A prologue to protein structure prediction

Proteins are a major class of biological macromolecules. They carry out many of the catalytic, structural, transport, signaling, and regulatory functions required by cells. Much of this functional diversity begins with the enormous number of possible amino-acid sequences. A sequence constrains how a polypeptide folds, moves, and interacts with other molecules, although its environment and binding partners can also affect the structures it adopts.

Reflecting their diverse functions, proteins also have diverse shapes and sizes. Some proteins, such as hemoglobin, are globular, whereas others, such as collagen, are fibrous. A protein’s structure is closely connected to what it can do [Mattaini, 2020].

How different can the overall shapes of proteins be?

The compact, globular examples and the elongated, fibrous examples make shape itself a biological variable rather than a cosmetic feature of the drawing.

Protein structure prediction asks a deceptively simple question:

Given a protein’s amino-acid sequence, what three-dimensional structure is it likely to have?

From a computer-science point of view, we want to map a 1D sequence to a 3D geometric object.

Background on amino acids

So what is an amino acid? An amino acid is a small organic molecule that can serve as a building block of proteins. The standard amino acids share an alpha carbon bonded to:

• An amino group ($\ce{NH2}$),
• A carboxyl group ($\ce{COOH}$),
• A hydrogen atom ($\ce{H}$), and
• A variable side chain ($\ce{R}$).

A common shorthand for the uncharged form is $\ce{NH2-CH(R)-COOH}$, although proline’s side chain closes back onto the amino nitrogen. Protonation states depend on the chemical environment; near physiological pH, free amino acids are commonly represented as zwitterions with positively charged amino ($\ce{NH3^+}$) and negatively charged carboxylate groups ($\ce{COO^-}$) [Reddy, 2026].

Which part of this molecular scaffold is shared, and which part is allowed to vary?

The side chain $\ce{R}$ is what mostly distinguishes one amino acid from another. Different side chains have different sizes, charges, polarities, and chemical behaviors.

For our purposes, the important idea is simple:

A protein sequence is not a sequence of interchangeable symbols. Each symbol corresponds to a chemically different residue.

What can change at the side chain while the common amino-acid scaffold remains recognizable?

Now ask the same question in three dimensions: when you replace methionine with another residue, which atoms remain part of the common backbone and which atoms change with the side chain? Use the residue codes to compare the structures, and toggle the hydrogens when they obscure the heavier-atom scaffold.

Across the choices, the amino group, $\ce{C}\alpha$, and carboxyl group remain recognizable while the side chain changes in size, branching, and chemical composition. The viewer supports geometric inspection; it does not show which conformation is most stable in a particular environment.

The peptide bond

Amino acids are connected into chains by peptide bonds. A peptide bond is the covalent bond between the carbonyl carbon of one amino acid and the amino nitrogen of the next.

For formal atom accounting, peptide-bond formation can be pictured as removing $\ce{OH}$ from the carboxyl group of one amino acid and $\ce{H}$ from the amino group of another. The remaining atoms form a $\ce{C(=O)-N}$ linkage and $\ce{H2O}$.

Which atoms are removed from the two amino acids, and which new linkage remains between the residues?

The schematic is formal atom bookkeeping: $\ce{OH}$ and $\ce{H}$ account for the water molecule, while the carbonyl carbon and amino nitrogen remain connected in the peptide group.

Does the same atom accounting remain visible in three dimensions? Toggle between the free components and formal products, and track the carbonyl carbon, amino nitrogen, and separated water molecule.

The product view adds the $\ce{C(=O)-N}$ peptide linkage and displays $\ce{H2O}$ separately. This comparison represents the formal reactants and products; it is not a time-resolved reaction mechanism.

Suppose we have the chain

Once amino acids have been incorporated into a chain, the units are called amino-acid residues or residues for short. In this example, methionine is one residue in the chain $\ce{MGSAKE}$.

N-terminus and C-terminus

Once many residues have been linked together, the result is a polypeptide chain.

