Fig. 1.

Informational analysis of protein complex TusBCD, chains B and C. (A) Three-dimensional representation of stochastic variables X^N and Y^N as defined from physically coupled amino acids at short-range cutoff distances r_c ≤ 8.0 Å (turquoise) and physically uncoupled amino-acids at long-range cutoff distances r_c > 8.0 Å (gray). Calculation of r_c involved C^β-C^β atomic separation distances. (B) Conditional mutual information <I(X^N; Y^N|z)>_M−n as a function of the number M − n of randomly paired proteins in the reference (native) MSA, for 0 ≤ n ≤ M. < I(X^N; Y^N|z)>_M−n are expectation values estimated from a generated ensemble of 500 MSA models. Mutual information of fully “scrambled” models featuring M unpaired sequences is similar to that calculated from randomized sequence alignments generated by aleatory swapping of lines within columns. (C) Mutual information gap ΔI_M between reference and 100 fully “scrambled” models featuring M unpaired sequences. (D) Per-contact mutual information gap N⁻¹ΔI_M,rc. (E) Mutual information decomposition $\left(N^{-1}\mathrm{\Delta }\mathrm{\Delta }{I}_{M,r_c\le 8\text{Å}}^{\mathit{Cov}}\right)$ according to Eq. (11) and comparison with functional mutual information (MI_p,rc≤8Å) and direct information (DI_rc≤8Å). In B, C, D and E error bars correspond to standard deviations.