Protein folding and phylogenetic tree reconstruction using stochastic approximation Monte Carlo

Recently, the stochastic approximation Monte Carlo algorithm has been proposed by Liang et al. (2005) as a general-purpose stochastic optimization and simulation algorithm. An annealing version of this algorithm was developed for real small protein folding problems. The numerical results indicate that it outperforms simulated annealing and conventional Monte Carlo algorithms as a stochastic optimization algorithm. We also propose one method for the use of secondary structures in protein folding. The predicted protein structures are rather close to the true structures. Phylogenetic trees have been used in biology for a long time to graphically represent evolutionary relationships among species and genes. An understanding of evolutionary relationships is critical to appropriate interpretation of bioinformatics results. The use of the sequential structure of phylogenetic trees in conjunction with stochastic approximation Monte Carlo was developed for phylogenetic tree reconstruction. The numerical results indicate that it has a capability of escaping from local traps and achieving a much faster convergence to the global likelihood maxima than other phylogenetic tree reconstruction methods, such as BAMBE and MrBayes

Thermodynamics of RNA structures by Wang–Landau sampling

Motivation: Thermodynamics-based dynamic programming RNA secondary structure algorithms have been of immense importance in molecular biology, where applications range from the detection of novel selenoproteins using expressed sequence tag (EST) data, to the determination of microRNA genes and their targets. Dynamic programming algorithms have been developed to compute the minimum free energy secondary structure and partition function of a given RNA sequence, the minimum free-energy and partition function for the hybridization of two RNA molecules, etc. However, the applicability of dynamic programming methods depends on disallowing certain types of interactions (pseudoknots, zig-zags, etc.), as their inclusion renders structure prediction an nondeterministic polynomial time (NP)-complete problem. Nevertheless, such interactions have been observed in X-ray structures