thus the rate at which the temperature increases, is maximal immediately after the blast of cold air–when the temperature is lowest. As temperature increases, the rate of heat production by the furnace gradually decreases and the rate of heat withdrawal by the air conditioner gradually increases. Thus, the difference (Jheat – Jcold) gradually becomes smaller until, at the original temperature of 22°C, Jheat = Jcold and the system returns once again to its original steady state (i.e., T/t = 0). Similarly for cells that are recovering from an acute acid load, the difference between acid-loading and acid-extrusion rates is greatest when pHi is lowest, and gradually falls to zero as pHi rises toward its original steady-state value. During the course of a temperature recovery, the net amount of heat introduced by the temperature-control system (i.e., the increment in Jheat – Jcold integrated over time) is exactly equal to the net amount of cold introduced by the blast of cold air. We can make a comparable statement for cells, where the net amount of alkali extruded during a pHi recovery exactly equals the amount of acid introduced by the insult—acute acid load.
The solid curve in Fig. 2B illustrates the hypothetical time course of the temperature recovery when the house has a normal heat capacity. If we wished to be more precise, we could express Eq. 6 as a differential equation, which we could solve to obtain an exponential expression that would describe the time course of T vs. time (t). Knowing the heat capacity of our house and the amount of heat withdrawn by the blast of cold air, we could compute the initial T. Knowing the actual value of Jheat and Jcold over the relevant range of temperatures, we could compute the entire time course of T vs. t from the instant of the big blast to the eventual reachievement of the steady state.
The dashed curve in Fig. 2B illustrates how the system would respond if we were to double the heat capacity of our house (or buffering power of a cell) by adding that 50-m3 swimming pool (or buffers to a cell). Notice that, for the same acute cold load (or acute acid load), the magnitude of the initial temperature (or pHi) decrease is half of what it was before. Also notice that the time course of the exponential recovery of temperature (or pHi) is stretched out by a factor of 2 (i.e., the time constant has doubled). Nevertheless, the total amount of heat withdrawn by the blast of cold air (or acid introduced by the acute acid load) equals the net amount of heat (or alkali) subsequently introduced by the temperature-control (or pHi control) system, and both values are identical to their counterparts in the first example (solid curve in Fig. 2B), in which the heat capacity (or ß) was normal.
Response to an acute heat load.
The solid curve in Fig. 2C illustrates the hypothetical response of our temperature-control (or pHi control) system, assuming a normal heat capacity (or ß), to an acute heat (or alkali) load, such as we might observe upon opening an exterior door on a hot summer day (or injecting a cell with alkali). For the sake of symmetry, we assume that the magnitude of the acute heat load in this example is exactly the same as the magnitude of the acute cold in the previous one. Thus the blast of hot air causes the temperature to rise to 40°C. Our temperature-control (or pHi control) system will respond by immediately reducing the rate of heat output by the furnace (or acid extrusion) and increasing the rate of heat withdrawal by the air conditioner (or acid loading), in a manner analogous to that shown in Fig. 2A. As a result, the temperature (or pHi) falls with an exponential time course, with Jheat (or the chronic acid-extrusion rate) gradually rising and Jcold (or the chronic acid loading rate) gradually falling until these two parameters once again come into balance at the original temperature of 22°C (or pHi).
As we saw in the blast-of-cold-air example, doubling the heat capacity reduces the initial T by a factor of 2 and increases the time constant of the temperature recovery by a factor of 2. However, the final temperature is the same.
It is worth emphasizing three points. First, a high heat capacity (or buffering power) can reduce the magnitude of a temperature (or pHi) perturbation, but cannot eliminate the perturbation. Second, the magnitude of the heat capacity (or buffering power) has no effect whatsoever on the final steady-state temperature (or pHi). Third, final steady-state temperature (or pHi) depends solely on the relationship between Jheat (chronic acid extrusion) and Jcold (chronic acid loading).
Regarding this last point, as long as both Jheat-vs.-T and Jcold-vs.-T remain unchanged, the final steady-state temperature must also remain unchanged. As we will see in the next section, the steady-state temperature can change only as the result of a fundamental change in the kinetics of Jheat and/or Jcold.
