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Using an all-atom representation, we exhaustively enumerate all sterically allowed conformations for short polyalanyl chains. Only intrachain interactions are considered, including one adjustable parameter, a favorable backbone energy (e.g., a peptide hydrogen bond). The counting is used to reevaluate Flory's isolated-pair hypothesis, the simplifying assumption that each phi,psi pair is sterically independent. This hypothesis is a conceptual linchpin in helix-coil theories and protein folding. Contrary to the hypothesis, we find that systematic local steric effects can extend beyond nearest-chain neighbors and can restrict the size of accessible conformational space significantly. As a result, the entropy price that must be paid to adopt any specific conformation is far less than previously thought.

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Although energetic and phylogenetic methods have been very successful for prediction of nucleic acid secondary structures, arrangement of these secondary structure elements into tertiary structure has remained a difficult problem. Here we explore the packing arrangements of DNA, RNA, and DNA/RNA hybrid molecules in crystals. In the conventional view, the highly charged double helix will be pushed toward isolation by favorable solvation effects; interactions with other like-charged stacks would be strongly disfavored. Contrary to this expectation, we find that most of the cases analyzed ( approximately 80%) exhibit specific, preferential packing between elements of secondary structure, which falls into three categories: (i) interlocking of major grooves of two helices, (ii) side-by-side parallel packing of helices, and (iii) placement of the ribose-phosphate backbone ridge of one helix into the major groove of another. The preponderance of parallel packing motifs is especially surprising. This category is expected to be maximally disfavored by charge repulsion. Instead, it comprises in excess of 50% of all packing interactions in crystals of A-form RNA and has also been observed in crystal structures of large RNA molecules. To explain this puzzle, we introduce a novel model for RNA folding. A simple calculation suggests that the entropy gained by a cloud of condensed cations surrounding the helices more than offsets the Coulombic repulsion of parallel arrangements. We propose that these condensed counterions are responsible for entropy-driven RNA collapse, analogous to the role of the hydrophobic effect in protein folding.

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A physical theory of protein secondary structure is proposed and tested by performing exceedingly simple Monte Carlo simulations. In essence, secondary structure propensities are predominantly a consequence of two competing local effects, one favoring hydrogen bond formation in helices and turns, the other opposing the attendant reduction in sidechain conformational entropy on helix and turn formation. These sequence specific biases are densely dispersed throughout the unfolded polypeptide chain, where they serve to preorganize the folding process and largely, but imperfectly, anticipate the native secondary structure.

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A simple stereochemical framework for understanding RNA structure has remained elusive to date. We present a comprehensive conformational map for two nucleoside-5',3'-diphosphates and for a truncated dinucleotide derived from a grid search of all potential conformers using hard sphere steric exclusion criteria to define allowed conformers. The eight-dimensional conformational space is presented as a series of two-dimensional projections. These projections reveal several well-defined allowed and disallowed regions which correlate well with data obtained from X-ray crystallography of both large and small RNA molecules. Furthermore, the two-dimensional projections show that consecutive and ribose ring-proximal torsion angles are interdependent, while more distant torsion angles are not. Remarkably, using steric criteria alone, it is possible to generate a predictive conformational map for RNA.

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It is now possible to compare life forms at high levels of detail and completeness due to the increasing availability of whole genomes from all three domains. However, exploration of interesting hypotheses requires the ability to recognize a correspondence between proteins that may since have diverged beyond the threshold of detection by sequence-based methods. Since protein structure is far better conserved than protein sequence, structural information can enhance detection sensitivity, and this is the basis for the field of structural genomics. Demonstrating the effectiveness of this approach, we identify two important but previously elusive Archaeal enzymes: a homolog of dihydropteroate synthase and a thymidylate synthase. The former is especially noteworthy in that no Archaeal homolog of a bacterial folate biosynthetic enzyme has been found to date. Experimental confirmation of the deduced activity of both enzymes is described. Identification of two different proteins was attempted deliberately to help allay concern that predictive success is merely a lucky accident.

