Selection applied to an elastic protein model leads to a statistical signature among sequences.

(a) Cartoon representation of the third PDZ domain of the rat postsynaptic density protein 95 from the RSCB PDB [32] (gray: ligand free, 1BFE; blue: ligand bound, 1BE9 (ligand not shown)). (b) Elastic network model for 1BFE, where each amino-acid residue is represented by its alpha carbon (Cα, black node) and beta carbon (Cβ, purple node). Nearby nodes interact through a harmonic spring [20] (S1 Appendix). (c) Relation between protein sequence and elastic network: 0 denotes the reference state, while 1 denotes a mutated residue, which weakens interactions of the corresponding Cβ with all its neighbors by ϵ. (d) Histogram of the energy δE required to deform the domain from its ligand-free to its ligand-bound conformation, for randomly sampled sequences where 0 and 1 are equally likely at each site. Sequences are selectively weighted using a narrow Gaussian window (orange) around δE*. (e) Eigenvalues of the covariance matrix C for the selectively weighted protein sequences. (f) Upper panel: last principal component of C (red) and average mutant fraction 〈Sl〉* (green) at site l after selection; lower panel: effect Δl of a single mutation at site l on δE. (g) Schematic representation of the selected ensemble in sequence space, where each dot is a highly-weighted sequence; thus dots are restricted to a narrow region around a plane perpendicular to . (h) Recovery of for all principal components , with maximum Recovery = 1 (Eq 8). Gray dashed line: random expectation of Recovery (S1 Appendix).