Hydrophobic-polar Model Research Articles

A novel algorithm based on a modified PSO to predict 3D structure for proteins in HP model using Transfer Learning

Most intracellular activities of living organisms are performed by proteins that have unique and complex 3-Dimensional (3D) structures, playing very important roles in their operations. Due to importance and challenges of predicting 3D structures for proteins, laboratory methods with limitations such as time consuming and high cost have been developed. Computational methods use a sequence of amino acids to obtain the 3D structure. They encounter with a nondeterministic problem having polynomial completion time (NP-Complete problem); with a chain of amino acids as input, and a protein, with 3D structure, as output. In this paper, a new population-based algorithm, under Predatory Search Strategy-Particle Swarm Optimization (PSS-PSO) framework, is presented for predicting the 3D structure; using Hydrophobic-Polar (HP) model on Face-Centered Cubic (FCC) lattice. In this approach, name TRL-PSSPSO, two new moves are proposed to direct each solution toward the native structure: Local Move for reaching a dense hydrophobic core and large H-H contacts and Meta Move for reaching optimal structure, by using Transfer learning. Two datasets are considered for evaluating and the results on some set of standard protein benchmarks show outperforming the state-of-the-art approaches. They show that the proposed approach can improve the accuracy of template-free prediction in an acceptable manner.

Maximum mutational robustness in genotype-phenotype maps follows a self-similar blancmange-like curve.

Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum phenotype robustness occurs when genotypes are organized as bricklayer's graphs, so-called because they resemble the way in which a bricklayer would fill in a Hamming graph. The value of the maximal robustness is given by a fractal continuous everywhere but differentiable nowhere sums-of-digits function from number theory. Interestingly, genotype-phenotype maps for RNA secondary structure and the hydrophobic-polar (HP) model for protein folding can exhibit phenotype robustness that exactly attains this upper bound. By exploiting properties of the sums-of-digits function, we prove a lower bound on the deviation of the maximum robustness of phenotypes with multiple neutral components from the bricklayer's graph bound, and show that RNA secondary structure phenotypes obey this bound. Finally, we show how robustness changes when phenotypes are coarse-grained and derive a formula and associated bounds for the transition probabilities between such phenotypes.

Globular Proteins and Where to Find Them within a Polymer Brush-A Case Study.

Protein adsorption by polymerized surfaces is an interdisciplinary topic that has been approached in many ways, leading to a plethora of theoretical, numerical and experimental insight. There is a wide variety of models trying to accurately capture the essence of adsorption and its effect on the conformations of proteins and polymers. However, atomistic simulations are case-specific and computationally demanding. Here, we explore universal aspects of the dynamics of protein adsorption through a coarse-grained (CG) model, that allows us to explore the effects of various design parameters. To this end, we adopt the hydrophobic-polar (HP) model for proteins, place them uniformly at the upper bound of a CG polymer brush whose multibead-spring chains are tethered to a solid implicit wall. We find that the most crucial factor affecting the adsorption efficiency appears to be the polymer grafting density, while the size of the protein and its hydrophobicity ratio come also into play. We discuss the roles of ligands and attractive tethering surfaces to the primary adsorption as well as secondary and ternary adsorption in the presence of attractive (towards the hydrophilic part of the protein) beads along varying spots of the backbone of the polymer chains. The percentage and rate of adsorption, density profiles and the shapes of the proteins, alongside with the respective potential of mean force are recorded to compare the various scenarios during protein adsorption.

Protein folding in 3D lattice HP model using a combining cuckoo search with the Hill-Climbing algorithms

A protein is a linear chain containing a set of amino acids, which folds on itself to create a specific native structure, called the minimum energy conformation. It is the native structure that determines the functionality of each protein. The Protein Folding Problem (PFP) remains one of the most strenuous computational and chemical biology. The principal challenge of PFP is to predict the optimal conformation of a given protein by considering only its amino acid sequence. Since the conformational space contains a colossal number of possibilities, even when considering short sequences, different simplified models have been developed and applied to make the PFP less complex. Experimental methods can be used to predict the native structure of small and specific proteins. Given the limitations of experimental methods, in the last few years many computational approaches have been proposed to solve the PFP. Based on the folding process, the PFP was formulated as an optimization problem. They are based on simplified lattice models such as the hydrophobic-polar model. In this paper, we present a new Hybrid Cuckoo Search Algorithm (HCSA) to solve the 3D-HP protein folding optimization problem. Our proposed algorithm consists of combining the Cuckoo Search Algorithm (CSA) with the Hill Climbing (HC) algorithm. Simulation results on different benchmark sequences are presented and compared to the state-of-the-art algorithms.

