Coarse-grained versus atomistic simulations: realistic interaction free energies for real proteins

Why Na+ has higher propensity than K+ to condense DNA in a crowded environment

Experimentally, in the presence of the crowding agent polyethylene glycol (PEG), sodium ions compact double-stranded DNA more readily than potassium ions. Here, we have used molecular dynamics simulations and the "ion binding shells model" of DNA condensation to provide an explanation for the observed variations in condensation of short DNA duplexes in solutions containing different monovalent cations and PEG; several predictions are made. According to the model we use, externally bound ions contribute the most to the ion-induced aggregation of DNA duplexes. The simulations reveal that for two adjacent DNA duplexes, the number of externally bound Na+ ions is larger than the number of K+ ions over a wide range of chloride concentrations in the presence of PEG, providing a qualitative explanation for the higher propensity of sodium ions to compact DNA under crowded conditions. The qualitative picture is confirmed by an estimate of the corresponding free energy of DNA aggregation that is at least 0.2kBT per base pair more favorable in solution with NaCl than with KCl at the same ion concentration. The estimated attraction free energy of DNA duplexes in the presence of Na+ depends noticeably on the DNA sequence; we predict that AT-rich DNA duplexes are more readily condensed than GC-rich ones in the presence of Na+. Counter-intuitively, the addition of a small amount of a crowding agent with high affinity for the specific condensing ion may lead to the weakening of the ion-mediated DNA-DNA attraction, shifting the equilibrium away from the DNA condensed phase.

Effects of Nitro-Oxidative Stress on Biomolecules: Part 1-Non-Reactive Molecular Dynamics Simulations

Plasma medicine, or the biomedical application of cold atmospheric plasma (CAP), is an expanding field within plasma research. CAP has demonstrated remarkable versatility in diverse biological applications, including cancer treatment, wound healing, microorganism inactivation, and skin disease therapy. However, the precise mechanisms underlying the effects of CAP remain incompletely understood. The therapeutic effects of CAP are largely attributed to the generation of reactive oxygen and nitrogen species (RONS), which play a crucial role in the biological responses induced by CAP. Specifically, RONS produced during CAP treatment have the ability to chemically modify cell membranes and membrane proteins, causing nitro-oxidative stress, thereby leading to changes in membrane permeability and disruption of cellular processes. To gain atomic-level insights into these interactions, non-reactive molecular dynamics (MD) simulations have emerged as a valuable tool. These simulations facilitate the examination of larger-scale system dynamics, including protein-protein and protein-membrane interactions. In this comprehensive review, we focus on the applications of non-reactive MD simulations in studying the effects of CAP on cellular components and interactions at the atomic level, providing a detailed overview of the potential of CAP in medicine. We also review the results of other MD studies that are not related to plasma medicine but explore the effects of nitro-oxidative stress on cellular components and are therefore important for a broader understanding of the underlying processes.

Pangenomic Study of Fusobacterium nucleatum Reveals the Distribution of Pathogenic Genes and Functional Clusters at the Subspecies and Strain Levels

Fusobacterium nucleatum is a prevalent periodontal pathogen and is associated with many systemic diseases. Our knowledge of the genomic characteristics and pathogenic effectors of different F. nucleatum strains is limited. In this study, we completed the whole genome assembly of the 4 F. nucleatum strains and carried out a comprehensive pangenomic study of 30 strains with their complete genome sequences. Phylogenetic analysis revealed that the F. nucleatum strains are mainly divided into 4 subspecies, while 1 of the sequenced strains was classified into a new subspecies. Gene composition analysis revealed that a total of 517 "core/soft-core genes" with housekeeping functions widely distributed in almost all the strains. Each subspecies had a unique gene cluster shared by strains within the subspecies. Analysis of the virulence factors revealed that many virulence factors were widely distributed across all the strains, with some present in multiple copies. Some virulence genes showed no consistent occurrence rule at the subspecies level and were specifically distributed in certain strains. The genomic islands mainly revealed strain-specific characteristics instead of subspecies level consistency, while CRISPR types and secondary metabolite biosynthetic gene clusters were identically distributed in F. nucleatum strains from the same subspecies. The variation in amino acid sites in the adhesion protein FadA did not affect the monomer and dimer 3D structures, but it may affect the binding surface and the stability of binding to host receptors. This study provides a basis for the pathogenic study of F. nucleatum at the subspecies and strain levels. IMPORTANCE We used F. nucleatum as an example to analyze the genomic characteristics of oral pathogens at the species, subspecies, and strain levels and elucidate the similarities and differences in functional genes and virulence factors among different subspecies/strains of the same oral pathogen. We believe that the unique biological characteristics of each subspecies/strain can be attributed to the differences in functional gene clusters or the presence/absence of certain virulence genes. This study showed that F. nucleatum strains from the same subspecies had similar functional gene compositions, CRISPR types, and secondary metabolite biosynthetic gene clusters, while pathogenic genes, such as virulence genes, antibiotic resistance genes, and GIs, had more strain level specificity. The findings of this study suggest that, for microbial pathogenicity studies, we should carefully consider the subspecies/strains being used, as different strains may vary greatly.