A linear polypeptide chain has direction:

• The N-terminus is the end containing the terminal amino group.
• The C-terminus is the end containing the terminal carboxyl group.
• Protein sequences are conventionally written from the N-terminus to the C-terminus.

For our example,

• $\ce{M}$ is the N-terminal residue.
• $\ce{E}$ is the C-terminal residue.
• $\ce{M}$ is residue 1, $\ce{G}$ is residue 2, and so forth.

This N-terminus to C-terminus ordering is important because AlphaFold2 receives an ordered sequence, not an unordered collection of residues.

The four levels of protein structure

Before naming the structural levels, what does a folded single chain look like when we can rotate it as one three-dimensional object? The figure below shows crambin (PDB 1CRN)Show sidenoteThe Protein Data Bank, or PDB, stores experimentally determined three-dimensional structures of proteins, nucleic acids, and other biological macromolecules., a compact 46-residue plant proteinShow sidenoteThe structure contains local patterns such as $\alpha$-helices and $\beta$-strands, together with the global arrangement that packs them into one fold..

Rotating crambin reveals local helices, strands, and loops packed into one compact global fold. This is an experimental coordinate model, so it illustrates the geometric object that structure prediction targets rather than the dynamics by which a protein folds.

The terms primary, secondary, tertiary, and quaternary describe different levels of protein organization:

• The ordered amino-acid sequence is the primary structure.
• Recurring backbone patterns, such as $\alpha$-helices and $\beta$-strands, form secondary structure.
• The complete arrangement of one chain in 3D space is its tertiary structure.
• When multiple polypeptide chains assemble, their arrangement is the quaternary structure of the complex [Branden et al., 1999].

How do these four labels change the scale at which we describe the same molecular organization?

The diagram nests an ordered sequence inside local motifs, those motifs inside one chain’s fold, and folded chains inside a multi-chain assembly. These are levels of description, not four independent kinds of molecule.

Primary structure

The primary structure is the ordered 1D amino-acid sequence. Reusing our example,

This is the primary structure of the example chainShow sidenoteYou can track the current structural level in the figure below. .

Order matters. $\ce{MGSAKE}$ and $\ce{MEASKG}$ are different sequences and generally correspond to different polypeptides.

What does a primary-structure diagram specify, and what geometric information does it leave unknown?

From a machine-learning point of view, the target sequence is the starting input. It provides each residue’s amino-acid identity and order. Once the residues are indexed, we can compute sequence separation, such as $j-i$, but the corresponding separation in 3D is still unknown.

Secondary structure: local backbone patterns

Secondary structure refers to recurring local conformations of the protein backbone, commonly characterized by their backbone geometry and hydrogen-bonding patternsShow sidenote.

Which backbone patterns recur locally, before we consider the complete fold?

The two most common regular patterns are:

• $\alpha$-helix: Notice the dotted lines in the top right of the diagram. In a standard $\alpha$-helix, the carbonyl oxygen of residue $i$ hydrogen-bonds with the backbone $\ce{N-H}$ group of residue $i+4$. Repeating this pattern coils a nearby stretch of the chain into a helix.
• $\beta$-sheet: It looks like folded paper or a zig-zagging plane. It is formed by multiple segments of the protein chain (called $\beta$-strands) lining up next to each other. Those strands can be far apart in the sequence even though they are neighbors in 3D.

The important distinction: an $\alpha$-helix is built from one continuous stretch of sequence, whereas neighboring $\beta$-strands may come from distant parts of the chain.

Secondary-structure labels describe recurring backbone geometry and hydrogen-bonding patterns. A residue can therefore have a local role, such as belonging to a helix, and a global role determined by how that helix is positioned relative to the rest of the protein.

What do an $\alpha$-helix and a $\beta$-sheet look like at closer range, and what holds their repeated shapes together?

The first panel contrasts the continuous winding of an $\alpha$-helix with neighboring $\beta$-strands. The second makes the repeated backbone hydrogen bonds between strands explicit.

Tertiary structure: the complete fold of one chain

Tertiary structure is the overall three-dimensional arrangement of a single polypeptide chain. It describes how helices, sheets, loops, and side chains are positioned relative to one anotherShow sidenote.

