Biochemistry: every practice question

Every amino acid has the same core: a central α-carbon bonded to an α-amino group (–NH₂, –NH₃⁺ at pH 7.4), an α-carboxyl group (–COOH, –COO⁻ at pH 7.4), a hydrogen atom and a variable side chain. The side chain gives each amino acid its size, charge and polarity, and so decides its class.

• Hydroxyl instead of carboxyl: an –OH alone is not an acid; without the carboxyl there is nothing to form the peptide bond.
• Imino + methyl: the methyl is alanine's R group, not a fixed fourth substituent; 'imino' describes proline only.

Amino acids are the building blocks of proteins and also precursors of many other biomolecules. Over 300 occur in nature (many in plants, microbes or as metabolic intermediates such as ornithine and citrulline), but the genetic code specifies only 20 for protein synthesis.

• 30 overstates the protein set.
• 'The only amino acids in nature' is false: most natural amino acids never enter proteins.

A carbon is chiral (asymmetric) when its four substituents are all different, so it has two non-superimposable mirror-image forms. Glycine's R group is just –H; with two hydrogens on the α-carbon it has no mirror-image isomer, so glycine is the one amino acid with no D/L forms.

• Alanine (R = –CH₃) has four different groups, so it is chiral.
• Proline's side chain loops back onto its nitrogen, but its α-carbon still has four different neighbours, so it is chiral.

Glycine, the smallest amino acid (its side chain is a hydrogen atom), has several special jobs:

• Collagen: glycine is every third residue (Gly-X-Y), because only its tiny side chain fits in the centre of the tight triple helix.
• Creatine: made from glycine and arginine, then methylated by S-adenosylmethionine.
• Purine ring: the whole glycine molecule supplies C4, C5 and N7.

It also feeds haem and glutathione synthesis. Wrong choices: carnitine is made from lysine and methionine, and the pyrimidine ring from aspartate and carbamoyl phosphate; serotonin comes from tryptophan and melanin from tyrosine.

An amino acid with an asymmetric α-carbon has two stereoisomers, mirror images labelled L and D by the arrangement around the α-carbon. Ribosomes and tRNA charging use only L amino acids, so every residue in a human protein (except achiral glycine) is L.

• D isomers occur in bacterial cell walls and some antibiotics, not in mammalian proteins.
• A racemic mix (50:50 D and L) is what a non-enzymatic chemical synthesis gives; biology is stereospecific.

The α-amino and α-carboxyl groups are the same in every amino acid, so they cannot tell amino acids apart. The R group does. The course scheme:

• Hydrophobic (nonpolar): aliphatic, aromatic, imino (proline).
• Hydrophilic (polar): uncharged; charged → acidic or basic.

The carboxyl and α-amino options fail because those groups are shared by all 20 and are both ionised at pH 7.4.

These four are the classic code traps because the obvious first letters are taken (G = glycine, A = alanine). The amides (glutamine, asparagine) carry the 'odd' letters Q and N; the acids carry E and D.

• E, Q, D, N swaps each amide with its acid.
• G, E, A, D uses glycine's and alanine's letters.

Asx (B) and Glx (Z) mean 'Asn or Asp' and 'Gln or Glu' when the amide is not known. Hook: 'Q-tamine' (glutamine), 'asparagi-N-e'. The Q in 'polyQ' diseases is glutamine.

• Ser carries an –OH and is polar uncharged.
• Phe has a benzene ring, so it is aromatic, not aliphatic.

This primer places cysteine with the aliphatic group; many textbooks list it as polar uncharged.

Methionine's side chain (–CH₂–CH₂–S–CH₃) has no charge and no hydrogen-bonding group; the sulfur sits in a thioether, unlike cysteine's free –SH. It is buried in protein cores like leucine and isoleucine.

• Glutamine ends in an amide (–CONH₂): polar uncharged.
• Lysine ends in an amino group that is –NH₃⁺ at pH 7.4: basic, positively charged.

All three carry a large flat aromatic ring: benzene (Phe), phenol (Tyr) and indole (Trp). Their bulky rings make them more common in β-sheets than in α-helices.

• Proline has a ring, but it is a saturated (non-aromatic) pyrrolidine ring; it is the separate 'imino' class.
• Histidine's imidazole ring is aromatic, but it is a weak base and is classed as hydrophilic, basic.

Tyrosine is phenylalanine with an –OH on the ring. The OH makes it somewhat polar and lets it hydrogen-bond, yet the aromatic ring keeps it mostly hydrophobic, so the course places it with the aromatics.

• Charged at pH 7.4: the phenol OH has a pK_a near 10, so it is almost fully protonated (uncharged) at 7.4.
• Cannot hydrogen-bond: it can; that is the point of the slide.

The same slide says tryptophan's indole nitrogen does not form hydrogen bonds (textbooks note it can act as a weak donor), so Trp also counts as hydrophobic.

In proline the side chain loops round and attaches to the α-amino nitrogen, giving a secondary amine (imino group) inside a five-membered ring. That ring locks the N–Cα rotation (Φ) and leaves no N–H to donate a backbone hydrogen bond, so proline kinks the chain and is found in turns and bends.

• Flexible chain, helix centre: the reverse; proline is the 'helix breaker'.
• Glycine is not an imino acid, and its flexibility also makes it a poor helix former.

Cysteine (–SH) and tyrosine (phenol –OH) are borderline: each has a weakly polar group that can hydrogen-bond and can ionise at high pH (Cys pK_a ~8.3, Tyr ~10), but each is largely nonpolar. The primer files them as hydrophobic; the review slides' nonpolar list (Gly, Ala, Val, Leu, Ile, Met, Phe, Trp, Pro) leaves them out. Know both views.

• Serine and threonine are polar uncharged in every scheme.
• Glycine and proline are nonpolar in every scheme.

These side chains carry hydroxyl or amide groups that hydrogen-bond with water and with other side chains, but none ionises at physiological pH. Serine and threonine hydroxyls are also sites of phosphorylation and O-linked glycosylation.

• Asp and Glu are the acids of Asn and Gln: their carboxylates are negatively charged at pH 7.4.
• His is basic; Cys is placed with the aliphatic hydrophobics in this primer.

The side-chain carboxyls of Asp and Glu have pK_as near 4. At any pH well above the pK_a a group gives up its proton, so at 7.4 both carry −1. They form ionic bonds (salt bridges) with lysine and arginine.

• Positive: a carboxylate cannot be positive; positive charge comes from amino, guanidinium or imidazole groups.
• Asn and Gln are the amides of Asp and Glu: polar but uncharged.