Asynchronous Reciprocal Coupling of Martini 2.2 Coarse-Grained and CHARMM36 All-Atom Simulations in an Automated Multiscale Framework

The appeal of multiscale modeling approaches is predicated on the promise of combinatorial synergy. However, this promise can only be realized when distinct scales are combined with reciprocal consistency. Here, we consider multiscale molecular dynamics (MD) simulations that combine the accuracy and macromolecular flexibility accessible to fixed-charge all-atom (AA) representations with the sampling speed accessible to reductive, coarse-grained (CG) representations. AA-to-CG conversions are relatively straightforward because deterministic routines with unique outcomes are achievable. Conversely, CG-to-AA conversions have many solutions due to a surge in the number of degrees of freedom. While automated tools for biomolecular CG-to-AA transformation exist, we find that one popular option, called Backward, is prone to stochastic failure and the AA models that it does generate frequently have compromised protein structure and incorrect stereochemistry. Although these shortcomings can likely be circumvented by human intervention in isolated instances, automated multiscale coupling requires reliable and robust scale conversion. Here, we detail an extension to Multiscale Machine-learned Modeling Infrastructure (MuMMI), including an improved CG-to-AA conversion tool called sinceCG. This tool is reliable (∼98% weakly correlated repeat success rate), automatable (no unrecoverable hangs), and yields AA models that generally preserve protein secondary structure and maintain correct stereochemistry. We describe how the MuMMI framework identifies CG system configurations of interest, converts them to AA representations, and simulates them at the AA scale while on-the-fly analyses provide feedback to update CG parameters. Application to systems containing the peripheral membrane protein RAS and proximal components of RAF kinase on complex eight-component lipid bilayers with ∼1.5 million atoms is discussed in the context of MuMMI.

Unifying structural descriptors for biological and bioinspired nanoscale complexes

Biomimetic nanoparticles are known to serve as nanoscale adjuvants, enzyme mimics and amyloid fibrillation inhibitors. Their further development requires better understanding of their interactions with proteins. The abundant knowledge about protein-protein interactions can serve as a guide for designing protein-nanoparticle assemblies, but the chemical and biological inputs used in computational packages for protein-protein interactions are not applicable to inorganic nanoparticles. Analysing chemical, geometrical and graph-theoretical descriptors for protein complexes, we found that geometrical and graph-theoretical descriptors are uniformly applicable to biological and inorganic nanostructures and can predict interaction sites in protein pairs with accuracy >80% and classification probability ~90%. We extended the machine-learning algorithms trained on protein-protein interactions to inorganic nanoparticles and found a nearly exact match between experimental and predicted interaction sites with proteins. These findings can be extended to other organic and inorganic nanoparticles to predict their assemblies with biomolecules and other chemical structures forming lock-and-key complexes.

