Heuristic-based tabu search algorithm for folding two-dimensional AB off-lattice model proteins

The protein structure prediction problem is a classical NP hard problem in bioinformatics. The lack of an effective global optimization method is the key obstacle in solving this problem. As one of the global optimization algorithms, tabu search (TS) algorithm has been successfully applied in many optimization problems. We define the new neighborhood conformation, tabu object and acceptance criteria of current conformation based on the original TS algorithm and put forward an improved TS algorithm. By integrating the heuristic initialization mechanism, the heuristic conformation updating mechanism, and the gradient method into the improved TS algorithm, a heuristic-based tabu search (HTS) algorithm is presented for predicting the two-dimensional (2D) protein folding structure in AB off-lattice model which consists of hydrophobic (A) and hydrophilic (B) monomers. The tabu search minimization leads to the basins of local minima, near which a local search mechanism is then proposed to further search for lower-energy conformations. To test the performance of the proposed algorithm, experiments are performed on four Fibonacci sequences and two real protein sequences. The experimental results show that the proposed algorithm has found the lowest-energy conformations so far for three shorter Fibonacci sequences and renewed the results for the longest one, as well as two real protein sequences, demonstrating that the HTS algorithm is quite promising in finding the ground states for AB off-lattice model proteins.     

A comparison of heuristic search algorithms for molecular docking

This paper describes the implementation and comparison of four heuristic search algorithms (genetic algorithm, evolutionary programming, simulated annealing and tabu search) and a random search procedure for flexible molecular docking. To our knowledge, this is the first application of the tabu search algorithm in this area. The algorithms are compared using a recently described fast molecular recognition potential function and a diverse set of five protein–ligand systems. Statistical analysis of the results indicates that overall the genetic algorithm performs best in terms of the median energy of the solutions located. However, tabu search shows a better performance in terms of locating solutions close to the crystallographic ligand conformation. These results suggest that a hybrid search algorithm may give superior results to any of the algorithms alone.     

Hybrid particle swarm optimization and tabu search approach for selecting genes for tumor classification using gene expression data

Gene expression data are characterized by thousands even tens of thousands of measured genes on only a few tissue samples. This can lead either to possible overfitting and dimensional curse or even to a complete failure in analysis of microarray data. Gene selection is an important component for gene expression-based tumor classification systems. In this paper, we develop a hybrid particle swarm optimization (PSO) and tabu search (HPSOTS) approach for gene selection for tumor classification. The incorporation of tabu search (TS) as a local improvement procedure enables the algorithm HPSOTS to overleap local optima and show satisfactory performance. The proposed approach is applied to three different microarray data sets. Moreover, we compare the performance of HPSOTS on these datasets to that of stepwise selection, the pure TS and PSO algorithm. It has been demonstrated that the HPSOTS is a useful tool for gene selection and mining high dimension data.     

Lattice models of peptide aggregation: evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.     

Flexible protein‐protein docking based on Best‐First search algorithm

We developed a new high resolution protein‐protein docking method based on Best‐First search algorithm that loosely imitates protein‐protein associations. The method operates in two stages: first, we perform a rigid search on the unbound proteins. Second, we search alternately on rigid and flexible degrees of freedom starting from multiple configurations from the rigid search. Both stages use heuristics added to the energy function, which causes the proteins to rapidly approach each other and remain adjacent, while optimizing on the energy. The method deals with backbone flexibility explicitly by searching over ensembles of conformations generated before docking. We ran the rigid docking stage on 66 complexes and grouped the results into four classes according to evaluation criteria used in Critical Assessment of Predicted Interactions (CAPRI; “high,” “medium,” “acceptable,” and “incorrect”). Our method found medium binding conformations for 26% of the complexes and acceptable for additional 44% among the top 10 configurations. Considering all the configurations, we found medium binding conformations for 55% of the complexes and acceptable for additional 39% of the complexes. Introducing side‐chains flexibility in the second stage improves the best found binding conformation but harms the ranking. However, introducing side‐chains and backbone flexibility improve both the best found binding conformation and the best found conformation in the top 10. Our approach is a basis for incorporating multiple flexible motions into protein‐protein docking and is of interest even with the current use of a simple energy function. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Hybrid genetic algorithm–tabu search approach for optimising multilayer optical coatings

Constructing multilayer optical coatings (MOCs) is a difficult large-scale optimisation problem due to the enormous size of the search space. In the present paper, a new approach for designing MOCs is presented using genetic algorithms (GAs) and tabu search (TS). In this approach, it is not necessary to specify how many layers will be present in a design, only a maximum needs to be defined. As it is generally recognised that the existence of specific repeating blocks is beneficial for a design, a specific GA representation of a design is used which promotes the occurrence of repeating blocks. Solutions found by GAs are improved by a new refinement method, based on TS, a global optimisation method which is loosely based on artificial intelligence. The improvements are demonstrated by creating a visible transmitting/infrared reflecting filter with a wide variety of materials.     

