Structural Biology from Zero · 2: The Twenty Amino Acids and the Backbone

This article covers the building blocks of almost all natural proteins: the twenty amino acids, the bond that links them into a chain, and the surprisingly rigid geometry of that chain.

A protein is a linear polymer built from a repeating backbone and one of twenty standard side chains at each residue. The backbone provides regular geometry, while the side chains provide much of the chemical variation. Their sequence and the conformation of the chain together determine the structures discussed in the rest of this series.

The twenty amino acids

Every one of the twenty standard amino acids follows the same template. At the center sits the α-carbon, or $C\alpha$ , bonded to an amino group ( $-\mathrm{NH_2}$ ), a carboxyl group ( $-\mathrm{COOH}$ ), a hydrogen, and a variable side chain written $\mathrm{R}$ . Changing $\mathrm{R}$ changes the amino acid while the rest of the template remains shared.

The common amino-acid scaffold. The $\mathrm{R}$ group is the part that changes between the twenty standard amino acids; in water near pH 7.4, the $-\mathrm{NH_2}$ and $-\mathrm{COOH}$ groups become $-\mathrm{NH_3^+}$ and $-\mathrm{COO^-}$ .

Because the $C\alpha$ carries four different substituents (for every amino acid except one), it is a chirality center — it comes in left- and right-handed mirror images, exactly like your two hands. Life, almost without exception, uses only the left-handed form, the L-amino acids. This is not a deep law of physics; it is a frozen historical accident that all of biochemistry inherited. The lone exception to the chirality is glycine, whose side chain is just a second hydrogen, making its $C\alpha$ symmetric and achiral. Hold on to glycine — its smallness and flexibility will keep mattering.

In water at the pH of your cells (about 7.4), amino acids don't actually carry a neutral amino group and a neutral acid. The carboxyl has given up its proton to become $-\mathrm{COO^-}$ , and the amino group has grabbed one to become $-\mathrm{NH_3^+}$ . The molecule is a zwitterion: positive at one end, negative at the other, neutral overall. This matters the moment we start talking about charge.

Reading the alphabet by chemistry

The twenty amino acids become easier to use when grouped by side-chain chemistry. Each side chain contributes characteristic size, polarity, charge, and conformational preferences to the folded structure.

Nonpolar / hydrophobic. These side chains are made mostly of carbon and hydrogen, carry no charge, and do not like water. Glycine (just $-\mathrm{H}$ ), alanine, valine, leucine, isoleucine, methionine, and proline. Add the bulky aromatic phenylalanine and tryptophan here too. In water, these are the residues that get buried in the protein's interior — a fact that, as we'll see in Part 3, is the single most important force in folding.

Polar, uncharged. Serine, threonine, cysteine, asparagine, glutamine, and tyrosine. These carry $-\mathrm{OH}$ , $-\mathrm{SH}$ , or amide groups that can donate or accept hydrogen bonds. They are comfortable at the water-facing surface, and they show up constantly in active sites doing chemistry.

Positively charged (basic). Lysine, arginine, and histidine. At physiological pH, lysine and arginine are reliably protonated and positive; histidine sits right at the tipping point, which makes it biology's favorite pH-sensitive switch (more on that below).

Negatively charged (acidic). Aspartate and glutamate — carboxylic acid side chains that lose their proton and sit as $-\mathrm{COO^-}$ at physiological pH.

A few residues deserve individual attention because they break the rules:

Glycine is the flexibility residue. With no side chain to get in the way, its backbone can adopt angles no other residue can, so it turns up wherever the chain needs to make a tight turn.
Proline is the rigidity residue. Its side chain loops back and bonds to its own backbone nitrogen, forming a ring that locks part of the backbone and removes the amide hydrogen. Proline kinks chains and breaks helices.
Cysteine carries a reactive thiol ( $-\mathrm{SH}$ ). Two cysteines can be oxidized together into a covalent disulfide bond, the only common covalent cross-link within a folded protein — a molecular staple.

