An iterative knowledge-based scoring function for protein-protein recognition

Using an efficient iterative method, we have developed a distance-dependent knowledge-based scoring function to predict protein-protein interactions. The function, referred to as ITScore-PP, was derived using the crystal structures of a training set of 851 protein-protein dimeric complexes containing true biological interfaces. The key idea of the iterative method for deriving ITScore-PP is to improve the interatomic pair potentials by iteration, until the pair potentials can distinguish true binding modes from decoy modes for the protein-protein complexes in the training set. The iterative method circumvents the challenging reference state problem in deriving knowledge-based potentials. The derived scoring function was used to evaluate the ligand orientations generated by ZDOCK 2.1 and the native ligand structures on a diverse set of 91 protein-protein complexes. For the bound test cases, ITScore-PP yielded a success rate of 98.9% if the top 10 ranked orientations were considered. For the more realistic unbound test cases, the corresponding success rate was 40.7%. Furthermore, for faster orientational sampling purpose, several residue-level knowledge-based scoring functions were also derived following the similar iterative procedure. Among them, the scoring function that uses the side-chain center of mass (SCM) to represent a residue, referred to as ITScore-PP(SCM), showed the best performance and yielded success rates of 71.4% and 30.8% for the bound and unbound cases, respectively, when the top 10 orientations were considered. ITScore-PP was further tested using two other published protein-protein docking decoy sets, the ZDOCK decoy set and the RosettaDock decoy set. In addition to binding mode prediction, the binding scores predicted by ITScore-PP also correlated well with the experimentally determined binding affinities, yielding a correlation coefficient of R = 0.71 on a test set of 74 protein-protein complexes with known affinities. ITScore-PP is computationally efficient. The average run time for ITScore-PP was about 0.03 second per orientation (including optimization) on a personal computer with 3.2 GHz Pentium IV CPU and 3.0 GB RAM. The computational speed of ITScore-PP(SCM) is about an order of magnitude faster than that of ITScore-PP. ITScore-PP and/or ITScore-PP(SCM) can be combined with efficient protein docking software to study protein-protein recognition.     

Physical scoring function based on AMBER force field and Poisson-Boltzmann implicit solvent for protein structure prediction

A well-behaved physics-based all-atom scoring function for protein structure prediction is analyzed with several widely used all-atom decoy sets. The scoring function, termed AMBER/Poisson-Boltzmann (PB), is based on a refined AMBER force field for intramolecular interactions and an efficient PB model for solvation interactions. Testing on the chosen decoy sets shows that the scoring function, which is designed to consider detailed chemical environments, is able to consistently discriminate all 62 native crystal structures after considering the heteroatom groups, disulfide bonds, and crystal packing effects that are not included in the decoy structures. When NMR structures are considered in the testing, the scoring function is able to discriminate 8 out of 10 targets. In the more challenging test of selecting near-native structures, the scoring function also performs very well: for the majority of the targets studied, the scoring function is able to select decoys that are close to the corresponding native structures as evaluated by ranking numbers and backbone Calpha root mean square deviations. Various important components of the scoring function are also studied to understand their discriminative contributions toward the rankings of native and near-native structures. It is found that neither the nonpolar solvation energy as modeled by the surface area model nor a higher protein dielectric constant improves its discriminative power. The terms remaining to be improved are related to 1-4 interactions. The most troublesome term is found to be the large and highly fluctuating 1-4 electrostatics term, not the dihedral-angle term. These data support ongoing efforts in the community to develop protein structure prediction methods with physics-based potentials that are competitive with knowledge-based potentials.     

Energy-based graph convolutional networks for scoring protein docking models

Structural information about protein-protein interactions, often missing at the interactome scale, is important for mechanistic understanding of cells and rational discovery of therapeutics. Protein docking provides a computational alternative for such information. However, ranking near-native docked models high among a large number of candidates, often known as the scoring problem, remains a critical challenge. Moreover, estimating model quality, also known as the quality assessment problem, is rarely addressed in protein docking. In this study, the two challenging problems in protein docking are regarded as relative and absolute scoring, respectively, and addressed in one physics-inspired deep learning framework. We represent protein and complex structures as intra- and inter-molecular residue contact graphs with atom-resolution node and edge features. And we propose a novel graph convolutional kernel that aggregates interacting nodes’ features through edges so that generalized interaction energies can be learned directly from 3D data. The resulting energy-based graph convolutional networks (EGCN) with multihead attention are trained to predict intra- and inter-molecular energies, binding affinities, and quality measures (interface RMSD) for encounter complexes. Compared to a state-of-the-art scoring function for model ranking, EGCN significantly improves ranking for a critical assessment of predicted interactions (CAPRI) test set involving homology docking; and is comparable or slightly better for Score_set, a CAPRI benchmark set generated by diverse community-wide docking protocols not known to training data. For Score_set quality assessment, EGCN shows about 27% improvement to our previous efforts. Directly learning from 3D structure data in graph representation, EGCN represents the first successful development of graph convolutional networks for protein docking.     

