Fast de novo discovery of low‐energy protein loop conformations

In the prediction of protein structure from amino acid sequence, loops are challenging regions for computational methods. Since loops are often located on the protein surface, they can have significant roles in determining protein functions and binding properties. Loop prediction without the aid of a structural template requires extensive conformational sampling and energy minimization, which are computationally difficult. In this article we present a new de novo loop sampling method, the Parallely filtered Energy Targeted All‐atom Loop Sampler (PETALS) to rapidly locate low energy conformations. PETALS explores both backbone and side‐chain positions of the loop region simultaneously according to the energy function selected by the user, and constructs a nonredundant ensemble of low energy loop conformations using filtering criteria. The method is illustrated with the DFIRE potential and DiSGro energy function for loops, and shown to be highly effective at discovering conformations with near‐native (or better) energy. Using the same energy function as the DiSGro algorithm, PETALS samples conformations with both lower RMSDs and lower energies. PETALS is also useful for assessing the accuracy of different energy functions. PETALS runs rapidly, requiring an average time cost of 10 minutes for a length 12 loop on a single 3.2 GHz processor core, comparable to the fastest existing de novo methods for generating an ensemble of conformations. Proteins 2017; 85:1402–1412. © 2017 Wiley Periodicals, Inc.     

Modeling of loops in protein structures

Comparative protein structure prediction is limited mostly by the errors in alignment and loop modeling. We describe here a new automated modeling technique that significantly improves the accuracy of loop predictions in protein structures. The positions of all nonhydrogen atoms of the loop are optimized in a fixed environment with respect to a pseudo energy function. The energy is a sum of many spatial restraints that include the bond length, bond angle, and improper dihedral angle terms from the CHARMM-22 force field, statistical preferences for the main-chain and side-chain dihedral angles, and statistical preferences for nonbonded atomic contacts that depend on the two atom types, their distance through space, and separation in sequence. The energy function is optimized with the method of conjugate gradients combined with molecular dynamics and simulated annealing. Typically, the predicted loop conformation corresponds to the lowest energy conformation among 500 independent optimizations. Predictions were made for 40 loops of known structure at each length from 1 to 14 residues. The accuracy of loop predictions is evaluated as a function of thoroughness of conformational sampling, loop length, and structural properties of native loops. When accuracy is measured by local superposition of the model on the native loop, 100, 90, and 30% of 4-, 8-, and 12-residue loop predictions, respectively, had <2 A RMSD error for the mainchain N, C(alpha), C, and O atoms; the average accuracies were 0.59 +/- 0.05, 1.16 +/- 0.10, and 2.61 +/- 0.16 A, respectively. To simulate real comparative modeling problems, the method was also evaluated by predicting loops of known structure in only approximately correct environments with errors typical of comparative modeling without misalignment. When the RMSD distortion of the main-chain stem atoms is 2.5 A, the average loop prediction error increased by 180, 25, and 3% for 4-, 8-, and 12-residue loops, respectively. The accuracy of the lowest energy prediction for a given loop can be estimated from the structural variability among a number of low energy predictions. The relative value of the present method is gauged by (1) comparing it with one of the most successful previously described methods, and (2) describing its accuracy in recent blind predictions of protein structure. Finally, it is shown that the average accuracy of prediction is limited primarily by the accuracy of the energy function rather than by the extent of conformational sampling.     

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.     

Atomic-Accuracy Prediction of Protein Loop Structures through an RNA-Inspired Ansatz