Limitations of field-theory simulation for exploring phase separation: The role of repulsion in a lattice protein model.

Field-theory simulation by the complex Langevin method offers an alternative to conventional sampling techniques for exploring the forces driving biomolecular liquid-liquid phase separation. Such simulations have recently been used to study several polyampholyte systems. Here, we formulate a field theory corresponding to the hydrophobic/polar (HP) lattice protein model, with finite same-site repulsion and nearest-neighbor attraction between HH bead pairs. By direct comparison with particle-based Monte Carlo simulations, we show that complex Langevin sampling of the field theory reproduces the thermodynamic properties of the HP model only if the same-site repulsion is not too strong. Unfortunately, the repulsion has to be taken weaker than what is needed to prevent condensed droplets from assuming an artificially compact shape. Analysis of a minimal and analytically solvable toy model hints that the sampling problems caused by repulsive interaction may stem from loss of ergodicity.

Прогнозування третинної структури білка на двомірній трикутній ґратці гібридним еволюційним алгоритмом

This work discusses the problem of forecasting the tertiary structure of a protein, based on its primary sequence. The problem is that science, with all its computing power and a set of experimental data, has not learned to build models that describe the process of protein molecule coagulation and predict the tertiary structure of a protein, based on its primary structure. However, it is wrong to assume that nothing is happening in this field of science. The regularities of folding (convolution) of the protein are known, methods for its modelling have been developed. Analysis of the current state of research in the field of these problems indicates the presence of shortcomings associated with the accuracy of forecasting and the time necessary to obtain the optimal solution. Consequently, the development of new computational methods, deprived of these shortcomings, seems relevant. In this work, the authors focused on the lattice model, which is a special case of the known hydrophobic-polar dill. protein conformation according to the chosen model, hybrid algorithms of cloning selection, differential are proposed. Since the processes of protein coagulation have not been fully understood, the researchers proposed several simplified models based on the physical properties of molecules and which leads to problems of combinatorial optimization. A hydrophobic-polar simplified model on the planar triangular lattice is chosen as a protein model. From the point of view of the optimization problem, the problem of protein folding comes down to finding a conformation with minimal energy. In lattice models, the conformation is represented as a non-self-cutting pathway. A hybrid artificial immune system in the form of a combination of clonal selection and differential evolution algorithms is proposed to solve this problem. The paper proposes a hybrid method and algorithm to solve the protein folding problem using the HP model on a planar triangular lattice. In this paper, a hybrid method and algorithm for solving the protein folding problem using the HP model on a planar triangular lattice are proposed. The developed hybrid algorithm uses special methods for encoding and decoding individuals, as well as the affinity function, which allows reducing the number of incorrect conformations (self-cutting solutions). Experimental studies on test hp-sequences were conducted to verify the effectiveness of the algorithm. The results of these experiments showed some advantages of the developed algorithm over other known methods. Experiments have been taught to verify the effectiveness of the proposed approach. The results labelled "Best" show the minimum energy values achieved over 30 runs, while the results labelled "Medium" show the robustness of the algorithm to achieve minima. Regarding robustness, the hybrid algorithm also offers an advantage, showing higher results. A comparative analysis of the performance results of the proposed algorithm on test sequences with similar results of other published methods allows us to conclude the high efficiency of the developed method. In particular, the result is more stable, and, in some cases, conformations with lower energy are obtained. Keywords: protein folding; hydrophobic-polar model; clonal selection; differential evolution; artificial immune systems; hydrophobic-polar model.

