Jan 2, 2007

2007 week 01: Articles in Folding


Steiner minimal trees, twist angles, and the protein folding problem

The Steiner Minimal Tree (SMT) problem determines the minimal length network for connecting a given set of vertices in three-dimensional space. SMTs have been shown to be useful in the geometric modeling and characterization of proteins. Even though the SMT problem is an NP-Hard Optimization problem, one can define planes within the amino acids that have a surprising regularity property for the twist angles of the planes. This angular property is quantified for all amino acids through the Steiner tree topology structure. The twist angle properties and other associated geometric properties unique for the remaining amino acids are documented in this paper. We also examine the relationship between the Steiner ratio [rho] and the torsion energy in amino acids with respect to the side chain torsion angle [chi]1. The [rho] value is shown to be inversely proportional to the torsion energy. Hence, it should be a useful approximation to the potential energy function. Finally, the Steiner ratio is used to evaluate folded and misfolded protein structures. We examine all the native proteins and their decoys at . and compare their Steiner ratio values. Because these decoy structures have been delicately misfolded, they look even more favorable than the native proteins from the potential energy viewpoint. However, the [rho] value of a decoy folded protein is shown to be much closer to the average value of an empirical Steiner ratio for each residue involved than that of the corresponding native one, so that we recognize the native folded structure more easily. The inverse relationship between the Steiner ratio and the energy level in the protein is shown to be a significant measure to distinguish native and decoy structures. These properties should be ultimately useful in the ab initio protein folding prediction. Proteins 2007. © 2006 Wiley-Liss, Inc.

Cooperative folding mechanism of a [beta]-hairpin peptide studied by a multicanonical replica-exchange molecular dynamics simulation

G-peptide is a 16-residue peptide of the C-terminal end of streptococcal protein G B1 domain, which is known to fold into a specific [beta]-hairpin within 6 [mu]s. Here, we study molecular mechanism on the stability and folding of G-peptide by performing a multicanonical replica-exchange (MUCAREM) molecular dynamics simulation with explicit solvent. Unlike the preceding simulations of the same peptide, the simulation was started from an unfolded conformation without any experimental information on the native conformation. In the 278-ns trajectory, we observed three independent folding events. Thus MUCAREM can be estimated to accelerate the folding reaction more than 60 times than the conventional molecular dynamics simulations. The free-energy landscape of the peptide at room temperature shows that there are three essential subevents in the folding pathway to construct the native-like [beta]-hairpin conformation: (i) a hydrophobic collapse of the peptide occurs with the side-chain contacts between Tyr45 and Phe52, (ii) then, the native-like turn is formed accompanying with the hydrogen-bonded network around the turn region, and (iii) finally, the rest of the backbone hydrogen bonds are formed. A number of stable native hydrogen bonds are formed cooperatively during the second stage, suggesting the importance of the formation of the specific turn structure. This is also supported by the accumulation of the nonnative conformations only with the hydrophobic cluster around Tyr45 and Phe52. These simulation results are consistent with high [phis]-values of the turn region observed by experiment. Proteins 2007. © 2006 Wiley-Liss, Inc.

Exploring zipping and assembly as a protein folding principle

It has been proposed that proteins fold by a process called "Zipping and Assembly" (Z&A). Zipping refers to the growth of local substructures within the chain, and assembly refers to the coming together of already-formed pieces. Our interest here is in whether Z&A is a general method that can fold most of sequence space, to global minima, efficiently. Using the HP model, we can address this question by enumerating full conformation and sequence spaces. We find that Z&A reaches the global energy minimum native states, even though it searches only a very small fraction of conformational space, for most sequences in the full sequence space. We find that Z&A, a mechanism-based search, is more efficient in our tests than the replica exchange search method. Folding efficiency is increased for chains having: (a) small loop-closure steps, consistent with observations by Plaxco et al. 1998;277;985-994 that folding rates correlate with contact order, (b) neither too few nor too many nucleation sites per chain, and (c) assembly steps that do not occur too early in the folding process. We find that the efficiency increases with chain length, although our range of chain lengths is limited. We believe these insights may be useful for developing faster protein conformational search algorithms. Proteins 2007. © 2006 Wiley-Liss, Inc.

Strategies for high-throughput comparative modeling: Applications to leverage analysis in structural genomics and protein family organization

The technological breakthroughs in structural genomics were designed to facilitate the solution of a sufficient number of structures, so that as many protein sequences as possible can be structurally characterized with the aid of comparative modeling. The leverage of a solved structure is the number and quality of the models that can be produced using the structure as a template for modeling and may be viewed as the "currency" with which the success of a structural genomics endeavor can be measured. Moreover, the models obtained in this way should be valuable to all biologists. To this end, at the Northeast Structural Genomics Consortium (NESG), a modular computational pipeline for automated high-throughput leverage analysis was devised and used to assess the leverage of the 186 unique NESG structures solved during the first phase of the Protein Structure Initiative (January 2000 to July 2005). Here, the results of this analysis are presented. The number of sequences in the nonredundant protein sequence database covered by quality models produced by the pipeline is [sim]39,000, so that the average leverage is [sim]210 models per structure. Interestingly, only 7900 of these models fulfill the stringent modeling criterion of being at least 30% sequence-identical to the corresponding NESG structures. This study shows how high-throughput modeling increases the efficiency of structure determination efforts by providing enhanced coverage of protein structure space. In addition, the approach is useful in refining the boundaries of structural domains within larger protein sequences, subclassifying sequence diverse protein families, and defining structure-based strategies specific to a particular family. Proteins 2007. © 2006 Wiley-Liss, Inc.

A knowledge-based move set for protein folding

The free energy landscape of protein folding is rugged, occasionally characterized by compact, intermediate states of low free energy. In computational folding, this landscape leads to trapped, compact states with incorrect secondary structure. We devised a residue-specific, protein backbone move set for efficient sampling of protein-like conformations in computational folding simulations. The move set is based on the selection of a small set of backbone dihedral angles, derived from clustering dihedral angles sampled from experimental structures. We show in both simulated annealing and replica exchange Monte Carlo (REMC) simulations that the knowledge-based move set, when compared with a conventional move set, shows statistically significant improved ability at overcoming kinetic barriers, reaching deeper energy minima, and achieving correspondingly lower RMSDs to native structures. The new move set is also more efficient, being able to reach low energy states considerably faster. Use of this move set in determining the energy minimum state and for calculating thermodynamic quantities is discussed. Proteins 2007. © 2006 Wiley-Liss, Inc.

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