The recovery of temperature in Fig. 2, B and C, is an indication of temperature regulation, the ability of the system-complete with its system of sensors, a coordinating center, and effectors-to return temperature to some steady-state value. To quantify temperature regulation, we focus on the rate at which the system can return temperature to normal following an acute cold or heat load. We might express this rate as an absolute rate of temperature recovery (dT/dt, expressed as°C/s) measured at some defined temperature, a series of dT/dt values measured over a range of temperatures, or as the time constant (measured in seconds) that characterizes the trajectory of the temperature recovery. We will see later that we can use analogous terms to quantitate pHi regulation.
Changes in steady-state temperature.
As we noted in our discussion of Fig. 1C, the Jheat and Jcold curves could change due to alterations in nonregulatory heat or cold loading, or to changes in the furnace and air conditioner themselves. In this section, we will examine three examples that illustrate how changes in Jheat and/or Jcold affect steady-state temperature as well as the time course of temperature as the system achieves a new steady state.
Response to inhibiting the furnace.
We begin our first experiment in this series with normal Jheat-vs.-T and Jcold-vs.-T profiles, and thus a normal steady-state temperature of 22°C. What would happen if—in an instant—we were to reduce the output of our furnace by a constant fraction across a wide range of temperatures? In Fig. 3A, we represent such a fall in heat flow by decreasing the negative slope of the Jheat-vs.-T curve (dashed red curve in Figs. 3A and step 1 in Fig. 3A). At the instant of the perturbation, the temperature would still be 22°C. However, because we have rotated the Jheat-vs.-T curve downward, Jheat at 22°C is now substantially less than Jcold at 22°C. As a result, Jheat – Jcold is a relatively large negative number, so that according to Eq. 6, temperature begins to fall rather rapidly (step 2 in Fig. 3B). As the temperature falls, however, Jheat gradually rises and Jcold gradually falls until the two come into balance at a new, lower, steady-state temperature that, in this example, is 17°C (step 3a and 3b in Fig. 3A). The solid curve in Fig. 3C shows the time course of temperature for a normal heat capacity.
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Response to stimulating nonregulatory cooling.
Rather than inhibiting the furnace (or an acid extruder), as in the previous example, we can produce an identical decrease in steady-state temperature (or pHi) either by stimulating the air conditioner (or an acid loader) or by lowering the outside temperature (or extracellular pH). In this next temperature-regulation example, we will do the latter by raising the non-regulatory component of Jcold by a constant fraction across a wide range of temperatures. We represent this effect in Fig. 4A the increased cooling by increasing the slope of the Jcold-vs.-T curve (dashed curve). At the instant of the perturbation, Jcold is now substantially greater than Jheat at 22°C. As in the previous example, Jheat – Jcold is now a relatively large negative number, so that temperature begins to fall rather rapidly. Eventually, the falling temperature brings Jheat and Jcold into balance at the same new, lower, steady-state temperature as in the previous example. The solid and dashed curves in Fig. 4B are exactly the same curves that described the time course of temperature when we inhibited the furnace in Fig. 3B.
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Response to compound perturbations.
Imagine that it is a gorgeous late summer’s day with an outside temperature of 28°C. All the windows of the house are open. While you are on a walk, a cold front moves in and lowers the outside temperature to 0°C. You rush home and close the windows, but the interior temperature has already fallen to 4°C. The temperature-regulating system senses the acute cold load (step 1a in Fig. 5A). Simultaneously, the system’s coordinating center recognizes that low outside temperature has rotated upward the Jcold-vs.-T curve (dashed curve and step 1b in Fig. 5A). Nevertheless, at the temperature of 4°C, Jheat greatly exceeds Jcold, so that Eq. 6 predicts that temperature should rise rapidly (step 2 in Fig. 5B). Of course, as the temperature rises, Jheat gradually falls and Jcold gradually rises (steps 3a and 3b in Fig. 5B) until the two eventually come into balance, not at the initial steady-state temperature of 22°C, but at the new steady-state temperature of 17°C, as dictated by the intersection of the Jheat-vs.-T curve and the newly rotated Jcold-vs.-T curve.
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Similar compound perturbations commonly occur in the world of pHi regulation. As an example, consider respiratory acidosis, in which a rise in extracellular [CO2] causes extracellular pH to fall. The rise in [CO2] leads to an influx of CO2 and thus an acute intracellular acid load. The fall in extracellular pHo inhibits acid extruders and stimulates acid loaders and thus causes a chronic intracellular acid load.
One way to quantify the ability of our temperature-control system to maintain a stable steady-state interior temperature in the face of an altered exterior temperature would be to define a parameter called temperature stability or Ti/To—the change in steady-state interior temperature for an imposed change in exterior temperature. Later, we will discuss a similar definition in the domain of acid-base physiology.
