We investigated the correlation between the Shannon information entropy, 'sequence entropy', with respect to the local flexibility of native globular proteins as described by inverse packing density. These are determined at each residue position for a total set of 130 query proteins, where sequence entropies are calculated from each set of aligned residues. For the accompanying aggregate set of 130 alignments, a strong linear correlation is observed between the calculated sequence entropy and the corresponding inverse packing density determined at an associated residue position. This region of linearity spans the range of C(alpha) packing densities from 12 to 25 amino acids within a sphere of 9 angstrom radius. Three different hydrophobicity scales all mimic the behavior of the sequence entropies. This confirms the idea that the ability to accommodate mutations is strongly dependent on the available space and on the propensity for each amino acid type to be buried. Future applications of these types of methods may prove useful in identifying both core and flexible residues within a protein.

Amino acid-amino acid interaction energies have been derived from crystal structure data for a number of years. Here is reported the first derivation of normalized relative interaction from binding data for each of the four bases interacting with a specific amino acid, utilizing data from combinatorial multiplex DNA binding of zinc finger domains [Desjarlais, J. R. and Berg, J. M. (1994) Proc. Natl. Acad. Sci. USA, 91, 11099-11103]. The five strongest interactions are observed for lysine-guanine, lysine-thymine, arginine-guanine, aspartic acid-cytosine and asparagine-adenine. These rankings for interactions with the four bases appear to be related to base-amino acid partial charges. Also, similar normalized relative interaction energies are derived by using DNA binding data for Cro and lambda repressors and the R2R3 c-Myb protein domain [Takeda, Y., Sarai, A. and Rivera, V. M. (1989) Proc. Natl. Acad. Sci. USA, 86, 439-443; Sarai, A. and Takeda, Y. (1989) Proc. Natl. Acad. Sci. USA, 86, 6513-6517; Ogata, K. et al. (1995) submitted]. These energies correlate well with the combinatorial multiplex energies, and the strongest cases are similar between the two sets. They also correlate well with similar relative interaction energies derived directly from frequencies of bases in the bacteriophage lambda operator sequences. These results suggest that such potentials are general and that extensive combinatorial binding studies can be used to derive potential energies for DNA-protein interactions.

For the binding of peptides to wild-type HIV-1 and BIV TAR RNA and to mutants with bulges of various sizes, changes in the DeltaDelta G values of binding were determined from experimental K d values. The corresponding entropies of these bulges are estimated by enumerating all possible RNA bulge conformations on a lattice and then applying the Boltzmann relationship. Independent calculations of entropies from fluctuations are also carried out using the Gaussian network model (GNM) recently introduced for analyzing folded structures. Strong correlations are seen between the changes in free energy determined for binding and the two different unbound entropy calculations. The fact that the calculated entropy increase with larger bulge size is correlated with the enhanced experimental binding free energy is unusual. This system exhibits a dependence on the entropy of the unbound form that is opposite to usual binding models. Instead of a large initial entropy being unfavorable since it would be reduced upon binding, here the larger entropies actually favor binding. Several interpretations are possible: (i) the higher conformational freedom implies a higher competence for binding with a minimal strain, by suitable selection amongst the set of already accessible conformations; (ii) larger bulge entropies enhance the probability of the specific favorable conformation of the bound state; (iii) the increased freedom of the larger bulges contri-butes more to the bound state than to the unbound state; (iv) indirectly the large entropy of the bound state might have an unfavorable effect on the solvent structure. Nonetheless, this unusual effect is interesting.

We investigate RNA base-amino acid interactions by counting their contacts in structures and their implicit contacts in various functional sequences where the structures can be assumed to be preserved. These frequencies are cast into equations to extract relative interaction energetics. Previously we used this approach in considering the major groove interactions of DNA, and here we apply it to the more diverse interactions observed in RNA. Structures considered are the three different tRNA synthetase complexes, the U1A spliceosomal protein with an RNA hairpin and the BIV TAR-Tat complex. We use binding data for the base frequencies for the seryl, aspartyl and glutaminyl tRNA-synthetase and U1 RNA-protein complexes. We compare with the previously reported DNA major groove peptide contacts the results for atoms of RNA bases, usually in the major groove. There are strong similarities between the rank orders of interacting bases in the DNA and the RNA cases. The apparent strongest RNA interaction observed is between arginine and guanine which was also one of the strongest DNA interactions. The similar data for base atomic interactions, whether base paired or not, support the importance of strong atomic interactions over local structure considerations, such as groove width and alpha-helicity.