A combinatorial scoring function for protein–RNA docking

Protein–RNA docking is still an open question. One of the main challenges is to develop an effective scoring function that can discriminate near‐native structures from the incorrect ones. To solve the problem, we have constructed a knowledge‐based residue‐nucleotide pairwise potential with secondary structure information considered for nonribosomal protein–RNA docking. Here we developed a weighted combined scoring function RpveScore that consists of the pairwise potential and six physics‐based energy terms. The weights were optimized using the multiple linear regression method by fitting the scoring function to L_rmsd for the bound docking decoys from Benchmark II. The scoring functions were tested on 35 unbound docking cases. The results show that the scoring function RpveScore including all terms performs best. Also RpveScore was compared with the statistical mechanics‐based method derived potential ITScore‐PR, and the united atom‐based statistical potentials QUASI‐RNP and DARS‐RNP. The success rate of RpveScore is 71.6% for the top 1000 structures and the number of cases where a near‐native structure is ranked in top 30 is 25 out of 35 cases. For 32 systems (91.4%), RpveScore can find the binding mode in top 5 that has no lower than 50% native interface residues on protein and nucleotides on RNA. Additionally, it was found that the long‐range electrostatic attractive energy plays an important role in distinguishing near‐native structures from the incorrect ones. This work can be helpful for the development of protein–RNA docking methods and for the understanding of protein–RNA interactions. RpveScore program is available to the public at http://life.bjut.edu.cn/kxyj/kycg/2017116/14845362285362368_1.html Proteins 2017; 85:741–752. © 2016 Wiley Periodicals, Inc.     

Sampling and scoring: A marriage made in heaven

Most structure prediction algorithms consist of initial sampling of the conformational space, followed by rescoring and possibly refinement of a number of selected structures. Here we focus on protein docking, and show that while decoupling sampling and scoring facilitates method development, integration of the two steps can lead to substantial improvements in docking results. Since decoupling is usually achieved by generating a decoy set containing both non‐native and near‐native docked structures, which can be then used for scoring function construction, we first review the roles and potential pitfalls of decoys in protein–protein docking, and show that some type of decoys are better than others for method development. We then describe three case studies showing that complete decoupling of scoring from sampling is not the best choice for solving realistic docking problems. Although some of the examples are based on our own experience, the results of the CAPRI docking and scoring experiments also show that performing both sampling and scoring generally yields better results than scoring the structures generated by all predictors. Next we investigate how the selection of training and decoy sets affects the performance of the scoring functions obtained. Finally, we discuss pathways to better alignment of the two steps, and show some algorithms that achieve a certain level of integration. Although we focus on protein–protein docking, our observations most likely also apply to other conformational search problems, including protein structure prediction and the docking of small molecules to proteins.Proteins 2013; 81:1874–1884. © 2013 Wiley Periodicals, Inc.     

CScore: a simple yet effective scoring function for protein-ligand binding affinity prediction using modified CMAC learning architecture

Protein-ligand docking is a computational method to identify the binding mode of a ligand and a target protein, and predict the corresponding binding affinity using a scoring function. This method has great value in drug design. After decades of development, scoring functions nowadays typically can identify the true binding mode, but the prediction of binding affinity still remains a major problem. Here we present CScore, a data-driven scoring function using a modified Cerebellar Model Articulation Controller (CMAC) learning architecture, for accurate binding affinity prediction. The performance of CScore in terms of correlation between predicted and experimental binding affinities is benchmarked under different validation approaches. CScore achieves a prediction with R = 0.7668 and RMSE = 1.4540 when tested on an independent dataset. To the best of our knowledge, this result outperforms other scoring functions tested on the same dataset. The performance of CScore varies on different clusters under the leave-cluster-out validation approach, but still achieves competitive result. Lastly, the target-specified CScore achieves an even better result with R = 0.8237 and RMSE = 1.0872, trained on a much smaller but more relevant dataset for each target. The large dataset of protein-ligand complexes structural information and advances of machine learning techniques enable the data-driven approach in binding affinity prediction. CScore is capable of accurate binding affinity prediction. It is also shown that CScore will perform better if sufficient and relevant data is presented. As there is growth of publicly available structural data, further improvement of this scoring scheme can be expected.     