Thermodynamics of hydrophobic-polar model proteins on the face-centered cubic lattice.

The HP model, a coarse-grained protein representation with only hydrophobic (H) and polar (P) amino acids, has already been extensively studied on the simple cubic (SC) lattice. However, this geometry severely restricts possible bond angles, and a simple improvement is to instead use the face-centered cubic (fcc) lattice. In this paper, the density of states and ground state energies are calculated for several benchmark HP sequences on the fcc lattice using the replica-exchange Wang-Landau algorithm and a powerful set of Monte Carlo trial moves. Results from the fcc lattice proteins are directly compared with those obtained from a previous lattice protein folding study with a similar methodology on the SC lattice. A thermodynamic analysis shows comparable folding behavior between the two lattice geometries, but with a greater rate of hydrophobic-core formation persisting into lower temperatures on the fcc lattice.

Lattice protein design using Bayesian learning.

Protein design is the inverse approach of the three-dimensional (3D) structure prediction for elucidating the relationship between the 3D structures and amino acid sequences. In general, the computation of the protein design involves a double loop: A loop for amino acid sequence changes and a loop for an exhaustive conformational search for each amino acid sequence. Herein, we propose a novel statistical mechanical design method using Bayesian learning, which can design lattice proteins without the exhaustive conformational search. We consider a thermodynamic hypothesis of the evolution of proteins and apply it to the prior distribution of amino acid sequences. Furthermore, we take the water effect into account in view of the grand canonical picture. As a result, on applying the 2D lattice hydrophobic-polar (HP) model, our design method successfully finds an amino acid sequence for which the target conformation has a unique ground state. However, the performance was not as good for the 3D lattice HP models compared to the 2D models. The performance of the 3D model improves on using a 20-letter lattice proteins. Furthermore, we find a strong linearity between the chemical potential of water and the number of surface residues, thereby revealing the relationship between protein structure and the effect of water molecules. The advantage of our method is that it greatly reduces computation time, because it does not require long calculations for the partition function corresponding to an exhaustive conformational search. As our method uses a general form of Bayesian learning and statistical mechanics and is not limited to lattice proteins, the results presented here elucidate some heuristics used successfully in previous protein design methods.

A new hybrid genetic algorithm for protein structure prediction on the 2D triangular lattice

The flawless functioning of the protein is essentially related to its three-dimensional structure. Therefore,predicting protein structure from its amino acid sequence is a fundamental problem that draws researchers' attentionin many areas. The protein structure prediction problem (PSP) can be formulated as a combinatorial optimization problem based on simplified lattice models such as the hydrophobic-polar model. In this paper, we propose a new hybridalgorithm that combines three different known heuristic algorithms: the genetic algorithm, the tabu search strategy,and the local search algorithm to solve the PSP problem. Regarding the evaluation of the proposed approach, wepresent an experimental study, where we consider the quality of the product solution as the main assessment criterion.Furthermore, we compared the proposed algorithm with state-of-the-art algorithms using a selection of well-studiedbenchmark instances.

Resource-efficient quantum algorithm for protein folding

Predicting the three-dimensional structure of a protein from its primary sequence of amino acids is known as the protein folding problem. Due to the central role of proteins’ structures in chemistry, biology and medicine applications, this subject has been intensively studied for over half a century. Although classical algorithms provide practical solutions for the sampling of the conformation space of small proteins, they cannot tackle the intrinsic NP-hard complexity of the problem, even when reduced to the simplest Hydrophobic-Polar model. On the other hand, while fault-tolerant quantum computers are beyond reach for state-of-the-art quantum technologies, there is evidence that quantum algorithms can be successfully used in noisy state-of-the-art quantum computers to accelerate energy optimization in frustrated systems. In this work, we present a model Hamiltonian with {mathcal{O}}({N}^{4}) scaling and a corresponding quantum variational algorithm for the folding of a polymer chain with N monomers on a lattice. The model reflects many physico-chemical properties of the protein, reducing the gap between coarse-grained representations and mere lattice models. In addition, we use a robust and versatile optimization scheme, bringing together variational quantum algorithms specifically adapted to classical cost functions and evolutionary strategies to simulate the folding of the 10 amino acid Angiotensin on 22 qubits. The same method is also successfully applied to the study of the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM 20-qubit quantum computer. Bringing together recent advances in building gate-based quantum computers with noise-tolerant hybrid quantum-classical algorithms, this work paves the way towards accessible and relevant scientific experiments on real quantum processors.