Each basic side chain contains nitrogen that accepts a proton: lysine's ε-amino group (pK_a ~10.5), arginine's guanidinium (~12.5) and histidine's imidazole (~6). Lys and Arg are fully positive at 7.4; His is only weakly basic and mostly uncharged at 7.4, although the course lists it with the positive group.

• Asn is an amide: polar uncharged, not basic.
• Negative: proton-accepting groups gain positive charge, never negative.

The lecture labels arginine's side-chain group guanidinium and histidine's imidazole; lysine ends in a terminal (ε) amino group. Guanidinium shares its positive charge over three nitrogens, which makes it the strongest base of the three.

• Imidazole belongs to histidine, the weakly basic one.
• ε-Amino group is lysine's terminal –NH₃⁺.

The acidic pair carry a carboxylic acid group.

At a pH above a group's pK_a, the deprotonated form dominates. With pK_a ~6 and pH 7.4, only a small fraction of imidazole rings carry the extra proton. Because its pK_a is so close to physiological pH, histidine easily gains or loses a proton, which makes it the key buffering and catalytic residue (enzyme active sites, haemoglobin).

• Fully positive fits lysine and arginine, whose pK_as are far above 7.4.
• Negative: imidazole accepts a proton; it never carries a negative charge in proteins.

The slide still files His under 'net positive' with the basic group, and review keys mark it '+' at physiological pH: when a question asks which amino acids are basic or positively charged, include histidine.

Histidine has a ring, which tempts students to group it with the aromatics. But its imidazole contains a nitrogen that accepts a proton, so it is polar and classed as charged, basic.

• Glycine: R = H; tiny but counted as hydrophobic aliphatic.
• Tryptophan: large indole ring; hydrophobic aromatic.

Other classic 'not hydrophobic' answers: Glu, Asp, Lys, Arg, Ser, Thr, Asn, Gln.

These seven have three pK_as (pK₁ α-carboxyl, pK₂ α-amino, pK_R side chain), so their pI is the average of the two nearest pK_as. Cysteine (pK_a ~8.3) and tyrosine (~10) ionise only at high pH and are uncharged at 7.4.

• Asn, Gln: amides do not ionise.
• Ser, Thr: aliphatic hydroxyls (pK_a ~13) do not ionise in the physiological range.

The hydrophobic effect pushes nonpolar side chains away from water. In a cytosolic or plasma protein that means the interior, with charged and polar residues on the surface. In the lipid bilayer the surroundings are themselves hydrophobic, so a membrane-spanning segment shows its nonpolar residues outward to the fatty-acid tails.

• Soluble outward would expose nonpolar groups to water and destabilise the fold.
• Membrane inward, away from lipid would leave polar groups facing the lipid, which is unfavourable.

A soluble protein folds so that hydrophilic side chains (charged Arg, Lys, Asp, Glu; polar Ser, Thr, Asn, Gln) are on the outside, where they hydrogen-bond with water, and hydrophobic side chains are packed inside.

• Isoleucine is hydrophobic aliphatic: core.
• Phenylalanine is hydrophobic aromatic: core.

Natural selection acts on what a protein does, and what it does depends on its 3-D fold. Because many different sequences can fold into the same shape, related proteins from distant species often keep nearly the same fold while their sequences have drifted apart. This is why structural elements, and the chemistry of the residues that build them, can be used to predict function: seven hydrophobic transmembrane α-helices mark a G-protein-coupled receptor.

• DNA sequence is the least conserved: silent (synonymous) codon changes alter the gene without changing the protein at all.
• Amino acid sequence changes more than structure: conservative substitutions (e.g. leucine → isoleucine in the core) keep the fold while changing the sequence.

The receptor's extracellular domain binds the ligand, the seven transmembrane helices anchor it in the bilayer and transmit the shape change, and the intracellular domain activates a G protein. Hydrophobic residues facing hydrophobic lipid give a favourable interaction. This is the 'structure = function' example: the sequence alone predicts a membrane protein.

• A single helix describes single-pass receptors such as receptor tyrosine kinases.
• A β-barrel is how porins in bacterial and mitochondrial outer membranes cross; GPCRs use helices.

About 20 residues in an α-helix (1.5 Å rise per residue) give ~30 Å, the thickness of the bilayer's hydrophobic core. Val, Leu and Ile are hydrophobic aliphatic, so a run of them is happiest inside the lipid. Seven such helices is the GPCR signature.

• Binding TSH is the job of the extracellular N-terminal domain, which is polar and faces water.
• Phosphorylating tyrosines is kinase activity (receptor tyrosine kinases), not a property of hydrophobic helices.

Glu6 sits on the surface of the β chain. Valine's nonpolar side chain there creates a hydrophobic patch that, in deoxy-HbS, fits into a pocket on a neighbouring tetramer, so HbS polymerises into long fibres and the red cells sickle.

• Basic → hydrophobic: glutamate is acidic; the basic residues are Lys, Arg and His. (HbC is Glu6 → Lys: acidic → basic.)
• Acidic → polar uncharged: valine has no polar group; Glu → Gln would be that change.

Threonine's hydroxyl hydrogen-bonds with water, substrates or drugs; leucine's branched hydrocarbon chain cannot, so the site becomes more hydrophobic.

• Hydrophobic → polar is the reverse direction.
• Negative → neutral: threonine carries no charge at pH 7.4; only Asp and Glu are negative.

A substitution within the same class (polar uncharged → polar uncharged) usually preserves folding and surface properties. Glutamine (amide) and serine (hydroxyl) both hydrogen-bond and carry no charge at pH 7.4.

• Leucine is hydrophobic: it would put a nonpolar group where a polar one was.
• Aspartate is close in shape (it is the acid form of asparagine) but adds a negative charge.

The pK_a is the pH at which a group is half protonated. Below it the protonated form dominates; above it the deprotonated form does. With one pK_a far below 7.4 and the other far above, both groups are charged at physiological pH.

• ~4.2 / ~7.4: ~4 is the side-chain carboxyl of Asp/Glu; 7.4 is blood pH, not a pK_a of these groups.
• Swapped values would make the carboxyl the weaker acid, which it is not.

pH 7.4 is far above the carboxyl pK_a (~2.2), so it has lost its proton; it is far below the amino pK_a (~9.4), so the amino group keeps an extra proton. One + and one − give a net charge of zero for an amino acid with an uncharged side chain: a zwitterion.

• –COOH and –NH₃⁺ is the form below pH ~2 (net +1).
• –COOH and –NH₂ never predominates: it would need the carboxyl protonated and the amine deprotonated at the same time.

