Dr. C.S. Gasser's excellent Acid-Base Tutorial

K_eq, K_w and pH

As H₂O is the medium of biological systems one must consider the role of this molecule in the dissociation of ions from biological molecules. Water is essentially a neutral molecule but will ionize to a small degree. This can be described by a simple equilibrium equation:

H₂O <------->H⁺ + OH^- Eqn. 1

This equilibrium can be calculated as for any reaction:

K_eq = [H⁺][OH^-]/[H₂O] Eqn. 2

Since the concentration of H₂O is very high (55.5M) relative to that of the [H⁺] and [OH^-], consideration of it is generally removed from the equation by multiplying both sides by 55.5 yielding a new term, K_w:

K_w = [H⁺][OH^-] Eqn. 3

This term is referred to as the ion product. In pure water, to which no acids or bases have been added:

K_w = 1 x 10^-14 M² Eqn. 4

As K_w is constant, if one considers the case of pure water to which no acids or bases have been added:

[H⁺] = [OH^-] = 1 x 10^-7 M Eqn. 5

This term can be reduced to reflect the hydrogen ion concentration of any solution. This is termed the pH, where:

pH = -log[H⁺] Eqn. 6back to the top

pK_a

Acids and bases can be classified as proton donors and proton acceptors, respectively. This means that the conjugate base of a given acid will carry a net charge that is more negative than the corresponding acid. In biologically relavent compounds various weak acids and bases are encountered, e.g. the acidic and basic amino acids, nucleotides, phospholipids etc.

Weak acids and bases in solution do not fully dissociate and, therefore, there is an equilibrium between the acid and its conjugate base. This equilibrium can be calculated and is termed the equilibrium constant = K_a. This is also sometimes referred to as the dissociation constant as it pertains to the dissociation of protons from acids and bases.

In the reaction of a weak acid:

HA <----->A^- + H⁺ Eqn. 7

the equlibrium constant can be calculated from the following equation:

K_a = [H⁺][A^-]/[HA] Eqn. 8

As in the case of the ion product:

pK_a = -logK_a Eqn. 9

Therefore, in obtaining the -log of both sides of the equation describing the dissociation of a weak acid we arrive at the following equation:

-logK_a = -log[H⁺][A^-]/[HA] Eqn. 10

Since as indicated above -logK_a = pK_a and taking into account the laws of logrithms:

pK_a = -log[H⁺] -log[A^-]/[HA] Eqn. 11

pK_a = pH -log[A^-]/[HA] Eqn. 12

From this equation it can be seen that the smaller the pK_a value the stronger is the acid. This is due to the fact that the stronger an acid the more readily it will give up H⁺ and, therefore, the value of [HA] in the above equation will be relatively small.
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The Henderson-Hasselbalch Equation

By rearranging the above equation we arrive at the Henderson-Hasselbalch equation:

pH = pK_a + log[A^-]/[HA] Eqn. 13

It should be obvious now that the pH of a solution of any acid (for which the equilibrium constant is known, and there are numerous tables with this information) can be calculated knowing the concentration of the acid, HA, and its conjugate base [A^-].

At the point of the dissociation where the concentration of the conjugate base [A^-] = to that of the acid [HA]:

pH = pK_a + log[1] Eqn. 14

The log of 1 = 0. Thus, at the mid-point of a titration of a weak acid:

pK_a = pH Eqn. 15

In other words, the term pK_a is that pH at which an equivalent distribution of acid and conjugate base (or base and conjugate acid) exists in solution.
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Buffering

It should be noted that around the pK_a the pH of a solution does not change appreciably even when large amounts of acid or base are added. This phenomenon is known as buffering. In most biochemical studies it is important to perform experiments, that will consume H⁺ or OH^- equivalents, in a solution of a buffering agent that has a pK_a near the pH optimum for the experiment.
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Clinical Significance of Blood Buffering

The pH of blood is maintained in a narrow range around 7.4. Even relatively small changes in this value of blood pH can lead to severe metabolic consequences. Therefore, blood buffering is extremely important in order to maintain homeostasis. Although the blood contains numerous cations (e.g., Na⁺, K⁺, Ca²⁺ and Mg²⁺) and anions (e.g., Cl^-, PO₄^3- and SO₄^2-) that can, as a whole, play a role in buffering, the primary buffers in blood are hemoglobin in erythrocytes and bicarbonate ion (HCO₃^-) in the plasma. Buffering by hemoglobin is accomplished by ionization of the imidazole ring of histidines in the protein.

The formation of bicarbonate ion in blood from CO₂ and H₂O allows the transfer of relatively insoluble CO₂ from the tissues to the lungs, where it is expelled. The major source of CO₂ in the tissues comes from the oxidation of ingested carbon compounds.

