Excluded volume in protein side-chain packing

The excluded volume occupied by protein side-chains and the requirement of high packing density in the protein interior should severely limit the number of side-chain conformations compatible with a given native backbone. To examine the relationship between side-chain geometry and side-chain packing, we use an all-atom Monte Carlo simulation to sample the large space of side-chain conformations. We study three models of excluded volume and use umbrella sampling to effectively explore the entire space. We find that while excluded volume constraints reduce the size of conformational space by many orders of magnitude, the number of allowed conformations is still large. An average repacked conformation has 20 % of its chi angles in a non-native state, a marked reduction from the expected 67 % in the absence of excluded volume. Interestingly, well-packed conformations with up to 50 % non-native chi angles exist. The repacked conformations have native packing density as measured by a standard Voronoi procedure. Entropy is distributed non-uniformly over positions, and we partially explain the observed distribution using rotamer probabilities derived from the Protein Data Bank database. In several cases, native rotamers that occur infrequently in the database are seen with high probability in our simulation, indicating that sequence-specific excluded volume interactions can stabilize rotamers that are rare for a given backbone. In spite of our finding that 65 % of the native rotamers and 85 % of chi(1) angles can be predicted correctly on the basis of excluded volume only, 95 % of positions can accommodate more than one rotamer in simulation. We estimate that, in order to quench the side-chain entropy observed in the presence of excluded volume interactions, other interactions (hydrophobic, polar, electrostatic) must provide an additional stabilization of at least 0.6 kT per residue in order to single out the native state.     

GEM: a Gaussian Evolutionary Method for predicting protein side-chain conformations

We have developed an evolutionary approach to predicting protein side-chain conformations. This approach, referred to as the Gaussian Evolutionary Method (GEM), combines both discrete and continuous global search mechanisms. The former helps speed up convergence by reducing the size of rotamer space, whereas the latter, integrating decreasing-based Gaussian mutations and self-adaptive Gaussian mutations, continuously adapts dihedrals to optimal conformations. We tested our approach on 38 proteins ranging in size from 46 to 325 residues and showed that the results were comparable to those using other methods. The average accuracies of our predictions were 80% for chi(1), 66% for chi(1 + 2), and 1.36 A for the root mean square deviation of side-chain positions. We found that if our scoring function was perfect, the prediction accuracy was also essentially perfect. However, perfect prediction could not be achieved if only a discrete search mechanism was applied. These results suggest that GEM is robust and can be used to examine the factors limiting the accuracy of protein side-chain prediction methods. Furthermore, it can be used to systematically evaluate and thus improve scoring functions.     

Improved side-chain prediction accuracy using an ab initio potential energy function and a very large rotamer library

Accurate prediction of the placement and comformations of protein side chains given only the backbone trace has a wide range of uses in protein design, structure prediction, and functional analysis. Prediction has most often relied on discrete rotamer libraries so that rapid fitness of side-chain rotamers can be assessed against some scoring function. Scoring functions are generally based on experimental parameters from small-molecule studies or empirical parameters based on determined protein structures. Here, we describe the NCN algorithm for predicting the placement of side chains. A predominantly first-principles approach was taken to develop the potential energy function incorporating van der Waals and electrostatics based on the OPLS parameters, and a hydrogen bonding term. The only empirical knowledge used is the frequency of rotameric states from the PDB. The rotamer library includes nearly 50,000 rotamers, and is the most extensive discrete library used to date. Although the computational time tends to be longer than most other algorithms, the overall accuracy exceeds all algorithms in the literature when placing rotamers on an accurate backbone trace. Considering only the most buried residues, 80% of the total residues tested, the placement accuracy reaches 92% for chi(1), and 83% for chi(1 + 2), and an overall RMS deviation of 1 A. Additionally, we show that if information is available to restrict chi(1) to one rotamer well, then this algorithm can generate structures with an average RMS deviation of 1.0 A for all heavy side-chains atoms and a corresponding overall chi(1 + 2) accuracy of 85.0%.     

