Free energy of burying hydrophobic residues in the interface between protein subunits

We have obtained an experimental estimate of the free energy change associated with variations at the interface between protein subunits, a subject that has raised considerable interest since the concept of accessible surface area was introduced by Lee and Richards [Lee, B. & Richards, F. M. (1971) J. Mol. Biol. 55, 379–400]. We determined by analytical ultracentrifugation the dimer–tetramer equilibrium constant of five single and three double mutants of human Hb. One mutation is at the stationary α1β1 interface, and all of the others are at the sliding α1β2 interface where cleavage of the tetramer into dimers and ligand-linked allosteric changes are known to occur. A surprisingly good linear correlation between the change in the free energy of association of the mutants and the change in buried hydrophobic surface area was obtained, after corrections for the energetic cost of losing steric complementarity at the αβ dimer interface. The slope yields an interface stabilization free energy of −15 ± 1.2 cal/mol upon burial of 1 Å2 of hydrophobic surface, in very good agreement with the theoretical estimate given by Eisenberg and McLachlan [Eisenberg, D. & McLachlan, A. D. (1986) Nature (London) 319, 199–203].

Bond orientational order, molecular motion, and free energy of high-density DNA mesophases.

By equilibrating condensed DNA arrays against reservoirs of known osmotic stress and examining them with several structural probes, it has been possible to achieve a detailed thermodynamic and structural characterization of the change between two distinct regions on the liquid-crystalline phase diagram: (i) a higher density hexagonally packed region with long-range bond orientational order in the plane perpendicular to the average molecular direction and (ii) a lower density cholesteric region with fluid-like positional order. X-ray scattering on highly ordered DNA arrays at high density and with the helical axis oriented parallel to the incoming beam showed a sixfold azimuthal modulation of the first-order diffraction peak that reflects the macroscopic bond-orientational order. Transition to the less-dense cholesteric phase through osmotically controlled swelling shows the loss of this bond orientational order, which had been expected from the change in optical birefringence patterns and which is consistent with a rapid onset of molecular positional disorder. This change in order was previously inferred from intermolecular force measurements and is now confirmed by 31P NMR. Controlled reversible swelling and compaction under osmotic stress, spanning a range of densities between approximately 120 mg/ml to approximately 600 mg/ml, allow measurement of the free-energy changes throughout each phase and at the phase transition, essential information for theories of liquid-crystalline states.

Recent improvements in prediction of protein structure by global optimization of a potential energy function

Recent improvements of a hierarchical ab initio or de novo approach for predicting both α and β structures of proteins are described. The united-residue energy function used in this procedure includes multibody interactions from a cumulant expansion of the free energy of polypeptide chains, with their relative weights determined by Z-score optimization. The critical initial stage of the hierarchical procedure involves a search of conformational space by the conformational space annealing (CSA) method, followed by optimization of an all-atom model. The procedure was assessed in a recent blind test of protein structure prediction (CASP4). The resulting lowest-energy structures of the target proteins (ranging in size from 70 to 244 residues) agreed with the experimental structures in many respects. The entire experimental structure of a cyclic α-helical protein of 70 residues was predicted to within 4.3 Å α-carbon (Cα) rms deviation (rmsd) whereas, for other α-helical proteins, fragments of roughly 60 residues were predicted to within 6.0 Å Cα rmsd. Whereas β structures can now be predicted with the new procedure, the success rate for α/β- and β-proteins is lower than that for α-proteins at present. For the β portions of α/β structures, the Cα rmsd's are less than 6.0 Å for contiguous fragments of 30–40 residues; for one target, three fragments (of length 10, 23, and 28 residues, respectively) formed a compact part of the tertiary structure with a Cα rmsd less than 6.0 Å. Overall, these results constitute an important step toward the ab initio prediction of protein structure solely from the amino acid sequence.