The lecture defines three terms: cation = net (+) charge, anion = net (−) charge, zwitterion = neutral molecule with equal (+) and (−) charges. An amino acid with an uncharged side chain is a zwitterion at pH 7.4 (–NH₃⁺ and –COO⁻).

• Net positive is a cation.
• No ionised groups is simply uncharged; a zwitterion is neutral because its charges cancel, not because it has none.

At the pI the positive and negative charges balance exactly. Below it the molecule carries extra protons (net +); above it it has lost them (net −). Because the net charge is zero, a molecule at its pI does not move in an electric field and is least soluble.

• Greatest net charge is reached at the extremes of pH, far from the pI.
• Side chain becomes charged describes the side-chain pK_R, not the pI.

Lowering the pH adds protons: carboxylates become neutral –COOH while amino groups stay –NH₃⁺, so + wins. Raising the pH strips protons: amino groups become neutral –NH₂ while carboxylates stay –COO⁻, so − wins.

• The reversed pairing is the common slip.
• Net zero below pI: net zero happens only at the pI itself.

The lecture slide calls the negatively charged form 'cationic'; the correct word is anionic (an anion is negative). Hook: 'below the pI, protons pile on → positive'.

Electrophoresis separates molecules by net charge: net-negative molecules move to the anode (+), net-positive ones to the cathode (−). At the pI the charges cancel. Isoelectric focusing uses this: each protein stops where the pH gradient equals its pI.

• Toward the anode happens when the buffer pH is above the pI (net −).
• Toward the cathode happens when the buffer pH is below the pI (net +).

The titration slide shows three forms of alanine:

• Form I (pH < 2): –COOH, –NH₃⁺, net +1.
• Form II (pH ~6, the pI 5.7): –COO⁻, –NH₃⁺, net 0, the zwitterion.
• Form III (pH > 10): –COO⁻, –NH₂, net −1.

pH 1 is below pK₁ (2.3), so even the carboxyl keeps its proton: form I.

At any pH equal to a group's pK_a, that group is exactly half protonated. At 2.3, half of the alanine carboxyls are –COOH (net +1 molecules) and half are –COO⁻ (net 0 zwitterions), so [I] = [II] and the average is +½. Likewise at pK₂ (9.1), [II] = [III] and the average is −½.

• +1 holds well below pH 2.3.
• 0 holds at the pI, 5.7.

A buffer resists pH change when it holds plenty of both the proton donor and the proton acceptor. That happens at pH = pK_a (± ~1 unit), the flat 'regions of buffering' shaded on the alanine curve at 2.3 and 9.1. At the pI only one form (the zwitterion) dominates, so the curve is steep and buffering is poorest there.

• pI (5.7) is the worst buffering region.
• pH 7.4 is far from both of alanine's pK_as; only histidine's side chain (pK_a ~6) buffers near there.

A group buffers well within about one pH unit of its pK_a. Histidine is the only side chain with a pK_a near neutral, which is why histidine-rich proteins (haemoglobin, albumin) are important blood buffers and why histidine is common in enzyme active sites.

• Lysine (pK_a ~10.5) is fully protonated at 7.4 and cannot absorb more H⁺.
• Aspartate (pK_a ~4) is fully deprotonated at 7.4.

The zwitterion dominates between the two pK_as, and the point of exact charge balance lies midway between them. For an amino acid with an uncharged side chain, pK₁ is the α-carboxyl and pK₂ the α-amino group.

• The higher pK_a is where half the amino groups have lost their proton (net −½), not where net charge is zero.
• The sum gives a number above any possible pH (e.g. 11.4 for alanine).

Alanine's side chain (–CH₃) does not ionise, so only the α-carboxyl and α-amino groups count. Their average is 5.7: at that pH alanine is the zwitterion (form II) with net charge 0.

• 11.4 is the sum without dividing by 2.
• 6.8 is simply 9.1 − 2.3, the difference of the two pK_as.

Write out the forms from low to high pH and find the one with net charge 0; the pI is the average of the pK_as on either side of it.

• Acidic amino acids (Asp, Glu): the neutral form lies between the two low pK_as → average pK₁ and pK_R.
• Basic amino acids (Lys, Arg): the neutral form lies between the two high pK_as → average pK₂ and pK_R.

Averaging all three, or using pK_R alone, does not land at the point of zero charge.

Going up in pH, aspartate passes through net +1 (all protonated), 0 (α-carboxyl lost its proton at 2.0), −1 (side-chain carboxyl lost its proton at 4.0) and −2 (amino group deprotonated at 9.5). The zero-charge form lies between 2.0 and 4.0, so the pI is 3.0. An acidic amino acid always has a low pI.

• 5.75 averages the two α-groups and ignores the side chain.
• 6.75 averages the wrong pair: between 4.0 and 9.5 aspartate is already net −1.

Going up in pH, arginine passes through +2 (all protonated), +1 (carboxyl deprotonated at 2.1), 0 (α-amino deprotonated at 9.0) and −1 (guanidinium deprotonated at 12.5). Zero charge lies between 9.0 and 12.5. A basic amino acid always has a high pI.

• 5.55 averages the two low pK_as; at that pH arginine is still +1.
• 7.30 averages the outermost pK_as, which is never the rule.

Method for any peptide at pH 7.4:

• Free N-terminus +1, free C-terminus −1 (they cancel).
• Each Asp or Glu −1; each Lys or Arg +1.
• His: the course lists it with the positive (basic) residues and review keys count it +1, although with a pK_a ~6 most His side chains are uncharged at 7.4. Cys and Tyr are uncharged.
• All other residues 0.

Here: −1 (Glu) +1 (Lys) −1 (Asp) −1 (Asp) = −2. −1 forgets one acidic residue; +1 reverses the signs.

Count only the side chains once the N-terminal +1 and C-terminal −1 cancel:

• Acidic: Glu (−1), Asp (−1) → −2.
• Basic: Arg (+1), Lys (+1), Lys (+1) → +3.

Sum = +1. +3 forgets the two acidic residues; −1 swaps the signs of the acidic and basic groups.

After the termini cancel:

• Glu-Pro-Lys-Val-Leu: Glu −1 + Lys +1 = 0.
• Met-Thr-Asn-Asp-Gly: Asp −1 = −1 (Asn and Thr are polar but uncharged).
• Ile-Val-Gln-Ser-Arg: Arg +1 = +1.

Trap: Gln and Asn look like Glu and Asp but carry no charge.

