2D HP Model Research Articles

Emergent protein folding modeled with evolved neural cellular automata using the 3D HP model.

We used cellular automata (CA) for the modeling of the temporal folding of proteins. Unlike the focus of the vast research already done on the direct prediction of the final folded conformations, we will model the temporal and dynamic folding process. To reduce the complexity of the interactions and the nature of the amino acid elements, lattice models like HP were used, a model that categorizes the amino acids regarding their hydrophobicity. Taking into account the restrictions of the lattice model, the CA model defines how the amino acids interact through time to obtain a folded conformation. We extended the classical CA models using artificial neural networks for their implementation (neural CA), and we used evolutionary computing to automatically obtain the models by means of Differential Evolution. As the iterative folding also provides the final folded conformation, we can compare the results with those from direct prediction methods of the final protein conformation. Finally, as the neural CA that provides the iterative folding process can be evolved using several protein sequences and used as operators in the folding of another protein with different length, this represents an advantage over the NP-hard complexity of the original problem of the direct prediction.

Solving Two-Dimensional HP Model by Firefly Algorithm and Simplified Energy Function

In order to solve the HP model of the protein folding problem, we investigated traditional energy function and pointed out that its discrete property cannot give direction of the next step to the searching point, causing a challenge to optimization algorithms. Therefore, we introduced the simplified energy function into a turn traditional discrete energy function to continuous one. The simplified energy function totals the distance between all pairs of hydrophobic amino acids. To optimize the simplified energy function, we introduced the latest swarm intelligence algorithm, the firefly algorithm (FA). FA is a hot nature-inspired technique and has been used for solving nonlinear multimodal optimization problems in dynamic environment. We also proposed the code scheme strategy to apply FA to the simplified HP model with the clash test strategy. The experiment took 14 sequences of different chain lengths from 18 to 100 as the dataset and compared the FA with standard genetic algorithm and immune genetic algorithm. Each algorithm ran 20 times. The averaged energy convergence results show that FA achieves the lowest values. It concludes that it is effective to solve 2D HP model by the firefly algorithm and the simplified energy function.

Particle swarm optimization approach for protein structure prediction in the 3D HP model

The primary structure of proteins consists of a linear chain of amino acids that can vary in length. Proteins fold, under the influence of several chemical and physical factors, into their 3D structures, which determine their biological functions and properties. Misfolding occurs when the protein folds into a 3D structure that does not represent its native structure, which can lead to diseases. Due to the importance of this problem and since laboratory techniques are not always feasible, computational methods for characterizing protein structures have been proposed. In this paper, we present a particle swarm optimization (PSO) based algorithm for predicting protein structures in the 3D hydrophobic polar model. Starting from a small set of candidate solutions, our algorithm efficiently explores the search space and returns 3D protein structures with minimal energy. To test our algorithm, we used two sets of benchmark sequences of different lengths and compared our results to published results. Our algorithm performs better than previous algorithms by finding lower energy structures or by performing fewer numbers of energy evaluations.

Annealing genetic algorithm for protein folding simulations in the 3D HP model

The protein folding problem, i.e., the prediction of the tertiary structures of protein molecules from their amino acid sequences is one of the most important problems in computational biology. This problem has been widely studied under the HP model in which each amino acid is classified, based on its hydrophobicity, as a hydrophobic (H) residue or a hydrophilic (or polar, P) one. The protein folding problem in the HP model is in fact to find conformations with the lowest energies for some benchmark amino acid sequences. A genetic algorithm (GA) is used to find the lowest energy conformation in this paper. Each time for a newly produced offspring individual, which is originated from the selection, crossover and mutation operator of two parent individuals, we adopt the new acceptance criteria based on the annealing strategy to let it pass into the next generation, and propose a so-called annealing genetic algorithm (aGA) to predict efficiently the protein folding conformations in the three-dimensional (3D) HP model. Eleven benchmarks are tested to verify the effectiveness of the proposed approach and the computational results show that aGA explores the conformation surfaces more efficiently than other methods, and finds new lower energies in several cases, which means that aGA is an efficient tool for the protein folding simulations.

Protein 3D HP Model Folding Simulation Using a Hybrid of Genetic Algorithm and Particle Swarm Optimization

Given the amino-acid sequence of a protein, the prediction of a protein's tertiary structure is known as the protein folding problem. The protein folding problem in the hydrophobic-hydrophilic lattice model is the problem of finding the lowest energy conformation. This is the NP-complete problem. In order to enhance the procedure performance for predicting protein structures, a hybrid genetic-based particle swarm optimization (PSO) is proposed. Simulation results indicate that our approach outperforms the existing evolutionary algorithms. The method can be applied successfully to the protein folding problem based on the three-dimensional hydrophobic- hydrophilic lattice model.