An important lesson that we learned from Figs. 3–5 is that an isolated change in kinetics that affects the value of either Jheat or Jcold at the original steady-state temperature will always cause the steady-state temperature to change. We could draw a comparable conclusion concerning steady-state pHi. Of course, it is possible for coordinated change in both Jheat and Jcold to leave the steady-state temperature unaltered. In this case, the intersection of the old Jheat-vs.-T and old Jcold-vs.-T curves would occur at the same temperature (but not the same energy flux) as the intersection of the new Jheat-vs.-T and new Jcold-vs.-T curves—as we shall see in the next section.
Environmental Sensors
The experiment in Fig. 5 revealed a flaw in our temperature-control system: environmental changes may lead to a change in steady-state temperature. We might compensate for the flaw by introducing one or more environmental sensors that warn the coordinating center of impending changes in the unregulated components of Jheat and/or Jcold.
Environmental temperature.
The most obviously useful environmental sensor might be one that detects changes in exterior temperature (To). For example, we could program our temperature-regulating system to respond to a decrease in To by increasing the output of the furnace and/or decreasing the output of the air conditioner. Such a To-dependent shift in the temperature-sensitivity of a furnace could counteract the shift in steady-state temperature that we saw in Fig. 5C. However, we will underplay this type of sensor inasmuch as there is presently no evidence that the analogous pHo sensors play a role in coordinating pHi regulation. Sensors for pHo clearly exist. For example, vascular smooth muscle cells dilate in response specifically to a fall in pHo (2, 3). In sensory neurons the acid sensing ionic channel, which is primarily permeable to Na+, mediates a fast-rising and desensitizing inward current when pHo falls below 6.9 (25, 46). Other examples of pHo-sensitive channels are the tandem pore-domain acid-sensitive K+ channels, which are inhibited by decreases in both pHo and pHi below values of 
7.3, and the human pancreatic tandem-pore K+ channel, which is stimulated at pHo values >7.4 and inhibited by pHo values <7.4 (22, 26, 30).
Snow sensors.
Whereas a To sensor would provide direct information about a key parameter that directly influences unregulated Jheat and Jcold, a snow sensor would provide information about a parameter that is associated with increased passive heat loss. We might program the coordinating center to respond to the appearance of snow by increasing the output of the furnace over a range of temperatures, and by decreasing the output of the air conditioner, as shown in Fig. 6A. With these modifications, the system might appropriately detect the approach of a blizzard and prevent the house temperature from falling. As we will see later, an analogous sensor in cells might detect extracellular CO2 and signal certain cells to stimulate acid-base transporters.
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Integrated responses to environmental sensors.
Of course, we might wish to provide additional data concerning such relevant environmental parameters as wind speed. Even more important, we might wish to program the coordinating center to integrate appropriately information on all of the environmental parameters so that it would respond intelligently to a mixed message–such as those provided by bright sunlight when theexterior temperature is –30°C. In the ideal situation, our temperature-control system would respond to varying environmental cues by fine tuning the Jheat-vs.-T and Jcold-vs.-T relationships so that they always intersected at the target temperature of 22°C (Fig. 6C). As we will see later, when certain neurons are challenged by metabolic acidosis–a fall in extracellular pH caused by a decrease in the extracellular HCO3– concentration at a fixed level of CO2–they are somehow able to maintain a near-stable pHi.
Overview of pHi Homeostasis
The foregoing discussion, in which we treated the problem of pHi regulation as if it were a problem in temperature regulation, is very likely to be true a century from now. The discussion that follows, in which we examine pHi regulation per se, necessarily will be less complete and more tentative. It will be less complete because cells use many different transporters as the analogs of furnaces and air conditions, and because different cell types make use of different subsets of these transporters. Our pHi discussion will be more tentative than our temperature discussion because I am not aware of a single cell type for which, as of this writing, we know at the molecular level just which transporters make which contribution to pHi homeostasis. Moreover, we are only beginning to understand the regulation of individual transporters and the interactions among them. Thus much of what one might write today about the details of pHi regulation will be outdated a year or a decade from now. However, our discussion of temperature regulation has laid the groundwork for understanding the fundamental concepts of pHi regulation, and these concepts will likely withstand the test of time.
