Multicanonical study of coarse-grained off-lattice models for folding heteropolymers

Supervised and unsupervised machine learning of structural phases of polymers adsorbed to nanowires

We identify configurational phases and structural transitions in a polymer nanotube composite by means of machine learning. We employ various unsupervised dimensionality reduction methods, conventional neural networks, as well as the confusion method, an unsupervised neural-network-based approach. We find neural networks are able to reliably recognize all configurational phases that have been found previously in experiment and simulation. Furthermore, we locate the boundaries between configurational phases in a way that removes human intuition or bias. This could be done before only by relying on preconceived, ad hoc order parameters.

Effects of lattice constraints in coarse-grained protein models

We compare and contrast folding behavior in several coarse-grained protein models, both on- and off-lattice, in an attempt to uncover the effect of lattice constraints in these kinds of models. Using modern, extended ensemble Monte Carlo methods-Wang-Landau sampling, multicanonical sampling, replica-exchange Wang-Landau sampling, and replica-exchange multicanonical sampling, we investigate the thermodynamic and structural behavior of the protein Crambin within the context of the hydrophobic-polar, hydrophobic-"neutral"-polar (H0P), and semi-flexible H0P model frameworks. We uncover the folding process in all cases; all models undergo, at least, the two major structural transitions observed in nature-the coil-globule collapse and the folding transition. As the complexity of the model increases, these two major transitions begin to split into multi-step processes, wherein the lattice coarse-graining has a significant impact on the details of these processes. The results show that the level of structural coarse-graining is coupled to the level of interaction coarse-graining.

Microstructural Capture of Living Ultrathin Polymer Brush Evolution via Kinetic Simulation Studies

Performing dynamic off-lattice multicanonical Monte Carlo simulations, we study the statics, dynamics, and scission-recombination kinetics of a self-assembled in situ-polymerized polydisperse living polymer brush (LPB), designed by surface-initiated living polymerization. The living brush is initially grown from a two-dimensional substrate by end-monomer polymerization-depolymerization reactions through seeding of initiator arrays on the grafting plane which come in contact with a solution of nonbonded monomers under good solvent conditions. The polydispersity is shown to significantly deviate from the Flory-Schulz type for low temperatures because of pronounced diffusion limitation effects on the rate of the equilibration reaction. The self-avoiding chains take up fairly compact structures of typical size R_g(N) ∼ N^ν in rigorously two-dimensional (d = 2) melt, with ν being the inverse fractal dimension (ν = 1/d). The Kratky description of the intramolecular structure factor F(q), in keeping with the concept of generalized Porod scattering from compact particles with fractal contour, discloses a robust nonmonotonic fashion with q^dF(q) ∼ (qR_g)^-3/4 in the intermediate-q regime. It is found that the kinetics of LPB growth, given by the variation of the mean chain length, follows a power law ⟨N(t)⟩ ∝ t^1/3 with elapsed time after the onset of polymerization, whereby the instantaneous molecular weight distribution (MWD) of the chains c(N) retains its functional form. The variation of ⟨N(t)⟩ during quenches of the LPB to different temperatures T can be described by a single master curve in units of dimensionless time t/τ_∞, where τ_∞ is the typical (final temperature T^∞-dependent) relaxation time which is found to scale as τ_∞ ∝ ⟨N(t = ∞)⟩⁵ with the ultimate average length of the chains. The equilibrium monomer density profile ϕ(z) of the LPB varies as ϕ(z) ∝ ϕ^-α with the concentration of segments ϕ in the system and the probability distribution c(N) of chain lengths N in the brush layer scales as c(N) ∝ N^-τ. The computed exponents α ≈ 0.64 and τ ≈ 1.70 are in good agreement with those predicted within the context of the Diffusion-Limited Aggregation theory, α = 2/3 and τ = 7/4.

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.

Size-guided multi-seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size-guided multi-seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest-energy configurations of the cluster with n - 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.