Side-chain modeling with an optimized scoring function

Modeling side-chain conformations on a fixed protein backbone has a wide application in structure prediction and molecular design. Each effort in this field requires decisions about a rotamer set, scoring function, and search strategy. We have developed a new and simple scoring function, which operates on side-chain rotamers and consists of the following energy terms: contact surface, volume overlap, backbone dependency, electrostatic interactions, and desolvation energy. The weights of these energy terms were optimized to achieve the minimal average root mean square (rms) deviation between the lowest energy rotamer and real side-chain conformation on a training set of high-resolution protein structures. In the course of optimization, for every residue, its side chain was replaced by varying rotamers, whereas conformations for all other residues were kept as they appeared in the crystal structure. We obtained prediction accuracy of 90.4% for chi(1), 78.3% for chi(1 + 2), and 1.18 A overall rms deviation. Furthermore, the derived scoring function combined with a Monte Carlo search algorithm was used to place all side chains onto a protein backbone simultaneously. The average prediction accuracy was 87.9% for chi(1), 73.2% for chi(1 + 2), and 1.34 A rms deviation for 30 protein structures. Our approach was compared with available side-chain construction methods and showed improvement over the best among them: 4.4% for chi(1), 4.7% for chi(1 + 2), and 0.21 A for rms deviation. We hypothesize that the scoring function instead of the search strategy is the main obstacle in side-chain modeling. Additionally, we show that a more detailed rotamer library is expected to increase chi(1 + 2) prediction accuracy but may have little effect on chi(1) prediction accuracy.     

Beyond the rotamer library: genetic algorithm combined with the disturbing mutation process for upbuilding protein side-chains

The disturbing genetic algorithm, incorporating the disturbing mutation process into the genetic algorithm flow, has been developed to extend the searching space of side-chain conformations and to improve the quality of the rotamer library. Moreover, the growing generation amount idea, simulating the real situation of the natural evolution, is introduced to improve the searching speed. In the calculations using the pseudo energy scoring function of the root mean squared deviation, the disturbing genetic algorithm method has been shown to be highly efficient. With the real energy function based on AMBER force field, the program has been applied to rebuilding side-chain conformations of 25 high-quality crystallographic structures of single-protein and protein-protein complexes. The averaged root mean standard deviation of atom coordinates in side-chains and veracities of the torsion angles of chi(1) and chi(1) + chi(2) are 1.165 A, 88.2 and 72.9% for the buried residues, respectively, and 1.493 A, 79.2 and 64.7% for all residues, showing that the method has equal precision to the program SCWRL, whereas it performs better in the prediction of buried residues and protein-protein interfaces. This method has been successfully used in redesigning the interface of the Basnase-Barstar complex, indicating that it will have extensive application in protein design, protein sequence and structure relationship studies, and research on protein-protein interaction.     

Analysis of the relationship between side-chain conformation and secondary structure in globular proteins

The relationship between the preferred side-chain dihedral angles and the secondary structure of a residue was examined. The structures of 61 proteins solved to a resolution of 2.0 A (1 A = 0.1 nm) or better were analysed using a relational database to store the information. The strongest feature observed was that the chi 1 distribution for most side-chains in an alpha-helix showed an absence of the g- conformation and a shift towards the t conformation when compared to the non-alpha/beta structures. The exceptions to this tendency were for short polar side-chains that form hydrogen bonds with the main-chain which prefer g+. Shifts in the chi 1 preferences for residues in the beta-sheet were observed. Other side-chain dihedral angles (chi 2, chi 3, chi 4) were found to be influenced by the main-chain. This paper presents more accurate distributions for the side-chain dihedral angles which were obtained from the increased number of proteins determined to high resolution. The means and standard deviations for chi 1 and chi 2 angles are presented for all residues according to the secondary structure of the main-chain. The means and standard deviations are given for the most popular conformations for side-chains in which chi 3 and chi 4 rotations affect the position of C atoms.     

IRECS: a new algorithm for the selection of most probable ensembles of side-chain conformations in protein models

We introduce a new algorithm, IRECS (Iterative REduction of Conformational Space), for identifying ensembles of most probable side-chain conformations for homology modeling. On the basis of a given rotamer library, IRECS ranks all side-chain rotamers of a protein according to the probability with which each side chain adopts the respective rotamer conformation. This ranking enables the user to select small rotamer sets that are most likely to contain a near-native rotamer for each side chain. IRECS can therefore act as a fast heuristic alternative to the Dead-End-Elimination algorithm (DEE). In contrast to DEE, IRECS allows for the selection of rotamer subsets of arbitrary size, thus being able to define structure ensembles for a protein. We show that the selection of more than one rotamer per side chain is generally meaningful, since the selected rotamers represent the conformational space of flexible side chains. A knowledge-based statistical potential ROTA was constructed for the IRECS algorithm. The potential was optimized to discriminate between side-chain conformations of native and rotameric decoys of protein structures. By restricting the number of rotamers per side chain to one, IRECS can optimize side chains for a single conformation model. The average accuracy of IRECS for the chi1 and chi1+2 dihedral angles amounts to 84.7% and 71.6%, respectively, using a 40 degrees cutoff. When we compared IRECS with SCWRL and SCAP, the performance of IRECS was comparable to that of both methods. IRECS and the ROTA potential are available for download from the URL http://irecs.bioinf.mpi-inf.mpg.de.     