Here is the full alphabet, sorted the way I actually think about it:

| Amino acid | 3-letter | 1-letter | Class | Side-chain note | |---|---|---|---|---| | Glycine | Gly | G | Nonpolar | No side chain; maximally flexible | | Alanine | Ala | A | Nonpolar | Smallest real side chain (methyl) | | Valine | Val | V | Nonpolar | Branched, bulky | | Leucine | Leu | L | Nonpolar | Branched, common in cores | | Isoleucine | Ile | I | Nonpolar | Branched isomer of Leu | | Methionine | Met | M | Nonpolar | Sulfur-containing; start codon | | Proline | Pro | P | Nonpolar | Ring locks the backbone | | Phenylalanine | Phe | F | Nonpolar (aromatic) | Benzene ring | | Tryptophan | Trp | W | Nonpolar (aromatic) | Largest; indole ring | | Serine | Ser | S | Polar | $-\mathrm{OH}$ , small | | Threonine | Thr | T | Polar | $-\mathrm{OH}$ , branched | | Cysteine | Cys | C | Polar | $-\mathrm{SH}$ ; forms disulfides | | Tyrosine | Tyr | Y | Polar (aromatic) | Phenol; ionizes at high pH | | Asparagine | Asn | N | Polar | Amide | | Glutamine | Gln | Q | Polar | Amide, one carbon longer | | Aspartate | Asp | D | Acidic ( $-$ ) | Carboxylate, pKa ≈ 3.9 | | Glutamate | Glu | E | Acidic ( $-$ ) | Carboxylate, pKa ≈ 4.1 | | Lysine | Lys | K | Basic ( $+$ ) | Amine, pKa ≈ 10.5 | | Arginine | Arg | R | Basic ( $+$ ) | Guanidinium, pKa ≈ 12.5 | | Histidine | His | H | Basic ( $+$ ) | Imidazole, pKa ≈ 6.0 |

Twenty letters still produce an enormous sequence space.

# How much can a 20-letter alphabet say?
alphabet = 20
for length in (5, 20, 100, 300):
    print(f"{length:>4} residues: {alphabet**length:.2e} possible sequences")
# 100 residues -> 1.27e+130 sequences — more than the number of atoms
# in the observable universe (~1e80), by fifty orders of magnitude.

A typical protein is a few hundred residues long, so the space of possible sequences is combinatorially vast. Evolution samples only a small, structured subset of it. Protein design and machine learning both attempt to characterize and navigate that subset.

Charge as a function of pH

Calling aspartate "negative" and lysine "positive" is a useful shorthand, but it hides something we'll need later. Whether an ionizable group carries its charge depends on the pH of its surroundings, through the Henderson–Hasselbalch relation. For an acidic group that loses a proton ( $\mathrm{HA} \rightleftharpoons \mathrm{H^+ + A^-}$ ),

$\mathrm{pH} = \mathrm{p}K_a + \log_{10}\frac{[\mathrm{A^-}]}{[\mathrm{HA}]},$

which rearranges to a clean expression for the fraction of molecules in the deprotonated (charged, for an acid) form:

$f_{\text{deprotonated}} = \frac{1}{1 + 10^{\,\mathrm{p}K_a - \mathrm{pH}}}.$

Sanity-check the limits, because you should always sanity-check a formula like this: when $\mathrm{pH} = \mathrm{p}K_a$ the exponent is zero and $f = \tfrac{1}{2}$ , exactly the definition of $\mathrm{p}K_a$ (half deprotonated). When $\mathrm{pH} \gg \mathrm{p}K_a$ , $f \to 1$ ; when $\mathrm{pH} \ll \mathrm{p}K_a$ , $f \to 0$ . Good.