Polymer adsorption on curved surfaces

The conformational behavior of a coarse-grained finite polymer chain near an attractive spherical surface was investigated by means of multicanonical Monte Carlo computer simulations. In a detailed analysis of canonical equilibrium data over a wide range of sphere radius and temperature, we have constructed entire phase diagrams both for nongrafted and end-grafted polymers. For the identification of the conformational phases, we have calculated several energetic and structural observables such as gyration tensor based shape parameters and their fluctuations by canonical statistical analysis. Despite the simplicity of our model, it qualitatively represents in the considered parameter range real systems that are studied in experiments. The work discussed here could have experimental implications from protein-ligand interactions to designing nanosmart materials.

Two Perturbations for Geometry Optimization of Off-lattice Bead Protein Models

Referring to the optimization algorithm previously developed for atomic clusters, the present author develops an efficient method for geometry optimization of a coarse-grained protein model expressed with two kinds of beads (hydrophilic and hydrophobic ones). In the method, two types of geometrical perturbations, center-directed bead move and one bead rotation, are used to explore new configurations and local optimizations are performed after the perturbations. The center-directed bead move is used for hydrophobic beads and the one bead rotation is performed for both hydrophobic and hydrophilic beads. The optimization method was applied to protein models consisting of 13, 20, 21, and 34 beads. The present method produced the global minima of the 13-, 21-, and 34-bead models reported in the literature and updated the lowest energies of the protein models with 20 beads. These results indicate that the present method is efficient for searching for optimal structures of proteins.

Dilute Semiflexible Polymers with Attraction: Collapse, Folding and Aggregation

We review the current state on the thermodynamic behavior and structural phases of self- and mutually-attractive dilute semiflexible polymers that undergo temperature-driven transitions. In extreme dilution, polymers may be considered isolated, and this single polymer undergoes a collapse or folding transition depending on the internal structure. This may go as far as to stable knot phases. Adding polymers results in aggregation, where structural motifs again depend on the internal structure. We discuss in detail the effect of semiflexibility on the collapse and aggregation transition and provide perspectives for interesting future investigations.

Knots as a Topological Order Parameter for Semiflexible Polymers

Using a combination of the multicanonical Monte Carlo algorithm and the replica-exchange method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudophase diagram for the complete range of semiflexible polymers, from flexible to stiff. Although it is a simple model, we observe a rich variety of conformational phases, reminiscent of conformations observed for synthetic polymers or biopolymers. Depending on the bending stiffness, the model exhibits different pseudophases like bent, hairpin, or toroidal. In particular, we find thermodynamically stable knots and unusual transitions into these knotted phases with a clear phase coexistence, but almost constant mean total energy, and hence almost no latent heat.

Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations

Over the last decade flat-histogram Monte Carlo simulations, especially multi-canonical and Wang-Landau simulations, have emerged as a strong tool to study the statistical mechanics of polymer chains. These investigations have focused on coarse-grained models of polymers on the lattice and in the continuum. Phase diagrams of chains in bulk as well as chains attached to surfaces were studied, for homopolymers as well as for protein-like models. Also, aggregation behavior in solution of these models has been investigated. We will present here the theoretical background for these simulations, explain the algorithms used and discuss their performance and give an overview over the systems studied with these methods in the literature, where we will limit ourselves to studies of coarse-grained model systems. Implementations of these algorithms on parallel computers will be also briefly described. In parallel to the development of these simulation methods, the power of a micro-canonical analysis of such simulations has been recognized, and we present the current state of the art in applying the micro-canonical analysis to phase transitions in nanoscopic polymer systems.