Assessing Site-specific PEGylation of TEM-1 β-lactamase with Cell-free Protein Synthesis and Coarse-grained Simulation

PEGylation is a broadly used strategy to enhance the pharmacokinetic properties of therapeutic proteins. It is well established that the location and extent of PEGylation have a significant impact on protein properties. However, conventional PEGylation techniques have limited control over PEGylation sites. Emerging site-specific PEGylation technology provides control of PEG placement by conjugating PEG polymers via click chemistry reaction to genetically encoded non-canonical amino acids. Unfortunately, a method to rapidly determine the optimal PEGylation location has yet to be established. Here we seek to address this challenge. In this work, coarse-grained molecular dynamic simulations are paired with high-throughput experimental screening utilizing cell-free protein synthesis to investigate the effect of site-specific PEGylation on the two-state folder protein TEM-1 β-lactamase. Specifically, the conjugation efficiency, thermal stability, and enzymatic activity are studied for the enzyme PEGylated at several different locations. The results of this analysis confirm that the physical properties of the PEGylated protein vary considerably with PEGylation site and that traditional design recommendations are insufficient to predict favorable PEGylation sites. In this study, the best predictor of the most favorable conjugation site is coarse-grained simulation. Thus, we propose a dual combinatorial screening approach in which coarse-grained molecular simulation informs site selection for high-throughput experimental verification.

Simulated Breathing: Application of Molecular Dynamics Simulations to Pulmonary Lung Surfactant

In this review, we delve into the topic of the pulmonary surfactant (PS) system, which is present in the respiratory system. The total composition of the PS has been presented and explored, from the types of cells involved in its synthesis and secretion, down to the specific building blocks used, such as the various lipid and protein components. The lipid and protein composition varies across species and between individuals, but ultimately produces a PS monolayer with the same role. As such, the composition has been investigated for the ways in which it imposes function and confers peculiar biophysical characteristics to the system as a whole. Moreover, a couple of theories/models that are associated with the functions of PS have been addressed. Finally, molecular dynamic (MD) simulations of pulmonary surfactant have been emphasized to not only showcase various group’s findings, but also to demonstrate the validity and importance that MD simulations can have in future research exploring the PS monolayer system.

Molecular Dynamics Simulations of Human Beta-Defensin Type 3 Crossing Different Lipid Bilayers

Human β defensin type 3 (hBD-3) is a small cationic cysteine-rich peptide. It has a broad spectrum of antimicrobial activities. However, at high concentrations, it also shows hemolytic activity by interrupting red blood cells. To understand the selectivity of hBD-3 disrupting cell membranes, investigating the capability of hBD-3 translocating through different membranes is important. Since hBD-3 in the analogue form in which all three pairs of disulfide bonds are broken has similar antibacterial activities to the wild-type, this project investigates the structure and dynamics of an hBD-3 analogue in monomer, dimer, and tetramer forms through both zwitterionic and negatively charged lipid bilayers using molecular dynamics (MD) simulations. One tetramer structure of hBD-3 was predicted by running all-atom MD simulations on hBD-3 in water at a high concentration, which was found to be stable in water during 400 ns all-atom simulations based on root-mean-squared deviation, root-mean-squared fluctuation, buried surface area, and binding interaction energy calculations. After that, hBD-3 in different forms was placed inside different membranes, and then steered MD simulation was conducted to pull the hBD-3 out of the membrane along the z-direction to generate different configurational windows to set up umbrella-sampling (US) simulations. Because extensive sampling is important to obtain accurate free energy barriers, coarse-grained US MD simulations were performed in each window. Based on the long-term simulation result, membrane thinning was found near hBD-3 in different lipid bilayers and in different hBD-3 oligomer systems. By calculating the root-mean-squared deviation of the z-coordinate of hBD-3 molecules, rotation of the oligomer inside the bilayer and stretching of the oligomer structure along the z-direction were observed. Although reorientation of lipid heads toward the hBD-3 tetramer was observed based on the density profile calculation, the order parameter calculation shows that hBD-3 disrupts 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-l-serine (POPS) lipids more significantly and makes it less ordered than on 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipids. Calculating the free energy of hBD-3 through different lipid bilayers, it was found that generally hBD-3 encounters a lower energy barrier through negatively charged lipid membranes than the zwitterionic membrane. hBD-3 in different forms needs to overcome a lower energy barrier crossing the combined POPC+POPS bilayer through the POPS leaflet than through the POPC leaflet. Besides that, the potential of mean force result suggests that hBD-3 forms an oligomer translocating negatively charged lipid membranes at a low concentration. This study supplied new insight into the antibacterial mechanism of hBD-3 through different membranes.