Contributions of topological polar-polar contacts to achieve better folding stability of 2D/3D HP lattice proteins: An <i>in silico</i> 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, S<sub>1</sub>-S<sub>8</sub> folded in 2D-square lattice, and S<sub>9</sub>-S<sub>11</sub> 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>

RETRACTED ARTICLE: Solving the protein folding problem in hydrophobic-polar model using deep reinforcement learning

The present article focuses on solving the protein folding problem with deep reinforcement learning (DRL) approach. The protein folding problem is an NP-hard problem and as we are proposing our approach in the hydrophobic-polar model, we deal with an NP-complete problem. Also, the protein folding problem is a combinatorial optimization problem. Combinatorial optimization problems are hard to solve optimally, that is why any attempt to improve their solutions is beneficent. Generally, this problem refers to the process of predicting the structure of a protein from its amino acids sequence. During recent years, the protein folding problem has attracted a lot of attention. The amount of time and expenses of using nuclear magnetic resonance imaging and crystallography for identifying the three-dimensional structure is the main reason of many proposed approaches. In this study, our approach models the problem as a DRL problem, and for enhancing its performance, we adopt long short-term memory networks for the approximation phase in the reinforcement learning algorithm. Using deep Q-learning approach and actor–critic algorithm with an experience replay mechanism overcomes the complexity of other proposed approaches which leads to better accuracy in less time. In addition, we analyzed the efficiency and effectiveness of the dueling deep Q-network technique for solving the protein folding problem. Providing a step-by-step implementation and modeling for solving the bi-dimensional protein folding problem with the DRL approach is the purpose of the present study which could be helpful for solving other omics and computational biology problems. However, a comparison between the DRL approach and other notable approaches (as it is available in Sect. 6) shows that our approach outperforms other approaches in finding the minimum value of the free energy, which is the main factor in the protein folding problem, in less time in any available case.

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.

A Novel Branch-and-Bound Algorithm for the Protein Folding Problem in the 3D HP Model.

The protein folding problem (PFP) is an important issue in bioinformatics and biochemical physics. One of the most widely studied models of protein folding is the hydrophobic-polar (HP) model introduced by Dill. The PFP in the three-dimensional (3D) lattice HP model has been shown to be NP-complete; the proposed algorithms for solving the problem can therefore only find near-optimal energy structures for most long benchmark sequences within acceptable time periods. In this paper, we propose a novel algorithm based on the branch-and-bound approach to solve the PFP in the 3D lattice HP model. For 10 48-monomer benchmark sequences, our proposed algorithm finds the lowest energies so far within comparable computation times than previous methods.

Elucidating thermal behavior, native contacts, and folding funnels of simple lattice proteins using replica exchange Wang-Landau sampling.

We studied the folding behavior of two coarse-grained, lattice models, the HP (hydrophobic-polar) model and the semi-flexible H0P model, whose 124 monomer long sequences were derived from the protein Ribonuclease A. Taking advantage of advanced parallel computing techniques, we applied replica exchange Wang-Landau sampling and calculated the density of states over the models entire energy ranges to high accuracy. We then determined both energetic and structural quantities in order to elucidate the folding behavior of each model completely. As a result of sufficiently long sequences and model complexity, yet computational accessibility, we were able to depict distinct free energy folding funnels for both models. In particular, we found that the HP model folds in a single-step process with a very highly degenerate native state and relatively flat low temperature folding funnel minimum. By contrast, the semi-flexible H0P model folds via a multi-step process and the native state is almost four orders of magnitude less degenerate than that for the HP model. In addition, for the H0P model, the bottom of the free energy folding funnel remains rough, even at low temperatures.