Confinement effects upon the separation of structural transitions in linear systems with restricted bond fluctuation ranges

By means of advanced parallel replica-exchange Monte Carlo methods we examine the influence of elasticity and confinement on the structural transitions of linear systems with restricted bonded interaction. For this purpose, we adopt a model for coarse-grained flexible polymers of finite length in the dilute regime. Hyperphase diagrams are constructed using energy-dependent canonical quantities to demonstrate the effects of the changes in the range of the confined interaction on the liquid and solid structural phases. With increasing bonded interaction range we observe the disappearance of the liquid phase and the fusion of the gas-liquid (or Θ) and the liquid-solid transitions. One of the most remarkable features, the liquid-gas transition, changes from second to first order if the confined interaction range exceeds a threshold that separates polymeric from nonpolymeric systems. The notoriously difficult sampling of the entropically suppressed conformations in the region of very strong first-order transitions is improved by using multiple Gaussian modified ensembles.

Protein structure prediction with local adjust tabu search algorithm

Background

Protein folding structure prediction is one of the most challenging problems in the bioinformatics domain. Because of the complexity of the realistic protein structure, the simplified structure model and the computational method should be adopted in the research. The AB off-lattice model is one of the simplification models, which only considers two classes of amino acids, hydrophobic (A) residues and hydrophilic (B) residues.

Results

The main work of this paper is to discuss how to optimize the lowest energy configurations in 2D off-lattice model and 3D off-lattice model by using Fibonacci sequences and real protein sequences. In order to avoid falling into local minimum and faster convergence to the global minimum, we introduce a novel method (SATS) to the protein structure problem, which combines simulated annealing algorithm and tabu search algorithm. Various strategies, such as the new encoding strategy, the adaptive neighborhood generation strategy and the local adjustment strategy, are adopted successfully for high-speed searching the optimal conformation corresponds to the lowest energy of the protein sequences. Experimental results show that some of the results obtained by the improved SATS are better than those reported in previous literatures, and we can sure that the lowest energy folding state for short Fibonacci sequences have been found.

Conclusions

Although the off-lattice models is not very realistic, they can reflect some important characteristics of the realistic protein. It can be found that 3D off-lattice model is more like native folding structure of the realistic protein than 2D off-lattice model. In addition, compared with some previous researches, the proposed hybrid algorithm can more effectively and more quickly search the spatial folding structure of a protein chain.

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.

Wang-Landau sampling in face-centered-cubic hydrophobic-hydrophilic lattice model proteins

Finding the global minimum-energy structure is one of the main problems of protein structure prediction. The face-centered-cubic (fcc) hydrophobic-hydrophilic (HP) lattice model can reach high approximation ratios of real protein structures, so the fcc lattice model is a good choice to predict the protein structures. The lacking of an effective global optimization method is the key obstacle in solving this problem. The Wang-Landau sampling method is especially useful for complex systems with a rough energy landscape and has been successfully applied to solving many optimization problems. We apply the improved Wang-Landau (IWL) sampling method, which incorporates the generation of an initial conformation based on the greedy strategy and the neighborhood strategy based on pull moves into the Wang-Landau sampling method to predict the protein structures on the fcc HP lattice model. Unlike conventional Monte Carlo simulations that generate a probability distribution at a given temperature, the Wang-Landau sampling method can estimate the density of states accurately via a random walk, which produces a flat histogram in energy space. We test 12 general benchmark instances on both two-dimensional and three-dimensional (3D) fcc HP lattice models. The lowest energies by the IWL sampling method are as good as or better than those of other methods in the literature for all instances. We then test five sets of larger-scale instances, denoted by the S, R, F90, F180, and CASP target instances on the 3D fcc HP lattice model. The numerical results show that our algorithm performs better than the other five methods in the literature on both the lowest energies and the average lowest energies in all runs. The IWL sampling method turns out to be a powerful tool to study the structure prediction of the fcc HP lattice model proteins.