With the termini cancelling:

• Gly-Tyr-Asp-Glu-Phe-Cys: Asp −1, Glu −1 → −2.
• Leu-Met-Ser-Asn-Glu-Val: Glu −1 → −1 (Asn is uncharged).
• Lys-Arg-Pro-Tyr-Phe-Cys: Lys +1, Arg +1 → +2 (basic).

Tyr (pK_a ~10) and Cys (~8.3) are protonated and uncharged at 7.4.

The carbonyl carbon of residue 1 bonds to the nitrogen of residue 2 (–CO–NH–). Repeating this gives the polypeptide backbone, with the side chains hanging off the α-carbons. Peptide bonds are what hold the primary structure together.

• α-Amino + side chain: side chains are not part of the backbone link (a side-chain amide bond is an isopeptide, e.g. ubiquitin conjugation).
• Ester link: esters join carboxyl and hydroxyl groups (as in triacylglycerols), not amino acids in a chain.

The –OH of one carboxyl and an –H of the next amino group leave as a water molecule, joining the two residues. Putting the water back cleaves the bond, which is what proteases and gastric/pancreatic digestion do. Hydrolysis is thermodynamically favourable but very slow without an enzyme, so proteins are kinetically stable.

• ATP: ATP pays for amino acid activation (tRNA charging) but is not a product of the bond itself.
• CO₂: no carbon is lost; decarboxylation makes amines (e.g. histamine), not peptides.

The lone pair on the amide nitrogen delocalises toward the carbonyl oxygen. The C–N bond is therefore shorter than a single bond and behaves like ~40% double bond: it cannot twist, and the six atoms around it lie in one plane (the peptide unit).

• Side-chain clash explains why the R groups prefer trans, not why the bond cannot rotate.
• Full double bond overstates it: the bond is intermediate between single and double, and the C=O keeps partial double-bond character too.

Because the C–N bond cannot rotate, these six atoms (Cα, C, O, N, H, Cα) are locked in a flat plate. A protein backbone is a chain of these rigid plates hinged at each α-carbon.

• Including R groups: the side chains attach to the α-carbons and project out of the plane; they are not part of the unit.
• Rotating freely: the unit is rigid; rotation happens only at the Cα hinges (Φ and Ψ).

In the trans arrangement the two α-carbons, and so their side chains, sit on opposite sides of the rigid C–N bond, as far apart as possible. Cis would bump the side chains together.

• Cis is rare; it occurs mainly in bonds preceding proline, whose ring reduces the energy difference.
• Random: the preference for trans is strong (>99.9% for non-proline bonds).

Each peptide unit is a rigid plane; the planes meet at the α-carbons, which act as swivels. The pair of angles (Φ, Ψ) at every residue determines the local backbone shape, and particular pairs give the α-helix or β-sheet. Proline's ring fixes its Φ, which is part of why it breaks helices.

• Φ and Ψ swapped mislabels the bonds: Φ is the N–Cα bond.
• C–N peptide bond cannot rotate (partial double bond).

This matches the direction of synthesis on the ribosome, which adds each new amino acid to the free carboxyl end. The name follows the same order: all residues but the last end in '-yl', so Tyr-Gly-Gly-Phe-Leu (Leu-enkephalin) is tyrosylglycylglycylphenylalanylleucine.

• C → N is backwards.
• N on the right puts the ends on the wrong sides.

By convention the residue on the left (first in the name, with the '-yl' ending) is the N-terminal residue with a free –NH₃⁺. The last residue, leucine, keeps its full name and is the C-terminal residue with a free –COO⁻.

• Leucine carries the free α-carboxyl, not the free amino group.
• Phenylalanine is internal: both its α-groups are tied up in peptide bonds.

The sequence (read N → C) is the level encoded by the gene, and it determines every higher level. A single change in it can alter the whole protein (Glu → Val in sickle haemoglobin).

• Hydrogen bonds hold secondary structure (backbone C=O···H–N).
• Disulfide bonds are side-chain cross-links that stabilise tertiary structure.

The carbonyl oxygen of one peptide unit accepts a hydrogen bond from the amide N–H of another. In an α-helix these bonds lie within one stretch of chain; in a β-sheet they link neighbouring strands. Both the helix and the sheet are held by hydrogen bonds.

• Peptide bonds make the chain itself (primary).
• Side-chain hydrogen bonds are a tertiary interaction; secondary structure uses backbone atoms only.

Secondary elements pack together into motifs and domains. The fold is stabilised by hydrophobic interactions, hydrogen bonds, ionic bonds, metal ions and covalent disulfide bonds between side chains.

• Covalent only is wrong twice: that is the local (secondary) level, and most tertiary forces are non-covalent.
• Several chains is quaternary structure.

Common trap: 'tertiary structure involves only non-covalent interactions' is false.

The subunits are separate folded chains that associate through hydrogen bonds, ionic bonds, hydrophobic contacts and metal ions. Haemoglobin (2α + 2β) is the standard example; myoglobin, a single chain, has none.

• One chain is tertiary.
• Peptide bonds join residues within a chain, never separate subunits.

Textbook note: a few multi-chain proteins (e.g. antibodies) also have inter-chain disulfide bonds; for this exam answer 'non-covalent'.

It is a rigid, rod-like structure that forms spontaneously and looks like a spiral staircase turning clockwise as it moves away from the viewer. 3.6 residues per turn means residue n sits almost directly below residue n + 4, the partner it hydrogen-bonds with.

• Left-handed helices are strained for L amino acids and almost never occur in proteins (collagen's individual chains are a special left-handed polyproline-type helix).
• 5.0 per turn does not match the α-helix geometry.

Twelve residues is just over three turns (3.6 per turn). Transmembrane helices are at the longer end (~20 residues) because they must span the ~30 Å hydrophobic core of the bilayer.

• ~4 residues is barely one turn, the size of a β-turn.
• ~40 residues overstates the average, though single helices can reach 45.

Every backbone C=O and N–H inside the helix is paired, which is what makes the helix stable. Because each bond links residues one turn apart, the bonds point along the helix axis, and the peptide-unit planes are parallel to that axis.

• Side chain to backbone: helix hydrogen bonds are backbone-to-backbone only.
• Neighbouring chain, perpendicular: that describes a β-sheet, where bonds run between strands.

The tightly wound backbone fills the centre of the helix, leaving no room inside; the side chains project out like the steps of a spiral staircase. Their chemistry then decides how the helix packs: a membrane helix shows hydrophobic R groups to the lipid; an amphipathic helix has a polar face and a nonpolar face.