Thus far we mentioned the word "pH"—and associated acid-base terms—only parenthetically. Nevertheless, if you understand the concepts that we have developed in our discussion of temperature regulation, then you understand the principles necessary for being a midlevel expert in the field of pHi regulation. You merely must change the names of the terms we have been using: replace temperature with pH, heat capacity with buffering power, cold loading with acid loading, furnace with acid extruder, and so on.
pH is defined as the negative logarithm (base 10) of the H+ activity (a parameter that measures the effect that the ion produces, which is usually less than its actual concentration). If we make the simplifying assumption that the H+ concentration is the same as activity
 | (7) |
The pH scale is a scale of ratios. Because the log10 of 10 is 1 and the log10 of 2 is 0.3, tenfold changes in [H+] correspond to pH changes of 1 and twofold changes in [H+] correspond to pH changes of 0.3.
Buffering (Heat Capacity)
Buffers.
According to Brønsted’s definition, an acid is any substance that is capable of donating a proton. In the general sense
 | (8) |
where n is the valence. In this example, HB(n+1) is a weak acid, and B(n) is its conjugate weak base.1 Viewed differently, B(n) is a weak base, and HB(n+1) is its conjugate weak acid. Other common examples of weak acids include ammonium (NH4+), carbonic acid (H2CO3), and monobasic inorganic phosphate (H2PO4–):
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 | (9) |
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The corresponding conjugate weak bases are NH3, HCO3–, and dibasic inorganic phosphate HPO4=. For each of these buffers, the equilibrium is described by an equation of the form:
 | (10) |
where K is the equilibrium constant. In its logarithmic form, the relationship becomes:
 | (11) |
where pK is –log10K. Thus when pH = pK (i.e., when [H+] = K), [B(n)] = [HB(n+1)].
We could write a similar equation for the CO2/HCO3– buffer system:
 | (12) |
The concentration of dissolved CO2 is given by Henry’s law,
 | (13) |
where s is the solubility of CO2 (in mM/mmHg) and PCO2 is the partial pressure of CO2 in the gas phase with which the aqueous solution is in equilibrium. Combining Eq. 12 and Eq. 13 yields the Henderson-Hasselbalch equation:
 | (14) |
Buffering power.
Together, a weak acid and its conjugate weak base constitute a buffer pair. That is, the members of the buffer pair are capable of reversibly releasing or binding a proton, and thereby acting as a buffer. Buffering power (ß) is defined as the amount of strong base (e.g., NaOH)—or the negative of the amount of strong acid (e.g., HCl)—that one would have to add to a liter of solution to raise the pH of the solution by 1 pH unit:
 | (15) |
The amount of strong acid or strong base is generally given in millimoles. Strictly speaking, pH is unitless, so that it is correct to give buffering power in units of mM. However, authors often explicitly include pH: mM/pH unit. This designation has the advantage of making it easier to keep track of units in complex calculations.
Buffering in a closed system.
As it happens, buffering power varies with pH. How might we measure the pH dependence of buffering power? In this example, we will work with a closed-system buffer, that is, one in which neither member of the buffer pair can escape from (or be added to) the beaker either by equilibrating with the atmosphere or by some biochemical or transport reaction. Inorganic phosphate or HEPES would be such a buffer. For simplicity, let us assume that the buffer has a pK of 7. We will start with a beaker of buffer solution at a pH of, say, 4. We will now add a small amount of NaOH (i.e., Strong Base in Eq. 15). The added OH– will have two fates: (1) Some will be neutralized (i.e., buffered) as HB(n+1) dissociates into B(n) and H+, and the H+ then combines with the OH– to form H2O; this sequence of reactions will result in no pH change (2). The rest of the added OH– will equilibrate with H+ and H2O and thereby raise the pH of the solution by a small amount (i.e., pH in Eq. 15), raising the pH to slightly more than 4. We then use Eq. 15 to compute the mean ß over the pH range 4 – (4 + pH). We plot this computed ß in Fig. 7A at the mean pH of 4 + pH/2, and repeat the whole procedure many times as the computed ß rises to a maximum at a pH of 7 and then falls to near-zero values as we approach a pH of 10.
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[B(n)], and that
 | (16) |
If we would combine Eq. 10 and Eq. 16, and then take the partial derivative of B(n) with respect to pH (holding the amount of total buffer constant), we would see that
 | (17) |
Here, [TB] is [HB(n+1)] + [B(n)], the total buffer concentration. If we would plot ßclosed as a function of pH, we would obtain the bell-shaped curve in Fig. 7A. The maximal ßclosed is 58% of [TB].