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.     

Gradient tabu search

This paper presents a modification of the tabu search called gradient tabu search (GTS). It uses analytical gradients for a fast minimization to the next local minimum and analytical diagonal elements of the Hessian to escape local minima. For an efficient blocking of already visited areas tabu regions and tabu directions are introduced into the tabu list (TL). Trials with various well-known test functions indicate that the GTS is a very promising approach to determine local and global minima of differentiable functions. Possible application areas could be optimization routines for force field parameters or conformational searches for large molecules.     

Efficiency of tabu‐search‐based conformational search algorithms

Efficient conformational search or sampling approaches play an integral role in molecular modeling, leading to a strong demand for even faster and more reliable conformer search algorithms. This article compares the efficiency of a molecular dynamics method, a simulated annealing method, and the basin hopping (BH) approach (which are widely used in this field) with a previously suggested tabu‐search‐based approach called gradient only tabu search (GOTS). The study emphasizes the success of the GOTS procedure and, more importantly, shows that an approach which combines BH and GOTS outperforms the single methods in efficiency and speed. We also show that ring structures built by a hydrogen bond are useful as starting points for conformational search investigations of peptides and organic ligands with biological activities, especially in structures that contain multiple rings. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Protein structure predictions by parallel simulated annealing molecular dynamics using genetic crossover

We propose a conformational search method to find a global minimum energy structure for protein systems. The simulated annealing is a powerful method for local conformational search. On the other hand, the genetic crossover can search the global conformational space. Our method incorporates these attractive features of the simulated annealing and genetic crossover. In the previous works, we have been using the Monte Carlo algorithm for simulated annealing. In the present work, we use the molecular dynamics algorithm instead. To examine the effectiveness of our method, we compared our results with those of the normal simulated annealing molecular dynamics simulations by using an α-helical miniprotein. We used genetic two-point crossover here. The conformations, which have lower energy than those obtained from the conventional simulated annealing, were obtained.     

An ant colony approach for clustering

This paper presents an ant colony optimization methodology for optimally clustering N objects into K clusters. The algorithm employs distributed agents which mimic the way real ants find a shortest path from their nest to food source and back. This algorithm has been implemented and tested on several simulated and real datasets. The performance of this algorithm is compared with other popular stochastic/heuristic methods viz. genetic algorithm, simulated annealing and tabu search. Our computational simulations reveal very encouraging results in terms of the quality of solution found, the average number of function evaluations and the processing time required.     

Molecular properties from conformational ensembles. 1. Dipole moments of molecules with multiple internal rotations

We present a novel method for constructing the stable conformational space of small molecules with many rotatable bonds that uses our iterative stochastic elimination (ISE) algorithm, a robust stochastic search method capable of finding ensembles of best solutions for large combinatorial problems. To validate the method, we show that ISE reproduces the best conformers found in a fully exhaustive search, as well as compare computed dipole moments to experimental values, based on molecular ensembles and their Boltzmann distributions. Results were also compared to the alternative molecular dynamics and simulated annealing methods. Our results clarify that many low energy conformations may be required to reproduce molecular properties, while single low energy conformers or ensembles of low energy conformers cannot account for the experimental properties of flexible molecules. Whereas ISE well reproduces conformations that are not separated by very large energy barriers, it has not been successful in reproducing conformations of strained molecules.     

Kick: constraining a stochastic search procedure with molecular fragments

An extension of the Kick program developed by Bera et al. (J Phys Chem A 2006, 110, 4287) is described in which chemically sensible molecular fragments are used in an automated stochastic search algorithm. This results in a vastly reduced region of the potential energy surface which can be explored very quickly. We present use of this modified algorithm to the search for low-lying isomers, and we present candidates for the global energy minimum, for a range of chemical systems. We highlight the usefulness of this procedure for exploring reactions of molecules with transition metal clusters and to the microsolvation of a small dipeptide.     

Low-mode conformational search elucidated: Application to C39H80 and flexible docking of 9-deazaguanine inhibitors into PNP

We previously described a new conformational search method, termed low-mode search (LMOD), and discussed its utility for conformational searches performed on cycloalkanes and a cyclic penta-peptide. 1 In this report, we discuss a rigorous implementation of mode following (c-LMOD) for conformational searching, and we demonstrate that for a conformational search involving cycloheptadecane, this rigorous implementation is capable of finding all of the previously known structures. To the best of our knowledge, this is the first computational proof that mode following can be used for conformational searches conducted on a complex molecular system. We show, however, that, as expected, it is generally inefficient to perform a conformational search in this manner. Nonetheless, c-LMOD has been shown to be an excellent method for conducting conformational analyses involving conformational interconversions, where the location of saddle points is important. We also describe refinement to our original LMOD procedure (l-LMOD) and discuss its utility for a difficult conformational search problem, namely locating the global minimum energy conformation of C₃₉H₈₀. For this search, l-LMOD combined with limited torsional Monte Carlo movement was able to locate the lowest energy structures yet reported, and significantly outperformed a pure torsional Monte Carlo and a genetic algorithm-based search. Furthermore, we also demonstrate the utility of l-LMOD combined with random translation/rotation of a ligand for the extremely difficult problem of docking flexible ligands into flexible protein binding sites on a system that includes 9-deaza-guanine-based inhibitors docked into the flexible biding site of PNP. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1671–1684, 1999     