Thermodynamic Integration in 3n Dimensions without Biases or Alchemy for Protein Interactions

Thermodynamic integration (TI), a powerful formalism for computing Gibbs free energy, has been implemented for many biophysical processes with alchemical schemes that require delicate human efforts to choose/design biasing potentials for sampling the desired biophysical events and to remove their artifactitious consequences afterwards. Theoretically, an alchemical scheme is exact but practically, an unsophisticated implementation of this exact formula can cause error amplifications. Small relative errors in the input parameters can be amplified many times in their propagation into the computed free energy [due to subtraction of similar numbers such as (105 ± 5)‒(100 ± 5) = 5 ± 7]. In this paper, we present an unsophisticated implementation of TI in 3n dimensions (3nD) (n=1,2,3…) for the potential of mean force along a 3nD path connecting one state in the bound state ensemble to one state in the unbound state ensemble. Fluctuations in these 3nD are integrated in the bound and unbound state ensembles but not along the 3nD path. Using TI3nD, we computed the standard binding free energies of three protein complexes: trometamol in Salmonella effector SpvD (n=1), biotin-avidin (n=2), and Colicin E9 endonuclease with cognate immunity protein Im9 (n=3). We employed three different protocols in three independent computations of E9-Im9 to show TI3nD's robustness. We also computed the hydration energies of ten biologically relevant compounds (n=1 for water, acetamide, urea, glycerol, trometamol, ammonium and n=2 for erythritol, 1,3-propanediol, xylitol, biotin). Each of the 15 computations is accomplishable within one (for hydration) to ten (for E9-Im9) days on an inexpensive GPU workstation. The computed results all agree with the available experimental data.

Computational Modeling of Realistic Cell Membranes

Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.

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.

Design and Development of Biomimetic Nanovesicles Using a Microfluidic Approach

The advancement of nanotechnology toward more sophisticated bioinspired approaches has highlighted the gap between the advantages of biomimetic and biohybrid platforms and the availability of manufacturing processes to scale up their production. Though the advantages of transferring biological features from cells to synthetic nanoparticles for drug delivery purposes have recently been reported, a standardizable, batch-to-batch consistent, scalable, and high-throughput assembly method is required to further develop these platforms. Microfluidics has offered a robust tool for the controlled synthesis of nanoparticles in a versatile and reproducible approach. In this study, the incorporation of membrane proteins within the bilayer of biomimetic nanovesicles (leukosomes) using a microfluidic-based platform is demonstrated. The physical, pharmaceutical, and biological properties of microfluidic-formulated leukosomes (called NA-Leuko) are characterized. NA-Leuko show extended shelf life and retention of the biological functions of donor cells (i.e., macrophage avoidance and targeting of inflamed vasculature). The NA approach represents a universal, versatile, robust, and scalable tool, which is extensively used for the assembly of lipid nanoparticles and adapted here for the manufacturing of biomimetic nanovesicles.

Fast Calculation of Protein-Protein Binding Free Energies Using Umbrella Sampling with a Coarse-Grained Model

Determination of protein–protein binding affinity values is key to understanding various underlying biological phenomena, such as how missense variations change protein–protein binding. Most existing non-rigorous (fast) and rigorous (slow) methods that rely on all-atom representation of the proteins force the user to choose between speed and accuracy. In an attempt to achieve balance between speed and accuracy, we have combined rigorous umbrella sampling molecular dynamics simulation with a coarse-grained protein model. We predicted the effect of missense variations on binding affinity by selecting three protein–protein systems and comparing results to empirical relative binding affinity values and to non-rigorous modeling approaches. We obtained significant improvement both in our ability to discern stabilizing from destabilizing missense variations and in the correlation between predicted and experimental values compared to non-rigorous approaches. Overall our results suggest that using a rigorous affinity calculation method with coarse-grained protein models could offer fast and reliable predictions of protein–protein binding free energies.