Buffering powers are additive, so that if we had a solution containing a mixture of many closed-system buffers, we could simply add their individual buffering powers to obtain the total buffering power of the solution. In the example of Fig. 7B, the hypothetical solution consists of nine buffers, each at a concentration of 1 mM, with their pK values evenly spaced at intervals of 0.5. Note that in the center of this pH range, the total buffering power is remarkable constant. Indeed, the total closed-system buffering power of cells is remarkably constant over a wide pH range, tending to fall gradually as pHi rises. Thus the relative constancy of ßclosed in a cell is not terribly different from the absolute constancy of heat capacity in our house.
Buffering in an open system.
Although the foregoing analysis works quite well for most buffers, it fails badly when [TB] is not constant. The most common example in which [TB] is not constant is the CO2/HCO3– buffer pair, where the volatile CO2 freely exchanges with its environment. In this case, [CO2] is constant, but [TB] can vary over a very wide range. Open-system buffering by CO2/HCO3– is extremely important in pHi regulation because we can generally regard the extracellular solution as an infinite sink for CO2, which can freely diffuse across most cell membranes. Thus we can generally regard [CO2]i as fixed.
Imagine an experiment in which we begin with a beaker that contains one liter of an aqueous solution that—in terms of CO2/HCO3– and pH—mimics mammalian blood plasma (Fig. 8). However, the beaker contains no other buffers. The atmosphere has a PCO2 of 40 mmHg, the dissolved [CO2] is 1.2 mM (as determined by Henry’s law), the pH of the solution is 7.4, and [HCO3–] is 24 mM. We now add 10 mmol of HCl to the beaker (two panels at top right). Nearly all of the added 10 mmol of H+ are neutralized as they combine with nearly 10 mmol of HCO3– to form nearly 10 mmol of H2CO3, which in turn forms nearly 10 mmol of CO2. The excess CO2 evolves into the atmosphere so that the final [CO2] is the same as the initial [CO2]. Because the buffering reaction is not limited by the buildup of the ultimate reaction product (i.e., CO2), buffering is quite effective, and pH falls by only 0.23 (i.e., from 7.40 to 7.17). If we had instead performed this same experiment in a closed bottle, the newly formed CO2 would not have been able to escape the aqueous solution, the reaction product would have limited the extent of the overall buffer reaction, and pH would have fallen by a substantially greater amount.
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If we were to repeat the experiments in Fig. 8, but add much smaller amounts of HCl or NaOH, we could compute the pH dependence of the CO2/HCO3– buffer system over a wide pH range. The steadily rising curve in Fig. 9 shows the result of such series of hypothetical experiments. If we would combine Eq. 10 and Eq. 16, and then take the partial derivative B(n) with respect to pH, holding [CO2] = [HB(n+1)] constant, we would see that
 | (18) |
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The flattened, bell-shaped curve in Fig. 9 shows what the buffering power of the CO2/HCO3– system would be if we put the starting solution from Fig. 8 into a closed glass bottle. The ßclosed for CO2/HCO3– is maximal at the overall pK of the CO2/HCO3– equilibrium, 6.1.
Total buffering power in a cell.
The buffering power that is most relevant for a cell is that of the cytosol–the compartment in direct contact with the plasma membrane and most other membrane–enclosed cellular compartments. The total intracellular buffering power is the sum of the individual buffering powers of all cytosolic buffers, regardless of whether they behave as closed- or open-system buffers. These cytosolic buffers generally can be divided into two classes. The intrinsic buffers are the closed system buffers, the aggregate buffering power of which one would measure experimentally (36). The extrinsic buffers are the open-system buffers, like the CO2/HCO3– buffer pair, that one has the option of adding to the system. In principle, these extrinsic buffers could be any buffer pair in which one of the members could readily cross the cell membrane. Examples might include butyrate/butyric acid (the neutral weak acid is often permeant) and NH3/NH4+ (the neutral NH3 is generally permeant). One computes the buffering power of these open-system buffers using an expression analogous to Eq. 18. In mammalian cells (exposed to a PCO2 of 40 mmHg), the open-system CO2/HCO3– buffering power accounts for one-half to two-thirds of the total buffering power at the resting pHi. Of course, the total intracellular buffering power, as well as the contribution of CO2/HCO3–, increase at higher pHi values.
Perturbations: Acute and Chronic Acid and Alkali (Heat/Cold) Loads
Acute acid and alkali loads: microinjection.