GRID: A high‐resolution protein structure refinement algorithm

The energy‐based refinement of protein structures generated by fold prediction algorithms to atomic‐level accuracy remains a major challenge in structural biology. Energy‐based refinement is mainly dependent on two components: (1) sufficiently accurate force fields, and (2) efficient conformational space search algorithms. Focusing on the latter, we developed a high‐resolution refinement algorithm called GRID. It takes a three‐dimensional protein structure as input and, using an all‐atom force field, attempts to improve the energy of the structure by systematically perturbing backbone dihedrals and side‐chain rotamer conformations. We compare GRID to Backrub, a stochastic algorithm that has been shown to predict a significant fraction of the conformational changes that occur with point mutations. We applied GRID and Backrub to 10 high‐resolution (≤ 2.8 Å) crystal structures from the Protein Data Bank and measured the energy improvements obtained and the computation times required to achieve them. GRID resulted in energy improvements that were significantly better than those attained by Backrub while expending about the same amount of computational resources. GRID resulted in relaxed structures that had slightly higher backbone RMSDs compared to Backrub relative to the starting crystal structures. The average RMSD was 0.25 ± 0.02 Å for GRID versus 0.14 ± 0.04 Å for Backrub. These relatively minor deviations indicate that both algorithms generate structures that retain their original topologies, as expected given the nature of the algorithms. © 2012 Wiley Periodicals, Inc.     

A Comparison of Three Heuristic Algorithms for Molecular Docking

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Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function

A novel and robust automated docking method that predicts the bound conformations of flexible ligands to macromolecular targets has been developed and tested, in combination with a new scoring function that estimates the free energy change upon binding. Interestingly, this method applies a Lamarckian model of genetics, in which environmental adaptations of an individual's phenotype are reverse transcribed into its genotype and become heritable traits (sic). We consider three search methods, Monte Carlo simulated annealing, a traditional genetic algorithm, and the Lamarckian genetic algorithm, and compare their performance in dockings of seven protein–ligand test systems having known three-dimensional structure. We show that both the traditional and Lamarckian genetic algorithms can handle ligands with more degrees of freedom than the simulated annealing method used in earlier versions of AUTO DOCK , and that the Lamarckian genetic algorithm is the most efficient, reliable, and successful of the three. The empirical free energy function was calibrated using a set of 30 structurally known protein–ligand complexes with experimentally determined binding constants. Linear regression analysis of the observed binding constants in terms of a wide variety of structure-derived molecular properties was performed. The final model had a residual standard error of 9.11 kJ mol⁻¹ (2.177 kcal mol⁻¹) and was chosen as the new energy function. The new search methods and empirical free energy function are available in AUTO DOCK , version 3.0. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1639–1662, 1998     

An ant algorithm for the conformational analysis of flexible molecules

Originally, the ant system was developed for optimization in discrete search spaces such as the traveling salesman problem. We detail our adaptation of the algorithm to optimization in the continuous search space of conformational analysis. The parameters of the algorithm were tuned using a simple test molecule, undecane, and a drug molecule, imatinib. The algorithm is further tested on four more drug or drug-like molecules, on vitamin A and on alanine tetrapeptide.     

A consensus line search algorithm for molecular potential energy functions

Force field based energy minimization of molecular structures is a central task in computational chemistry and biology. Solving this problem usually requires efficient local minimization techniques, i.e., iterative two‐step methods that search first for a descent direction and then try to estimate the step width. The second step, the so called line search, typically uses polynomial interpolation schemes to estimate the next trial step. However, dependent on local properties of the objective function alternative schemes may be more appropriate especially if the objective function shows singularities or exponential behavior. As the choice of the best interpolation scheme cannot be made a priori, we propose a new consensus line search approach that performs several different interpolation schemes at each step and then decides which one is the most reliable at the current position. Although a naive consensus approach would lead to severe performance impacts, our method does not require additional evaluations of the energy function, imposing only negligible computational overhead. Additionally, our method can be easily adapted to the local behavior of other objective functions by incorporating suitable interpolation schemes or omitting non‐fitting schemes. The performance of our consensus line search approach has been evaluated and compared to established standard line search algorithms by minimizing the structures of a large set of molecules using different force fields. The proposed algorithm shows better performance in almost all test cases, i.e., it reduces the number of iterations and function and gradient evaluations, leading to significantly reduced run times. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009