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Does a protein's secondary structure determine its three-dimensional fold? This question is tested directly by analyzing proteins of known structure and constructing a taxonomy based solely on secondary structure. The taxonomy is generated automatically, and it takes the form of a tree in which proteins with similar secondary structure occupy neighboring leaves. Our tree is largely in agreement with results from the structural classification of proteins (SCOP), a multidimensional classification based on homologous sequences, full three-dimensional structure, information about chemistry and evolution, and human judgment. Our findings suggest a simple mechanism of protein evolution.

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The folding reactions of some small proteins show clear evidence of a hierarchic process, whereas others, lacking detectable intermediates, do not. Nevertheless, we argue that both classes fold hierarchically and that folding begins locally. If this is the case, then the secondary structure of a protein is determined largely by local sequence information. Experimental data and theoretical considerations support this argument. Part I of this article reviews the relationship between secondary structures in proteins and their counterparts in peptides.

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The folding reactions of some small proteins show clear evidence of a hierarchic process, whereas others, lacking detectable intermediates, do not. Evidence from folding intermediates and transition states suggests that folding begins locally, and that the formation of native secondary structure precedes the formation of tertiary interactions, not the reverse. Some notable examples in the literature have been interpreted to the contrary. For these examples, we have simulated the local structures that form when folding begins by using the LINUS program with nonlocal interactions turned off. Our results support a hierarchic model of protein folding.

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We have developed a simple procedure to identify protein homologs in genomic databases. The program, called ORF, is based on comparisons of predicted secondary structure. Protein structure is far better conserved than amino acid sequence, and structure-based methods have been effective in exploiting this fact to find homologs, even among proteins with scant sequence identity. ORF is a secondary structure-based method that operates solely on predictions from sequence and requires no experimentally determined information about the structure. The approach is illustrated by an example: Thymidylate synthase, a highly conserved enzyme essential to thymidine biosynthesis in both prokaryotes and eukaryotes, is thought to be used by Archaea, but a corresponding gene has yet to be identified. Here, a candidate thymidylate synthase is identified as a previously unassigned open reading frame from the genome of Methanococcus jannaschii, viz., MJ0757. Using primary structure information alone, the optimally aligned sequence identity between MJ0757 and Escherichia coli thymidylate synthase is 7%, well below the threshold of sensitivity for detection by sequence-based methods.

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Helix-capping motifs are specific patterns of hydrogen bonding and hydrophobic interactions found at or near the ends of helices in both proteins and peptides. In an alpha-helix, the first four >N-H groups and last four >C=O groups necessarily lack intrahelical hydrogen bonds. Instead, such groups are often capped by alternative hydrogen bond partners. This review enlarges our earlier hypothesis (Presta LG, Rose GD. 1988. Helix signals in proteins. Science 240:1632-1641) to include hydrophobic capping. A hydrophobic interaction that straddles the helix terminus is always associated with hydrogen-bonded capping. From a global survey among proteins of known structure, seven distinct capping motifs are identified-three at the helix N-terminus and four at the C-terminus. The consensus sequence patterns of these seven motifs, together with results from simple molecular modeling, are used to formulate useful rules of thumb for helix termination. Finally, we examine the role of helix capping as a bridge linking the conformation of secondary structure to supersecondary structure.

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Buried surface area is often used as a measure of the contribution to protein folding from the hydrophobic effect. Quantitatively, the surface buried upon folding is reckoned as the difference in area between the native and unfolded states. This calculation is well defined for a known structure but model-dependent for the unfolded state. In a previous paper [Creamer, T. P., Srinivasan, R., & Rose, G. D. (1995) Biochemistry 34, 16245-16250], we developed two models that bracket the surface area of the unfolded state between limiting extremes. Using these extrema, it was shown that earlier models, such as an extended tripeptide, overestimate the surface area of side chains in the unfolded state. In this sequel to our previous paper, we focus on backbone surface in the unfolded state, again adopting the strategy of trapping the area between limiting extrema. A principal conclusion of this present study is that most backbone surface in proteins is buried within local structure.