• Inward is the classic trap; the core is occupied by backbone atoms.
• Along the axis describes the hydrogen bonds, not the side chains.

Each β-strand is an almost fully extended stretch of chain. Strands line up side by side, and the C=O of one strand bonds the N–H of the neighbour, so the bonds run roughly perpendicular to the strands. The strands can come from distant parts of one chain or from different chains.

• Four apart, same strand is the α-helix pattern (intrachain).
• Side chains: like the helix, the sheet uses backbone atoms, not R groups.

Summary: α-helix = within the same chain; β-sheet = between adjacent strands.

Direction is judged from N- to C-terminus of each strand. Antiparallel sheets, often formed by a chain folding back on itself through a β-turn, have straighter, slightly stronger hydrogen bonds; parallel sheets need a longer crossover connection between strands.

• Coiled describes coiled coils of α-helices, not sheet strands.
• Left/right-handed describes helices; sheet strands are classed by direction only.

The pleats (zigzag) of the extended chain make successive side chains alternate sides. So one face of a sheet can be hydrophobic and the other polar if the sequence alternates nonpolar and polar residues, as when one face of the sheet packs against the protein core.

• All on one face ignores the alternation.
• Between the strands is where the hydrogen bonds run; the R groups stick out of the plane.

'Random' does not mean disordered or useless: these loops have a defined structure in a given protein, often form the active or binding site, and link the regular elements. They simply lack a repeating hydrogen-bond pattern.

• β-turn is a regular, tight four-residue U-turn with a specific hydrogen bond (C=O of residue 1 to N–H of residue 4).
• Domain is a large, independently folded tertiary unit, not a local backbone shape.

Alanine's methyl side chain is small enough to fit the tight helix without clashing, yet it restricts the backbone enough to favour the helical Φ/Ψ angles. On the lecture's helix-propensity table (energy penalty for placing a residue in a helix) alanine is the reference at 0.

• Glycine is smaller still, but its flexibility makes it lose entropy when held in a helix (penalty 1.00 kcal/mol).
• Proline is the worst (3.16 kcal/mol): the helix breaker.

In a helix every residue's N–H donates a hydrogen bond to the C=O four back. Proline's nitrogen is bonded to its own side chain, so it has no hydrogen to donate, and its ring fixes Φ at an angle that does not fit the helix. Proline is therefore never found inside an α-helix, only at its ends and in bends.

• Glycine has no ring at all (R = H); it is a weak helix former because it is too flexible.
• Charged: proline's side chain is nonpolar and uncharged.

The scale lists the energy cost of placing each residue in a helix, relative to alanine (0). Proline cannot fit (rigid ring, no N–H); glycine is so flexible that pinning it into a helix costs entropy. The same two residues are what build β-turns.

• Alanine and leucine are at the top of the table (0.00 and 0.21): strong helix formers.
• Tryptophan and tyrosine sit in the middle (~0.5); the slide notes they are more often found in β-sheets.

Haemoglobin and myoglobin chains are all-α proteins, so their fold depends on intact helices. Proline's ring cannot adopt helical angles and lacks the N–H the helix needs, so it kinks the helix at the mutation. Unstable haemoglobins of this kind tend to denature and precipitate in red cells.

• Disulfide bond: only cysteine forms disulfides; proline cannot.
• Better O₂ delivery would need a specific shift in O₂ affinity, not a broken helix.

In a helix the side chains crowd together around the tight spiral; bulky rings clash. In a β-sheet the chain is extended and successive side chains alternate above and below the sheet, so there is more room.

• Rings form the inter-strand hydrogen bonds: sheet hydrogen bonds are backbone C=O to N–H.
• Covalent cross-links: only cysteine disulfides cross-link chains covalently.

Note: the same lecture also says 'small amino acids are common, large amino acids destabilise β-sheets' (true for very tightly stacked sheets such as silk). The point tested is the slide's: aromatic residues favour sheets over helices.

A β-turn spans four residues and lets the chain fold back on itself, connecting antiparallel β-strands and making the protein compact. Glycine's tiny R group allows the sharp angles, and proline's ring naturally kinks the chain.

• Cys and Met: cysteine makes disulfide bonds and methionine is the start residue; neither is a turn-former.
• Trp and Tyr: bulky aromatic rings are too big for a tight turn.

Both helix and sheet are secondary structures held by C=O···H–N hydrogen bonds. In a sheet they link adjacent strands; in a helix they link residues four apart in the same chain. Converting one to the other breaks one set and forms the other, without touching covalent bonds. The reverse switch (helix → sheet) is what happens in amyloid and prion diseases.

• Peptide bonds make the primary sequence; breaking them would cut the protein.
• Disulfide bonds are tertiary side-chain cross-links, not part of secondary structure.

Tertiary structure is the overall fold of a chain. Within it, helices and strands assemble into motifs, and motifs into domains that often fold independently and carry one function. The globin fold is eight α-helices; green fluorescent protein is eleven β-strands forming a barrel ('β-can') around its chromophore.

• Separate chains are subunits (quaternary), not domains.
• Swapped examples: globins contain no β-sheet.

Four are non-covalent; the disulfide bond is the one covalent cross-link. Mnemonic 'HHIDM': Hydrophobic, Hydrogen, Ionic, Disulfide, Metal.

• Phosphodiester bonds join nucleotides in DNA/RNA.
• Peptide and glycosidic bonds: peptide bonds make primary structure; glycosidic bonds join sugars.

Quaternary structure uses the same forces minus the disulfide bond (non-covalent only).

Tertiary forces act between side chains that may be far apart in the sequence but close in space: hydrophobic interactions, hydrogen bonds, ionic bonds (salt bridges), disulfide bonds and metal-ion coordination. Peptide bonds link neighbouring residues along the backbone and are the same whether the protein is folded or unfolded; denaturing a protein breaks the tertiary forces but leaves the peptide bonds intact.

• Ionic bonds, e.g. Asp–Lys, are a tertiary force.
• Metal ions, e.g. zinc in zinc fingers, are a tertiary force.

Hydrophobic interactions are not true bonds: nonpolar side chains gather because this releases the ordered water that would otherwise surround them (the hydrophobic effect). This is the main driving force of folding. The lecture's example shows isoleucine and leucine side chains packed against each other.

• Serine and threonine have –OH groups: they form hydrogen bonds.
• Aspartate and lysine carry opposite charges: they form an ionic bond.

A hydrogen bond forms when an H on an electronegative atom (O or N) is attracted to a lone pair on another O or N. Serine is polar uncharged, so it cannot form a salt bridge, but its hydroxyl readily hydrogen-bonds with charged or polar partners.

