Figure 1. Relative fold complexities of the chorismate mutase monomer and the β-lactamase large domain. a, The AroQ-type chorismate mutase examined by Taylor et al.⁹ is formed by symmetrical association of a pair of 93 residue monomers with this three helix structure (PDB entry 1ECM). b, The TEM-1 penicillinase, a typical class A β-lactamase, functions as a 263 residue monomer with two structural domains, the larger one shown here (153 residues; PDB entry 1ERM). This fold is made more complex by its larger size, and by the number of structural components (loops, helices, and strands) and the degree to which formation of these components is intrinsically coupled to the formation of tertiary structure (as is generally the case for strands and loops, but not for helices).

Figure 2. Importance of starting sequence and selection threshold on local side-chain randomization experiments. A generic enzyme is represented schematically as a backbone conformation (curved line) stabilized by a large number of interactions among side-chains (appendages) distributed throughout the structure, resulting in formation of a working active site (Y-shaped appendages). Each black appendage represents an “optimal” side-chain, meaning that it stabilizes the native fold at least as well as any of its 19 possible replacements would in the same context. Grey appendages represent side-chains that are in this sense suboptimal. A set of structurally local side-chains (broken lines) is chosen for randomization with subsequent functional selection. Folding stabilities of the starting sequence and a passing randomized sequence are represented by a qualitative graph, with the dotted line representing the minimum stability for passing under the chosen selection conditions. a, Natural selection ensures that a wild-type starting sequence (left) has relatively few suboptimal side-chains. (Substitutions that improve the stability of natural proteins are therefore relatively rare, as data collated by Guerois et al. bear out. See Figure 5 of Guerois et al.,⁴⁷ disregarding data from reverse mutations [cyan squares]. Consequently, anything but the most stringent selection will count randomized variants that are significantly less stable (right) as “active”. b, A uniformly suboptimal starting sequence having just enough activity to pass a very low selection threshold (left) ensures that randomized variants passing that threshold (right) retain interactions within the randomized region that are comparable in quality to those of the starting sequence. Although these interactions are not optimal, they favour the folded structure to a degree that is characteristic of a marginally functional enzyme fold, which cannot be said of the randomized interactions of a (right).

Figure 3. Structural importance of the 36 residue segment missing from a deletion mutant. The backbone structure is shown in stereo for the TEM-1 large-domain (PDB entry 1FQG) with space-filling representation of the small domain. The missing segment (yellow) includes two important active-site side-chains (Ser130 and Asn132, green). Two other active-site side-chains (Ser70 and Lys73, also green) are found not to be important for the low-level activity of the deletion mutant. Penicillin (white) is shown attached covalently via Ser70, representing the normal acyl-enzyme intermediate in the hydrolysis reaction.¹⁴ As a consequence of the deletion, the blue portion of the chain cannot adopt its normal conformation.

Figure 4. Superposition of the large-domain backbone structures of 11 class A β-lactamases. Structural data are from PDB entries: 1BSG, 1BUE, 1BZA, 1DY6, 1ERM, 1G6A, 1GHP, 1HZO, 1MFO, 1SHV, and 4BLM. Excluding hydrogen atoms, backbone RMS deviations from the TEM-1 structure (1ERM) are, in the above order: 0.82, 0.85, 0.85, 0.89, 0, 0.76, 1.24, 0.75, 0.86, 0.44, and 0.63 Å over alignments covering at least 87% of the full domain. The 1BSG and 1GHP structures show the largest RMS deviation (1.50 Å over an alignment covering 90% of the domain).

Figure 5. Sequence-identity matrix for the 44 aligned large-domain sequences. Residue identities (%) are based upon the full domain sequences (identified by SwissProt and/or PDB accession codes) as aligned in Figure 6.

Figure 6. Alignment of 44 homologous large-domain sequences. Position numbering corresponds to the TEM-1 sequence, shown at the top and identified within the alignment by its SwissProt and PDB accession codes (P00810/1ERM). Shading indicates the four sets of ten positions chosen for randomization (coloured according to Figure 7b). Positions showing no variation are indicated below the alignment by asterisks (*). Those showing a high level of variation, meaning both a hydropathic constraint score of x (see Results and Discussion: subsection The hydropathy signature…) and six or more amino acid residues represented in the alignment, are indicated by slashes (/). Below the signature and reference sequences (explained in the text) are the allowed substitutions at the first four groups of positions subjected to limited substitution (see Results and Discussion, subsection Finding a reference sequence), the top row showing where the TEM-1 residue was included as an option.

Figure 7. Location of reference-sequence substitutions and ten residue sets in the TEM-1 large domain (PDB 1FQG). Penicillin substrate (white) identifies the active-site pocket. a, Stereo image showing TEM-1 side-chains substituted in the reference sequence as red. b, Stereo image showing the four sets of ten residues chosen for randomization enclosed by transparent surfaces (see Results and Discussion, subsection Local side-chain randomization). Set 1 (green) includes positions 80, 83, 84, 86, 87, 88, 89, 90, 91, and 93; set 2 (gold) includes positions 106, 107, 108, 109, 111, 112, 117, 125, 129, 131; set 3 (cyan) includes positions 161, 163, 164, 171, 173, 176, 177, 178, 179, 180; set 4 (magenta) includes positions 194, 205, 206, 207, 208, 209, 210, 211, 212 and 213. Locations of reference-sequence substitutions are again indicated by red side-chains.

Figure 8. Functional residue combinations identified from four separate randomization experiments. Wild-type TEM-1 residues, reference-sequence residues, and signature scores are listed for each set in ascending order according to position (see Figure 6 or Figure 7 for unlabeled position numbers). Functional combinations found by sequencing complete genes of passing clones are listed below the signature scores, with matches to the TEM-1 sequence shown in boldface. For sets 1 and 4, these clones were among those counted in the assessment of pass rates (Table 2). The three functional combinations shown for set 3 were isolated as described (Materials and Methods) after the initial selective plating produced no colonies. No functional variants could be isolated following randomization of set 2.

Figure 9. Alternative models of how function might map onto sequence space. A quantifiable function, performed with a high level of efficiency by a natural protein, is represented in the vertical dimension, the logarithmic scale indicating a wide range of measurable activity. For the purpose of this comparative illustration, sequence possibilities are imagined to be represented within the horizontal scales such that neighbouring sequences occupy neighbouring positions on these scales. Dotted lines represent two selection thresholds, function being much rarer at the higher threshold. (a) Global-ascent model, with optimal sequence in the middle. (b) Local-ascent model, with optimal sequence in the middle.

Figure 10. Relationships between key sets and subsets of sequences. See the text for a full explanation.

Characteristics of the ten residue sets

Calculation of pass rates from local side-chain randomization experiments

See Materials and Methods for a full description of the calculation.