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A protein is a biological molecule made of one or more polypeptide chains: ordered amino acid residues joined by peptide bonds. Biological translation assembles a chain in the order specified by messenger RNA codons. Protein folding then brings parts of that chain into spatial relationships that support its function. See Cooper, The Cell: protein composition and structure. These processes can overlap in a biological cell; the sequence-to-shape explanation does not require waiting until biological translation finishes before any folding begins. See Cooper, The Cell: protein folding and processing.

The useful connection is from information to physical work. A protein's protein primary structure records an order; its protein tertiary structure can bring distant amino acid residues together at an active site. An enzyme uses such an arrangement to recognize a substrate and accelerate a chemical reaction. Other proteins serve as receptors, membrane transport proteins or structural material. For example, actin assembles into filaments whose mechanical properties can be described by biopolymer mechanics. See Alberts et al., Molecular Biology of the Cell: protein function and binding.

Order matters beyond composition. Let A stand for alanine and M for methionine, and read from the N-terminus to the C-terminus. The illustrative strings AMAMAMAMAMAM and AAAAAAMMMMMM each contain exactly six A and six M amino acid residues. Each has $12-1=11$ peptide bonds when made into one unbranched polypeptide chain. In the first string all eleven neighboring pairs have different letters; in the second only the pair at positions 6 and 7 does. A composition histogram therefore loses information about which amino acid residues are neighbors. Their arrangements can affect protein folding and function; these short invented strings neither specify a known functional protein nor establish what shape either would adopt.

Protein structure is a moving arrangement, not a permanently rigid outline. Substrate binding can change an enzyme's shape through induced fit, and a functional protein can include flexible regions. Sequence, surroundings and interacting molecules must therefore be considered together. See Alberts et al.: binding, conformational changes and protein function.

Protein aggregation is the association of proteins into clusters, often involving exposed regions of partly folded or unfolded polypeptide chains. It can prevent recovery of normal function while leaving the protein primary structures intact. It is distinct from both unfolding one chain and the functional assembly described by protein quaternary structure. See Cooper: partly folded chains, aggregation and chaperone protection.

The protein primary structure specifies the ordered amino acid residues of each polypeptide chain, joined through peptide bonds. A chain is conventionally written from its N-terminus to its C-terminus. In the broader chemical sense, a complete protein primary structure also specifies covalent bond crosslinks between chain positions, including protein disulfide bonds; a bare sequence string leaves that information unstated. This describes chemical connectivity rather than the spatial arrangement of protein tertiary structure or protein quaternary structure. See IUPAC Gold Book: primary structure, sequence and chain crosslinking and IUPAC-IUB, 3AA-16: writing residue sequences from the amino end. Some conventions reserve protein primary structure for sequence alone and call the complete chemical connectivity the covalent structure; the distinction should be stated when comparing descriptions. See IUPAC-IUB polypeptide-conformation recommendations, section 6.1: the narrower sequence-only convention.

In this toy example M denotes methionine, A alanine and G glycine. Both polypeptide chains have six amino acid residues, five peptide bonds, an M at the N-terminus and a G at the C-terminus. Their amino acid composition is identical, yet position 2 is A in MAGAMG and M in MMAAGG. There are $6!/(2!2!2!)=90$ distinct orders with these counts, a multinomial coefficient. Even fixing those two end residues leaves $4!/(1!2!1!)=12$ orders. The counts constrain the answer without determining it.

For multiple polypeptide chains, record each sequence separately and specify any protein disulfide bonds between cysteine positions. Mature insulin, for example, has an A chain of 21 amino acid residues and a B chain of 30 amino acid residues. Their combined 51 residues give $(21-1)+(30-1)=49$ peptide bonds, rather than the 50 of one unbroken 51-residue chain. See Cooper, The Cell: insulin's two chains and cysteine crosslinks, figure 2.16. A protein disulfide bond joins side groups; it does not concatenate the C-terminus of one chain with the N-terminus of another. The three insulin protein disulfide bonds connect A6 to A11 within the A chain, and A7 to B7 and A20 to B19 between chains. Positions are numbered from each chain's N-terminus. See Replacement of the interchain disulfide bridge-forming amino acids A7 and B7 by glutamate impairs the structure and activity of insulin: native disulfide positions.