Localization of binding sites in protein structures by optimization of a composite scoring function

The rise in the number of functionally uncharacterized protein structures is increasing the demand for structure-based methods for functional annotation. Here, we describe a method for predicting the location of a binding site of a given type on a target protein structure. The method begins by constructing a scoring function, followed by a Monte Carlo optimization, to find a good scoring patch on the protein surface. The scoring function is a weighted linear combination of the z-scores of various properties of protein structure and sequence, including amino acid residue conservation, compactness, protrusion, convexity, rigidity, hydrophobicity, and charge density; the weights are calculated from a set of previously identified instances of the binding-site type on known protein structures. The scoring function can easily incorporate different types of information useful in localization, thus increasing the applicability and accuracy of the approach. To test the method, 1008 known protein structures were split into 20 different groups according to the type of the bound ligand. For nonsugar ligands, such as various nucleotides, binding sites were correctly identified in 55%-73% of the cases. The method is completely automated (http://salilab.org/patcher) and can be applied on a large scale in a structural genomics setting.     

Score_set: A CAPRI benchmark for scoring protein complexes

Critical Assessment of PRedicted Interactions (CAPRI) has proven to be a catalyst for the development of docking algorithms. An essential step in docking is the scoring of predicted binding modes in order to identify stable complexes. In 2005, CAPRI introduced the scoring experiment, where upon completion of a prediction round, a larger set of models predicted by different groups and comprising both correct and incorrect binding modes, is made available to all participants for testing new scoring functions independently from docking calculations. Here we present an expanded benchmark data set for testing scoring functions, which comprises the consolidated ensemble of predicted complexes made available in the CAPRI scoring experiment since its inception. This consolidated scoring benchmark contains predicted complexes for 15 published CAPRI targets. These targets were subjected to 23 CAPRI assessments, due to existence of multiple binding modes for some targets. The benchmark contains more than 19,000 protein complexes. About 10% of the complexes represent docking predictions of acceptable quality or better, the remainder represent incorrect solutions (decoys). The benchmark set contains models predicted by 47 different predictor groups including web servers, which use different docking and scoring procedures, and is arguably as diverse as one may expect, representing the state of the art in protein docking. The data set is publicly available at the following URL: http://cb.iri.univ‐lille1.fr/Users/lensink/Score_set . Proteins 2014; 82:3163–3169. © 2014 Wiley Periodicals, Inc.     

Native fold and docking pose discrimination by the same residue‐based scoring function

Structure prediction and quality assessment are crucial steps in modeling native protein conformations. Statistical potentials are widely used in related algorithms, with different parametrizations typically developed for different contexts such as folding protein monomers or docking protein complexes. Here, we describe BACH‐SixthSense, a single residue‐based statistical potential that can be successfully employed in both contexts. BACH‐SixthSense shares the same approach as BACH, a knowledge‐based potential originally developed to score monomeric protein structures. A term that penalizes steric clashes as well as the distinction between polar and apolar sidechain‐sidechain contacts are crucial novel features of BACH‐SixthSense. The performance of BACH‐SixthSense in discriminating correctly the native structure among a competing set of decoys is significantly higher than other state‐of‐the‐art scoring functions, that were specifically trained for a single context, for both monomeric proteins (QMEAN, Rosetta, RF_CB_SRS_OD, benchmarked on CASP targets) and protein dimers (IRAD, Rosetta, PIE*PISA, HADDOCK, FireDock, benchmarked on 14 CAPRI targets). The performance of BACH‐SixthSense in recognizing near‐native docking poses within CAPRI decoy sets is good as well. Proteins 2015; 83:621–630. © 2015 Wiley Periodicals, Inc.     

Modulation of interaction of mutant TP53 and wild type BRCA1 by alkaloids: a computational approach towards targeting protein-protein interaction as a futuristic therapeutic intervention strategy for breast cancer impediment

Protein–protein interactions (PPI) are a new emerging class of novel therapeutic targets. In order to probe these interactions, computational tools provide a convenient and quick method towards the development of therapeutics. Keeping this in view the present study was initiated to analyse interaction of tumour suppressor protein p53 (TP53) and breast cancer associated protein (BRCA1) as promising target against breast cancer. Using computational approaches such as protein–protein docking, hot spot analyses, molecular docking and molecular dynamics simulation (MDS), stepwise analyses of the interactions of the wild type and mutant TP53 with that of wild type BRCA1 and their modulation by alkaloids were done. Protein–protein docking method was used to generate both wild type and mutant complexes of TP53-BRCA1. Subsequently, the complexes were docked using sixteen different alkaloids, fulfilling ADMET and Lipinski’s rule of five criteria, and were compared with that of a well-known inhibitor of PPI, namely nutlin. The alkaloid dicentrine was found to be the best docked alkaloid among all the docked alklaloids as well as that of nutlin. Furthermore, MDS analyses of both wild type and mutant complexes with the best docked alkaloid i.e. dicentrine, revealed higher stability of mutant complex than that of the wild one, in terms of average RMSD, RMSF and binding free energy, corroborating the results of docking. Results suggested more pronounced interaction of BRCA1 with mutant TP53 leading to increased expression of mutated TP53 thus showing a dominant negative gain of function and hampering wild type TP53 function leading to tumour progression.     