Extending the accuracy limits of prediction for side-chain conformations

Current techniques for the prediction of side-chain conformations on a fixed backbone have an accuracy limit of about 1.0-1.5 A rmsd for core residues. We have carried out a detailed and systematic analysis of the factors that influence the prediction of side-chain conformation and, on this basis, have succeeded in extending the limits of side-chain prediction for core residues to about 0.7 A rmsd from native, and 94 % and 89 % of chi(1) and chi(1+2 ) dihedral angles correctly predicted to within 20 degrees of native, respectively. These results are obtained using a force-field that accounts for only van der Waals interactions and torsional potentials. Prediction accuracy is strongly dependent on the rotamer library used. That is, a complete and detailed rotamer library is essential. The greatest accuracy was obtained with an extensive rotamer library, containing over 7560 members, in which bond lengths and bond angles were taken from the database rather than simply assuming idealized values. Perhaps the most surprising finding is that the combinatorial problem normally associated with the prediction of the side-chain conformation does not appear to be important. This conclusion is based on the fact that the prediction of the conformation of a single side-chain with all others fixed in their native conformations is only slightly more accurate than the simultaneous prediction of all side-chain dihedral angles.     

A graph-theory algorithm for rapid protein side-chain prediction

Fast and accurate side-chain conformation prediction is important for homology modeling, ab initio protein structure prediction, and protein design applications. Many methods have been presented, although only a few computer programs are publicly available. The SCWRL program is one such method and is widely used because of its speed, accuracy, and ease of use. A new algorithm for SCWRL is presented that uses results from graph theory to solve the combinatorial problem encountered in the side-chain prediction problem. In this method, side chains are represented as vertices in an undirected graph. Any two residues that have rotamers with nonzero interaction energies are considered to have an edge in the graph. The resulting graph can be partitioned into connected subgraphs with no edges between them. These subgraphs can in turn be broken into biconnected components, which are graphs that cannot be disconnected by removal of a single vertex. The combinatorial problem is reduced to finding the minimum energy of these small biconnected components and combining the results to identify the global minimum energy conformation. This algorithm is able to complete predictions on a set of 180 proteins with 34342 side chains in <7 min of computer time. The total chi(1) and chi(1 + 2) dihedral angle accuracies are 82.6% and 73.7% using a simple energy function based on the backbone-dependent rotamer library and a linear repulsive steric energy. The new algorithm will allow for use of SCWRL in more demanding applications such as sequence design and ab initio structure prediction, as well addition of a more complex energy function and conformational flexibility, leading to increased accuracy.     

SymmRef: a flexible refinement method for symmetric multimers

Symmetric protein complexes are abundant in the living cell. Predicting their atomic structure can shed light on the mechanism of many important biological processes. Symmetric docking methods aim to predict the structure of these complexes given the unbound structure of a single monomer, or its model. Symmetry constraints reduce the search-space of these methods and make the prediction easier compared to asymmetric protein-protein docking. However, the challenge of modeling the conformational changes that the monomer might undergo is a major obstacle. In this article, we present SymmRef, a novel method for refinement and reranking of symmetric docking solutions. The method models backbone and side-chain movements and optimizes the rigid-body orientations of the monomers. The backbone movements are modeled by normal modes minimization and the conformations of the side-chains are modeled by selecting optimal rotamers. Since solved structures of symmetric multimers show asymmetric side-chain conformations, we do not use symmetry constraints in the side-chain optimization procedure. The refined models are re-ranked according to an energy score. We tested the method on a benchmark of unbound docking challenges. The results show that the method significantly improves the accuracy and the ranking of symmetric rigid docking solutions. SymmRef is available for download at http:// bioinfo3d.cs.tau.ac.il/SymmRef/download.html.     