Histidine is especially useful in acid–base chemistry because its side-chain $\mathrm{p}K_a \approx 6.0$ lies near physiological pH. Changes in its local environment can shift the balance between protonated and neutral states, allowing histidine to shuttle protons in many enzyme active sites. Aspartate, glutamate, lysine, and arginine usually carry their conventional charges near pH 7.4, although burial, nearby charges, and hydrogen bonding can shift any residue's $\mathrm{p}K_a$ .

Sum the signed charge over all of a peptide's ionizable groups and you get its net charge as a function of pH; the pH where that net charge crosses zero is the isoelectric point, $\mathrm{pI}$ — a number every biochemist uses to purify proteins.

import numpy as np

# pKa values: (pKa, +1 if the protonated form is charged else 0-based sign)
# Acids are negative when deprotonated; bases are positive when protonated.
groups = [
    ("C-terminus", 2.0, -1),  # acidic
    ("Asp",        3.9, -1),
    ("N-terminus", 9.0, +1),  # basic
    ("Lys",       10.5, +1),
]

def net_charge(pH):
    q = 0.0
    for _, pKa, sign in groups:
        if sign < 0:                      # acid: charged (–) when deprotonated
            q -= 1 / (1 + 10**(pKa - pH))
        else:                             # base: charged (+) when protonated
            q += 1 / (1 + 10**(pH - pKa))
    return q

pH = np.linspace(0, 14, 1401)
charge = np.array([net_charge(p) for p in pH])
pI = pH[np.argmin(np.abs(charge))]
print(f"Net charge at pH 7.4: {net_charge(7.4):+.2f}")   # ~ 0.00
print(f"Isoelectric point pI ≈ {pI:.1f}")                # ~6.5, midway
# between the Asp (3.9) and N-terminus (9.0) pKa's that bracket neutrality.

Keep this in the back of your mind: a protein's surface is a patchwork of charges that can be tuned by pH, and those charges will form salt bridges — the electrostatic contacts we'll meet in Part 3.

The peptide bond: a flat, rigid link

Now we join the amino acids. The carboxyl of one and the amino group of the next react, spitting out a water molecule and forming a peptide bond — an amide linkage. Do this repeatedly and you get a polypeptide: a backbone of the repeating unit $(-\mathrm{N}-C\alpha-\mathrm{C}-)$ , with side chains hanging off each $C\alpha$ . The chain has a direction. One end has a free amino group (the N-terminus), the other a free carboxyl (the C-terminus), and by universal convention we read and write sequences N-to-C, the same direction the ribosome builds them.

Here is the first genuinely non-obvious fact about the backbone, and it controls everything that follows: the peptide bond is planar and rigid. You might expect the $\mathrm{C-N}$ amide bond to rotate freely, the way single bonds usually do. It does not. The lone pair on the nitrogen delocalizes onto the neighbouring carbonyl, giving the $\mathrm{C-N}$ bond roughly 40% double-bond character:

$\mathrm{O=C-N} \;\longleftrightarrow\; \mathrm{O^- -C=N^+}.$

A double bond cannot twist without breaking the $\pi$ overlap, so rotating around the peptide bond costs a large barrier — around $20\ \mathrm{kcal/mol}$ ( $\approx 84\ \mathrm{kJ/mol}$ ), far more than thermal energy at body temperature ( $RT \approx 0.6\ \mathrm{kcal/mol}$ ). The consequence is that the six atoms of each peptide unit — the $C\alpha$ and $\mathrm{C{=}O}$ of one residue, and the $\mathrm{N-H}$ and $C\alpha$ of the next — are locked into a single flat plane. You can measure it in the numbers: the amide $\mathrm{C-N}$ bond is about $1.33\ \text{Å}$ , noticeably shorter than a normal $\mathrm{C-N}$ single bond ( $1.45\ \text{Å}$ ) and longer than a full double bond, exactly what "partial double bond" predicts.

The backbone can therefore be viewed as a chain of comparatively rigid, planar peptide units connected by rotatable bonds around the $C\alpha$ atoms. This geometry sharply reduces the conformational space available to a protein chain.

