Biochemistry: pH, Buffers, and Ionization Notes

Taxol interactions with beta-tubulin (Page 1)

• Topic: Taxol (paclitaxel) anti-cancer mechanism and protein interactions.
• Key beta-tubulin residues implicated in Taxol binding: \text{His}{229}, \;\text{Leu}{230}, \;\text{Phe}_{275}.
• Question presented: Which statement is LEAST likely true about Taxol-tubulin interactions?
  • A. Taxol has both hydrophobic (including aromatic) and hydrophilic functional groups. (True; Taxol contains hydrophobic regions/aromatic rings and polar functionalities.)
  • B. Tubulin H229 H-bonds to a hydroxyl group of Taxol. (Possible; histidine can H-bond; specific hydroxyl interactions plausible.)
  • C. Tubulin L230 is part of a hydrophobic pocket that is close to a phenyl ring of Taxol. (Plausible; leucine residues form hydrophobic pockets near ligands.)
  • D. Tubulin F275 forms an aromatic stacking interaction with a phenyl ring of Taxol. (Plausible; aromatic stacking with phenyl rings is common.)
  • E. The R-group of L230 forms a H-bond with a carbonyl group of Taxol. (Least plausible; leucine side chain is aliphatic/hydrophobic and not a hydrogen-bond donor/acceptor.)
• Answer highlight: E is least likely; leucine’s aliphatic side chain is not typically a hydrogen-bond donor/acceptor.

Prior knowledge expected (Page 2)

• Four core concepts students should know from earlier classes:
  • 1) Difference between a strong and a weak acid/base.
  • 2) How to calculate the pH of strong and weak acids/bases and why this matters.
  • 3) What information a titration curve of a weak acid/base provides and its relevance.
  • 4) What buffers are and why buffers are needed in biology.

Quick recall: pH basics (Page 3)

• Statements about pH truth values:
  • 1. The pH tells us whether a solution is acidic or basic. (True)
  • 2. The pH is quite unimportant for biological processes. (False)
  • 3. The pH is the negative logarithm of the proton concentration, [H+]. (True)
  • 4. A 100 mM HCl solution would have pH = 9. (False; 0.1 M HCl would have pH ≈ 1; 100 mM is 0.1 M.)
  • 5. Water’s neutrality (pH 7) is tied to [H+] = 10^{-7} M. (True)
• Answer: 1, 3, and 5 are correct (Option E).

Quick practice: pH of 0.1 mM HCl (strong acid) (Page 4 and 6)

• Calculation:
  • For HCl (strong acid): [H^+] = 0.1\,\text{mM} = 1\times 10^{-4}\,\text{M}
  • Therefore \mathrm{pH} = -\log[H^+] = -\log(10^{-4}) = 4.
• Quick note on bases (for comparison): 0.1 mM NaOH → [OH^-] = 1\times10^{-4}\,\text{M}; \mathrm{pOH}=4\Rightarrow \mathrm{pH}=14-4=10.
• Unit prefixes: 1\,\text{M} = 1\,\text{M}, \quad 1\,\text{mM} = 10^{-3}\,\text{M}, \quad 1\,\mu\text{M} = 10^{-6}\,\text{M}, \quad 1\,\text{nM} = 10^{-9}\,\text{M}.

Strong vs weak acids and pH concepts (Page 5 and 6)

• Strong acid/base definition:
  • A strong acid (HA) fully dissociates in water: \mathrm{HA} \rightarrow \mathrm{H^+} + \mathrm{A^-}
  • Arrow indicates the reaction is effectively in one direction (nearly complete).
• pH relation:
  • \mathrm{pH} = -\log[\mathrm{H^+}].
• Note on the concept of molar concentration: The square-bracket notation [\text{} \text{] } indicates molar concentration (moles per liter).

Weak acids and Ka; pKa concept (Page 8)

• Weak acid CH3COOH (acetic acid, HAc) partially dissociates: \mathrm{HAc} \rightleftharpoons \mathrm{H^+} + \mathrm{Ac^-}
• Acid dissociation constant: K_a = \frac{[\mathrm{H^+}][\mathrm{Ac^-}]}{[\mathrm{HAc}]}
• Example data (from text): When 1 M HAc is diluted to equilibrium, values approximate to:
  • K_a = 1.77 \times 10^{-5}\,\text{M}
  • pKa = -\log Ka = 4.76
  • At equilibrium: [\mathrm{H^+}] = 0.0042\,\text{M}, \; pH = 2.38.
• Relationship: pKa = -\log Ka.

Henderson–Hasselbalch equation (Page 9, 11, 12)

• For a weak acid and its conjugate base: \mathrm{pH} = pK_a + \log\left(\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}\right).
• Alternate form (solving for ratio): \frac{[\mathrm{A^-}]}{[\mathrm{HA}]} = 10^{\mathrm{pH} - pK_a}.
• Key implications:
  • If pH > pK_a, more A^- (base form) is present.
  • If pH < pK_a, more HA (acid form) is present.
• Example calculation (0.1 mM CH3COOH, 0.01 mM CH3COO^-; pK_a = 4.76):
  • \mathrm{pH} = 4.76 + \log\left(\frac{0.01}{0.1}\right) = 4.76 + \log(0.1) = 4.76 - 1 = 3.76.