Docking and scoring with alternative side-chain conformations

We describe a scoring and modeling procedure for docking ligands into protein models that have either modeled or flexible side-chain conformations. Our methodical contribution comprises a procedure for generating new potentials of mean force for the ROTA scoring function which we have introduced previously for optimizing side-chain conformations with the tool IRECS. The ROTA potentials are specially trained to tolerate small-scale positional errors of atoms that are characteristic of (i) side-chain conformations that are modeled using a sparse rotamer library and (ii) ligand conformations that are generated using a docking program. We generated both rigid and flexible protein models with our side-chain prediction tool IRECS and docked ligands to proteins using the scoring function ROTA and the docking programs FlexX (for rigid side chains) and FlexE (for flexible side chains). We validated our approach on the forty screening targets of the DUD database. The validation shows that the ROTA potentials are especially well suited for estimating the binding affinity of ligands to proteins. The results also show that our procedure can compensate for the performance decrease in screening that occurs when using protein models with side chains modeled with a rotamer library instead of using X-ray structures. The average runtime per ligand of our method is 168 seconds on an Opteron V20z, which is fast enough to allow virtual screening of compound libraries for drug candidates.     

Construction of side-chains in homology modelling. Application to the C-terminal lobe of rhizopuspepsin

A detailed and rule-based side-chain modelling procedure for globular proteins is presented. It uses the conformational information contained in a homologous (template) structure as a starting point and includes recipes for atom placement and for checking and improving the atomic positions. The scheme does not rely on intuitive judgements or visual examination of the model during construction or refinement. It comprises four stages; the first three are relatively simple and the fourth is more complex. In the first stage, initial conformations for as many atoms as possible are transferred from the template structure based on the application of trends reported previously. Second, these trends are used to correct poor van der Waals overlaps. Third, the remaining side-chains atoms (those for which no information is contained in the template) are placed by evaluating their rigid rotation, van der Waals surfaces. The fourth stage consists of a hierarchial series of conformational checks. They involve the evaluation of individual residue energies in the absence and presence of the rest of the protein relative to statistical trends observed in the template structure, the comparison of hydrogen-bonding patterns and side-chain accessibilities in the model and template and brief energy minimization followed by an evaluation of the rigid rotation potential energy surfaces of each side-chain. The checks pinpoint "incorrectly" modelled side-chains, suggest conformational changes and provide a means for determining the portions of the model that are likely to be correct and those likely to be in error. The procedure developed in the paper is tested by modelling the side-chains of the C-terminal lobe of the aspartyl proteinase rhizopuspepsin, using the rhizopuspepsin backbone and the homologous protein, penicillopepsin, as a template for the side-chains. The resultant model was compared to the high-resolution X-ray structure of rhizopuspepsin. Using penicillopepsin data only (stage I), 58% of the chi 1 dihedrals and 44% of the chi 2 dihedrals were modelled correctly. Once poor van der Waals overlaps had been corrected and all of the atoms had been placed (stages II and III), 86% of the chi 1 dihedrals and 75% of the chi 2 dihedrals were correct. After the refinement had been completed (stage IV), 92% of the chi 1 dihedrals and 81% of the chi 2 dihedrals were correctly positioned.(ABSTRACT TRUNCATED AT 400 WORDS)     

High-resolution solution structure of reduced French bean plastocyanin and comparison with the crystal structure of poplar plastocyanin