• Ionic bond needs two opposite full charges, e.g. aspartate with lysine; serine is uncharged.
• Disulfide bond needs two cysteines.

At pH 7.4 Asp and Glu carboxylates are −1 and Lys and Arg are +1; when a negative and a positive side chain come close, they attract. Ionic bonds are also called electrostatic interactions or salt bridges, and they are sensitive to pH because pH changes the charges.

• Leucine and valine are nonpolar: hydrophobic interaction.
• Lysine and arginine are both positive: they repel.

Two cysteine sulfhydryls are oxidised to a disulfide (the paired residue is sometimes called cystine). Disulfides are common in secreted and extracellular proteins (insulin, immunoglobulins), where they lock the fold against denaturation. Insulin has two interchain disulfides between its A and B chains and one within the A chain.

• Methionine contains sulfur, but as a thioether with no free –SH, so it cannot form disulfides.
• Serine has –OH, not –SH; myoglobin has no disulfide bonds.

A metal ion coordinates side chains from different parts of the chain (in zinc fingers, cysteine and often histidine side chains), pulling them together and fixing the fold. Steroid-hormone receptors (glucocorticoid, vitamin D, oestrogen receptors) use zinc fingers to bind DNA. This is a tertiary-structure interaction.

• Magnesium or iron in a zinc finger: the name gives the metal away.
• Copper in haemoglobin: haemoglobin's metal is iron in haem, and it carries O₂; plastocyanin is the copper protein.

Quaternary structure needs more than one polypeptide subunit; the subunits can be identical (insulin hexamer) or different (haemoglobin's α and β). Insulin is stored in pancreatic β-cell granules as a zinc-bound hexamer and acts as a monomer.

• Myoglobin is a single chain (monomer): no quaternary structure.
• 2α + 2γ is fetal haemoglobin, and insulin's metal is zinc, not copper.

In cooperative binding, O₂ binding to one haemoglobin subunit shifts the tetramer from the T (tense) to the R (relaxed) state and raises the affinity of the remaining subunits. That produces the sigmoidal O₂-dissociation curve, which lets haemoglobin load O₂ in the lungs and unload it in tissues.

• Only independently ignores cooperativity, the main reason haemoglobin is a tetramer.
• Myoglobin is a monomer; its O₂ curve is hyperbolic, not cooperative.

The amino acid sequence encodes the fold: which residues are hydrophobic (to be buried), which are charged or polar (to face water), where prolines and glycines put turns. A denatured protein can often refold on its own when the denaturant is removed (Anfinsen's experiment).

• Chaperones help a chain reach its native fold faster and avoid aggregation, but they do not encode the final shape.
• Disulfide bonds stabilise the fold once it forms; which cysteines pair is itself set by the sequence.

Water forms ordered 'cages' around exposed nonpolar groups. Burying those groups releases the water, raising the entropy of the solvent; that gain outweighs the loss of chain flexibility, so folding is favourable. The folded protein settles at its lowest free energy. Hydrogen bonds, ionic interactions and van der Waals forces then fine-tune the fold.

• Hydrogen bonding stabilises the fold but is not the main driver; polar side chains mostly stay on the surface.
• Nonpolar on the surface is the reverse of what happens in a soluble protein.

Folding is spontaneous because the native state has lower free energy (ΔG < 0) than the unfolded chain, mainly thanks to the hydrophobic effect. Folding pathways can get trapped in local energy minima, and chaperones use ATP to help chains escape them.

• Highest free energy would be the least stable state.
• Highest chain entropy describes the unfolded chain; folding lowers the chain's own entropy (offset by the water's gain).

Their name comes from their induction by heat and other stresses that make proteins unfold. ATP hydrolysis drives repeated cycles of binding and release, which helps a folding chain escape local energy minima and avoid aggregation.

• Ubiquitin ligases tag proteins for proteasomal degradation; they are the disposal system, not the folding helpers.
• GTP is used by G proteins and in translation, not by Hsp70/Hsp60 folding cycles.

A newly made chain leaving the ribosome exposes hydrophobic stretches before the rest of the protein exists to bury them. Hsp70 clamps onto those stretches (with Hsp40 helping), using ATP, and releases them in cycles so the chain can fold.

• Cleaves: chaperones do not cut proteins; proteases do.
• Encloses as a template is Hsp60 (the barrel-shaped chaperonin).

Hook: Hsp70 = holds the chain (binds); Hsp60 = a 'chamber' around it.

Hsp60 forms a barrel-shaped chamber. The chain folds inside this protected space, away from other proteins it might stick to, with ATP-driven cycles of opening and closing.

• Degrades: degradation is the job of the proteasome, not chaperonins.
• Binds hydrophobic stretches at the ribosome is Hsp70.

A mutation can change the sequence so the native fold is no longer the most stable state (e.g. familial prion disease, where the mutant protein folds into PrP^Sc more easily). Even a normal sequence can misfold if folding is disrupted (stress, chaperone overload, ageing).

• Glycosylation and phosphorylation are normal post-translational modifications.
• Ubiquitination marks misfolded proteins for destruction; it is a consequence, not a cause.

Chaperones first try to refold a misfolded chain. If they fail, it is tagged with ubiquitin and destroyed by the proteasome, or aggregates are removed by autophagy. Disease arises when misfolded proteins resist this clearance and form insoluble aggregates or toxic fibrils.

• Secreted: quality control in the endoplasmic reticulum holds back misfolded secretory proteins rather than exporting them.
• Amyloid plaque is the pathological exception, not the usual fate.

In amyloid, β-strands from many molecules stack into long, protease-resistant fibrils, held by inter-strand hydrogen bonds. Amyloid β, α-synuclein, TDP-43, polyglutamine proteins and prions all follow this pattern.

• Soluble monomers only: fibrils are insoluble aggregates; that is why they deposit as plaques.
• α-Helix: the disease change is helix → sheet; a drug that pushes the protein back to α-helix is the therapeutic idea.

Aβ is a 40- or 42-residue fragment cut from amyloid precursor protein (APP). It spontaneously adopts β-sheet structure and aggregates into fibrils that accumulate as plaques between neurons.

α-Synuclein is a neuronal protein that misfolds into β-sheet-rich aggregates inside dopaminergic neurons of the substantia nigra.

• Huntingtin with an expanded polyglutamine tract causes Huntington disease.
• Amyloid β is the Alzheimer protein.

TDP-43 is an RNA/DNA-binding protein that normally lives in the nucleus; in ALS it misfolds and aggregates in the cytoplasm of motor neurons.