Carbonic acid is formed from the reaction of dissolved CO₂ with H₂O. The relationship between carbonic acid and bicarbonate ion formation is shown in equations 16 and 17.

CO₂ + H₂O <------> H₂CO₃ Eqn. 16

H₂CO₃ <-------> H⁺ + HCO₃^- Eqn. 17

The reactions shown in equations 16 and 17 occur predominately in the erythrocytes, since nearly all of the CO₂ leaving tissues via the capillary endothelium is taken up by these cells. This reaction is catalyzed by carbonic anhydrase. Ionization of carbonic acid then occurs spontaneously (as shown in equation 17), yielding bicarbonate ion.

Carbonic acid is a relatively strong acid with a pK_a of 3.8. However, carbonic acid is in equilibrium with dissolved CO₂. Therefore, the equilibrium equation for the sum of equations 16 and 17 requires a conversion factor, since CO₂ is a dissolved gas. This factor has been shown to be approximately 0.03 times the partial pressure of CO₂ (PCO₂). When this is entered into the Henderson-Hasselbalch equation:

pH = 6.1 + log [HCO₃^-/(0.03)(PCO₂)] Eqn. 18

where the apparent pKa for bicarbonate formation, 6.1, has been introduced into equation 18.

The PCO₂ in the peripheral tissues is approximately 50mm Hg, whereas in the blood entering the peripheral tissues it is approximately 40mm Hg. This difference results in the diffusion of CO₂ from the tissues into the blood in the capillaries of the periphery. When the CO₂ is converted to H₂CO₃ within the erythrocytes and then ionizes, the hydrogen ions (H⁺) are buffered by hemoglobin. The production of H⁺ ions within erythrocytes and their subsequent buffering by hemoglobin results in a reduced affinity of hemoglobin for oxygen. This leads to a release of O₂ to the peripheral tissues, a phenomenon is termed the Bohr effect.

Representation of the transport of CO₂ from the tissues to the blood with delivery of O₂ to the tissues. The opposite process occurs when O₂ is taken up from the alveoli of the lungs and the CO₂ is expelled. All of the processes of the transport of CO₂ and O₂ are not shown such as the formation and ionization of carbonic acid in the plasma. The latter is a major mechanism for the transport of CO₂ to the lungs, i.e. in the plasma as HCO₃^-. The H⁺ produced in the plasma by the ionization of carbonic acid is buffered by phosphate (HPO₄^2-) and by proteins. Additionally, some 15% of the CO₂ is transported from the tissues to the lungs as hemoglobin carbamate as shown in Eqn. 19.

As CO₂ passes from the tissues to the plasma a minor amount of carbonic acid takes form and ionizes. The H⁺ ions are then buffered predominantly by proteins and phosphate ions in the plasma. As the concentration of bicarbonate ions rises in erythrocytes, an osmotic imbalance occurs. The imbalance is relieved as bicarbonate ion leaves the erythrocytes in exchange for chloride ions from the plasma. This phenomenon is known as the chloride shift which is also shown in the diagram above. Therefore, the majority of the bicarbonate ion formed as CO₂ leaves the peripheral tissues is transported by the plasma to the lungs.

Around 15% of CO₂ transport from the tissues to the lungs occurs through a reversible combination with non-ionized amino groups (-NH₂) of hemoglobin forming what is termed hemoglobin carbamate.

Hemoglobin-NH₂ + CO₂ <---> Hemoglobin-NH-COO^- + H⁺ Eqn. 19

The formation of hemoglobin carbamate results in a reduced affinity of hemoglobin for O₂ thus favoring dissociation of bound oxygen in the tissues where the concentration of CO₂ is high. The process is reversed when the erythrocytes enter the lungs and the partial pressure of O₂ is elevated.

The partial pressure of O₂ (PO₂) in the pulmonary alveoli is higher than the PO₂ of the entering erythrocytes that contain predominantly deoxygenated hemoglobin. This increased PO₂ leads to oxygenation of hemoglobin and release of H⁺ ions from the hemoglobin. The released H⁺ ions combine with the bicarbonate ions to form H₂CO₃. Cellular carbonic anhydrase then catalyzes the reverse of reaction 17, leading to release of CO₂ from erythrocytes. Owing to the PCO₂ gradient (described above), the CO₂ diffuses from the blood to the alveoli where it is expelled.

The great utility of bicarbonate as a physiological buffer stems from the fact that if excess acid is added to the blood the concentration of bicarbonate ion declines and the level of CO₂ increases. The CO₂ then passes from capillaries in the pulmonary alveoli and is expelled. As a consequence, the H⁺ ion concentration drives reaction 17 to the left and bicarbonate ion acts as a buffer until all of the hydrogen ion is consumed. Conversely, when excess base is added to the blood, CO₂ is consumed by carbonic acid and replaced by metabolic reactions within the body.

