On the characterization and software implementation of general protein lattice models

Contributions of topological polar-polar contacts to achieve better folding stability of 2D/3D HP lattice proteins: An in silico approach

<abstract> <p>Many of the simplistic hydrophobic-polar lattice models, such as Dill's model (called <bold>Model 1</bold> herein), are aimed to fold structures through hydrophobic-hydrophobic interactions mimicking the well-known hydrophobic collapse present in protein structures. In this work, we studied 11 designed hydrophobic-polar sequences, S₁-S₈ folded in 2D-square lattice, and S₉-S₁₁ folded in 3D-cubic lattice. And to better fold these structures we have developed <bold>Model 2</bold> as an approximation to convex function aimed to weight hydrophobic-hydrophobic but also polar-polar contacts as an augmented version of <bold>Model 1</bold>. In this partitioned approach hydrophobic-hydrophobic ponderation was tuned as <italic>α</italic>-1 and polar-polar ponderation as <italic>α</italic>. This model is centered in preserving required hydrophobic substructure, and at the same time including polar-polar interactions, otherwise absent, to reach a better folding score now also acquiring the polar-polar substructure. In all tested cases the folding trials were better achieved with <bold>Model 2</bold>, using <italic>α</italic> values of 0.05, 0.1, 0.2 and 0.3 depending of sequence size, even finding optimal scores not reached with <bold>Model 1</bold>. An important result is that the better folding score, required the lower <italic>α</italic> weighting. And when <italic>α</italic> values above 0.3 are employed, no matter the nature of the hydrophobic-polar sequence, banning of hydrophobic-hydrophobic contacts started, thus yielding misfolding of sequences. Therefore, the value of <italic>α</italic> to correctly fold structures is the result of a careful weighting among hydrophobic-hydrophobic and polar-polar contacts.</p> </abstract>

Effective hybrid approach for protein structure prediction in a two-dimensional Hydrophobic-Polar model

Hydrophobic-polar (HP) models are widely used to predict protein folding and hydrophobic interactions. Numerous optimization algorithms have been proposed to predict protein folding using the two-dimensional (2D) HP model. However, to obtain an optimal protein structure from the 2D HP model remains challenging. In this study, an algorithm integrating particle swarm optimization (PSO) and Tabu search (TS), named PSO-TS, was proposed to predict protein structures based on the 2D HP model. TS can help PSO to avoid getting trapped in a local optima and thus to remove the limitation of PSO in predicting protein folding by the 2D HP model. In this study, a total of 28 protein sequences were used to evaluate the accuracy of PSO-TS in protein folding prediction. The proposed PSO-TS method was compared with 15 other approaches for predicting short and long protein sequences. Experimental results demonstrated that PSO-TS provides a highly accurate, reproducible, and stabile prediction ability for the protein folding by the 2D HP model.

Protein folding prediction in the HP model using ions motion optimization with a greedy algorithm

Background

The function of a protein is determined by its native protein structure. Among many protein prediction methods, the Hydrophobic-Polar (HP) model, an ab initio method, simplifies the protein folding prediction process in order to reduce the prediction complexity.

Results

In this study, the ions motion optimization (IMO) algorithm was combined with the greedy algorithm (namely IMOG) and implemented to the HP model for the protein folding prediction based on the 2D-triangular-lattice model. Prediction results showed that the integration method IMOG provided a better prediction efficiency in a HP model. Compared to others, our proposed method turned out as superior in its prediction ability and resilience for most of the test sequences. The efficiency of the proposed method was verified by the prediction results. The global search capability and the ability to escape from the local best solution of IMO combined with a local search (greedy algorithm) to the new algorithm IMOG greatly improve the search for the best solution with reliable protein folding prediction.

Conclusion

Overall, the HP model integrated with IMO and a greedy algorithm as IMOG provides an improved way of protein structure prediction of high stability, high efficiency, and outstanding performance.

A Particle Swarm Optimization-Based Approach with Local Search for Predicting Protein Folding

The hydrophobic-polar (HP) model is commonly used for predicting protein folding structures and hydrophobic interactions. This study developed a particle swarm optimization (PSO)-based algorithm combined with local search algorithms; specifically, the high exploration PSO (HEPSO) algorithm (which can execute global search processes) was combined with three local search algorithms (hill-climbing algorithm, greedy algorithm, and Tabu table), yielding the proposed HE-L-PSO algorithm. By using 20 known protein structures, we evaluated the performance of the HE-L-PSO algorithm in predicting protein folding in the HP model. The proposed HE-L-PSO algorithm exhibited favorable performance in predicting both short and long amino acid sequences with high reproducibility and stability, compared with seven reported algorithms. The HE-L-PSO algorithm yielded optimal solutions for all predicted protein folding structures. All HE-L-PSO-predicted protein folding structures possessed a hydrophobic core that is similar to normal protein folding.

A firefly-inspired method for protein structure prediction in lattice models

We introduce a Firefly-inspired algorithmic approach for protein structure prediction over two different lattice models in three-dimensional space. In particular, we consider three-dimensional cubic and three-dimensional face-centred-cubic (FCC) lattices. The underlying energy models are the Hydrophobic-Polar (H-P) model, the Miyazawa–Jernigan (M-J) model and a related matrix model. The implementation of our approach is tested on ten H-P benchmark problems of a length of 48 and ten M-J benchmark problems of a length ranging from 48 until 61. The key complexity parameter we investigate is the total number of objective function evaluations required to achieve the optimum energy values for the H-P model or competitive results in comparison to published values for the M-J model. For H-P instances and cubic lattices, where data for comparison are available, we obtain an average speed-up over eight instances of 2.1, leaving out two extreme values (otherwise, 8.8). For six M-J instances, data for comparison are available for cubic lattices and runs with a population size of 100, where, a priori, the minimum free energy is a termination criterion. The average speed-up over four instances is 1.2 (leaving out two extreme values, otherwise 1.1), which is achieved for a population size of only eight instances. The present study is a test case with initial results for ad hoc parameter settings, with the aim of justifying future research on larger instances within lattice model settings, eventually leading to the ultimate goal of implementations for off-lattice models.