Growth algorithms for lattice heteropolymers at low temperatures

Abstract

Two improved versions of the pruned-enriched-Rosenbluth method ͑PERM͒ are proposed and tested on simple models of lattice heteropolymers. Both are found to outperform not only the previous version of PERM, but also all other stochastic algorithms which have been employed on this problem, except for the core directed chain growth method ͑CG͒ of Beutler and Dill. In nearly all test cases they are faster in finding low-energy states, and in many cases they found new lowest energy states missed in previous papers. The CG method is superior to our method in some cases, but less efficient in others. On the other hand, the CG method uses heavily heuristics based on presumptions about the hydrophobic core and does not give thermodynamic properties, while the present method is a fully blind general purpose algorithm giving correct Boltzmann-Gibbs weights, and can be applied in principle to any stochastic sampling problem.

Re‐examination of structure optimization of off‐lattice protein AB models by conformational space annealing

“…We note that the degrees of freedom of the system S n in three dimensions increases as 2n which corresponds to the number of backbone angles of a protein with n residues. Table 1 shows the results of the lowest energy of model1 in two dimensions, along with the values reported in the literature by nPERMis, 4 ACMC, 5 our previous work, 6 and STMD 7 for comparison. All methods except nPERMis report identical results for S 13 , S 21 , and S 34 .…”

“…Although putative groundstate conformations have been reported, they are continually being updated, [4][5][6][7][8][9] and thus it is not clear if they correspond to true ground-state conformations.…”

Thermodynamics of Protein Folding from Coarse-Grained Models’ Perspectives

“…In the recently developed new variants nPERMss and nPERMis [33], the number of copies is not constant and depends on the ratio of the weight W PERM n compared to the upper threshold value W > n and the copies are necessarily chosen to be different. The method of selecting the copies is based on simple sampling (ss) in nPERMss and a kind of importance sampling (is) in nPERMis.…”

“…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].…”

“…For practical applications of this algorithm, in particular for studies of heteropolymers, it is more favorable to replace the original pruning-enrichment core, i.e., PERM [30], by the modern, improved variants nPERMss or nPERMis [33]. The combination of this more efficient chain-growth strategy with multicanonical sampling is straightforward.…”