The three-dimensional solution structure of reduced (CuI) plastocyanin from French bean leaves has been determined by distance geometry and restrained molecular dynamics methods using constraints obtained from 1H n.m.r. (nuclear magnetic resonance) spectroscopy. A total of 1244 experimental constraints were used, including 1120 distance constraints, 103 dihedral angle constraints and 21 hydrogen bond constraints. Stereospecific assignments were made for 26 methylene groups and the methyls of 11 valines. Additional constraints on copper co-ordination were included in the restrained dynamics calculations. The structures are well defined with average atomic root-mean-square deviations from the mean of 0.45 A for all backbone heavy atoms and 1.08 A for side-chain heavy atoms. French bean plastocyanin adopts a beta-sandwich structure in solution that is similar to the X-ray structure of reduced poplar plastocyanin; the average atomic root-mean-square difference between 16 n.m.r. structures and the X-ray structure is 0.76 A for all backbone heavy atoms. The conformations of the side-chains that constitute the hydrophobic core of French bean plastocyanin are very well defined. Of 47 conserved residues that populate a single chi 1 angle in solution, 43 have the same rotamer in the X-ray structure. Many surface side-chains adopt highly preferred conformations in solution, although the 3J alpha beta coupling constants often indicate some degree of conformational averaging. Some surface side-chains are disordered in both the solution and crystal structures of plastocyanin. There is a striking correlation between measures of side-chain disorder in solution and side-chain temperature factors in the X-ray structure. Side-chains that form a distinctive acidic surface region, believed to be important in binding other electron transfer proteins, appear to be disordered. Fifty backbone amide protons form hydrogen bonds to carbonyls in more than 60% of the n.m.r. structures; 45 of these amide protons exchange slowly with solvent deuterons. Ten hydrogen bonds are formed between side-chain and backbone atoms, eight of which are correlated with decreased proton exchange. Of the 60 hydrogen bonds formed in French bean plastocyanin, 56 occur in the X-ray structure of the poplar protein; two of the missing hydrogen bonds are absent as a result of mutations. It appears that molecular dynamics refinement of highly constrained n.m.r. structures allows accurate prediction of the pattern of hydrogen bonding.     

Side-chain rotamers in protein α-α hairpins and a mechanism of their selection

Several regularities were observed for the distribution of side-chain rotamers in α-α hairpins of globular proteins. In left-turned α-α hairpins, most side chains adopt t rotamers in d-positions and g^? rotamers in g-positions. In right-turned α-α hairpins, most side-chains adopt g^? rotamers in a-positions and t rotamers in e-positions. Analysis of these regularities suggested that selection of the side-chain conformation in α-α hairpins depends on two main factors, the mode of α-helix packing and the positions of side chains in α-helices. The regularities were explained by the squeezing mechanism: interhelical interactions bring the α-helices close together so that the side chains are squeezed out of the helix-helix interface and adopt unique conformations.     

A consistent set of statistical potentials for quantifying local side-chain and backbone interactions

The frequencies of occurrence of atom arrangements in high-resolution protein structures provide some of the most accurate quantitative measures of interaction energies in proteins. In this report we extend our development of a consistent set of statistical potentials for quantifying local interactions between side-chains and the polypeptide backbone, as well as nearby side-chains. Starting with phi/psi/chi1 propensities that select for optimal interactions of the 20 amino acid side-chains with the 2 flanking peptide bonds, the following 3 new terms are added: (1) a distance-dependent interaction between the side-chain at i and the carbonyl oxygens and amide protons of the peptide units at i +/- 2, i +/- 3, and i +/- 4; (2) a distance-dependent interaction between the side-chain at position i and side-chains at positions i + 1 through i + 4; and (3) an orientation-dependent interaction between the side-chain at position i and side-chains at i + 1 through i + 4. The relative strengths of these 4 pseudo free energy terms are estimated by the average information content of each scoring matrix and by assessing their performance in a simple fragment threading test. They vary from -0.4 - -0.5 kcal/mole per residue for phi/psi/chi1 propensities to a range of -0.15 - -0.6 kcal/mole per residue for each of the other 3 terms. The combined energy function, containing no interactions between atoms more than 4 residues apart, identifies the correct structural fragment for randomly selected 15 mers over 40% of the time, after searching through 232,000 alternative conformations. For 14 out of 20 sets of all-atom Rosetta decoys analyzed, the native structure has a combined score lower than any of the 1700-1900 decoy conformations. The ability of this energy function to detect energetically important details of local structure is demonstrated by its power to distinguish high-resolution crystal structures from NMR solution structures.     

On the role of the crystal environment in determining protein side-chain conformations

The role of crystal packing in determining the observed conformations of amino acid side-chains in protein crystals is investigated by (1) analysis of a database of proteins that have been crystallized in different unit cells (space group or unit cell dimensions) and (2) theoretical predictions of side-chain conformations with the crystal environment explicitly represented. Both of these approaches indicate that the crystal environment plays an important role in determining the conformations of polar side-chains on the surfaces of proteins. Inclusion of the crystal environment permits a more sensitive measurement of the achievable accuracy of side-chain prediction programs, when validating against structures obtained by X-ray crystallography. Our side-chain prediction program uses an all-atom force field and a Generalized Born model of solvation and is thus capable of modeling simple packing effects (i.e. van der Waals interactions), electrostatic effects, and desolvation, which are all important mechanisms by which the crystal environment impacts observed side-chain conformations. Our results are also relevant to the understanding of changes in side-chain conformation that may result from ligand docking and protein-protein association, insofar as the results reveal how side-chain conformations change in response to their local environment.     