Consistently predicting biopolymer structure at atomic resolution from sequence alone remains a difficult problem, even for small sub-segments of large proteins. Such loop prediction challenges, which arise frequently in comparative modeling and protein design, can become intractable as loop lengths exceed 10 residues and if surrounding side-chain conformations are erased. Current approaches, such as the protein local optimization protocol or kinematic inversion closure (KIC) Monte Carlo, involve stages that coarse-grain proteins, simplifying modeling but precluding a systematic search of all-atom configurations. This article introduces an alternative modeling strategy based on a ‘stepwise ansatz’, recently developed for RNA modeling, which posits that any realistic all-atom molecular conformation can be built up by residue-by-residue stepwise enumeration. When harnessed to a dynamic-programming-like recursion in the Rosetta framework, the resulting stepwise assembly (SWA) protocol enables enumerative sampling of a 12 residue loop at a significant but achievable cost of thousands of CPU-hours. In a previously established benchmark, SWA recovers crystallographic conformations with sub-Angstrom accuracy for 19 of 20 loops, compared to 14 of 20 by KIC modeling with a comparable expenditure of computational power. Furthermore, SWA gives high accuracy results on an additional set of 15 loops highlighted in the biological literature for their irregularity or unusual length. Successes include cis-Pro touch turns, loops that pass through tunnels of other side-chains, and loops of lengths up to 24 residues. Remaining problem cases are traced to inaccuracies in the Rosetta all-atom energy function. In five additional blind tests, SWA achieves sub-Angstrom accuracy models, including the first such success in a protein/RNA binding interface, the YbxF/kink-turn interaction in the fourth ‘RNA-puzzle’ competition. These results establish all-atom enumeration as an unusually systematic approach to ab initio protein structure modeling that can leverage high performance computing and physically realistic energy functions to more consistently achieve atomic accuracy.     

Fast Protein Loop Sampling and Structure Prediction Using Distance-Guided Sequential Chain-Growth Monte Carlo Method

Loops in proteins are flexible regions connecting regular secondary structures. They are often involved in protein functions through interacting with other molecules. The irregularity and flexibility of loops make their structures difficult to determine experimentally and challenging to model computationally. Conformation sampling and energy evaluation are the two key components in loop modeling. We have developed a new method for loop conformation sampling and prediction based on a chain growth sequential Monte Carlo sampling strategy, called Distance-guided Sequential chain-Growth Monte Carlo (DiSGro). With an energy function designed specifically for loops, our method can efficiently generate high quality loop conformations with low energy that are enriched with near-native loop structures. The average minimum global backbone RMSD for 1,000 conformations of 12-residue loops is Å, with a lowest energy RMSD of Å, and an average ensemble RMSD of Å. A novel geometric criterion is applied to speed up calculations. The computational cost of generating 1,000 conformations for each of the x loops in a benchmark dataset is only about cpu minutes for 12-residue loops, compared to ca cpu minutes using the FALCm method. Test results on benchmark datasets show that DiSGro performs comparably or better than previous successful methods, while requiring far less computing time. DiSGro is especially effective in modeling longer loops (– residues).     

Ab initio structure prediction of the antibody hypervariable H3 loop

Antibodies have the capability of binding a wide range of antigens due to the diversity of the six loops constituting the complementarity determining region (CDR). Among the six loops, the H3 loop is the most diverse in structure, length, and sequence identity. Prediction of the three‐dimensional structures of antibodies, especially the CDR loops, is an important step in the computational design and engineering of novel antibodies for improved affinity and specificity. Although it has been demonstrated that the conformation of the five non‐H3 loops can be accurately predicted by comparing their sequences against databases of canonical loop conformations, no such connection has been established for H3 loops. In this work, we present the results for ab initio structure prediction of the H3 loop using conformational sampling and energy calculations with the program Prime on a dataset of 53 loops ranging in length from 4 to 22 residues. When the prediction is performed in the crystal environment and including symmetry mates, the median backbone root mean square deviation (RMSD) is 0.5 Å to the crystal structure, with 91% of cases having an RMSD of less than 2.0 Å. When the prediction is performed in a noncrystallographic environment, where the scaffold is constructed by swapping the H3 loops between homologous antibodies, 70% of cases have an RMSD below 2.0 Å. These results show promise for ab initio loop predictions applied to modeling of antibodies. © 2012 Wiley Periodicals, Inc.     

