pH, pka, Henderson Hasselbalch Equation

Definition of Keq, Kw and pH
Definition of pKa
The Henderson-Hasselbalch Equation
Definition of Buffering
Significance of Blood Buffering
Ampholyte, Polyampholyte, pI and Zwitterion
Definition of Solvation and Hydration
Kidneys and Acid-Base Balance
Sodium Bicarbonate Reabsorption
Excretion of Acid
Ammonia Secretion
Neurotoxicity of Ammonia
Acidosis and Alkalosis

Ionic Equilibrium

Keq, Kw 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:
Keq = [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, Kw:
Kw = [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:
Kw = 1 x 10-14 M2 Eqn. 4
As Kw 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. 6
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pKa
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 = Ka. 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:
Ka = [H+][A-]/[HA] Eqn. 8
As in the case of the ion product:
pKa = -logKa 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:
-logKa = -log[H+][A-]/[HA] Eqn. 10
Since as indicated above -logKa = pKa and taking into account the laws of logrithms:
pKa = -log[H+] -log[A-]/[HA] Eqn. 11
pKa = pH -log[A-]/[HA] Eqn. 12
From this equation it can be seen that the smaller the pKa 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. __________________________________________________________


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-, PO43- and SO42-) 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 pKa 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 (HPO42-) 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. Bicarbonate as a buffer
The major buffering systems in the body are proteins, particularly those with the amino acids histidine and cysteine exposed to the outside environment, phosphate, and bicarbonate. All three of these are weak acids with pKa values lower than physiological pH. As a consequence, buffering capacity increases as the pH is lowered from the physiological range. This meets the needs of most organisms because physiological pH excursions generally occur in the acid direction. Hence, the low pKa of these buffering systems is poised to respond to metabolic acidosis.
Of these three, only the bicarbonate system, which is critical for buffering extracellular fluids such as blood, is in steady-state between production and removal. Thus, pH changes via this dynamic bicarbonate system are taking place on a background provided by the more static protein and phosphate systems.
Production of Bicarbonate Cells generate and excrete large quantities of carbon dioxide (CO2) during aerobic metabolism of glucose and fats. CO2 is subsequently converted to carbonic acid (H2CO3), which serves as the basis for the bicarbonate buffering system. Hence, the body is not dependent on ingestion of exogenous compounds or complex syntheses to maintain this buffering system.
Removal of Bicarbonate The bicarbonate buffering system is in volatile equilibrium (via breathing) with the external environment (lungs and air). Thus it is able to respond rapidly to endogenous alterations. It can also be affected, either positively or negatively, by environmental manipulation.
Movement into and out of cells
The acid components of the bicarbonate system (i.e. H+ and CO2) cross biological membranes rapidly, thus do not depend on complex transport kinetics. The base component (HCO3-), on the other hand, is transported rapidly in all cells via anion exchange. Consequently, the bicarbonate buffering system helps to maintain both intracellular and extracellular pH.
Role of other blood components
The acid components of the bicarbonate system are transported from the tissues to the lungs by hemoglobin. Thus, this important protein participates in both the production and removal of metabolic acid.
Clinical Correlates: Acidosis & Alkalosis
CO2 produced by metabolism is normally balanced by CO2 expired from the lungs, resulting in no net production of H2CO3. However, as detailed in the table below, certain medically significant circumstances can throw the equation out of balance.
respiratory acidosis
apnea or impaired lung capacity, with a build-up of CO2 in the lungs
metabolic acidosis
ingestion of acid, production of ketoacids in uncontrolled diabetes, or kidney failure
Note: These conditions all result in build-up of H+ from sources other than excess CO2.


Condition
Possible causes
respiratory alkalosis
hyperventilation, with a net loss of CO2 from the blood.
metabolic alkalosis
ingestion of alkali, prolonged vomiting leading to a loss of HCl, or extreme dehydration leading to kidney retention of bicarbonate.
Note: The common thread here is the loss of H+ for reasons other than depletion of CO2.


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

For more complex molecules such as polyampholytes the pI is the average of the pKa 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. ­­­­­­­­­­­­­­­­­­ _______________________________________________________________

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. ___________________________________________________________

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.
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-, HPO42- 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.

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 pKa for the dibasic/monobasic phosphate buffering system (pKa = 6.8). The excess H+ reacts with dibasic phosphate (HPO42-) 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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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+.