How are local helices, sheets, and loops packed into the global fold of one chain?

Describing tertiary structure requires long-range relationships. For example:

Residue 15  ─...─...─...─...─ Residue 120

These residues are far apart in sequence, but folding may bring them close together in space:

sequence distance: large
spatial distance:  small

This is one of the central difficulties of protein-structure prediction. Local sequence neighborhoods are not enough. The model must infer:

• Which distant residues become spatial neighbors, and
• How they are oriented relative to one another.

That observation will later motivate one of AlphaFold2’s central design choices: representing relationships between pairs of residues, not only features attached to individual residues.

Quaternary structure: multiple chains together

Many functional proteins contain more than one polypeptide chain. Each chain has its own primary, secondary, and tertiary structure. The arrangement of multiple chains is called the quaternary structureShow sidenote.

For example:

Chain A + Chain B + Chain C → protein complex

In structure files, chains are commonly labelled A, B, C, and so on. A chain is also often called a subunit when it is part of a multi-chain complex.

The original AlphaFold2 system described in 2021 primarily targeted single-chain prediction [Jumper et al., 2021]. Predicting a multi-chain complex is a related problem, but it introduces additional questions:

• which chains interact
• where their interfaces lie
• how the chains are arranged

From a chain to three-dimensional geometry

The four structural levels tell us what scale we are describing. To understand the output of a structure-prediction model, we also need a more mechanical description of how the atoms are arranged.

A structure model records atomic coordinates, but those coordinates are one representation of the molecule rather than a preferred pose in space. We will approach that representation in two steps: first through the internal rotations of the chain, then through three-dimensional coordinates and local frames.

Each residue contributes three backbone atoms [Branden et al., 1999]:

• The peptide nitrogen $\ce{N}$,
• The alpha carbon $\ce{C}\alpha$, and
• The carbonyl carbon $\ce{C'}$

For residue $i$, we will write them as $\ce{N}_i$, $\ce{C}\alpha_i$, and $\ce{C'}_i$. The side chain branches from $\ce{C}\alpha_i$, while the peptide bond connects $\ce{C'}_i$ to $\ce{N}_{i+1}$.

Why is $\ce{C}\alpha$ a useful geometric anchor for a residue?

The three backbone neighbors locate $\ce{C}\alpha$ within the chain, while the fourth substituent gives most residues a definite handed arrangement. We will later use the ordered backbone atoms to construct a residue-local coordinate frame.

A backbone with rotatable joints

Bond lengths and bond angles fluctuate, but they stay close to strongly preferred values. If we temporarily hold them fixed, most of the backbone’s remaining flexibility comes from rotations around bonds. These rotations are described by torsion angles, also called dihedral angles.

A dihedral angle is determined by four consecutively bonded atoms. The first three atoms define one plane, the last three define another, and the signed angle between those planes measures the twist around the bond shared by the middle two atoms. We will use AlphaFold’s per-residue indexing, in which the peptide-bond torsion preceding residue $i$ is called $\operatorname{pre}\text{-}\omega_i$. For an internal residue $i$, the three backbone torsions are:

• $\operatorname{pre}\text{-}\omega_i$ (pre-omega) uses $\ce{C}\alpha_{i-1}-\ce{C'}_{i-1}-\ce{N}_i-\ce{C}\alpha_i$ and measures rotation around the peptide bond $\ce{C'}_{i-1}-\ce{N}_i$Show sidenoteThe IUPAC convention attaches a peptide-bond torsion to the preceding residue: $\omega_i$ uses $\ce{C}\alpha_i-\ce{C'}_i-\ce{N}_{i+1}-\ce{C}\alpha_{i+1}$. Therefore AlphaFold’s $\operatorname{pre}\text{-}\omega_i$ is the same geometric angle as IUPAC’s $\omega_{i-1}$. [IUPAC-IUB Commission on Biochemical Nomenclature, 1970].
• $\phi_i$ (phi) uses $\ce{C'}_{i-1}-\ce{N}_i-\ce{C}\alpha_i-\ce{C'}_i$ and measures rotation around $\ce{N}_i-\ce{C}\alpha_i$.
• $\psi_i$ (psi) uses $\ce{N}_i-\ce{C}\alpha_i-\ce{C'}_i-\ce{N}_{i+1}$ and measures rotation around $\ce{C}\alpha_i-\ce{C'}_i$.