Two angles to rule them all

If each peptide plate is rigid and the only hinges are the $C\alpha$ atoms, then the shape of the whole backbone is determined by the rotation angles at those hinges. There are two rotatable bonds per residue, and they have names you will see for the rest of your life in this field:

$\varphi$ (phi) — rotation about the $\mathrm{N}-C\alpha$ bond.
$\psi$ (psi) — rotation about the $C\alpha-\mathrm{C}$ bond.

There is a third angle, $\omega$ (omega), around the peptide bond. It is usually near $180°$ , the trans configuration, because resonance restricts rotation and trans avoids steric crowding. Peptide bonds preceding proline have a larger cis population than other peptide bonds, although trans remains favored. Most backbone descriptions therefore treat $\omega$ as fixed unless cis–trans isomerization is relevant.

So to a very good approximation, the entire three-dimensional path of a protein backbone is specified by the list of $(\varphi, \psi)$ pairs, one per residue. Two numbers per residue. That is an astonishing compression, and it is why structural biologists talk about backbone conformation almost entirely in terms of these angles.

A dihedral angle is the angle between two planes, each defined by three consecutive atoms. It can be calculated directly from atomic coordinates:

import numpy as np

def dihedral(p0, p1, p2, p3):
    """Signed dihedral angle (degrees) about the p1-p2 bond."""
    b0, b1, b2 = p0 - p1, p2 - p1, p3 - p2
    b1 /= np.linalg.norm(b1)
    # components of b0 and b2 perpendicular to the central bond b1
    v = b0 - np.dot(b0, b1) * b1
    w = b2 - np.dot(b2, b1) * b1
    x = np.dot(v, w)
    y = np.dot(np.cross(b1, v), w)
    return np.degrees(np.arctan2(y, x))

# phi uses C(i-1), N(i), CA(i), C(i);  psi uses N(i), CA(i), C(i), N(i+1).
# Run this over every residue of a PDB structure and you recover its
# (phi, psi) list — the backbone's entire fold, two numbers at a time.

The Ramachandran plot: geometry says no

Not every $(\varphi, \psi)$ combination is physically possible. Rotate to the wrong angles and backbone atoms — or the side chain and the carbonyl oxygen — would have to occupy the same space, which they cannot. In 1963 G. N. Ramachandran worked out, from nothing more than hard-sphere atomic radii, which combinations of $\varphi$ and $\psi$ are sterically allowed. Plot $\varphi$ on one axis and $\psi$ on the other, and the allowed combinations cluster into a few islands in a sea of forbidden angles. This is the Ramachandran plot, and it is one of the most quietly powerful diagrams in all of biology: pure geometry, no energy minimization, no experiment — and yet it predicts the two great structural motifs of proteins before you've even mentioned them.

Two islands dominate, both at negative $\varphi$ :

The right-handed α-helix region, around $\varphi \approx -60°,\ \psi \approx -45°$ .
The β-sheet region, around $\varphi \approx -120°,\ \psi \approx +130°$ — an extended conformation.

These clusters show how steric constraints contribute to the regularity developed further in Part 4. Glycine, with no side chain beyond hydrogen, can occupy regions unavailable to most other residues, including the left-handed helix region at positive $\varphi$ . Proline's ring confines it to a narrower range near $\varphi \approx -63°$ . The Ramachandran plot is also a useful validation tool: residues outside the expected regions deserve inspection because they may reflect unusual local geometry, refinement problems, or modeling errors.

The explorer below lets you feel this directly: drag a point across the $(\varphi, \psi)$ plane and watch which backbone conformation those two numbers imply — and whether geometry even allows it — with the classic favored regions and the helix and sheet basins drawn in. Toggle glycine to see the forbidden regions open up into their mirror images.

Interactive. Drag the marker or pick a preset to set the backbone dihedrals (φ, ψ); the panel reports whether the conformation is sterically allowed and which secondary-structure motif it belongs to. Favored regions are schematic contours after Ramachandran et al. (1963). Opens full-screen in a new tab.

