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The "operational" relationship between pKa and pH is mathematically represented by Henderson-Hasselback equation:
pH = pKa + log [A-] / [HA]
where [A-] represents the deprotonated form and [HA] represents the protonated form.
One often-cited solution to this equation is obtained by arbitrarily setting pH = pKa.
In this case, log([A-] / [HA]) = 0, and [A-] / [HA] = 1.
In words, this means that when the pH is equal to the pKa of the acid, there are equal amounts of protonated and deprotonated acid molecules. This same relationship holds for bases as well, with [B] substituting for [A-] as the deprotonated form, and [HB+] substituting for [HA] as the protonated form. It should be emphasized that the Henderson-Hasselbach relationship holds for a specified acid or base even if multiple acids or bases are present.
Example 1:
For [R-COOH < > RCOO- + H+], with a pKa of 3.2.
- If pH is decreased, then pH < pKa, the reaction will shift to the left, more acid will be formed (more HA)
For every drop in pH = 10 folds (10^1) of acid formation.
- If pH = 2.2 and pKa 3.2, then the ratio of HA:A- will be 10:1.
- If pH = 1.1 and pKa 3.2, then the ratio of HA:A- will be 100:1.
- If pH = 4.2 and pKa 3.2, then the ratio of HA:A- will be 1:10.
Example 2:
For [NH4+ < > NH3 + H+], with pKa [NH4+] = 9.5 and pH [in H20 solution] = 7.
- The difference between pKa and pH (9.5 - 7) is 2.5. So 10^2.5 = ~320
- Since the pH < pKa, the reaction will shift to the left, and ~320 of the NH4+ will be formed. The ration of HA:A- will be ~320:1.
Example 3:
For [NH2-C-COOH < > +NH3-C-COO-], with pKa's of 2.3 [COOH] and 9.6 [NH2], and pH of 7.4 [NH2]:
- For the [NH2 and +NH3], pH < pKa (~2 units), so more of the acid will be formed [NH2] and less of the base [+NH3], in 100:1 [HA:A-]. Therefore, the reaction will shift to the left.
- For the [COOH and COO-], pH > pKa (~5 units), so more of the base will be formed [COO-] and less of the acid [COOH], in 1:100,000 ratio (where 10^5 = 100,000).
Buffers:
An acid-base conjugate pair (such as acetic acid and acetate ion) has an important property: it resists changes in the pH of a solution. In other words, it acts as a buffer. Consider the addition of OH− to a solution of acetic acid (HA):
HA + OH− ⇌ A− + H2O
A plot of the dependence of the pH of this solution on the amount of OH− added is called a titration curve. Note that there is an inflection point in the curve at pH 4.8, which is the pKa of acetic acid. In the vicinity of this pH, a relatively large amount of OH− produces little change in pH. In other words, the buffer maintains the value of pH near a given value, despite the addition of other either protons or hydroxide ions. In general, a weak acid is most effective in buffering against pH changes in the vicinity of its pKa value.
Example:
Histodine and Buffer
Although histidine has a net positive charge under physiological conditions (around pH 7.4), most of the histidine under physiological conditions is uncharged; second, while histidine may be the best amino acid to buffer a solution at pH 6, it is not the best amino acid for buffering solutions at other pH's closer to the pKa's of the other charged amino acids. All of this gets to the point of the question, "how does a buffer work?" A buffer is defined chemically as any compound that minimizes the change in pH of a solution when other compounds are added to the solution. The ability of a compound to act as a buffer at a given pH is determined by how readily it will accept and donate protons at that pH.
- Tyrosine is a triprotic, dibasic amino acid with pKa of 9.6 [NH3+], 2.2 [COO-], and 10.9 [OH].
- The 1st proton is removed from the [COO-], the 2nd from [NH3+], and finally the phenolic proton is removed [OH].
- Since the acid is dibasic, the 2 basic pKa's [NH3+ and OH] are very similar, differing by only about 1 unit.
- At pH=pKa1, a [COOH] proton is removed at to give [COO-].
- At pH=(pKa1+pKa2)/2, [COO- and NH3+] are at equivalence.
- At pH=pKa2, [NH3+] proton is removed to give [NH2].
- At pH=(pKa2+pKa3)/2, [NH2 and phenolic-OH] are at equivalence.
- At pH=pKa3, [phenolic-OH] proton is removed to give [phenolic-O-]
The net charge of the molecule at the end of the titration [in high alkaline pH, like pH=12] is -2 (a -1 from COO- and another -1 from phenolic-O-]. If the titration was carried out under pH=7, then the net charge is 0.