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The hydrophobic effect is the major factor that drives a protein molecule toward collapse and folding. In this process, residues with apolar side chains associate to form a solvent-shielded hydrophobic core. Often, this hydrophobic contribution to folding is quantified by measuring buried apolar surface area, reckoned as the difference in area between hydrophobic groups in the folded protein and in a standard state. Typically, the standard state area of a residue is obtained from tripeptide models, with the results taken to implicitly represent values appropriate for the unfolded state. Here, we show that a tripeptide is a poor descriptor of the unfolded state, and its widespread use has prompted erroneous conclusions about folding. As an alternative, we explore two limiting models, chosen to bracket the expected behavior of the unfolded chain between reliable extremes. One extreme is represented by simulated hard-sphere peptides and shown to behave like a homopolymer with excluded volume in a good solvent. The other extreme is represented by fragments excised from folded proteins and conjectured to approximate the time-average behavior of a thermally denatured protein at Tm, the midpoint of the unfolding transition. Using these models, it is shown that the area buried by apolar side chains upon folding is considerably less than earlier estimates. For example, upon transfer from the unfolded state to the middle of an alpha-helix, an alanine side chain buries negligible area and, surprisingly, a valine side chain actually gains area. Among other applications, an improved model of the unfolded state can be used to better evaluate the driving force for helix formation in peptides and proteins.

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A rigid domain, defined here as a tertiary structure common to two or more different protein conformations, can be identified numerically from atomic coordinates by finding sets of residues, one in each conformation, such that the distance between any two residues within the set belonging to one conformation is the same as the distance between the two structurally equivalent residues within the set belonging to any other conformation. The distance between two residues is taken to be the distance between their respective alpha carbon atoms. With the methods of this paper we have found in the deoxy and oxy conformations of the human hemoglobin alpha 1 beta 1 dimer a rigid domain closely related to that previously identified by Baldwin and Chothia (J. Mol. Biol. 129: 175-220, 1979). We provide two algorithms, both using the difference-distance matrix, with which to search for rigid domains directly from atomic coordinates. The first finds all rigid domains in a protein but has storage and processing demands that become prohibitively large with increasing protein size. The second, although not necessarily finding every rigid domain, is computationally tractable for proteins of any size. Because of its efficiency we are able to search protein conformations recursively for groups of non-intersecting domains. Different protein conformations, when aligned by superimposing their respective domain structures, can be examined for structural differences in regions complementing a rigid domain.

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The thermodynamic basis of helix stability in peptides and proteins is a topic of considerable interest. Accordingly, we have computed the interactions between side chains of all hydrophobic residue pairs and selected triples in a model helix, using Boltzmann-weighted exhaustive modeling. Specifically, all possible pairs from the set Ala, Cys, His, Ile, Leu, Met, Phe, Trp, Tyr, and Val were modeled at spacings of (i, i + 2), (i, i + 3), and (i, i + 4) in the central turn of a model poly-alanyl alpha-helix. Significant interactions--both stabilizing and destabilizing-- were found to occur at spacings of (i, i + 3) and (i, i + 4), particularly in side chains with rings (i.e., Phe, Tyr, Trp, and His). In addition, modeling of leucine triples in a helix showed that the free energy can exceed the sum of pairwise interactions in certain cases. Our calculated interaction values both rationalize recent experimental data and provide previously unavailable estimates of the constituent energies and entropies of interaction.

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We describe LINUS, a hierarchic procedure to predict the fold of a protein from its amino acid sequence alone. The algorithm, which has been implemented in a computer program, was applied to large, overlapping fragments from a diverse test set of 7 X-ray-elucidated proteins, with encouraging results. For all proteins but one, the overall fragment topology is well predicted, including both secondary and supersecondary structure. The algorithm was also applied to a molecule of unknown conformation, groES, in which X-ray structure determination is presently ongoing. LINUS is an acronym for Local Independently Nucleated Units of Structure. The procedure ascends the folding hierarchy in discrete stages, with concomitant accretion of structure at each step. The chain is represented by simplified geometry and folds under the influence of a primitive energy function. The only accurately described energetic quantity in this work is hard sphere repulsion--the principal force involved in organizing protein conformation [Richards, F. M. Ann. Rev. Biophys. Bioeng. 6:151-176, 1977]. Among other applications, the method is a natural tool for use in the human genome initiative.

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