Protein folding optimization based on 3D off-lattice model via an improved artificial bee colony algorithm

Bilinear optimization of protein structure prediction: An exact approach via AB off-lattice model

Protein structure prediction (PSP) remains a central challenge in computational biology due to its inherent complexity and high dimensionality. While numerous heuristic approaches have appeared in the literature, their success varies. The AB off-lattice model, which characterizes proteins as sequences of A (hydrophobic) and B (hydrophilic) beads, presents a simplified perspective on PSP. This work presents a mathematical optimization-based methodology capitalizing on the off-lattice AB model. Dissecting the inherent non-linearities of the energy landscape of protein folding allowed for formulating the PSP as a bilinear optimization problem. This formulation was achieved by introducing auxiliary variables and constraints that encapsulate the nuanced relationship between the protein's conformational space and its energy landscape. The proposed bilinear model exhibited notable accuracy in pinpointing the global minimum energy conformations on a benchmark dataset presented by the Protein Data Bank (PDB). Compared to traditional heuristic-based methods, this bilinear approach yielded exact solutions, reducing the likelihood of local minima entrapment. This research highlights the potential of reframing the traditionally non-linear protein structure prediction problem into a bilinear optimization problem through the off-lattice AB model. Such a transformation offers a route toward methodologies that can determine the global solution, challenging current PSP paradigms. Exploration into hybrid models, merging bilinear optimization and heuristic components, might present an avenue for balancing accuracy with computational efficiency.

Effects of Residual Composition and Distribution on the Structural Characteristics of the Protein

The effect of ratio and consecutive number of hydrophobic residues in the repeating unit of protein chains was investigated by MD simulation. The modified off-lattice HNP model was applied in this study. The protein chains constituted by different HNP ratios or different numbers of consecutively hydrophobic residues with the same chain length were simulated under a broad temperature range. We concluded that the proteins with higher ratio or larger number of sequentially hydrophobic residues present more orientated and compact structure under a certain low temperature. It is attributed to the lower non-bonded potential energy between H-H residual pairs, especially more hydrophobic residues in a procession among the protein chain. Considering the microscopic structure of the protein, more residue contacts are achieved with the proteins with higher ratios and sequential H residues under the low temperature. Meanwhile, with the ratio and consecutive number of H residues increasing, the distribution of stem length showed a transition from exponential decline to unimodal and even multiple peaks, indicating the specific ordered structure formed. These results provide an insight into 3D structural properties of proteins from their residue sequences, which has a primary structure at molecular level and, ultimately, a practical possibility of applying in biotechnological applications.

Sequence-based protein structure optimization using enhanced simulated annealing algorithm on a coarse-grained model

The understanding of protein structure is vital to determine biological function. We presented an enhanced simulated annealing (ESA) algorithm to investigate protein three-dimensional (3D) structure on a coarse-grained model. Inside the algorithm, we adjusted exploration equations to achieve good search intensity. To that end, our algorithm used (i) a multivariable disturbance operator for diversification of solution, (ii) a sign function to improve randomness of solution, and (iii) taking remainder operation performed on floating-point number to tackle out-of-range solution. By monitoring energy value throughout the simulation, the energy-optimal state can be found. The ESA algorithm was tested on artificial and real protein sequences with different lengths. The results show that our algorithm outperforms conventional simulated annealing algorithm and can compete with the reported algorithms before. Especially, our algorithm can obtain folding conformations with specific structural features. Further analysis shows that simulating trajectory of seeking the lowest energy can exhibit thermodynamic behavior of protein folding. Graphical Abstract.

Protein structure optimization using improved simulated annealing algorithm on a three-dimensional AB off-lattice model

This paper proposed an improved simulated annealing (ISA) algorithm for protein structure optimization based on a three-dimensional AB off-lattice model. In the algorithm, we provided a general formula used for producing initial solution, and designed a multivariable disturbance term, relating to the parameters of simulated annealing and a tuned constant, to generate neighborhood solution. To avoid missing optimal solution, storage operation was performed in searching process. We applied the algorithm to test artificial protein sequences from literature and constructed a benchmark dataset consisting of 10 real protein sequences from the Protein Data Bank (PDB). Otherwise, we generated C_α space-filling model to represent protein folding conformation. The results indicate our algorithm outperforms the five methods before in searching lower energies of artificial protein sequences. In the testing on real proteins, our method can achieve the energy conformations with C_α-RMSD less than 3.0 Å from the PDB structures. Moreover, C_α space-filling model may simulate dynamic change of protein folding conformation at atomic level.

A benchmark of optimally folded protein structures using integer programming and the 3D-HP-SC model

The Protein Structure Prediction (PSP) problem comprises, among other issues, forecasting the three-dimensional native structure of proteins using only their primary structure information. Most computational studies in this area use synthetic data instead of real biological data. However, the closer to the real-world, the more the impact of results and their applicability. This work presents 17 real protein sequences extracted from the Protein Data Bank for a benchmark to the PSP problem using the tri-dimensional Hydrophobic-Polar with Side-Chains model (3D-HP-SC). The native structure of these proteins was found by maximizing the number of hydrophobic contacts between the side-chains of amino acids. The problem was treated as an optimization problem and solved by means of an Integer Programming approach. Although the method optimally solves the problem, the processing time has an exponential trend. Therefore, due to computational limitations, the method is a proof-of-concept and it is not applicable to large sequences. For unknown sequences, an upper bound of the number of hydrophobic contacts (using this model) can be found, due to a linear relationship with the number of hydrophobic residues. The comparison between the predicted and the biological structures showed that the highest similarity between them was found with distance thresholds around 5.2-8.2 Å. Both the dataset and the programs developed will be freely available to foster further research in the area.

An improved stochastic fractal search algorithm for 3D protein structure prediction

Protein structure prediction (PSP) is a significant area for biological information research, disease treatment, and drug development and so on. In this paper, three-dimensional structures of proteins are predicted based on the known amino acid sequences, and the structure prediction problem is transformed into a typical NP problem by an AB off-lattice model. This work applies a novel improved Stochastic Fractal Search algorithm (ISFS) to solve the problem. The Stochastic Fractal Search algorithm (SFS) is an effective evolutionary algorithm that performs well in exploring the search space but falls into local minimums sometimes. In order to avoid the weakness, Lvy flight and internal feedback information are introduced in ISFS. In the experimental process, simulations are conducted by ISFS algorithm on Fibonacci sequences and real peptide sequences. Experimental results prove that the ISFS performs more efficiently and robust in terms of finding the global minimum and avoiding getting stuck in local minimums.

Deoxynivalenol induces apoptosis in PC12 cells via the mitochondrial pathway

Deoxynivalenol (DON) has broad toxicity in animals and humans. In this study the impact of DON treatment on apoptotic pathways in PC12 cells was determined. The effects of DON were evaluated on (i) typical indicators of apoptosis, including cellular morphology, cell activity, lactate dehydrogenase (LDH) release, and apoptosis ratio in PC12 cells, and on (ii) the expression of key genes and proteins related to apoptosis, including Bcl-2, Bax, Bid, cytochrome C (Cyt C), apoptosis inducing factor (AIF), cleaved-Caspase9, and cleaved-Caspase3. DON treatment inhibited proliferation of PC12 cells, induced significant morphological changes and apoptosis, promoted the release of Cyt C and AIF from the mitochondria, and increased the activities of cleaved-Caspase9 and cleaved-Caspase3. Bcl-2 expression decreased with increasing DON concentrations, in contrast to Bax and Bid, which were increased with increasing DON concentration. These data demonstrate that DON induces apoptosis in PC12 cells through the mitochondrial apoptosis pathway.