Side-chain conformations in 4-alpha-helical bundles.

The distribution of the chi(1), chi(2) dihedral angles in a dataset consisting of 12 unrelated 4-alpha-helical bundle proteins was determined and qualitatively compared with that observed in globular proteins. The analysis suggests that the 4-alpha-helical bundle motif could occasionally impose steric constraints on side chains: (i) the side-chain conformations are limited to only a subset of the conformations observed in globular proteins and for some amino acids they are sterically more constrained than those in helical regions of globular proteins; (ii) aspartic acid and asparagine occasionally adopt rotamers that have not been previously reported for globular or helical proteins; (iii) some rotamers of tyrosine and isoleucine are predominantly or exclusively associated with hydrophobic core positions (a, d); (iv) mutations in the hydrophobic core occur preferentially between residue types which among other physicochemical properties also share a predominant rotamer.     

Incorporating knowledge-based biases into an energy-based side-chain modeling method: application to comparative modeling of protein structure

The performance of the self-consistent mean field theory (SCMFT) method for side-chain modeling, employing rotamer energies calculated with the flexible rotamer model (FRM), is evaluated in the context of comparative modeling of protein structure. Predictions were carried out on a test set of 56 model backbones of varying accuracy, to allow side-chain prediction accuracy to be analyzed as a function of backbone accuracy. A progressive decrease in the accuracy of prediction was observed as backbone accuracy decreased. However, even for very low backbone accuracy, prediction was substantially higher than random, indicating that the FRM can, in part, compensate for the errors in the modeled tertiary environment. It was also investigated whether the introduction in the FRM-SCMFT method of knowledge-based biases, derived from a backbone-dependent rotamer library, could enhance its performance. A bias derived from the backbone-dependent rotamer conformations alone did not improve prediction accuracy. However, a bias derived from the backbone-dependent rotamer probabilities improved prediction accuracy considerably. This bias was incorporated through two different strategies. In one (the indirect strategy), rotamer probabilities were used to reject unlikely rotamers a priori, thus restricting prediction by FRM-SCMFT to a subset containing only the most probable rotamers in the library. In the other (the direct strategy), rotamer energies were transformed into pseudo-energies that were added to the average potential energies of the respective rotamers, thereby creating hybrid energy-based/knowledge-based average rotamer energies, which were used by the FRM-SCMFT method for prediction. For all degrees of backbone accuracy, an optimal strength of the knowledge-based bias existed for both strategies for which predictions were more accurate than pure energy-based predictions, and also than pure knowledge-based predictions. Hybrid knowledge-based/energy-based methods were obtained from both strategies and compared with the SCWRL method, a hybrid method based on the same backbone-dependent rotamer library. The accuracy of the indirect method was approximately the same as that of the SCWRL method, but that of the direct method was significantly higher.     

Protein design using continuous rotamers

Optimizing amino acid conformation and identity is a central problem in computational protein design. Protein design algorithms must allow realistic protein flexibility to occur during this optimization, or they may fail to find the best sequence with the lowest energy. Most design algorithms implement side-chain flexibility by allowing the side chains to move between a small set of discrete, low-energy states, which we call rigid rotamers. In this work we show that allowing continuous side-chain flexibility (which we call continuous rotamers) greatly improves protein flexibility modeling. We present a large-scale study that compares the sequences and best energy conformations in 69 protein-core redesigns using a rigid-rotamer model versus a continuous-rotamer model. We show that in nearly all of our redesigns the sequence found by the continuous-rotamer model is different and has a lower energy than the one found by the rigid-rotamer model. Moreover, the sequences found by the continuous-rotamer model are more similar to the native sequences. We then show that the seemingly easy solution of sampling more rigid rotamers within the continuous region is not a practical alternative to a continuous-rotamer model: at computationally feasible resolutions, using more rigid rotamers was never better than a continuous-rotamer model and almost always resulted in higher energies. Finally, we present a new protein design algorithm based on the dead-end elimination (DEE) algorithm, which we call iMinDEE, that makes the use of continuous rotamers feasible in larger systems. iMinDEE guarantees finding the optimal answer while pruning the search space with close to the same efficiency of DEE. Availability: Software is available under the Lesser GNU Public License v3. Contact the authors for source code.