Loop prediction for a GPCR homology model: Algorithms and results

We present loop structure prediction results of the intracellular and extracellular loops of four G‐protein‐coupled receptors (GPCRs): bovine rhodopsin (bRh), the turkey β1‐adrenergic (β1Ar), the human β2‐adrenergic (β2Ar) and the human A2a adenosine receptor (A2Ar) in perturbed environments. We used the protein local optimization program, which builds thousands of loop candidates by sampling rotamer states of the loops' constituent amino acids. The candidate loops are discriminated between with our physics‐based, all‐atom energy function, which is based on the OPLS force field with implicit solvent and several correction terms. For relevant cases, explicit membrane molecules are included to simulate the effect of the membrane on loop structure. We also discuss a new sampling algorithm that divides phase space into different regions, allowing more thorough sampling of long loops that greatly improves results. In the first half of the paper, loop prediction is done with the GPCRs' transmembrane domains fixed in their crystallographic positions, while the loops are built one‐by‐one. Side chains near the loops are also in non‐native conformations. The second half describes a full homology model of β2Ar using β1Ar as a template. No information about the crystal structure of β2Ar was used to build this homology model. We are able to capture the architecture of short loops and the very long second extracellular loop, which is key for ligand binding. We believe this the first successful example of an RMSD validated, physics‐based loop prediction in the context of a GPCR homology model. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Protein loop modeling by using fragment assembly and analytical loop closure

Protein loops are often involved in important biological functions such as molecular recognition, signal transduction, or enzymatic action. The three dimensional structures of loops can provide essential information for understanding molecular mechanisms behind protein functions. In this article, we develop a novel method for protein loop modeling, where the loop conformations are generated by fragment assembly and analytical loop closure. The fragment assembly method reduces the conformational space drastically, and the analytical loop closure method finds the geometrically consistent loop conformations efficiently. We also derive an analytic formula for the gradient of any analytical function of dihedral angles in the space of closed loops. The gradient can be used to optimize various restraints derived from experiments or databases, for example restraints for preferential interactions between specific residues or for preferred backbone angles. We demonstrate that the current loop modeling method outperforms previous methods that employ residue‐based torsion angle maps or different loop closure strategies when tested on two sets of loop targets of lengths ranging from 4 to 12. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Validating a Coarse-Grained Potential Energy Function through Protein Loop Modelling

Coarse-grained (CG) methods for sampling protein conformational space have the potential to increase computational efficiency by reducing the degrees of freedom. The gain in computational efficiency of CG methods often comes at the expense of non-protein like local conformational features. This could cause problems when transitioning to full atom models in a hierarchical framework. Here, a CG potential energy function was validated by applying it to the problem of loop prediction. A novel method to sample the conformational space of backbone atoms was benchmarked using a standard test set consisting of 351 distinct loops. This method used a sequence-independent CG potential energy function representing the protein using -carbon positions only and sampling conformations with a Monte Carlo simulated annealing based protocol. Backbone atoms were added using a method previously described and then gradient minimised in the Rosetta force field. Despite the CG potential energy function being sequence-independent, the method performed similarly to methods that explicitly use either fragments of known protein backbones with similar sequences or residue-specific /-maps to restrict the search space. The method was also able to predict with sub-Angstrom accuracy two out of seven loops from recently solved crystal structures of proteins with low sequence and structure similarity to previously deposited structures in the PDB. The ability to sample realistic loop conformations directly from a potential energy function enables the incorporation of additional geometric restraints and the use of more advanced sampling methods in a way that is not possible to do easily with fragment replacement methods and also enable multi-scale simulations for protein design and protein structure prediction. These restraints could be derived from experimental data or could be design restraints in the case of computational protein design. C++ source code is available for download from http://www.sbg.bio.ic.ac.uk/phyre2/PD2/.     

Coarse-Grained Prediction of RNA Loop Structures

One of the key issues in the theoretical prediction of RNA folding is the prediction of loop structure from the sequence. RNA loop free energies are dependent on the loop sequence content. However, most current models account only for the loop length-dependence. The previously developed “Vfold” model (a coarse-grained RNA folding model) provides an effective method to generate the complete ensemble of coarse-grained RNA loop and junction conformations. However, due to the lack of sequence-dependent scoring parameters, the method is unable to identify the native and near-native structures from the sequence. In this study, using a previously developed iterative method for extracting the knowledge-based potential parameters from the known structures, we derive a set of dinucleotide-based statistical potentials for RNA loops and junctions. A unique advantage of the approach is its ability to go beyond the the (known) native structures by accounting for the full free energy landscape, including all the nonnative folds. The benchmark tests indicate that for given loop/junction sequences, the statistical potentials enable successful predictions for the coarse-grained 3D structures from the complete conformational ensemble generated by the Vfold model. The predicted coarse-grained structures can provide useful initial folds for further detailed structural refinement.     