The α-helix and β-sheet basins occupy distinct regions of the plot. Moving between them requires a substantial change in backbone conformation. This map provides the geometric basis for the next several articles.

The side chains have angles too

I've made a lot of the backbone's two angles, but the side chains are not rigid either. Every bond in a side chain that can rotate defines its own dihedral angle, named $\chi_1, \chi_2, \chi_3, \dots$ counting outward from the $C\alpha$ . Glycine and alanine have none; long residues like arginine and lysine have four. And here the Ramachandran logic repeats itself: because atoms can't overlap, the side-chain angles don't take arbitrary values either — they cluster into a small number of preferred combinations called rotamers.

This is more than a curiosity. It means a side chain, once you know its type, has only a handful of likely conformations, and those have been tabulated into rotamer libraries compiled from thousands of high-quality structures. That discreteness is what makes side-chain modeling tractable: when a program like Rosetta packs the interior of a designed protein, or when a structure-prediction model places side chains onto a predicted backbone, it is largely choosing from this discrete rotamer menu rather than searching a continuous space. The backbone $(\varphi, \psi)$ angles set the fold; the side-chain $\chi$ angles decide how the residues actually pack against each other, and both are quantized by the same unforgiving fact that two atoms cannot be in the same place.

Twenty, and then some

Why exactly twenty? There is no law that says a protein alphabet must have twenty letters — it is another frozen accident, though not an arbitrary one. The genetic code uses three-nucleotide codons, giving $4^3 = 64$ combinations; three are stop signals and the remaining sixty-one encode the twenty amino acids, so the code is degenerate (most amino acids have several codons). The particular set of twenty looks like an evolved compromise: enough chemical variety — acids and bases, greasy and polar, big and small, rigid and flexible — to build a working catalyst out of, without so many letters that the code becomes error-prone or the cell's biosynthesis too costly. It is a small, well-chosen palette.

"Standard twenty" is also a slight simplification in two directions worth knowing about.

First, life encodes two more amino acids in special contexts: selenocysteine (the 21st, a cysteine with selenium in place of sulfur) and pyrrolysine (the 22nd), each slipped in by recoding what is normally a stop codon. They are rare but real.

Second, and far more important in practice, side chains get chemically decorated after the protein is made. These post-translational modifications — phosphorylation of serine, threonine, and tyrosine; glycosylation of asparagine and serine; methylation, acetylation, hydroxylation (the hydroxyproline that makes collagen stable is a classic case) — dramatically expand what the twenty letters can do. A single phosphate added to a serine can switch an enzyme on or off. These modifications are decisive for function and yet they are invisible in the amino-acid sequence — which is precisely why models that read only the sequence have a blind spot here, and why structural and experimental data remain indispensable. The alphabet is twenty, but the working vocabulary is much larger.

Where this leaves us

Step back and look at what the backbone actually is. A directional chain of identical, rigid, planar peptide plates, hinged at the $C\alpha$ atoms, whose entire three-dimensional shape is set by two angles per residue that are themselves boxed into a couple of small allowed regions. Onto each hinge is grafted one of twenty side chains, whose chemistry — greasy or charged, bulky or tiny, rigid or flexible — decides how the chain will arrange itself. The alphabet supplies the chemistry; the backbone supplies the geometry; the two angles supply the degrees of freedom. Everything a protein does is written in that language.

What we have not explained is why a chain picks one particular set of $(\varphi, \psi)$ angles over the $10^{130}$ others available to it — why, out of that astronomical space, a given sequence reliably folds into one specific shape, and does it in milliseconds. That is the folding problem, and it is where the forces we've been quietly cataloguing — the hydrophobic burial of nonpolar side chains, the hydrogen bonds of the backbone, the salt bridges between charges — finally come together. Next time: how a chain finds its shape.