If blood is not adequately buffered, the result may be metabolic acidosis or metabolic alkalosis. These physiological states can be reached if a metabolic defect results in the inappropriate accumulation or loss of acidic or basic compounds. These compounds may be ingested , or they may accumulate as metabolic by-products such as acetoacetic acid and lactic acid. Both of these will ionize, thereby increasing the level of H⁺ ions that will in turn remove bicarbonate ions from the blood and alter blood pH. The predominant defect in acid or base elimination arises when the excretory system of the kidneys is impaired. Alternatively, if the lungs fail to expel accumulated CO₂ adequately and CO₂ accumulates in the body, the result will be respiratory acidosis. If a decrease in PCO₂ within the lungs occurs, as during hyperventilation, the result will be respiratory alkalosis.
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Ampholytes, Polyampholytes, pI and Zwitterion

Many substances in nature contain both acidic and basic groups as well as many different types of these groups in the same molecule. (e.g. proteins). These are called ampholytes (one acidic and one basic group) or polyampholytes (many acidic and basic groups). Proteins contains many different amino acids some of which contain ionizable side groups, both acidic and basic. Therefore, a useful term for dealing with the titration of ampholytes and polyampholytes (e.g. proteins) is the isoelectric point, pI. This is described as the pH at which the effective net charge on a molecule is zero.

For the case of a simple ampholyte like the amino acid glycine the pI, when calculated from the Henderson-Hasselbalch equation, is shown to be the average of the pK for the a-COOH group and the pK for the a-NH₂ group:

pI = [pK_a-(COOH) + pK_a-(NH₃⁺)]/2 Eqn. 20

For more complex molecules such as polyampholytes the pI is the average of the pK_a values that represent the boundaries of the zwitterionic form of the molecule. The pI value, like that of pK, is very informative as to the nature of different molecules. A molecule with a low pI would contain a predominance of acidic groups, whereas a high pI indicates predominance of basic groups.
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Solvation and Hydration shells

Depending on the pH of a solution, macromolecules such as proteins which contain many charged groups, will carry substantial net charge, either positive or negative. Cells of the body and blood contain many polyelectrolytes (molecules that contain multiple same charges, e.g. DNA and RNA) and polyampholytes that are in close proximity. The close association allows these molecules to interact through opposing charged groups. The presence, in cells and blood, of numerous small charged ions (e.g. Na⁺, Cl^-, Mg²⁺, Mn²⁺, K⁺) leads to the interaction of many small ions with the larger macroions. This interaction can result in a shielding of the electrostatic charges of like-charged molecules. This electrostatic shielding allows macroions to become more closely associated than predicted based upon their expected charge repulsion from one another. The net effect of the presence of small ions is to maintain the solubility of macromolecules at pH ranges near their pI. This interaction between solute (e.g. proteins, DNA, RNA, etc.) and solvent (e.g. blood) is termed solvation or hydration. The opposite effect to solvation occurs when the salt (small ion) concentration increases to such a level as to interfere with the solvation of proteins by H₂O. This results from the H₂O forming hydration shells around the small ions.
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Role of the Kidneys in Acid-Base Balance

The kidneys function to filter the plasma that passes through the nephrons. Filtration of the plasmas occurs in the glomerular capillaries of the nephron. These capillaries allow the passage of water and low molecular weight solutes (less than 70 kDa) into the capsular space. The filtrate then passes through the proximal and distal convoluted tubules where reabsorption of water and many solutes takes place. In the course of glomerular filtration and tubule reabsorption the composition of the plasma changes generating the typical composition of urine. From a biochemical standpoint the kidneys serve important roles in the regulation of plasma acid-base balance and the elimination of nitrogenous wastes.
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Sodium Bicarbonate Reabsorption

Regulation of plasma acid-base balance is primarily effected within the kidney through control over HCO₃^- reabsorption and secretion of H⁺. Secretion of H⁺, in excess of its capacity to react with HCO₃^- in the tubular lumenal fluid, requires the presence of other buffers (see below). The generation of HCO₃^- and H⁺ occurs by dissociation of carbonic acid (H₂CO₃), formed in the tubule cells from H₂O and CO₂, through the action of carbonic anhydrase. Secretion of H⁺ into the lumen of the tubule is accompanied by an exchange for Na⁺. This reabsorption of Na+ occurs by an antiport mechanism during the exchange for H⁺. Reduction in the intracellular concentration of Na⁺ occurs by an active transport process involving a Na⁺/K⁺-ATPase pump which pumps the excess Na⁺ into the interstitial fluid. The intracellular HCO₃^- then diffuses from the tubule cell into the interstitial fluid.