Microcanonical thermostatistics of coarse-grained proteins with amyloidogenic propensity

The formation of fibrillar aggregates seems to be a common characteristic of polypeptide chains, although the observation of these aggregates may depend on appropriate experimental conditions. Partially folded intermediates seem to have an important role in the generation of protein aggregates, and a mechanism for this fibril formation considers that these intermediates also correspond to metastable states with respect to the fibrillar ones. Here, using a coarse-grained (CG) off-lattice model, we carry out a comparative analysis of the thermodynamic aspects characterizing the folding transition with respect to the propensity for aggregation of four different systems: two isoforms of the amyloid β-protein, the Src SH3 domain, and the human prion proteins (hPrP). Microcanonical analysis of the data obtained from replica exchange method is conducted to evaluate the free-energy barrier and latent heat in these models. The simulations of the amyloid β isoforms and Src SH3 domain indicated that the folding process described by this CG model is related to a negative specific heat, a phenomenon that can only be verified in the microcanonical ensemble in first-order phase transitions. The CG simulation of the hPrP heteropolymer yielded a continuous folding transition. The absence of a free-energy barrier and latent heat favors the presence of partially unfolded conformations, and in this context, this thermodynamic aspect could explain the reason why the hPrP heteropolymer is more aggregation-prone than the other heteropolymers considered in this study. We introduced the hydrophobic radius of gyration as an order parameter and found that it can be used to obtain reliable information about the hydrophobic packing and the transition temperatures in the folding process.

Structural behavior of a polymer chain inside an attractive sphere

We analyze the structural behavior of a single polymer chain inside an attractive sphere. Our model is composed of a coarse-grained polymer and an attractive-sphere potential. By means of extensive multicanonical Monte Carlo simulations, it is shown that the system exhibits a rich phase diagram ranging from highly ordered compact to extended random coil structures and from desorbed to partially or even completely adsorbed conformations. These findings are identified with different structural observables.

STUDIES OF FINDING LOW ENERGY CONFIGURATIONS IN OFF-LATTICE PROTEIN MODELS

We studied two three-dimensional off-lattice protein models with two species of monomers, hydrophobic and hydrophilic. Low energy configurations in both models were optimized using the energy landscape paving (ELP) method and subsequent gradient descent. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. For all sequences with lengths 13 ≤ n ≤ 55, the algorithm finds states with lower energy than previously proposed putative ground states.

Effective 3D protein structure prediction with local adjustment genetic-annealing algorithm

The protein folding problem consists of predicting protein tertiary structure from a given amino acid sequence by minimizing the energy function. The protein folding structure prediction is computationally challenging and has been shown to be NP-hard problem when the 3D off-lattice AB model is employed. In this paper, the local adjustment genetic-annealing (LAGA) algorithm was used to search the ground state of 3D offlattice AB model for protein folding structure. The algorithm included an improved crossover strategy and an improved mutation strategy, where a local adjustment strategy was also used to enhance the searching ability. The experiments were carried out with the Fibonacci sequences. The experimental results demonstrate that the LAGA algorithm appears to have better performance and accuracy compared to the previous methods.

3D protein structure prediction with genetic tabu search algorithm

Background

Protein structure prediction (PSP) has important applications in different fields, such as drug design, disease prediction, and so on. In protein structure prediction, there are two important issues. The first one is the design of the structure model and the second one is the design of the optimization technology. Because of the complexity of the realistic protein structure, the structure model adopted in this paper is a simplified model, which is called off-lattice AB model. After the structure model is assumed, optimization technology is needed for searching the best conformation of a protein sequence based on the assumed structure model. However, PSP is an NP-hard problem even if the simplest model is assumed. Thus, many algorithms have been developed to solve the global optimization problem. In this paper, a hybrid algorithm, which combines genetic algorithm (GA) and tabu search (TS) algorithm, is developed to complete this task.

Results

In order to develop an efficient optimization algorithm, several improved strategies are developed for the proposed genetic tabu search algorithm. The combined use of these strategies can improve the efficiency of the algorithm. In these strategies, tabu search introduced into the crossover and mutation operators can improve the local search capability, the adoption of variable population size strategy can maintain the diversity of the population, and the ranking selection strategy can improve the possibility of an individual with low energy value entering into next generation. Experiments are performed with Fibonacci sequences and real protein sequences. Experimental results show that the lowest energy obtained by the proposed GATS algorithm is lower than that obtained by previous methods.