• α-Synuclein: Parkinson disease.
• Amyloid β: Alzheimer disease.

An expanded CAG repeat in the gene adds a long run of glutamine residues to huntingtin. The polyglutamine tract promotes β-sheet aggregation in neurons. ('Q' is the one-letter code for glutamine.)

• Prion diseases are transmissible spongiform encephalopathies caused by PrP^Sc.
• Synucleinopathies (Parkinson disease) involve α-synuclein.

The expanded CAG repeat in the gene codes for glutamine (CAG = Gln), producing a long polyglutamine tract that makes the protein aggregate.

• Glutamate is E (the acid; glutamine is its amide).
• Asparagine is N.

APP is a membrane protein. In the amyloidogenic pathway β-secretase cuts outside the membrane and γ-secretase cuts within it, releasing Aβ; the 42-residue form is the most aggregation-prone. Aβ adopts β-sheet structure and forms extracellular fibrils and plaques.

• α + β, ending in tangles: tangles are intracellular tau, not Aβ.
• α + γ: α-secretase cuts inside the Aβ region, so it prevents Aβ forming.

Cutting through the middle of the Aβ region destroys the sequence that would become the toxic peptide, so the α-secretase (non-amyloidogenic) route is protective. Only when β- and γ-secretase act instead is intact Aβ released.

• Pathological cut: that is β- plus γ-secretase.
• Usual cut that releases Aβ contradicts itself: the usual (α) cut destroys Aβ.

The review slide splits Alzheimer disease into sporadic (ApoE gene) and familial (the 'amyloid hypothesis': APP and its processing). The ε4 allele of apolipoprotein E raises risk and lowers age of onset.

• APP mutations (with presenilins) cause familial early-onset disease.
• SNCA encodes α-synuclein (Parkinson disease).

The prion protein gene is a normal part of the genome. Disease comes from a change of shape alone: α-helical PrP^C refolds into β-sheet-rich PrP^Sc. Prions are proteinaceous infectious agents that cause the transmissible spongiform encephalopathies.

• Extra disulfide bonds: the difference is conformation, not covalent change.
• Different sequence: sporadic and acquired cases have the normal sequence.

Each PrP^Sc molecule recruits PrP^C and refolds it, so the abnormal form multiplies exponentially without any genetic material. The aggregates resist proteolysis (like other amyloid fibrils), accumulate and destroy neurons, giving the spongy brain.

• Own nucleic acid: prions have none; that is what makes them unique among infectious agents.
• Soluble α-helical, templating back to PrP^C reverses the direction of the disease.

• Sporadic: most cases; PrP^C converts spontaneously.
• Inherited: a point mutation lowers the energy barrier for folding into PrP^Sc; autosomal dominant.
• Acquired: eating infected beef (variant CJD from bovine spongiform encephalopathy), cadaver-derived human growth hormone, contaminated instruments or grafts, ritual cannibalism (kuru).

The wrong options misplace 'most cases' and give the wrong inheritance pattern.

All are transmissible spongiform encephalopathies caused by PrP^Sc. Hook: sheep scrape themselves against fences; bovine = cattle; deer waste away.

The wrong options rotate scrapie, chronic wasting disease and bovine spongiform encephalopathy among the animals.

Globular proteins bury hydrophobic residues and display polar ones, so they dissolve in plasma and cytosol, where they work. Fibrous proteins assemble into long cables and sheets (collagen fibrils, keratin filaments) that must stay solid to bear load.

The wrong options swap the pairing or make both the same.

A repeating sequence builds a repeating structure, ideal for a long cable (collagen's Gly-X-Y repeat makes the triple helix). A globular protein needs a unique, irregular sequence to fold into a specific shape with a binding or active site.

The wrong options swap the pairing or make both repetitive.

A globular protein's function depends on a delicate tertiary fold held by many weak interactions; heat or a pH change that alters side-chain charges can unfold it (denaturation) and destroy its activity. Fibrous proteins are built for mechanical stability and keep their structure better.

The wrong options reverse the pairing or make both equal.

These form structural fibres: connective tissue (collagen, elastin), hair and skin (keratin), muscle filaments (actin, myosin) and clots (fibrin).

• Insulin and catalase are globular.
• Myoglobin and albumin are globular.

Textbook note: actin monomers (G-actin) are globular and polymerise into fibrous F-actin; the lecture table lists actin as fibrous.

Each is a compact, soluble protein with a specific function: O₂ transport, hormone signalling, enzyme (breaks down H₂O₂), antigen binding.

• Keratin is fibrous.
• Collagen is fibrous.

pH expresses [H⁺] (in mol/L) on a compressed scale: take the base-10 logarithm and change its sign. Blood [H⁺] is about 4 × 10⁻⁸ M, which becomes the handier number 7.4.

• log[H⁺] without the minus sign would give negative numbers (about −7.4 for blood); the minus sign is what makes pH positive and makes it fall as acidity rises.
• −ln[H⁺] uses the natural logarithm; pH is defined with log₁₀, which is why one pH unit equals a tenfold change.

Because pH = −log[H⁺], moving one pH unit multiplies or divides [H⁺] by 10, two units by 100, three by 1000. The minus sign reverses the direction: high [H⁺] = low pH = more acidic; low [H⁺] = high pH = more basic.

• Lower pH = less H⁺ has the direction backwards; this is the commonest trap (the school asks "which is NOT true: a low pH means a low [H⁺]").
• Twofold is the change for about 0.3 pH units (log 2 ≈ 0.3), not for one whole unit.

At pH 7.0, [H⁺] = 10⁻⁷ M; at pH 5.0, [H⁺] = 10⁻⁵ M. 10⁻⁵ / 10⁻⁷ = 10² = 100.

• Risen 2-fold treats the scale as linear ("two units = double"); pH is logarithmic.
• Fallen 100-fold has the right size but the wrong direction: a lower pH is more acidic, so [H⁺] rises.

Same logic the other way: pH 7.4 → 8.4 is a tenfold fall in [H⁺].

H₂O ⇌ H⁺ + OH⁻. The product [H⁺][OH⁻] is fixed at 1 × 10⁻¹⁴ (the ion product of water). In pure water the two ions are made in equal amounts, so each is the square root, 1 × 10⁻⁷ M, and pH = −log(10⁻⁷) = 7, neutral.

• 10⁻¹⁴ M is the product of the two concentrations, not each one.
• 10⁷ M drops the minus sign of the exponent: that would be an impossibly huge concentration.