Protein evolution speed depends on its stability and abundance and on chaperone concentrations

Proteins evolve at different rates. What drives the speed of protein sequence changes? Two main factors are a protein's folding stability and aggregation propensity. By combining the hydrophobic-polar (HP) model with the Zwanzig-Szabo-Bagchi rate theory, we find that: (i) Adaptation is strongly accelerated by selection pressure, explaining the broad variation from days to thousands of years over which organisms adapt to new environments. (ii) The proteins that adapt fastest are those that are not very stably folded, because their fitness landscapes are steepest. And because heating destabilizes folded proteins, we predict that cells should adapt faster when put into warmer rather than cooler environments. (iii) Increasing protein abundance slows down evolution (the substitution rate of the sequence) because a typical protein is not perfectly fit, so increasing its number of copies reduces the cell's fitness. (iv) However, chaperones can mitigate this abundance effect and accelerate evolution (also called evolutionary capacitance) by effectively enhancing protein stability. This model explains key observations about protein evolution rates.

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

BackgroundThe 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.ResultsIn 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.ConclusionOverall, 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 Novel Framework for Ab Initio Coarse Protein Structure Prediction.

Hydrophobic-Polar model is a simplified representation of Protein Structure Prediction (PSP) problem. However, even with the HP model, the PSP problem remains NP-complete. This work proposes a systematic and problem specific design for operators of the evolutionary program which hybrids with local search hill climbing, to efficiently explore the search space of PSP and thereby obtain an optimum conformation. The proposed algorithm achieves this by incorporating the following novel features: (i) new initialization method which generates only valid individuals with (rather than random) better fitness values; (ii) use of probability-based selection operators that limit the local convergence; (iii) use of secondary structure based mutation operator that makes the structure more closely to the laboratory determined structure; and (iv) incorporating all the above-mentioned features developed a complete two-tier framework. The developed framework builds the protein conformation on the square and triangular lattice. The test has been performed using benchmark sequences, and a comparative evaluation is done with various state-of-the-art algorithms. Moreover, in addition to hypothetical test sequences, we have tested protein sequences deposited in protein database repository. It has been observed that the proposed framework has shown superior performance regarding accuracy (fitness value) and speed (number of generations needed to attain the final conformation). The concepts used to enhance the performance are generic and can be used with any other population-based search algorithm such as genetic algorithm, ant colony optimization, and immune algorithm.

Influence of substrate pattern on the adsorption of HP lattice proteins

With the highly simplified hydrophobic-polar model representation of a protein, we can study essential qualitative physics without an unnecessarily large computational overhead. Using Wang-Landau sampling in conjunction with a set of efficient Monte Carlo trial moves, we studied the adsorption of short HP lattice proteins on various simple patterned substrates and in particular for checkered patterned surfaces. A set of single-site mutated HP proteins is used to investigate the role of hydrophobicity of a protein chain and surface pattern for substrates with various pattern cell sizes relative to the protein’s native configuration. For most cases, we found that the adsorption transition occurs at a lower temperature, while the hydrophobic core formation is less affected. The flattening procedure after the HP protein is adsorbed is more sensitive to the change in surface patterns and single-site mutations. These observations stay valid for both strongly and weakly attractive surfaces.

Approximation Algorithms for Protein Folding in the Hydrophobic-Polar Model on 3D Hexagonal Prism Lattice.

In this article, we study approximation algorithms for the protein folding problem in the hydrophobic-polar (HP) model on three-dimensional (3D) hexagonal prism lattice. We present two approximation algorithms based on previous work on two-dimensional (2D) square, 3D cubic, and 2D hexagonal lattice HP models. The first algorithm produces folds in which the H-H contacts are mainly on or between the hexagonal planes, and has approximation ratio [Formula: see text]. While in the folds produced by the second algorithm, the H-H contacts are mainly on or between the zigzag square planes. The theoretical approximation ratio bound of the second algorithm is no less than [Formula: see text], although no better than the first algorithm, it may perform much better for specific instances in practice.