The capacity of the kidney to secrete H⁺ is regulated by the maximal H⁺ gradient that can form between the tubule and lumen and still allow transport mechanisms to operate. This gradient is determined by the pH of the urine which in humans is near 4.5. The capacity to secrete H⁺ would be rapidly reached if it were not for the presence of buffers within the interstitial fluid. The H⁺ secreted into the tubular lumen can undergo three different fates depending upon the concentration of the three primary buffers of the interstitial fluid. These buffers are HCO₃^-, HPO₄^2- and NH₃. Reaction of H⁺ with HCO₃^- forms H₂O and CO₂ which diffuse back into the tubule cell. The net result of this process is the regeneration of HCO₃^- within the tubule cell. This process is termed reabsorption of sodium bicarbonate. The reabsorption of sodium bicarbonate takes place primarily within the proximal convoluted tubules.
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Excretion of Acid

As the concentration of HCO₃^- in the tubular lumen drops the pH of the fluid drops due to an increasing concentration of H⁺. The pH of the tubular fluid gradually approaches the pK_a for the dibasic/monobasic phosphate buffering system (pK_a = 6.8). The excess H⁺ reacts with dibasic phosphate (HPO₄^2-) forming monobasic phosphate (H₂PO₄^-). The H₂PO₄^- so formed is not reabsorbed and its excretion results in the net excretion of H⁺. The greatest extent of H₂PO₄^- formation occurs within the distal convoluted tubules and the collecting ducts.
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Ammonia Secretion

Buffering of H⁺ is also accomplished by reaction with ammonia, NH₃, to form ammonium ion, NH₄⁺. Elimination of NH₄⁺ is the major contributory factor in the ability of the body to excrete acid. Because the pK_a of NH₄⁺ is 9.3, excretion of acid in this form can be accomplished without lowering the pH of the urine. Additionally important is the fact that excretion of acid in the form of NH₄⁺ occurs without depleting Na⁺ nor K⁺.

Two principal reactions within tubule cells result in the generation of NH₃, conversion of glutamine to glutamate and conversion of glutamate to a-ketoglutarate. These reactions are catalyzed by glutaminase and glutamate dehydrogenase, respectively (Equations 21 and 22).

Glutamine ------> Glutamate + NH₄⁺ Eqn. 21

Glutamate -------> a-Ketoglutarate + NH₄⁺ Eqn. 22

Both of these enzymes are abundant in tubule cells. Ammonia is lipid soluble and will diffuse down its concentration gradient out of the tubule cell into the tubular fluid. There it reacts with H⁺ to yield NH₄⁺ which is excreted in the urine.
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Neurotoxicity of Ammonia

Excess ammonia is severely neurotoxic. Marked brain damage is seen in cases of failure to make urea via the urea cycle or to eliminate urea through the kidneys. The result of either of these events is a buildup of circulating levels of ammonium ion. Aside from its effect on blood pH, ammonia readily traverses the brain blood barrier and in the brain is converted to glutamate via glutamate dehydrogenase, depleting the brain of a-ketoglutarate. As the a-ketoglutarate is depleted, oxaloacetate falls correspondingly, and ultimately TCA cycle activity comes to a halt. In the absence of aerobic oxidative phosphorylation and TCA cycle activity, irreparable cell damage and neural cell death ensue.
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Acidosis and Alkalosis

The kidneys play an important role in the control of acidosis by responding with an increase in the excretion of H⁺. When H⁺ is excreted as a titratable acid such as H₂PO₄^- or when the anions of strong acids such as acetoacetate are excreted there is a requirement for simultaneous excretion of cations to maintain electrical neutrality. The principal cation excreted is Na⁺. As the level of excretable Na⁺ is depleted excretion of K⁺ increases. In conditions of acidosis the kidney will increase the production of NH₃ from tubular amino acids or amino acids absorbed from the plasma. As indicated the NH₃ can diffuse across the tubule cell membrane where it will react with H⁺ to form the excretable ammonium ion without a concomitant requirement for cation excretion. This demonstrates that an inability of the kidney to generate NH₃ would rapidly lead to fatal acidosis.

When the kidneys fail to modulate HCO₃^- excretion, metabolic alkalosis will develop. Alkalosis is normally countered quite effectively by the kidney allowing HCO₃^- to freely escape. Alkalosis generally only becomes problematic if the kidneys are restricted in their ability to secrete HCO₃^-. This situation can occur in patients taking diuretics since several of this class of drug cause a reduction in the ability of the kidney to reabsorb an anion (e.g. Cl^-) concomitant with the reabsorption of Na⁺.
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Michael W. King, Ph.D / IU School of Medicine / mking@medicine.indstate.edu

Last modified: Thursday, 10-May-01 10:12:52

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Keq, Kw and pH

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