Scaling of Folding Properties in Go Models of Proteins

Insights about scaling of folding properties of proteins are obtained bystudying folding in heteropolymers described by Go-like Hamiltonians. Bothlattice and continuum space models are considered. In the latter case, themonomer-monomer interactions correspond to the Lennard-Jones potential.Several statistical ensembles of the two- and three-dimensional targetnative conformations are considered. Among them are maximally compactconformations which are confined to a lattice and those which are obtainedeither through quenching or annealing of homopolymers to their compactlocal energy minima. Characteristic folding times are found to grow aspower laws with the system size. The corresponding exponents are notuniversal. The size related deterioration of foldability is found to beconsistent with the scaling behavior of the characteristic temperatures:asymptotically, the folding temperature becomes much lower than thetemperature at which glassy kinetics become important. The helicalconformations are found to have the lowest overall scaling exponent andthe best foldability among the classes of conformations studied. Thescaling properties of the Go-like models of the protein conformationsstored in the Protein Data Bank suggest that proteins are not optimizedkinetically.     

Long loop prediction using the protein local optimization program

We have developed an improved sampling algorithm and energy model for protein loop prediction, the combination of which has yielded the first methodology capable of achieving good results for the prediction of loop backbone conformations of 11 residue length or greater. Applied to our newly constructed test suite of 104 loops ranging from 11 to 13 residues, our method obtains average/median global backbone root-mean-square deviations (RMSDs) to the native structure (superimposing the body of the protein, not the loop itself) of 1.00/0.62 A for 11 residue loops, 1.15/0.60 A for 12 residue loops, and 1.25/0.76 A for 13 residue loops. Sampling errors are virtually eliminated, while energy errors leading to large backbone RMSDs are very infrequent compared to any previously reported efforts, including our own previous study. We attribute this success to both an improved sampling algorithm and, more critically, the inclusion of a hydrophobic term, which appears to approximately fix a major flaw in SGB solvation model that we have been employing. A discussion of these results in the context of the general question of the accuracy of continuum solvation models is presented.     

Kinetics of loop formation and breakage in the denatured state of iso-1-cytochrome c

The earliest events in protein folding involve the formation of simple loops. Observing the rates of loop closure under denaturing conditions can provide direct insight into the relative probability and sequence determinants for formation of loops of different sizes. The persistence of these initial contacts is equally important for efficient folding, so measurement of rates of loop breakage under denaturing conditions is also essential. We have used stopped-flow and continuous-flow methods to measure the rates of histidine-heme loop formation and breakage in the denatured state of iso-1-cytochrome c (in the presence of 3 M guanidine HCl). The data indicate that the mechanism for forming loops is a two-step process, the first step being the deprotonation of the histidine, and the second step being the binding of the histidine to the heme. This mechanism makes it possible to extract both the rate constants of formation, k(f), and breakage, k(b), of loops from the pH dependence of the observed rate constant, k(obs). To determine the dependence of k(f) and k(b) on loop size, we have carried out kinetic measurements for seven single surface histidine variants of iso-1-cytochrome c. A scaling factor (the dependence of k(f) on log[loop size]) of approximately -1.8 is observed for loop formation, similar to that observed in other systems. The magnitude of k(b) varies from 30 s(-1) to 300 s(-1), indicating that the stability of different loops varies considerably. The implications of the kinetics of loop formation and breakage in the denatured state for the mechanism of protein folding are discussed.     

Multiple copy sampling in protein loop modeling: computational efficiency and sensitivity to dihedral angle perturbations.

Multiple copy sampling and the bond scaling-relaxation technique are combined to generate 3-dimensional conformations of protein loop segments. The computational efficiency and sensitivity to initial loop copy dispersion are analyzed. The multicopy loop modeling method requires approximately 20-50% of the computational time required by the single-copy method for the various protein segments tested. An analytical formula is proposed to estimate the computational gain prior to carrying out a multicopy simulation. When 7-residue loops within flexible proteins are modeled, each multicopy simulation can sample a set of loop conformations with initial dispersions up to +/- 15 degrees for backbone and +/- 30 degrees for side-chain rotatable dihedral angles. The dispersions are larger for shorter and smaller for longer and/or surface loops. The degree of convergence of loop copies during a simulation can be used to complement commonly used target functions (such as potential energy) for distinguishing between native and misfolded conformations. Furthermore, this convergence also reflects the conformational flexibility of the modeled protein segment. Application to simultaneously building all 6 hypervariable loops of an antibody is discussed.     