The primer’s "Goldilocks zone" table: normal [H⁺] at pH 7.4 is 4.0 × 10⁻⁸ M; at 7.1 it is 7.9 × 10⁻⁸ M (+99%); at 7.0 it is 1.0 × 10⁻⁷ M (+151%); at 7.7 it is −50%. So the narrow-looking blood pH window hides large swings in [H⁺].

• About half is the direction for a pH rise of 0.3 (pH 7.7).
• Ten times would need a full pH unit (7.4 → 6.4).

HA ⇌ H⁺ + A⁻. The acid (protonated form) gives up H⁺; the deprotonated form A⁻ can take a proton back, so it is a base, the conjugate base of HA (acetic acid → acetate, lactic acid → lactate, carbonic acid → bicarbonate).

• Proton acceptor is the definition of a base.
• Electron donor belongs to redox chemistry (and the Lewis definition of a base), not to the proton definition used here.

B + H⁺ ⇌ BH⁺. Example from the primer: ammonia, NH₃ + H⁺ ⇌ NH₄⁺. The protonated form BH⁺ can give the proton back, so it is an acid, the conjugate acid of B.

• Proton donor describes an acid (BH⁺ giving up its proton is acting as an acid).
• Electron acceptor is redox (oxidising agent) language, not the proton definition.

Every weak acid/base reaction is a pair: weak acid ⇌ H⁺ + weak base. For ammonia: NH₄⁺ (proton donor, acid) ⇌ H⁺ + NH₃ (proton acceptor, base). The primer stresses that a molecule can be a weak acid or base regardless of its charge: NH₄⁺ is a positively charged weak acid.

• Conjugate base is what is left after an acid loses a proton; NH₄⁺ has gained one.
• Strong acid: NH₄⁺ dissociates only partly (it is the weak conjugate acid of a weak base), unlike HCl.

This is the form in which the kidney excretes H⁺ in urine.

"Strong" describes the extent of dissociation, not the concentration. HCl is essentially 100% H⁺ + Cl⁻ in water, so there is no meaningful HA left and no equilibrium to describe.

• Dissociates only partly is the definition of a weak acid or base.
• High concentration is a different property: concentrated acetic acid is still a weak acid (pK_a 4.8) because only a small fraction of its molecules dissociate.

Weak acids (acetic, lactic, carbonic acid) and weak bases (NH₃) exist as a mixture of protonated and deprotonated forms. Because both forms are present, the ratio between them can be described by the Henderson–Hasselbalch equation, and the pair can act as a buffer.

• Complete, one-way dissociation defines a strong acid (HCl).
• No dissociation at all would not make it an acid; a weak acid does release some H⁺.

The primer’s examples: strong = HCl (acid), NaOH (base), which dissociate completely; weak = acetic acid, lactic acid (acids) and NH₃ (base), which dissociate incompletely. The school asks this as "acetic acid dissociates completely in water: true or false?" (false).

• The list with hydrochloric acid, acetic acid, ammonia slips in one strong acid.
• The list with HCl, NaOH, lactic acid has two strong electrolytes.

K_a is the dissociation constant: high K_a = more H⁺ released = stronger acid. Taking −log flips the scale, so high K_a = low pK_a. The pK_a is also the pH at which the acid is exactly half dissociated: an acid with a low pK_a is already half dissociated at a very acidic pH.

• Weaker acid goes with a high pK_a (low K_a).
• Stronger base: a low pK_a describes the acid; its conjugate base is actually a weaker base.

The primer’s pK_a table: pyruvic acid 2.4, α-COOH of amino acids 2.2, aspartate R-group 3.7, formic acid 3.8, lactic acid 3.9, acetic acid 4.8, carbonic acid 6.4, α-NH₃⁺ 9.4. At pH 7.4 lactic acid is therefore almost entirely lactate, which is why lactic acidosis adds a free unmeasured anion to blood.

• Lactic 4.8, acetic 3.9 swaps the two values.
• 6.1 and 6.8 are the pK_a values of the bicarbonate and phosphate buffers.

Lower pK_a = higher K_a = more dissociated at any given pH. Pyruvic acid at 2.4 is a much stronger (though still weak) acid than acetic acid at 4.8.

• Acetic acid has a pK_a 2.4 units higher, so it is roughly 250 times weaker (10^2.4).
• Carbonic acid has the highest pK_a of the three, so it is the weakest acid here.

K_a is the equilibrium constant for deprotonation of a weak acid, written like any K_eq: product concentrations over reactant concentration (the same logic as the ion product of water). Taking −log of both sides gives pK_a = pH − log([A⁻]/[HA]), which rearranges to the Henderson–Hasselbalch equation. A large K_a means more dissociation, so a small pK_a means a stronger acid. For a weak base the constant is written for its conjugate acid, BH⁺ ⇌ H⁺ + B: K_a = [H⁺][B]/[BH⁺], giving pH = pK_a + log([B]/[BH⁺]).

• [HA]/([H⁺][A⁻]) is upside down: it is the constant for the reverse (association) reaction, H⁺ + A⁻ → HA.
• [H⁺][HA]/[A⁻] swaps the acid and its conjugate base; it does not follow from the reaction as written.

The Henderson–Hasselbalch (HH) equation links the pH of a solution to the ratio of the two forms of a weak acid. For a weak base it reads pH = pK_a + log([B]/[BH⁺]): again the deprotonated form on top.

• log([HA]/[A⁻]) inverts the ratio; it would make pH fall as the base form rises.
• pK_a = pH + log([A⁻]/[HA]) puts the log term on the wrong side: rearranged correctly, pK_a = pH − log([A⁻]/[HA]).

Hook: "base over acid", as in A over HA.

Put pH = pK_a into the HH equation: 0 = log(ratio), and log 1 = 0. This is the midpoint of the titration curve (0.5 equivalents of OH⁻ added), the point of maximum buffering.

• Ten times is the ratio when pH is one unit above the pK_a.
• Twice corresponds to pH about 0.3 above the pK_a (log 2 ≈ 0.3).

Every unit of pH above the pK_a multiplies [A⁻]/[HA] by 10 (pH = pK_a + 2 → 100 : 1); every unit below divides it by 10.

• 1 : 10 is the ratio one unit below the pK_a.
• 2 : 1 treats the log scale as linear; it is the ratio at about 0.3 units above the pK_a.

Plug into pH = pK_a + log([A⁻]/[HA]). The base form is ten times the acid form, log 10 = 1, so the pH sits one unit above the pK_a.

• 2 comes from inverting the ratio (log 0.1 = −1): acid on top instead of base.
• 13 comes from adding the ratio itself (10) instead of its logarithm.