Fast tree search for enumeration of a lattice model of protein folding

Abstract

Using a fast tree-searching algorithm and a Pentium cluster, we enumerated all the sequences and compact conformations (structures) for a protein folding model on a cubic lattice of size 4 × 3 × 3. We used two types of amino acids -hydrophobic (H) and polar (P) -to make up the sequences, so there were 2 36 ≈ 6.87 × 10 10 different sequences. The total number of distinct structures was 84, 731, 192. We made use of a simple solvation model in which the energy of a sequence folded into a structure is minus the number of hydrophobic amino acids in the "core" of the structure. For every sequence, we found its ground state or ground states, i.e., the structure or structures for which its energy is lowest. About 0.3% of the sequences have a unique ground state. The number of structures that are unique ground states of at least one sequence is 2, 662, 050, about 3% of the total number of structures. However, these "designable" structures differ drastically in their designability, defined as the number of sequences whose unique ground state is that structure. To understand this variation in designability, we studied the distribution of struc- * Present address: Sourcelight Technologies Inc., 906 University Place, Suite B-211, Evanston, IL 60201 † Present address: Yianilos Lab,

Exact sequence analysis for three-dimensional hydrophobic-polar lattice proteins

“…Thus we conclude that native conformations are very compact, but not necessarily maximally compact. This property has already been utilized in enumerations being performed a priori on compact lattices [2,11,47], where, however, the proteins are confined by hand to live in small cuboids (e.g. of size 3 × 3 × 3 or 4 × 3 × 3).…”

“…Therefore, sophisticated algorithms were applied to find lowest energy states for chains of up to 136 monomers. The methods applied are based on very different algorithms, ranging from exact enumeration in two dimensions [9,10] and three dimensions on cuboid (compact) lattices [2,11], and hydrophobic core construction methods [12,13] over genetic algorithms [14,15,16,17,18], Monte Carlo simulations with different types of move sets [19,20,21,22], and generalized ensemble approaches [23] to Rosenbluth chain growth methods [24] of the 'Go with the Winners' type [25,26,27,28,29,30]. With some of these algorithms, thermodynamic quantities of lattice heteropolymers were studied as well [23,27,29,30,31].…”

Exploration of the relationship between topology and designability of conformations

“…6 Numerous studies have been conducted on lattice models to understand protein designability. [6][7][8][9][10][11] Studies have also been done on off-lattice models 12 and semi-off-lattice models of proteins. 13 Emberly et al used off-lattice models of proteins and found that the surface exposure pattern of folded structures is related to their designability.…”

Thermodynamics of Protein Folding from Coarse-Grained Models’ Perspectives

“…Therefore, sophisticated algorithms were developed to find lowest-energy states for chains of up to 136 monomers. The methods applied are based on very different algorithms, ranging from exact enumeration in two dimensions [11,12] and three dimensions on cuboid (compact) lattices [4,[13][14][15], and hydrophobic-core construction methods [16,17] over genetic algorithms [18][19][20][21][22], Monte Carlo simulations with different types of move sets [23][24][25][26], and generalized ensemble approaches [27] to Rosenbluth chaingrowth methods [28] of the 'Go with the Winners' type [29][30][31][32][33][34][35]. With some of these algorithms, thermodynamic quantities of lattice heteropolymers were studied as well [14,27,31,[34][35][36].…”