ARTIST: an activated method in internal coordinate space for sampling protein energy landscapes

We present the first applications of an activated method in internal coordinate space for sampling all-atom protein conformations, the activation-relaxation technique for internal coordinate space trajectories (ARTIST). This method differs from all previous internal coordinate-based studies aimed at folding or refining protein structures in that conformational changes result from identifying and crossing well-defined saddle points connecting energy minima. Our simulations of four model proteins containing between 4 and 47 amino acids indicate that this method is efficient for exploring conformational space in both sparsely and densely packed environments, and offers new perspectives for applications ranging from computer-aided drug design to supramolecular assembly.     

Modeling protein loops using a phi i + 1, psi i dimer database.

We present an automated method for modeling backbones of protein loops. The method samples a database of phi i + 1 and psi i angles constructed from a nonredundant version of the Protein Data Bank (PDB). The dihedral angles phi i + 1 and psi i completely define the backbone conformation of a dimer when standard bond lengths, bond angles, and a trans planar peptide configuration are used. For the 400 possible dimers resulting from 20 natural amino acids, a list of allowed phi i + 1, psi i pairs for each dimer is created by pooling all such pairs from the loop segments of each protein in the nonredundant version of the PDB. Starting from the N-terminus of the loop sequence, conformations are generated by assigning randomly selected pairs of phi i + 1, psi i for each dimer from the respective pool using standard bond lengths, bond angles, and a trans peptide configuration. We use this database to simulate protein loops of lengths varying from 5 to 11 amino acids in five proteins of known three-dimensional structures. Typically, 10,000-50,000 models are simulated for each protein loop and are evaluated for stereochemical consistency. Depending on the length and sequence of a given loop, 50-80% of the models generated have no stereochemical strain in the backbone atoms. We demonstrate that, when simulated loops are extended to include flanking residues from homologous segments, only very few loops from an ensemble of sterically allowed conformations orient the flanking segments consistent with the protein topology. The presence of near-native backbone conformations for loops from five different proteins suggests the completeness of the dimeric database for use in modeling loops of homologous proteins. Here, we take advantage of this observation to design a method that filters near-native loop conformations from an ensemble of sterically allowed conformations. We demonstrate that our method eliminates the need for a loop-closure algorithm and hence allows for the use of topological constraints of the homologous proteins or disulfide constraints to filter near-native loop conformations.     

Toward better refinement of comparative models: predicting loops in inexact environments

Achieving atomic-level accuracy in comparative protein models is limited by our ability to refine the initial, homolog-derived model closer to the native state. Despite considerable effort, progress in developing a generalized refinement method has been limited. In contrast, methods have been described that can accurately reconstruct loop conformations in native protein structures. We hypothesize that loop refinement in homology models is much more difficult than loop reconstruction in crystal structures, in part, because side-chain, backbone, and other structural inaccuracies surrounding the loop create a challenging sampling problem; the loop cannot be refined without simultaneously refining adjacent portions. In this work, we single out one sampling issue in an artificial but useful test set and examine how loop refinement accuracy is affected by errors in surrounding side-chains. In 80 high-resolution crystal structures, we first perturbed 6-12 residue loops away from the crystal conformation, and placed all protein side chains in non-native but low energy conformations. Even these relatively small perturbations in the surroundings made the loop prediction problem much more challenging. Using a previously published loop prediction method, median backbone (N-Calpha-C-O) RMSD's for groups of 6, 8, 10, and 12 residue loops are 0.3/0.6/0.4/0.6 A, respectively, on native structures and increase to 1.1/2.2/1.5/2.3 A on the perturbed cases. We then augmented our previous loop prediction method to simultaneously optimize the rotamer states of side chains surrounding the loop. Our results show that this augmented loop prediction method can recover the native state in many perturbed structures where the previous method failed; the median RMSD's for the 6, 8, 10, and 12 residue perturbed loops improve to 0.4/0.8/1.1/1.2 A. Finally, we highlight three comparative models from blind tests, in which our new method predicted loops closer to the native conformation than first modeled using the homolog template, a task generally understood to be difficult. Although many challenges remain in refining full comparative models to high accuracy, this work offers a methodical step toward that goal.     

