Efficient generation of low-energy folded states of a model protein. II. Automated histogram filtering

Abstract

A number of short, Monte Carlo simulated annealing runs are performed on a highly frustrated 69-mer off-lattice model protein, consisting of a chain of 69 beads that are either hydrophobic, hydrophilic, or neutral in nature, and which demonstrably folds into a six-stranded ␤-barrel structure. We employ an iterative, consensus-based scheme to cluster the 725 nonbonded distances between the hydrophobic beads using, in tandem, Ward's method for hierarchical clustering and k-means partitional clustering. We also independently analyze the same data using computer-automated histogram filtering, a technology designed to cluster high-dimensional data, without the tedium and subjectivity required by our iterative implementation of the two classical clustering methods. The memberships of low-energy clusters obtained from both classical clustering and automated histogram filtering approaches are remarkably similar. Nonbonded distance constraints are derived from these clusters and from small sets of the original unclustered conformations obtained by simulated annealing. Employing a distance geometry approach, we efficiently generate novel, low-energy conformations from each set of distance constraints, including the apparent native structure, up to 40 times faster than by doing additional simulated annealing runs. Over 33 000 unique locally optimized conformations are generated in total, substantially augmenting the number of low-energy states located by the original simulated annealing runs.

An off-lattice frustrated model protein with a six-stranded β-barrel structure

“…Recently, Larrass et al 26 introduced the 69-residue BLN protein with the sequence B 9 N 3 ͑LB͒ 4 N 3 B 9 N 3 ͑LB͒ 4 N 3 B 9 N 3 ͑LB͒ 5 L and combining simulated annealing, the automated histogram filtering method, the distance geometry approach, and local minimization, located its global minimum-energy conformation, that is, the native structure of a six-stranded ␤-barrel. Using the statistical temperature molecular dynamics ͑STMD͒ and local minimization, Kim et al 14 found the same global minimumenergy conformation for the BLN 69-mer.…”

“…Using the statistical temperature molecular dynamics ͑STMD͒ and local minimization, Kim et al 14 found the same global minimumenergy conformation for the BLN 69-mer. It is shown 14,26 that the 69-mer has a larger number of local minima and much more highly frustrated energy landscape than the 46mer. Also, using the replica exchange Monte Carlo method, Pan et al 13 estimated the collapse and folding transition temperatures for the 69-mer, and using STMD Kim et al 14 studied the collapse and folding transitions of the 69-mer.…”

“…However, only three articles 13,14,26 have dealt with the BLN 69-mer. However, only three articles 13,14,26 have dealt with the BLN 69-mer.…”

Protein Structure Optimization with a "Lamarckian"' Ant Colony Algorithm

“…The 46-residue protein, B 9 N 3 (LB) 4 N 3 B 9 N 3 (LB) 5 L, folds into a four-strand -barrel and has a frustrated energy landscape, with several competing low-energy structures separated by high barriers [5], [6], [21], [22], [23], [24]. The 69-residue protein, B 9 N 3 (LB) 4 N 3 B 9 N 3 (LB) 4 N 3 B 9 N 3 (LB) 5 L, forms a six-strand -barrel and has a more frustrated energy landscape [5], [6], [25], [26], [27], [28]. These will be referred to as BLN-46 and BLN-69 in the rest of this manuscript.…”

Structure propensities in mutated polyglutamine peptides

“…We examined Thakur and Wetzel's PGQ 9 variants (Table 1) using simulated annealing molecular dynamics (SA-MD) (Kirkpatrick et al, 1983;, as was done previously (VanSchouwen et al, 2010). Structures generated by the simulations were then subjected to a number of structural analyses, including backbone dihedral calculations, local secondary structure assessment with the Dictionary of Protein Secondary Structure (DSSP) (Kabsch and Sander, 1983), automated histogram filtering (AHF) cluster analysis (Gordon and Rothstein, 2006;Larrass et al, 2003), and assessment of global β-sheet structure tendency by counting of "in-register contacts" (Chopra et al, 2008). It should be noted that although a β-helix had been proposed as another possible structure for assemblies of non-mutated polyQ (Perutz et al, 2002), we chose to focus our examination on the case of β-sheet structure given the evidence of preference for this structure type in the case of PGQ 9 (Khare et al, 2005).…”