Practical calculation: pH of weak acid with conjugate base (Pages 10-12)

• Practice result: pH = 3.76 for the given mixture above (CH3COOH/CH3COO^- with pK_a = 4.76).
• Recap: For any weak acid/base system, use \mathrm{pH} = pK_a + \log\left(\frac{[A^-]}{[HA]}\right).

Buffers: definitions and visualized buffering (Pages 13-17)

• BUFFER: A mixture of a weak acid (or base) and its conjugate base (or acid) that resists pH changes upon addition of small amounts of strong acid/base.
• Buffer behavior on titration curves:
  • Midpoint of the titration of a weak acid by a strong base occurs at pH = pK_a (50:50 ratio of conjugate base/acid).
  • Buffer regions extend around pH ≈ pK_a ± 1.
• Practical phrasing:
  • Start: 50:50 mixture in buffer has pH = pK_a.
  • Buffer zone provides resistance to pH shifts when acid/base are added.
• Example scenario (acid titration with base):
  • pK_a = 4.76 for CH3COOH/CH3COO^-; at 50:50, pH = 4.76.
  • Buffer with 90:10 or 10:90 ratios shifts pH according to Henderson–Hasselbalch (pH = pK_a + log([A^-]/[HA])).
• Quantitative illustration (buffer at pH 4.76, adding strong acid/base):
  • Addition of 1 mL of 10 M HCl to 999 mL water yields pH ~ 2 (not buffer-protected).
  • In a true buffer, adding acid/base changes pH by a small amount (e.g., less than a few tenths of a pH unit).
• Midpoints and buffer capacity:
  • HAc:Ac^- at 50:50 is a common reference point (pH = pKa).
  • Buffer capacity decreases as you move away from pH ≈ pK_a.

Practical buffer examples and calculations (Pages 14-21)

• Dilution example: 999 mL of water with 1 mL of 10 M HCl (1:1000 dilution):
  • Final [HCl] ≈ 10 mM; pH ≈ 2.
• Concept: Adding buffered solution (HAc/Ac^-) reduces pH change compared with unbuffered water.
• Quantitative buffer example (CH3COOH/CH3COO^- at pH 4.76; add 1 mL of 10 M HCl to 1 L buffer):
  • Start: CH3COOH/CH3COO^- ≈ 0.5 M / 0.5 M, pH = 4.76.
  • End: After adding 10 M HCl to buffer, end ratio is CH3COOH ≈ 0.51 M and CH3COO^- ≈ 0.49 M; pH ≈ 4.743 (calculated via \mathrm{pH} = pK_a + \log \frac{[A^-]}{[HA]} = 4.76 + \log(0.49/0.51)).
• General buffer behavior: Adding 1 mL of 10 M HCl to 1 L buffer changes pH by less than ~0.03 pH units, demonstrating buffer resistance.

Why buffers are crucial in biology (Pages 24-25)

• Why buffers matter:
  • Metabolic processes generate acids (e.g., lactic acid from anaerobic metabolism); without buffers, pH would drift, protonation states would change, and critical ionic interactions could be lost.
  • Changes in protonation states can alter enzyme activity, protein structure, and charge-based interactions.
• Physiological buffer systems:
  • Phosphate buffer (cytoplasm and extracellular): pKa ≈ 6.86 for the H2PO4^- ⇌ HPO4^{2-} + H^+ pair.
  • CO2/Bicarbonate buffer system in plasma: typically around pH ≈ 7.4; involves CO2(g), CO2(aq), H2CO3, HCO3^-, and carbonic anhydrase.

CO2/Bicarbonate buffer system: physiological context and mathematics (Pages 27-29)

• Core reactions (simplified):
  • CO2(g) ⇌ CO2(aq) (dissolution)
  • CO2(aq) + H2O ⇌ H2CO3 (hydration)
  • H2CO3 ⇌ H^+ + HCO3^- (dissociation)
• Key quantitative parameters (typical physiological values):
  • pK_a′ (bathed in body fluids) ≈ 6.1 for the CO2/HCO3^- system under physiological conditions.
  • [HCO3^-] ≈ 24 mM; [CO2(aq)] ≈ 1 mM; pCO2 ≈ 5.3 kPa (~40 mmHg).
  • The physiologic pH is around 7.40 (normal blood pH).
• Comprehensive Henderson–Hasselbalch form for CO2/HCO3^- buffer (accounting for dissolved CO2):
  • \mathrm{pH} = pKa' + \log \left( \frac{[\mathrm{HCO3^-}]}{0.03 \cdot p\mathrm{CO}2} \right) where pCO2 is in mmHg. In SI-like terms, the factor 0.03 represents Henry’s constant linking CO2 partial pressure to dissolved CO2 concentration.
• Example calculation (normal physiology):
  • With pCO2 ≈ 40 mmHg and [HCO3^-] ≈ 24 mM:
  • \mathrm{pH} \approx 6.1 + \log\left(\frac{24}{1.2}\right) \approx 7.4 (consistent with normal blood pH).
• Additional notes:
  • The CO2/bicarbonate system acts as a key buffer but is limited by pKa and the capacity of the kidneys to regulate bicarbonate and of the lungs to regulate CO2.
  • The equation provides intuition for how changes in ventilation (CO2 removal) or bicarbonate concentration shift pH.