Influence of rotational energy barriers to the conformational search of protein loops in molecular dynamics and ranking the conformations.

An adjustable-barrier dihedral angle potential was added as an extension to a novel, previously presented soft-core potential to study its contribution to the efficacy of the search of the conformational space in molecular dynamics. As opposed to the conventional soft-core potential functions, the leading principle in the design of the new soft-core potential, as well as of its extension, the soft-core and adjustable-barrier dihedral angle (SCADA) potential (referred as the SCADA potential), was to maintain the main equilibrium properties of the original force field. This qualifies the methods for a variety of a priori modeling problems without need for additional restraints typically required with the conventional soft-core potentials. In the present study, the different potential energy functions are applied to the problem of predicting loop conformations in proteins. Comparison of the performance of the soft-core and SCADA potential showed that the main hurdles for the efficient sampling of the conformational space of (loops in) proteins are related to the high-energy barriers caused by the Lennard-Jones and Coulombic energy terms, and not to the rotational barriers, although the conformational search can be further enhanced by lowering the rotational barriers of the dihedral angles. Finally, different evaluation methods were studied and a few promising criteria found to distinguish the near-native loop conformations from the wrong ones.     

A methodology for efficiently sampling the conformation space of molecular structures

Motivated by recently developed computational techniques for studying protein flexibility, and their potential applications in docking, we propose an efficient method for sampling the conformational space of complex molecular structures. We focus on the loop closure problem, identified in the work of Thorpe and Lei (2004 Phil. Mag. 84 1323-31) as a primary bottleneck in the fast simulation of molecular motions. By modeling a molecular structure as a branching robot, we use an intuitive method in which the robot holds onto itself for maintaining loop constraints. New conformations are generated by applying random external forces, while internal, attractive forces pull the loops closed. Our implementation, tested on several model molecules with low number of degrees of freedom but many interconnected loops, gives promising results that show an almost four times speed-up on the benchmark cube-molecule of Thorpe and Lei.     

New efficient statistical sequence-dependent structure prediction of short to medium-sized protein loops based on an exhaustive loop classification.

A bank of 13,563 loops from three to eight amino acid residues long, representing motifs between two consecutive regular secondary structures, has been derived from protein structures presenting less than 95 % sequence identity. Statistical analyses of occurrences of conformations and residues revealed length-dependent over-representations of particular amino acids (glycine, proline, asparagine, serine, and aspartate) and conformations (alphaL, epsilon, betaPregions of the Ramachandran plot). A position-dependent distribution of these occurrences was observed for N and C-terminal residues, which are correlated to the nature of the flanking regions. Loops of the same length were clustered into statistically meaningful families on the basis of their backbone structures when placed in a common reference frame, independent of the flanks. These clusters present significantly different distributions of sequence, conformations, and endpoint residue Calphadistances. On the basis of the sequence-structure correlation of this clustering, an automatic loop modeling algorithm was developed. Based on the knowledge of its sequence and of its flank backbone structures each query loop is assigned to a family and target loop supports are selected in this family. The support backbones of these target loops are then adjusted on flanking structures by partial exploration of the conformational space. Loop closure is performed by energy minimization for each support and the final model is chosen among connected supports based upon energy criteria. The quality of the prediction is evaluated by the root-mean-square deviation (rmsd) between the final model and the native loops when the whole bank is re-attributed on itself with a Jackknife test. This average rmsd ranges from 1.1 A for three-residue loops to 3.8 A for eight-residue loops. A few poorly predicted loops are inescapable, considering the high level of diversity in loops and the lack of environment data. To overcome such modeling problems, a statistical reliability score was assigned for each prediction. This score is correlated to the quality of the prediction, in terms of rmsd, and thus improves the selection accuracy of the model. The algorithm efficiency was compared to CASP3 target loop predictions. Moreover, when tested on a test loop bank, this algorithm was shown to be robust when the loops are not precisely delimited, therefore proving to be a useful tool in practice for protein modeling.