Conclusions

The hybrid algorithm has the advantages from both genetic algorithm and tabu search algorithm. It makes use of the advantage of multiple search points in genetic algorithm, and can overcome poor hill-climbing capability in the conventional genetic algorithm by using the flexible memory functions of TS. Compared with some previous algorithms, GATS algorithm has better performance in global optimization and can predict 3D protein structure more effectively.

Residue length and solvation model dependency of elastinlike polypeptides

We have performed exhaustive multicanonical Monte Carlo simulations of elastinlike polypeptides with a chain including amino acids (valine-proline-glycine-valine-glycine)n or in short (VPGVG)n, where n changes from 1 to 4, in order to investigate the thermodynamic and structural properties. To predict the characteristic secondary structure motifs of the molecules, Ramachandran plots were prepared and analyzed as well. In these studies, we utilized a realistic model where the interactions between all types of atoms were taken into account. Effects of solvation were also simulated by using an implicit-solvent model with two commonly used solvation parameter sets and compared with the vacuum case.

Adsorption of a hydrophobic-polar-model heteropolymer in an attractive nanotube

The adsorption of an off-lattice hydrophobic-polar-model heteropolymer in an attractive hydrophobic nanotube is presented by means of a multicanonical Monte Carlo simulation. In the model, the Lennard-Jones potential is assumed as an interaction potential between the effective monomers and the nanotube wall. The global minimum-energy configurations and the values of radius of gyration and end-to-end distance of these configurations are compared for both pure hydrophobic and polar heteropolymer models and with interaction term included model. The low-energy conformations for heteropolymers are extended when they interact with the nanotube which the conformational extensions are detected with some structural parameters.

Thermodynamics of tubelike flexible polymers

In this work, we discuss the general phase behavior of short tubelike flexible polymers. The geometric thickness constraint is implemented through the concept of the global radius of curvature. We use sophisticated Monte Carlo sampling methods to simulate small bead-stick polymer models with Lennard-Jones interaction among nonbonded monomers. We analyze energetic fluctuations and structural quantities to classify conformational pseudophases. We find that the tube thickness influences the thermodynamic behavior of simple tubelike polymers significantly, i.e., for a given temperature, the formation of secondary structures strongly depends on the tube thickness.

Comparative molecular dynamics and Monte Carlo study of statistical properties for coarse-grained heteropolymers

Employing a simple hydrophobic-polar heteropolymer model, we compare thermodynamic quantities obtained from Andersen and Nosé-Hoover molecular dynamics as well as replica-exchange Monte Carlo methods. We find qualitative correspondence in the results, but serious quantitative differences using the Nosé-Hoover chain thermostat. For analyzing the deviations, we study different parameterizations of the Nosé-Hoover chain thermostat. Autocorrelations from molecular dynamics and Metropolis Monte Carlo runs are also investigated.

Re-examination of structure optimization of off-lattice protein AB models by conformational space annealing

The global structural optimization is carried out for off-lattice protein AB models in two and three dimensions by conformational space annealing. The models consist of hydrophobic and hydrophilic monomers in Fibonacci sequences. To accelerate the convergence, we have introduced a shift operator in the internal coordinate system, and effectively reduced the search space by forming a quotient space. With this, we significantly improve our previous results on AB models, and provide new low energy conformations. This work provides insights on exploring complicated energy landscapes by exploiting the advantages and limitations of CSA.

Determination of the structure of the energy landscape for coarse-grained off-lattice models of folding heteropolymers

The structure of energy landscapes for a minimalist coarse-grained off-lattice protein model is presented to investigate the folding behaviors of heteropolymers. The obtained energy landscapes serve as a useful tool for visualization of the funnel-like structure of a considered system in the configuration space. Despite the simplicity of the model, the knowledge of the free-energy landscape enables us to show different folding characteristics known from real proteins and synthetic peptides, such as two-state folding and metastability.