With AlphaFold’s indexing:

• $\operatorname{pre}\text{-}\omega_1$ and $\phi_1$ are undefined because there is no preceding residue.
• $\psi_N$ is undefined because there is no following residue.

Which four atoms define each torsion angle, and which middle bond acts as its rotation axis?

The angles $\phi$ and $\psi$ provide most of the backbone’s conformational freedom, so we will focus on themShow sidenoteThe peptide bond has partial double-bond character, which makes it nearly planar and strongly restricts $\operatorname{pre}\text{-}\omega$. Most peptide bonds are near $180^\circ$ in the trans configuration. The cis configuration, near $0^\circ$, is uncommon but occurs more often before proline than before other residues. .

The backbone is not the whole structure. Most side chains have additional rotatable bonds described by side-chain torsion angles $\chi_1,\ldots,\chi_4$, although which angles exist depends on the residue type. Glycine and alanine have no side-chain $\chi$ angles, while longer side chains have one or more. Changing a $\chi$ angle repositions side-chain atoms without changing the backbone’s $\phi$ and $\psi$ angles [Branden et al., 1999]Show sidenoteAlthough a side-chain bond can rotate, experimentally observed side chains do not use every angle equally. For many $\chi$ angles, the observations cluster around a few recurring arrangements called rotamers. Which arrangements are favored depends on the residue type and, in some cases, on the backbone’s $\phi$ and $\psi$ angles, because different rotations can bring side-chain atoms too close to the backbone or to one another. A plausible backbone therefore does not determine one unique side-chain arrangement, but it constrains which arrangements are likely [Dunbrack Lab Team]. .

Rotating $\phi$ or $\psi$ changes the direction of the backbone, but these angles cannot vary freely. Some choices bring non-bonded atoms too close together, creating a steric clashShow sidenoteAtoms have a finite effective size. When two non-bonded atoms are forced much closer than their preferred separation, repulsion rises steeply; structural models call such an implausibly close contact a steric clash..

The same structure can have different coordinates

At the scientific level, protein structure prediction asks for a plausible three-dimensional structure of a polypeptide chain with amino-acid sequence

where $\mathcal{A}$ is the alphabet of standard residue types. For example, the six-residue sequence $\ce{MGSAKE}$ has $N=6$.

What would it mean for a model to return a structure? For each residue $i$, let $\mathcal{H}(a_i)$ be the set of heavy atoms present in residue type $a_i$. The main geometric output is

In plain language, we predict a three-dimensional coordinate for every non-hydrogen atom represented in the polypeptide chain. A simplified coordinate table looks like this:

Atom              x        y        z
Residue 1 N       ...
Residue 1 C-alpha ...
Residue 1 C       ...
Residue 1 O       ...
Residue 1 C-beta  ...
Other side-chain atoms ...
Residue 2 N       ...
...

These numbers are measured in a global coordinate system:

• a chosen origin, together with
• three perpendicular axes.

We could rotate a structure on the screen or move it to the other side of the scene without changing any bond, angle, or spatial relationship within the molecule.

Suppose every atomic coordinate $x$ is transformed in the same way:

where $Q\in\operatorname{SO}(3)$ is a rotation and $s\in\mathbb{R}^3$ is a translationShow sidenoteA matrix in $\operatorname{SO}(3)$ has orthonormal columns and determinant equal to $1$. It preserves lengths and angles without reflecting space.. The individual coordinate triples change, but the protein’s internal geometry does not.

For example, the distance between atoms $x_a$ and $x_b$ remains:

Bond lengths, bond angles, and torsion angles are likewise unchanged. The two coordinate sets therefore describe the same structure in different global poses.

