Leonidas Kapsokalivas

A Local Move Set for Protein Folding in Triangular Lattice Models

The HP model is one of the most popular discretized models for the protein folding problem, i.e., for computationally predicting the three-dimensional structure of a protein from its amino acid sequence. This model considers the interactions between hydrophobic amino acids to be the driving force in the folding process. Thus, it distinguishes between polar and hydrophobic amino acids only and asks for an embedding of the amino acid sequence into a rectangular grid lattice which maximizes the number of neighboring pairs (contacts) of hydrophobic amino acids in the lattice. In this paper, we consider an HP-like model which uses a more appropriate grid structure, namely the 2D triangular grid and the face-centered cubic lattice in 3D. We consider a local-search approach for finding an optimal embedding. For defining the local-search neighborhood, we design a move set, the so-called pull moves, and prove its reversibility and completeness. We then use these moves for a tabu search algorithm which is experimentally shown to lead into optimum energy configurations and improve the current best results for several sequences in 2D and 3D.

Protein Folding Simulation by Two-Stage Optimization

This paper proposes a two-stage optimization approach for protein folding simulation in the FCC lattice, inspired from the phenomenon of hydrophobic collapse. Given a protein sequence, the first stage of the approach produces compact protein structures with the maximal number of contacts among hydrophobic monomers, using the CPSP tools for optimal structure prediction in the HP model. The second stage uses those compact structures as starting points to further optimize the protein structure for the input sequence by employing simulated annealing local search and a 20 amino acid pairwise interactions energy function. Experiment results with PDB sequences show that compact structures produced by the CPSP tools are up to two orders of magnitude better, in terms of the pairwise energy function, than randomly generated ones. Also, initializing simulated annealing with these compact structures, yields better structures in fewer iterations than initializing with random structures. Hence, the proposed two-stage optimization outperforms a local search procedure based on simulated annealing alone.

Research article: Population-based local search for protein folding simulation in the MJ energy model and cubic lattices

We present experimental results on benchmark problems in 3D cubic lattice structures with the Miyazawa-Jernigan energy function for two local search procedures that utilise the pull-move set: (i) population-based local search (PLS) that traverses the energy landscape with greedy steps towards (potential) local minima followed by upward steps up to a certain level of the objective function; (ii) simulated annealing with a logarithmic cooling schedule (LSA). The parameter settings for PLS are derived from short LSA-runs executed in pre-processing and the procedure utilises tabu lists generated for each member of the population. In terms of the total number of energy function evaluations both methods perform equally well, however, PLS has the potential of being parallelised with an expected speed-up in the region of the population size. Furthermore, both methods require a significant smaller number of function evaluations when compared to Monte Carlo simulations with kink-jump moves.

Two Local Search Methods for Protein Folding Simulation in the HP and the MJ Lattice Models

We present experimental results on benchmark problems for two local search procedures that utilise the pull-move set: (i) simulated annealing with logarithmic cooling schedule and (ii) guided local search that traverses the energy landscape with greedy steps towards (potential) local minima followed by upwards steps to a certain level of the objective function. The latter method returns optimum values on established 2D and 3D HP benchmark problems faster than logarithmic simulated annealing (LSA), however, it performs worse on five benchmarks designed for the Miyazawa-Jernigan energy function, where LSA reaches optimum solutions on all five benchmarks. Moreover, the number of function evaluations executed by LSA is significantly smaller than the corresponding number for Monte Carlo simulations with kink-jump moves.

Uphill unfolding of native protein conformations in cubic lattices

We present results from simulations of unfolding in cubic lattices with two types of simplified energy functions, namely the Miyazawa–Jernigan (MJ) energy function and the hydrophobic-polar (HP) model. The simulations are executed on six benchmark problems for the MJ model proposed by Faisca and Plaxco [7] and ten well-known benchmark problems for the HP model devised by Beutler and Dill [2]. The unfolding procedure utilizes the pull-move set as a neighbourhood relation and a new population-based search method. For all sixteen benchmark problems we establish the existence of short pathways with monotonically increasing energy functions from ground states to contact-free unfolded states, which includes the three sequences with a high contact order number studied in the MJ model. The number of pull-move transitions (length of unfolding pathways) differs only slightly for the sixteen benchmark problems and ranges from 27 to 31 for both types of benchmarks. The computational effort of finding unfolding paths and subsequent refolding is discussed in the context of one-way functions.

A Symmetry-Free Subspace for Ab initio Protein Folding Simulations

Ab initio protein structure prediction usually tries to find a ground state in an extremely large phase space. Stochastic search algorithms are often employed by using a predefined energy function. However, for each valid conformation in the search phase space, there are usually several counterparts that are reflective, rotated or reflectively rotated forms of the current conformation, imprecisely called isometric conformations here. In protein folding, these isometric conformations correspond to the different rotation states caused by admissible protein structure transitions. In structure prediction, these isometric conformations, owning the same energy value, not only significantly increase the search complexity but also degrade the stability of some local search algorithms. In this paper, we will prove that there exists a subspace that is unique (no two conformations in the space are isometric) and complete (for any valid conformation, there exists a corresponding conformation in the subspace that is a reflective or rotated form of it). We demonstrate that this subspace, which is about 1/24 of the conventional search space in the 3D lattice model and 1/8 in the 2D model contains the lowest energy conformation, and all other isometric lowest energy forms can then be obtained by protein rotation. Our experiments show that the subspace can significantly speed up existing local search algorithms.

Stochastic local search for the optimization of secondary structure packing in proteins

We examine the problem of packing secondary structure fragments into low energy conformations via a local search optimization algorithm. We first describe a simplified off-lattice model for the representation of protein conformations and adapt the energy minimization problem behind protein folding into our model. We propose a move set that transforms a protein conformation into another in order to enable the use of local search algorithms for protein folding simulations and conformational search. Special care has been taken so that amino acids in a conformation do not overlap. The constraint of producing an overlapfree conformation can be seen as a objective that conflicts with the energy minimization. Therefore, we approach protein folding as a two-objective problem. We employ a monte carlo-based optimization algorithm in combination to the proposed move set. The algorithm deals with the energy minimization problem while maintaining overlap-free conformations. Initial conformations incorporate experimentally determined secondary structure, which is preserved throughout the execution of local search. Our method produced conformations with a minimum RMSD of alpha-carbon atoms in the range of 3.95A to 5.96A for all benchmarks apart from one for which the value was 7.8A.

A replica exchange monte carlo algorithm for the optimization of secondary structure packing in proteins

We approach the problem of packing secondary structure fragments into low energy conformations with a local search optimization algorithm. Protein conformations are represented in a simplified off-lattice model. In that model we propose a move set that transforms a protein conformation into another in order to enable the use of local search algorithms for protein folding simulations and conformational search. The energy minimization problem behind protein folding is adapted to our model. Special care has been taken so that amino acids in a conformation do not overlap. The constraint of producing an overlap-free conformation can be seen as a objective that conflicts with the energy minimization. Thus, we approach protein folding as a two-objective problem. We employ a replica exchange Monte Carlo algorithm in combination to the proposed move set. The algorithm deals with the energy minimization problem while maintaining overlap-free conformations. Initial conformations incorporate experimentally determined secondary structure, which is preserved throughout the execution of local search. Our method produced conformations with a minimum RMSD of alpha-carbon atoms in the range of 4.71A to 6.82A for all benchmarks apart from one for which the value was 9.68A.