Thermodynamics of peptide aggregation processes: an analysis from perspectives of three statistical ensembles

We employ a mesoscopic model for studying aggregation processes of proteinlike hydrophobic-polar heteropolymers. By means of multicanonical Monte Carlo computer simulations, we find strong indications that peptide aggregation is a phase separation process, in which the microcanonical entropy exhibits a convex intruder due to non-negligible surface effects of the small systems. We analyze thermodynamic properties of the conformational transitions accompanying the aggregation process from the multicanonical, canonical, and microcanonical perspective. It turns out that the microcanonical description is particularly advantageous as it allows for unraveling details of the phase-separation transition in the thermodynamic region, where the temperature is not a suitable external control parameter anymore.

Simulation via direct computation of partition functions

In this paper, we demonstrate the efficiency of simulations via direct computation of the partition function under various macroscopic conditions, such as different temperatures or volumes. The method can compute partition functions by flattening histograms, through, for example, the Wang-Landau recursive scheme, outside the energy space. This method offers a more general and flexible framework for handling various types of ensembles, especially ones in which computation of the density of states is not convenient. It can be easily scaled to large systems, and it is flexible in incorporating Monte Carlo cluster algorithms or molecular dynamics. High efficiency is shown in simulating large Ising models, in finding ground states of simple protein models, and in studying the liquid-vapor phase transition of a simple fluid. The method is very simple to implement and we expect it to be efficient in studying complex systems with rugged energy landscapes, e.g., biological macromolecules.

Structure optimization and folding mechanisms of off-lattice protein models using statistical temperature molecular dynamics simulation: Statistical temperature annealing

The recently proposed statistical temperature molecular dynamics (STMD) algorithm [Kim, Phys. Rev. Lett. 97, 050601 (2006)] is used as the core of an optimization algorithm, statistical temperature annealing (STA), for finding low-lying energy minima of complex potential energy landscapes. Since STMD realizes a random walk in energy, the idea is simply to initiate repeated minimizations from configurations in the low-energy segments of STMD trajectories. STA is tested in structural optimization of various off-lattice AB and extended AB protein models in two and three dimensions with different chain lengths. New putative ground states were found for the two- and three-dimensional AB 55-mer, and for the three-dimensional extended AB 21-mer and 55-mer. The distinct folding features of the models are analyzed in terms of the statistical temperature and other representations of the structure of the potential energy landscape. It is shown that the characteristic behavior of the statistical temperature undergoes a qualitative change with the inclusion of a torsional potential in the extended AB model, as the more rigid backbone makes the potential energy landscape more funnel-like.

Identification of characteristic protein folding channels in a coarse-grained hydrophobic-polar peptide model

Folding channels and free-energy landscapes of hydrophobic-polar heteropolymers are discussed on the basis of a minimalistic off-lattice coarse-grained model. We investigate how rearrangements of hydrophobic and polar monomers in a heteropolymer sequence lead to completely different folding behaviors. Studying three exemplified sequences with the same content of hydrophobic and polar residues, we can reproduce within this simple model two-state folding, folding through intermediates, as well as metastability.

A knowledge-based move set for protein folding

The free energy landscape of protein folding is rugged, occasionally characterized by compact, intermediate states of low free energy. In computational folding, this landscape leads to trapped, compact states with incorrect secondary structure. We devised a residue-specific, protein backbone move set for efficient sampling of protein-like conformations in computational folding simulations. The move set is based on the selection of a small set of backbone dihedral angles, derived from clustering dihedral angles sampled from experimental structures. We show in both simulated annealing and replica exchange Monte Carlo (REMC) simulations that the knowledge-based move set, when compared with a conventional move set, shows statistically significant improved ability at overcoming kinetic barriers, reaching deeper energy minima, and achieving correspondingly lower RMSDs to native structures. The new move set is also more efficient, being able to reach low energy states considerably faster. Use of this move set in determining the energy minimum state and for calculating thermodynamic quantities is discussed.