A New Branch and Bound Method for the Protein Folding Problem Under the 2D-HP Model

The protein folding problem is a fundamental problem in computational molecular biology and biochemical physics. The previously best known branch and bound method for the protein folding problem may find optimal or near-optimal energy structure from the benchmark sequences, but the total computation time is rather lengthy because it usually needs to run a great deal of simulating tests or else lack of accuracy. In this paper, we develop a new branch and bound method for the the protein folding problem under the two-dimensional HP model to overcome the mentioned drawbacks. By using benchmark sequences for evaluation, we demonstrate that the performance of our method is superior than previously known methods. Moreover, our method is a simple, flexible and easily implemented one for the protein folding problem.

Protein folding simulations of 2D HP model by the genetic algorithm based on optimal secondary structures

In this paper, based on the evolutionary Monte Carlo (EMC) algorithm, we have made four points of ameliorations and propose a so-called genetic algorithm based on optimal secondary structure (GAOSS) method to predict efficiently the protein folding conformations in the two-dimensional hydrophobic–hydrophilic (2D HP) model. Nine benchmarks are tested to verify the effectiveness of the proposed approach and the results show that for the listed benchmarks GAOSS can find the best solutions so far. It means that reasonable, effective and compact secondary structures (SSs) can avoid blind searches and can reduce time consuming significantly. On the other hand, as examples, we discuss the diversity of protein GSC for the 24-mer and 85-mer sequences. Several GSCs have been found by GAOSS and some of the conformations are quite different from each other. It would be useful for the designing of protein molecules. GAOSS would be an efficient tool for the protein structure predictions (PSP).

A filter-and-fan approach to the 2D HP model of the protein folding problem

We examine a prominent and widely-studied model of the protein folding problem, the two-dimensional (2D) HP model, by means of a filter-and-fan (F&F) solution approach. Our method is designed to generate compound moves that explore the solution space in a dynamic and adaptive fashion. Computational results for standard sets of benchmark problems show that the F&F algorithm is highly competitive with the current leading algorithms, requiring only a single solution trial to obtain best known solutions to all problems tested, in contrast to a hundred or more trials required in the typical case to evaluate the performance of the best of the alternative methods.

Optimal HP configurations of proteins by combining local search with elastic net algorithm

The prediction of protein conformation from its amino-acid sequence is one of the most prominent problems in computational biology. But it is NP-hard. Here, we focus on an abstraction widely studied of this problem, the two-dimensional hydrophobic-polar protein folding problem (2D HP PFP). Mathematical optimal model of free energy of protein is established. Native conformations are often sought using stochastic sampling methods, but which are slow. The elastic net (EN) algorithm is one of fast deterministic methods as travelling salesman problem (TSP) strategies. However, it cannot be applied directly to protein folding problem, because of fundamental differences in the two types of problems. In this paper, how the 2D HP protein folding problem can be framed in terms of TSP is shown. Combination of the modified elastic net algorithm and novel local search method is adopted to solve this problem. To our knowledge, this is the first application of EN algorithm to 2D HP model. The results indicate that our approach can find more optimal conformations and is simple to implement, computationally efficient and fast.

Structure-Approximating Inverse Protein Folding Problem in the 2D HP Model

The inverse protein folding problem is that of designing an amino acid sequence which has a particular native protein fold. This problem arises in drug design where a particular structure is necessary to ensure proper protein-protein interactions. In this paper, we show that in the 2D HP model of Dill it is possible to solve this problem for a broad class of structures. These structures can be used to closely approximate any given structure. One of the most important properties of a good protein (in drug design) is its stability--the aptitude not to fold simultaneously into other structures. We show that for a number of basic structures, our sequences have a unique fold.

Inverse protein folding in 2D HP mode (extended abstract).

The inverse protein folding problem is that of designing an amino acid sequence which has a particular native protein fold. This problem arises in drug design where a particular structure is necessary to ensure proper protein-protein interactions. In this paper we show that in the 2D HP model of Dill it is possible to solve this problem for a broad class of structures. These structures can be used to closely approximate any given structure. One of the most important properties of a good protein is its stability -- the aptitude not to fold simultanously into other structures. We show that for a number of basic structures, our sequences have a unique fold.

Protein Folding in the 2D HP Model

We study folding algorithms in the two-dimensional Hydrophobic-<br />Hydrophilic model (2D HP model) for protein structure formation. We<br />consider three generalizations of the best known approximation algorithm.<br />We show that two of the generalizations do not improve the worst<br />case approximation ratio. The third generalization seems to be better,<br />and the analysis of its approximation ratio leads to an interesting combinatorial<br />problem.