Why keep this information? Protein primary structure lets us distinguish changes of chemical identity from changes of shape, and compare corresponding positions between proteins. Protein folding can bring distant amino acid residues together at a protein binding site while preserving their sequence. The attractive idea is that a readable linear record can constrain a complicated three-dimensional object; it is not, by itself, a guarantee of a unique fold in every environment. See protein folding and the ribonuclease A refolding experiment. Merely bending an intact chain preserves its protein primary structure; hydrolysis of a peptide bond, or changing which positions a protein disulfide bond connects, changes its chemical connectivity.

Protein secondary structure consists of recurring local arrangements of the protein backbone, notably the alpha helix and beta sheet. Backbone hydrogen bonds help stabilize these patterns. A beta sheet can bring together stretches far apart in the protein primary structure; local refers to the pattern of backbone geometry, not necessarily neighboring sequence positions. See Alberts et al.: alpha helices, beta sheets and backbone interactions.

Protein structure describes both the chain's chemical organization and its spatial arrangement. Four levels answer different questions: protein primary structure gives the order; protein secondary structure gives recurring local patterns; protein tertiary structure gives one chain's overall arrangement; protein quaternary structure gives the assembly of multiple chains. These are levels of description, not four mandatory stages that every protein must pass through. See Clark, Douglas and Choi: four levels of protein structure.

The protein tertiary structure is the overall spatial arrangement of one polypeptide chain. It includes how its protein secondary structures and intervening regions fit together. For example, the schematic under protein places positions 4 and 9 near each other despite their separation in protein primary structure. Such cooperation can help construct an active site; sequence distance and spatial separation answer different questions. Hydrophobicity, backbone hydrogen bonds and other interactions help stabilize folds, and some proteins additionally contain protein disulfide bonds. See Cooper: tertiary structure and interactions between chain regions.

Ribonuclease A is an enzyme that catalyzes cleavage of RNA. The bovine pancreatic ribonuclease A studied by Anfinsen and colleagues has 124 amino acid residues and four internal protein disulfide bonds. It supplied a particularly informative test of the relationship between protein primary structure, protein folding and biological function: recovery could be measured through restored enzyme activity. See the primary sources under ribonuclease A refolding experiment.

Write a peptide's protein primary structure from its N-terminus toward its C-terminus. The usual simplified trypsin cleavage specificity rule places a cut immediately after K (lysine) or R (arginine), unless the next amino acid residue is P (proline). The following amino acid residue is essential: a terminal K or R has no following peptide bond to cut. The inspected institutional documentation describes proline as usually blocking cleavage, and explicitly lists sequence contexts in which that blocking is negligible. It also warns that experimental results can differ from sequence-based predictions. Thus “never before proline” is too strong.^[ref]

For an original worked example, stipulate complete cleavage at all sites allowed by that simplified rule in the twelve-amino acid residue sequenceA denotes alanine, G denotes glycine, and K, R and P have the meanings above. Cuts follow positions $3$, $7$ and $10$. Position $5$ is R, but its following P suppresses that cut in the stipulated rule; position $12$ is terminal K. Notice that the R in ARPK is retained inside the fragment, despite being a usually favoured trypsin target.

Near neutral pH, the lysine and arginine amino acid side chains undergo predominant protonation and carry positive electric charge. This helps distinguish those amino acid residues from the uncharged letter symbols used to write the sequence; those symbols specify identities, not whole-fragment electric charges.^[ref]

Fragment accounting checks the prediction: lengths $3+4+3+2=12$ conserve the twelve amino acid residues. The original linear chain has eleven peptide bonds; the four fragments retain $2+3+2+1=8$, so three were hydrolysed. Three water molecules are consumed per original chain in this formal stoichiometry. More generally, cutting $m$ distinct bonds of one linear peptide makes $m+1$ fragments: each cut splits one connected piece into two. This argument assumes an unbranched chain without additional links joining the pieces.

A missed trypsin cleavage at position $7$ would instead give $\mathrm{AGK}|\mathrm{ARPKAGR}|\mathrm{AK}$, merging two neighbouring fragments without changing their order. Even a correct cleavage preference does not guarantee complete proteolysis; predicted fragment boundaries describe a model, while actual boundaries require evidence from the digest.