The past and the future fate of the universe and the formation of structure in it

The history and the ultimate future fate of the universe as a whole depend on how much the expansion of the universe is decelerated by its own mass. In particular, whether the expansion of the universe will ever come to a halt can be determined from the past expansion. However, the mass density in the universe does not only govern the expansion history and the curvature of space, but in parallel also regulates the growth of hierarchical structure, including the collapse of material into the dense, virialized regions that we identify with galaxies. Hence, the formation of galaxies and their clustered distribution in space depend not only on the detailed physics of how stars are formed but also on the overall structure of the universe. Recent observational efforts, fueled by new large, ground-based telescopes and the Hubble Space Telescope, combined with theoretical progress, have brought us to the verge of determining the expansion history of the universe and space curvature from direct observation and to linking this to the formation history of galaxies.

Top-down free-energy minimization on protein potential energy landscapes

The hierarchical properties of potential energy landscapes have been used to gain insight into thermodynamic and kinetic properties of protein ensembles. It also may be possible to use them to direct computational searches for thermodynamically stable macroscopic states, i.e., computational protein folding. To this end, we have developed a top-down search procedure in which conformation space is recursively dissected according to the intrinsic hierarchical structure of a landscape's effective-energy barriers. This procedure generates an inverted tree similar to the disconnectivity graphs generated by local minima-clustering methods, but it fundamentally differs in the manner in which the portion of the tree that is to be computationally explored is selected. A key ingredient is a branch-selection algorithm that takes advantage of statistically predictive properties of the landscape to guide searches down the tree branches that are most likely to lead to the physically relevant macroscopic states. Using the computational folding of a β-hairpin-forming peptide as an example, we show that such predictive properties indeed exist and can be used for structure prediction by free-energy global minimization.

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.

Folding of a nascent polypeptide chain in vitro: cooperative formation of structure in a protein module.

We have prepared a family of peptide fragments of the 64-residue chymotrypsin inhibitor 2, corresponding to its progressive elongation from the N terminus. The growing polypeptide chain has little tendency to form stable structure until it is largely synthesized, and what structures are formed are nonnative and lack, in particular, the native secondary structural elements of alpha-helix and beta-sheet. These elements then develop as sufficient tertiary interactions are made in the nearly full-length chain. The growth of structure in the small module is highly cooperative and does not result from the hierarchical accretion of substructures.