Physiological responses to pH changes (Pages 29-33)

• When pH is too low (acidic):
  • Increase ventilation to blow off CO2 (reduces H^+ production) and/or renal excretion of H^+ (as NH4^+).
• When pH is too high (alkaline):
  • Decrease ventilation to retain CO2 and excrete bicarbonate to increase H^+ concentration.
• Clinical scenarios:
  • Metabolic acidosis: low HCO3^-; kidneys compensate by increasing H^+ excretion.
  • Respiratory acidosis: high CO2 due to impaired ventilation; kidneys compensate by increasing H^+ excretion and bicarbonate reabsorption.

Amino acids and pH: ionization and isoelectric point (Pages 34-38)

• Protonation states as pH varies:
  • Very acidic pH: carboxyl group is protonated (COOH, neutral) and amino group is protonated (NH3^+, +1 charge) → net positive charge.
  • Neutral pH (typical amino acids in proteins): carboxyl is deprotonated (COO^-, −1) and amino is protonated (NH3^+, +1) → zwitterion (net charge 0).
  • Very alkaline pH: carboxyl deprotonated (−) and amino deprotonated (0) → net negative charge.
• Typical pKa ranges (in free amino acids):
  • Carboxyl group (alpha-COOH): pK_a ≈ 2–4 (often ~2.0–2.5 for the main carboxyl)
  • α-amino group (NH3^+): pK_a ≈ 9–10
  • Side chains (examples):
  • Asp/Glu (side-chain carboxyl): pK_a ≈ 2.3
  • Lys/Arg (side-chain amine): pK_a ≈ 9.7
  • His (imidazole): pK_a ≈ 6
• Important caveats for proteins:
  • The α-amino and carboxyl groups on the backbone are involved in peptide bonds in proteins and are not freely ionizable; N- and C-termini remain ionizable.
  • Side-chain ionization depends on the local environment within the protein.
• Isoelectric point (pI):
  • For amino acids with two dissociable groups (NK): pI is the pH at which net charge is zero.
  • If the amino acid has two pKa values (typical for neutral amino acids), then: \mathrm{pI} = \frac{pKa1 + pKa2}{2}.
  • In amino acids with ionizable side chains, the pI can be computed by considering the predominant species around the net zero charge.
• Titratable groups: number of OH^- equivalents needed for titration equals the number of protonatable groups (e.g., Asp, Glu, His, Arg, Lys): often 3 for amino acids with side chains.
• Buffer regions for amino acids: can be observed around each titratable group, leading to multiple buffering zones (typically up to 3 for amino acids with multiple ionizable groups).
• Practical visual: pI occurs where the net charge is zero; at this point, the molecule has minimal mobility in an electric field.

Practice question recap (Pages 39)

• Question: Enzyme X has optimal activity at pH = 6.9; activity falls sharply when pH is much lower than 6.4. Which interpretation is most likely?
  • A. A Glu residue is involved at the reaction site. (Glu has pKa ~4; involvement would affect activity more around pH 4–5.)
  • B. A His residue is involved at the reaction site. (His has pKa ~6; activity sensitive near pH 6–7; fits the sharp drop as pH decreases below 6.4.)
  • C. The enzyme has a metallic cofactor. (Unrelated to the specific pH window described.)
  • D. The enzyme is found in gastric secretions. (Not directly tied to pH profile near 6.5.)
  • E. The reaction relies on phosphorylation of a Ser residue. (Phosphorylation state can be pH-dependent but less specific to the narrow window around 6–7.)
• Most likely answer: B (A Histidine residue). His side chain has a pKa around 6; protonation state changes in this region can modulate enzyme activity.

Quick reference: key equations and constants

• Brønsted acidity: Ka = \frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]}; pKa = -\log K_a
• Henderson–Hasselbalch (acid/base pair): \mathrm{pH} = pK_a + \log \left(\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}\right)
• Protonation state and pH:
  • At pH < pK_a, species is predominantly protonated.
  • At pH > pK_a, species is predominantly deprotonated.

Summary of practical takeaways

• Buffers resist pH changes around their pKa in the range of pH = pKa ± 1.
• The pH of biological fluids is tightly regulated by buffers such as phosphate and CO2/HCO3^- systems.
• The Henderson–Hasselbalch equation is essential for predicting pH and buffer ratios in biological systems.
• The pI of amino acids determines their charge state in different pH environments, influencing protein behavior and interactions.
• In enzyme active sites, residues with pKa values near physiological pH (notably Histidine ~6, Lys/Arg ~9–10, Asp/Glu ~2–4) can act as critical proton donors/acceptors; shifts in pH can dramatically affect activity.