Simulation of Reversible Protein-Protein Binding and Calculation of Binding Free Energies Using Perturbed Distance Restraints

Virtually all biological processes depend on the interaction between proteins at some point. The correct prediction of biomolecular binding free-energies has many interesting applications in both basic and applied pharmaceutical research. While recent advances in the field of molecular dynamics (MD) simulations have proven the feasibility of the calculation of protein–protein binding free energies, the large conformational freedom of proteins and complex free energy landscapes of binding processes make such calculations a difficult task. Moreover, convergence and reversibility of resulting free-energy values remain poorly described. In this work, an easy-to-use, yet robust approach for the calculation of standard-state protein–protein binding free energies using perturbed distance restraints is described. In the binding process the conformations of the proteins were restrained, as suggested earlier. Two approaches to avoid end-state problems upon release of the conformational restraints were compared. The method was evaluated by practical application to a small model complex of ubiquitin and the very flexible ubiquitin-binding domain of human DNA polymerase ι (UBM2). All computed free energy differences were closely monitored for convergence, and the calculated binding free energies had a mean unsigned deviation of only 1.4 or 2.5 kJ·mol^–1 from experimental values. Statistical error estimates were in the order of thermal noise. We conclude that the presented method has promising potential for broad applicability to quantitatively describe protein–protein and various other kinds of complex formation.

Self-assembling study of sarcolipin and its mutants in multiple molecular dynamic simulations

The Sarcolipin (SLN) is a single trans-membrane protein that can self-assembly to dimer and oligomer for playing importantphysiological function. In this work, we addressed the dimerization of wild type SLN (wSLN) and its mutants (mSLNs) - I17A and I20A, using both coarse-grained (CG) and atomistic (AT) molecular dynamics (MD) simulations. Our results demonstrated that wSLN homodimer assembled as a left-handed helical complex, while mSLNs heterodimers assembled as right-handed complexes. Analysis of residue-residue contacts map indicated that isoleucine (Ile)-leucione (Leu) zipper domain played an important role in dimerization. The potential of mean force (PMF) demonstrated that wSLN homodimer was more stable than mSLNs heterodimers. Meanwhile, the mSLNs heterodimers preferred right-handed rather than left-handed helix. AT-MD simulations for wSLN and mSLNs were also in line with CG-MD simulations. These results provided the insights for understanding the mechanisms of SLNs self-assembling. Proteins 2017; 85:1065-1077. © 2017 Wiley Periodicals, Inc.

CLUB-MARTINI: Selecting Favourable Interactions amongst Available Candidates, a Coarse-Grained Simulation Approach to Scoring Docking Decoys

Large-scale identification of native binding orientations is crucial for understanding the role of protein-protein interactions in their biological context. Measuring binding free energy is the method of choice to estimate binding strength and reveal the relevance of particular conformations in which proteins interact. In a recent study, we successfully applied coarse-grained molecular dynamics simulations to measure binding free energy for two protein complexes with similar accuracy to full-atomistic simulation, but 500-fold less time consuming. Here, we investigate the efficacy of this approach as a scoring method to identify stable binding conformations from thousands of docking decoys produced by protein docking programs. To test our method, we first applied it to calculate binding free energies of all protein conformations in a CAPRI (Critical Assessment of PRedicted Interactions) benchmark dataset, which included over 19000 protein docking solutions for 15 benchmark targets. Based on the binding free energies, we ranked all docking solutions to select the near-native binding modes under the assumption that the native-solutions have lowest binding free energies. In our top 100 ranked structures, for the ‘easy’ targets that have many near-native conformations, we obtain a strong enrichment of acceptable or better quality structures; for the ‘hard’ targets without near-native decoys, our method is still able to retain structures which have native binding contacts. Moreover, in our top 10 selections, CLUB-MARTINI shows a comparable performance when compared with other state-of-the-art docking scoring functions. As a proof of concept, CLUB-MARTINI performs remarkably well for many targets and is able to pinpoint near-native binding modes in the top selections. To the best of our knowledge, this is the first time interaction free energy calculated from MD simulations have been used to rank docking solutions at a large scale.

