Abstract
BackgroundThe ab initio protein folding problem consists of predicting protein tertiary structure from a given amino acid sequence by minimizing an energy function; it is one of the most important and challenging problems in biochemistry, molecular biology and biophysics. The ab initio protein folding problem is computationally challenging and has been shown to be -hard even when conformations are restricted to a lattice. In this work, we implement and evaluate the replica exchange Monte Carlo (REMC) method, which has already been applied very successfully to more complex protein models and other optimization problems with complex energy landscapes, in combination with the highly effective pull move neighbourhood in two widely studied Hydrophobic Polar (HP) lattice models.ResultsWe demonstrate that REMC is highly effective for solving instances of the square (2D) and cubic (3D) HP protein folding problem. When using the pull move neighbourhood, REMC outperforms current state-of-the-art algorithms for most benchmark instances. Additionally, we show that this new algorithm provides a larger ensemble of ground-state structures than the existing state-of-the-art methods. Furthermore, it scales well with sequence length, and it finds significantly better conformations on long biological sequences and sequences with a provably unique ground-state structure, which is believed to be a characteristic of real proteins. We also present evidence that our REMC algorithm can fold sequences which exhibit significant interaction between termini in the hydrophobic core relatively easily.ConclusionWe demonstrate that REMC utilizing the pull move neighbourhood significantly outperforms current state-of-the-art methods for protein structure prediction in the HP model on 2D and 3D lattices. This is particularly noteworthy, since so far, the state-of-the-art methods for 2D and 3D HP protein folding – in particular, the pruned-enriched Rosenbluth method (PERM) and, to some extent, Ant Colony Optimisation (ACO) – were based on chain growth mechanisms. To the best of our knowledge, this is the first application of REMC to HP protein folding on the cubic lattice, and the first extension of the pull move neighbourhood to a 3D lattice.
Highlights
The ab initio protein folding problem consists of predicting protein tertiary structure from a given amino acid sequence by minimizing an energy function; it is one of the most important and challenging problems in biochemistry, molecular biology and biophysics
In the same manner in which the parameters for replica exchange Monte Carlo (REMC) remain fixed for all experiments, the pruned enriched Rosenbluth method (PERM) and ACOHPPFP-3 parameters have been fixed to the values suggested by their authors
The parameter values for ACOHPPFP-3 have been taken from Shmygelska and Hoos [9], and those for PERM were optimized by P
Summary
The ab initio protein folding problem consists of predicting protein tertiary structure from a given amino acid sequence by minimizing an energy function; it is one of the most important and challenging problems in biochemistry, molecular biology and biophysics. Even for simplified protein models that use lattices to discretize the conformational space, the ab initio protein structure prediction problem has been shown to be -hard [1,2,3], and a polynomial-time algorithm is unlikely to exist. We restrict our attention to those HP models that embed all protein folds into the 2D square lattice or the 3D cubic lattice Many of these algorithms can be classified primarily as construction based (or chain growth) algorithms, which determine folds by sequentially placing residues onto the lattice. PERM is a Monte Carlo based chain growth algorithm that iteratively constructs partial conformations; it is heavily based on mechanisms for pruning unfavourable folds and for enriching promising partial conformations, to facilitate their further exploration
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