- The 1st proton is removed from the [COO-], the 2nd from [NH3+], and finally the phenolic proton is removed [OH].
- Since the acid is dibasic, the 2 basic pKa's [NH3+ and OH] are very similar, differing by only about 1 unit.
Of more importance to the prediction of the shape of the titration curve is the fact that there are several species in solution at the pH where the second equivalence point should be reached. The main effect of there being three species in solution at this point is to buffer the pH around the second equivalence point. Since the solution is effectively buffered by removing the NH3+ at the second equivalence point, we might not expect to observe a sharp change. In fact, this prediction is borne out in titration curve shown below.
- At pH=(pKa1+pKa2)/2, [COO- and NH3+] are at equivalence.
- At pH=pKa2, [NH3+] proton is removed to give [NH2].
- At pH=(pKa2+pKa3)/2, [NH2 and phenolic-OH] are at equivalence.
- At pH=pKa3, [phenolic-OH] proton is removed to give [phenolic-O-]
The net charge of the molecule at the end of the titration [in high alkaline pH, like pH=12] is -2 (a -1 from COO- and another -1 from phenolic-O-]. If the titration was carried out under pH=7, then the net charge is 0.
Although histidine has a net positive charge under physiological conditions (around pH 7.4), most of the histidine under physiological conditions is uncharged; second, while histidine may be the best amino acid to buffer a solution at pH 6, it is not the best amino acid for buffering solutions at other pH's closer to the pKa's of the other charged amino acids. All of this gets to the point of the question, "how does a buffer work?" A buffer is defined chemically as any compound that minimizes the change in pH of a solution when other compounds are added to the solution. The ability of a compound to act as a buffer at a given pH is determined by how readily it will accept and donate protons at that pH.
Review for the Quiz:
- Tables on chapter (relations of amino acids, functional groups and their properties).
- Protein structures from last year's notes.
- Titrations (which ways proteins are likely to move, based on pH and pKa).
- Don't need to know structures of amino acids (i.e. Aspartic acid is negatively charged, while glutamine is not. Cysteine can for disulfide bonds, etc..).
- Peptide bonds can be cleaved at differents sections (structures).
Protein Purification and Characterization
- Tables on chapter (relations of amino acids, functional groups and their properties).
- Protein structures from last year's notes.
- Titrations (which ways proteins are likely to move, based on pH and pKa).
- Don't need to know structures of amino acids (i.e. Aspartic acid is negatively charged, while glutamine is not. Cysteine can for disulfide bonds, etc..).
- Peptide bonds can be cleaved at differents sections (structures).
Protein Purification and Characterization
•-Isolate Protein
– * Separate and Purify
• * Fractionation
• * Centrifugation (mass separation through speed)
• * Dialysis (size separation by diffusion across conc. gradient)
• * Chromatography (how proteins are moving and interacting)
• * Electrophoresis (changes in pH and charges for identification)
Must know Gene Analysis and ELISA. NMR and x-ray crystallography purposes are for 3D structures.
- Determine structure
– * Primary
• * Sequence via Edman degradation
• * Make peptide digests (small pieces of overall protein formed by chemical or enzymatic digestion)
• * Genetic code analysis
– * Tertiary and Quarternary Structure
• * NMR evaluation of protein structure in solution
• * X-ray crystallography of crystallized proteins
Separate homogenized material by weight in centrifuge
Dialysis allows separation of small molecules from large molecules.
Molecular exclusion Chromatography makes it possible to separate molecules based on size
Ion Exchange Chromatography uses electrostatic interactions to separate proteins based on charge (you can change pH for forces to attract "electrostatic interaction", or even change solvent).
Affinity Chromatography, also takes advantage of interaction energies.
HPLC is a valuable tool for separating many molecules of clinical importance rapidly (has really high throughput).
Aromatic rings can be sensed spectrophotometrically (the following has high electron-rich rings) - you don't need to know this for quiz.
Aromatic rings can be sensed spectrophotometrically (the following has high electron-rich rings) - you don't need to know this for quiz.
PAGE: Polyacrylamide Gel Electrophoresis. Molecules will move in an applied electric field (see more on handout and SDS structure).
Isoelectric focusing - proteins stop moving in an electric field at their iso-electric point (PI). It allows of speration on intrinsic charge of pH (see notes).
Centrifugation allows separation of molecules by weight in a strong centrifugal field
Mass Spectrometry allows determination of molecular weight
Must know Gene Analysis and ELISA. NMR and x-ray crystallography purposes are for 3D structures.