Evaluation of the coarse-grained OPEP force field for protein-protein docking

Background

Knowing the binding site of protein–protein complexes helps understand their function and shows possible regulation sites. The ultimate goal of protein–protein docking is the prediction of the three-dimensional structure of a protein–protein complex. Docking itself only produces plausible candidate structures, which must be ranked using scoring functions to identify the structures that are most likely to occur in nature.

Methods

In this work, we rescore rigid body protein–protein predictions using the optimized potential for efficient structure prediction (OPEP), which is a coarse-grained force field. Using a force field based on continuous functions rather than a grid-based scoring function allows the introduction of protein flexibility during the docking procedure. First, we produce protein–protein predictions using ZDOCK, and after energy minimization via OPEP we rank them using an OPEP-based soft rescoring function. We also train the rescoring function for different complex classes and demonstrate its improved performance for an independent dataset.

Results

The trained rescoring function produces a better ranking than ZDOCK for more than 50 % of targets, rising to over 70 % when considering only enzyme/inhibitor complexes.

Conclusions

This study demonstrates for the first time that energy functions derived from the coarse-grained OPEP force field can be employed to rescore predictions for protein–protein complexes.

Inferring the microscopic surface energy of protein-protein interfaces from mutation data

Mutations at protein-protein recognition sites alter binding strength by altering the chemical nature of the interacting surfaces. We present a simple surface energy model, parameterized with empirical ΔΔG values, yielding mean energies of -48 cal mol(-1) Å(-2) for interactions between hydrophobic surfaces, -51 to -80 cal mol(-1) Å(-2) for surfaces of complementary charge, and 66-83 cal mol(-1) Å(-2) for electrostatically repelling surfaces, relative to the aqueous phase. This places the mean energy of hydrophobic surface burial at -24 cal mol(-1) Å(-2) . Despite neglecting configurational entropy and intramolecular changes, the model correlates with empirical binding free energies of a functionally diverse set of rigid-body interactions (r = 0.66). When used to rerank docking poses, it can place near-native solutions in the top 10 for 37% of the complexes evaluated, and 82% in the top 100. The method shows that hydrophobic burial is the driving force for protein association, accounting for 50-95% of the cohesive energy. The model is available open-source from http://life.bsc.es/pid/web/surface_energy/ and via the CCharpPPI web server http://life.bsc.es/pid/ccharppi/.

Conformational frustration in calmodulin-target recognition

Calmodulin (CaM) is a primary calcium (Ca(2+) )-signaling protein that specifically recognizes and activates highly diverse target proteins. We explored the molecular basis of target recognition of CaM with peptides representing the CaM-binding domains from two Ca(2+) -CaM-dependent kinases, CaMKI and CaMKII, by employing experimentally constrained molecular simulations. Detailed binding route analysis revealed that the two CaM target peptides, although similar in length and net charge, follow distinct routes that lead to a higher binding frustration in the CaM-CaMKII complex than in the CaM-CaMKI complex. We discovered that the molecular origin of the binding frustration is caused by intermolecular contacts formed with the C-domain of CaM that need to be broken before the formation of intermolecular contacts with the N-domain of CaM. We argue that the binding frustration is important for determining the kinetics of the recognition process of proteins involving large structural fluctuations.

A balance-evolution artificial bee colony algorithm for protein structure optimization based on a three-dimensional AB off-lattice model

Protein structure prediction is a fundamental issue in the field of computational molecular biology. In this paper, the AB off-lattice model is adopted to transform the original protein structure prediction scheme into a numerical optimization problem. We present a balance-evolution artificial bee colony (BE-ABC) algorithm to address the problem, with the aim of finding the structure for a given protein sequence with the minimal free-energy value. This is achieved through the use of convergence information during the optimization process to adaptively manipulate the search intensity. Besides that, an overall degradation procedure is introduced as part of the BE-ABC algorithm to prevent premature convergence. Comprehensive simulation experiments based on the well-known artificial Fibonacci sequence set and several real sequences from the database of Protein Data Bank have been carried out to compare the performance of BE-ABC against other algorithms. Our numerical results show that the BE-ABC algorithm is able to outperform many state-of-the-art approaches and can be effectively employed for protein structure optimization.