Why a reflection is not another pose

An object is chiral if it cannot be placed on top of its mirror image using only rotations and translations [International Union of Pure et al.]. Your left and right hands illustrate the exact geometric distinction: they have the same pattern of distances, but no rotation of one hand makes it coincide with the other. They have opposite handedness Show sidenoteThe labels L and D describe an amino acid’s configuration by a formal relationship to L- or D-glyceraldehyde; they do not mean that the molecule literally points left or right. By convention, an unmarked amino-acid symbol in a protein sequence denotes the L configuration when the residue is chiral. Glycine is achiral. [IUPAC-IUB Joint Commission on Biochemical Nomenclature, 1984] .

The same distinction appears in amino acids. Except for glycine, the $\ce{C}\alpha$ atom in a standard amino acid is bonded to four different groups, giving the residue a particular three-dimensional handedness. Reflecting all of its coordinates reverses that arrangement. The result is the mirror-image configuration, not the original residue viewed from another direction.

A reflection preserves all pairwise distances. Distances alone therefore cannot distinguish a protein from its mirror image; a complete geometric description must retain some information about direction or handedness.

Let each residue carry its own coordinate system

Global coordinates contain the geometry we need, but they also contain an arbitrary choice we do not care about: a global origin and its axes. We would like to describe where an atom lies relative to a residue, in a way that does not change when the whole molecule is moved.

The three ordered, non-collinear backbone atoms $\ce{N}_i$, $\ce{C}\alpha_i$, and $\ce{C'}_i$ provide enough information to attach a local coordinate frame to residue $i$. We can place its origin at $\ce{C}\alpha_i$, point one axis toward $\ce{C'}_i$, and use $\ce{N}_i$ to determine the backbone plane.

There are two possible directions perpendicular to that plane, so we choose one handedness convention and use it for every residue. The main AlphaFold2 article will develop the exact construction; here, we only need the idea that every residue receives its own origin and axes.

Let the frame of residue $i$ be represented by a rotation $R_i$ and translation $t_i$. Here:

• $t_i$ is the global position of the frame’s origin.
• The columns of $R_i$ are unit vectors pointing along its three local axes.

The frame maps a point with local coordinates $u$ into global coordinates

Because $R_i$ is a rotation, $R_i^{-1}=R_i^\top$. We can therefore express a global point $x$ in residue $i$‘s frame by reversing the transformation:

This equation answers a concrete geometric question:

Where is atom $x$ when residue $i$ is used as the origin and its backbone determines the axes?

Now move the whole protein by a rotation $Q$ and translation $s$. The atom and residue frame move together:

The coordinates seen from residue $i$ do not change:

The global coordinates changed, but the atom’s position relative to the residue did not. A local frame removes the arbitrary global pose while preserving directional information that distances alone would discard.

Torsion angles and local frames now have separate roles:

• Torsion angles describe how bonded parts of the chain turn around particular bonds.
• A residue-local frame describes the position and orientation of other atoms or residues from that residue’s point of view.

Can one idealized backbone connect these two ideas: how internal torsions change its shape, and why coordinates measured in a residue-local frame ignore the molecule’s global pose?

In the Torsion angles view, the $\alpha$-helix and $\beta$-strand presets change $\phi$ and $\psi$, so the highlighted four-atom definition and the resulting backbone bend change together. In Local frame, toggling the global pose rotates and translates the whole chain while the coordinates measured from the selected residue remain fixed. The figure demonstrates these geometric relationships for an idealized short backbone; it is not a simulation of protein-folding dynamics.

What a structure-prediction model must produce

A useful prediction is more than a table of coordinates. Its atoms must form the specified sequence, respect plausible local chemistry, bring the correct distant residues together, and preserve molecular handedness. Yet its absolute position and orientation do not matter: applying one rotation and translation to the entire structure gives an equivalent answer.

AlphaFold2 encodes these requirements using residue features, pair features, local frames, and torsion angles. The next article traces how those objects become parts of a concrete neural architecture.

References