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Divergence preserves a structural framework while function changes; convergence produces similar solutions within otherwise different frameworks. Evidence should compare the entire protein fold, the sequence order and connectivity of structural elements, and the geometry of functional residues. Similar activity alone cannot distinguish either history, because many unrelated structures can perform the same reaction.

The globin fold illustrates divergence. myoglobin and the alpha and beta chains of haemoglobin share a predominantly alpha-helical architecture and a homologous pocket for haem. The proximal histidine coordinates the iron, and the surrounding pocket modulates ligand binding. Myoglobin is principally a monomeric oxygen-binding protein, whereas haemoglobin subunits interact within a tetramer to give cooperative oxygen transport. Their conserved core architecture and alignable sequence positions support descent from an ancestral globin, with duplication and subsequent specialization. Structural similarity remains recognizable even when many surface residues have changed. The functional difference arises partly from new intersubunit interactions rather than construction of an entirely new oxygen-binding chemistry.

Trypsin, chymotrypsin and elastase provide a second divergent series. They retain the chymotrypsin-like fold and corresponding catalytic triad residues, but changes in the specificity pocket favour different side chains next to the scissile peptide bond. A negatively charged pocket in trypsin favours basic residues; a hydrophobic pocket in chymotrypsin favours bulky aromatic residues; obstruction of the pocket in elastase favours smaller side chains. Conserved topology, residue correspondence and related sequences support common ancestry. The particular numbering of homologous catalytic residues is useful shorthand, but matching residue numbers alone is not evolutionary evidence.

For convergence, compare chymotrypsin-like proteases with subtilisin. Both are serine proteases using a serine nucleophile, histidine as a proton-transfer partner and an aspartate that organizes the histidine. Both stabilize a tetrahedral intermediate and form an acyl-enzyme. Nevertheless, their global folds differ, and the catalytic residues occur in different orders along the polypeptide: His–Asp–Ser in the chymotrypsin family and Asp–His–Ser in subtilisin. The similar local catalytic arrangement embedded in distinct topologies is evidence for independent assembly of effective serine-protease chemistry. Early three-dimensional structures made comparison of these spatial arrangements possible.^[ref]

The contrast is between a conserved scaffold with modified chemistry or specificity and independently organized scaffolds converging on a favourable active-site geometry. Chemical constraints help explain convergence: catalysis benefits from appropriately positioned acids, bases, nucleophiles and stabilizing charges. They do not require the rest of the protein to become similar.

Structural inference has limits. A common small motif can occur by chance or reflect physical constraints; failure to detect sequence similarity does not prove absence of ancient homology. Strong conclusions combine global structural alignment, sequence-profile comparisons, taxonomic distribution and molecular phylogeny. Domain duplication, rearrangement and loss can complicate a simple family tree. Thus structural resemblance is most persuasive when its extent and topology are evaluated alongside independent evolutionary evidence, rather than classifying every shared helix or catalytic residue as proof of common descent.

There arepossible sequences of length 300 over the standard twenty-amino-acid alphabet. Sampling $10^{20}$ sequences would cover only about $4.9\times 10^{-371}$ of that space, even before allowing repeated sequences. We cannot conclude that all possible protein folds have been explored.

However, this sequence count is not a count of folds: many sequences can share a fold, and many arbitrary sequences may not form a stable folded protein. Evolution also samples sequences non-uniformly. The calculation establishes vastly incomplete sequence-space exploration; proving either exhaustive or non-exhaustive coverage of physically realizable folds needs an additional model relating sequences to structures. The observed structural-cluster count alone supplies no such proof.

Protein structure can remain similar after extensive protein sequence divergence has obscured a sequence-only relationship. A structural comparison may therefore reveal a conserved protein fold, plausible binding pocket or spatial arrangement of candidate catalytic residues that a direct sequence search misses. Such evidence can suggest a functional family and useful hypotheses.

A similar fold does not uniquely determine function. The same architecture can support different activities, and a predicted pocket does not demonstrate binding or catalysis. Confidence in the model, residue-level chemistry and independent biochemical evidence must be considered together. Structural classification complements rather than replaces sequence and experimental analysis.

For fixed length $n$ and the standard twenty-amino-acid alphabet, there are $20^n$ sequences: each position has twenty choices. This counts possible sequences, not stable protein folds; the sequence-to-structure relationship is many-to-one and some sequences do not form a stable folded protein.