In the laboratory, one can acutely acid load a cell by injecting or iontophoresing H+ into the cytosol, as was pioneered by Roger Thomas (42). Figure 10A illustrates a hypothetical experiment in which we microinject HCl into a cell. For the sake of simplicity, we will assume that the cell is bathed in a solution that does not contain any CO2/HCO3–. Thus only closed-system non-HCO3– buffers will neutralize the injected H+. The minute amount of injected H+ that does not react with B(n) causes intracellular pH to fall.
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Acute acid and alkali loads: permeant weak acids and bases.
Although the hypothetical experiments in Fig. 10 nicely illustrate the concept of imposing an acute acid or alkali load, microinjections are only possible in a laboratory setting and require not only a skilled experimenter but a large cell. As illustrated in Fig. 11A, a far easier way to acid load a cell-and one to which cells are regularly subjected in vivo-is to increase the concentration of CO2 in the extracellular fluid (8). CO2 crosses the plasma membranes of most cells very easily. Once in the cytosol, the CO2 can combine with H2O to form H2CO3, most of which (but not all) then very slowly dissociates to form HCO3– and H+. Most cells contain abundant carbonic anhydrase, an enzyme that in effect catalyzes the conversion of CO2 + H2O to H2CO3 and thus accelerates the acidification of the cell. Almost all the H+ formed in this reaction sequence is buffered by non-HCO3– buffers. Note that the CO2/HCO3– buffer pair cannot buffer the H+ produced by the influx of CO2. In this experiment, we are assuming that the cell has no pHi regulatory mechanism. Thus the influx of CO2 causes pHi to fall and then level off once [CO2]i has risen to the level of [CO2]o and the net influx of CO2 has stopped. When we remove the CO2, pHi returns to its initial value. Although we used CO2 as the permeant weak acid in this experiment, we could have used any permeant weak acid (e.g., acetic acid, butyric acid) to acid load the cell. The extent of the pHi decline in such an experiment depends on the intracellular buffering power (greater values of ß reduce the magnitude of the pHi decrease), the initial extracellular concentration of the weak acid, and the relationship between pHi and the pK of the buffer (the higher the pHi, and the lower the pK, the greater the net acidification).
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Once added to a cell, CO2 and NH3 behave as open-system buffers, and augment the total buffering power of the cell. Although the CO2/HCO3– system cannot buffer the protons produced as CO2 enters the cell in Fig. 11A, the CO2/HCO3– system could buffer the NH3 that enters the cell in Fig. 11B. The same is true in reverse for the NH3/NH4+ buffer system.
Chronic acid and alkali loads: passive fluxes across the plasma membrane.
The equilibrium (or Nernst) potential for H+ (EH) is the hypothetical membrane potential at which H+ would be in equilibrium across the membrane. According to the laws of electrochemistry
 | (19) |
where [H+]o is the extracellular H+ concentration, [H+]i is the intracellular [H+], and R, T, and F have their usual meanings. Figure 12 illustrates how we might compute EH when the relevant values are reasonably physiological: pHi is 7.2, pHo is 7.4, and the transmembrane voltage (Vm) is –60 mV. Under these conditions, EH is –12 mV. In other words, if Vm were –12 mV, no energy would be required or released to move H+ across the membrane in either direction. Because Vm is in fact –60 mV in this example, the voltage inside the cell is far too negative for H+ to be in equilibrium. As a result, protons tend to enter the cell passively down their electrochemical gradient. This influx of H+ is in principle never ending. As long as the gradient for H+ remains inward, and as long as the cell membrane remains permeable to H+, protons will enter the cell passively, imposing a chronic intracellular acid load.
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 | (20) |
Because Vm is more negative than ENH4, the positively charged NH4+-like H+-will tend to passively enter the cell. Conversely, because Vm is more negative than EOH and EHCO3, the negatively charged OH– and HCO3– will tend to passively exit the cell. All of these movements tend to impose a chronic intracellular acid load. Harkening back to our temperature-regulation model, these passive fluxes are akin to heat escaping from our house during the winter. The lower the pHo (the lower outside temperature), the greater the tendency for acid to accumulate inside the cell (the faster the house loses heat).
Regulation: acid extruders and loaders (furnaces and air conditioners).
Just as the house in our temperature-regulation analogy had a furnace and an air conditioner to regulate temperature, cells have a host of acid-base transporters that perform analogous functions. The so-called acid extruders—which are analogous to furnaces—use energy to extrude H+ from the cell or to accumulate a weak base, such as HCO3–. Just as a furnace raises temperature, an acid ext