Development and validation of an empirical free energy function for calculating protein–protein binding free energy surfaces

In a previous paper, we described a novel empirical free energy function that was used to accurately predict experimental binding free energies for a diverse test set of 31 protein–protein complexes to within ≈ 1.0 kcal. Here, we extend that work and show that an updated version of the function can be used to (1) accurately predict native binding free energies and (2) rank crystallographic, native-like and non-native binding modes in a physically realistic manner. The modified function includes terms designed to capture some of the unfavorable interactions that characterize non-native interfaces. The function was used to calculate one-dimensional binding free energy surfaces for 21 protein complexes. In roughly 90% of the cases tested, the function was used to place native-like and crystallographic binding modes in global free energy minima. Our analysis further suggests that buried hydrogen bonds might provide the key to distinguishing native from non-native interactions. To the best of our knowledge our function is the only one of its kind, a single expression that can be used to accurately calculate native and non-native binding free energies for a large number of proteins. Given the encouraging results presented in this paper, future work will focus on improving the function and applying it to the protein–protein docking problem.     

Linking structural features of protein complexes and biological function

Protein–protein interaction (PPI) establishes the central basis for complex cellular networks in a biological cell. Association of proteins with other proteins occurs at varying affinities, yet with a high degree of specificity. PPIs lead to diverse functionality such as catalysis, regulation, signaling, immunity, and inhibition, playing a crucial role in functional genomics. The molecular principle of such interactions is often elusive in nature. Therefore, a comprehensive analysis of known protein complexes from the Protein Data Bank (PDB) is essential for the characterization of structural interface features to determine structure–function relationship. Thus, we analyzed a nonredundant dataset of 278 heterodimer protein complexes, categorized into major functional classes, for distinguishing features. Interestingly, our analysis has identified five key features (interface area, interface polar residue abundance, hydrogen bonds, solvation free energy gain from interface formation, and binding energy) that are discriminatory among the functional classes using Kruskal-Wallis rank sum test. Significant correlations between these PPI interface features amongst functional categories are also documented. Salt bridges correlate with interface area in regulator-inhibitors (r = 0.75). These representative features have implications for the prediction of potential function of novel protein complexes. The results provide molecular insights for better understanding of PPIs and their relation to biological functions.     

Predicting flexible loop regions that interact with ligands: the challenge of accurate scoring

Flexible loop regions play a critical role in the biological function of many proteins and have been shown to be involved in ligand binding. In the context of structure-based drug design, using or predicting an incorrect loop configuration can be detrimental to the study if the loop is capable of interacting with the ligand. Three protein systems, each with at least one flexible loop region in close proximity to the known binding site, were selected for loop prediction using the CorLps program; a six residue loop region from phosphoribosylglycinamide formyltransferase (GART), two nine residue loop regions from cytochrome P450 (CYP) 119, and an 11 residue loop region from enolase were selected for loop prediction. The results of this study indicate that the statistically based DFIRE scoring function implemented in the CorLps program did not accurately rank native-like predicted loop configurations in any protein system. In an attempt to improve the ranking of the native-like predicted loop configurations, the MM/GBSA and the optimized MM/GBSA-dsr scoring functions were used to re-rank the predicted loops with and without bound ligand. In general, single snapshot MM/GBSA scoring provided the best ranking of native-like loop configurations. Based on the scoring function analyses presented, the optimal ranking of native-like loop configurations is still a difficult challenge and the choice of the "best" scoring function appears to be system dependent.     

Developing optimal non-linear scoring function for protein design

Motivation. Protein design aims to identify sequences compatible with a given protein fold but incompatible to any alternative folds. To select the correct sequences and to guide the search process, a design scoring function is critically important. Such a scoring function should be able to characterize the global fitness landscape of many proteins simultaneously. RESULTS: To find optimal design scoring functions, we introduce two geometric views and propose a formulation using a mixture of non-linear Gaussian kernel functions. We aim to solve a simplified protein sequence design problem. Our goal is to distinguish each native sequence for a major portion of representative protein structures from a large number of alternative decoy sequences, each a fragment from proteins of different folds. Our scoring function discriminates perfectly a set of 440 native proteins from 14 million sequence decoys. We show that no linear scoring function can succeed in this task. In a blind test of unrelated proteins, our scoring function misclassfies only 13 native proteins out of 194. This compares favorably with about three-four times more misclassifications when optimal linear functions reported in the literature are used. We also discuss how to develop protein folding scoring function.     

PPI spider: A tool for the interpretation of proteomics data in the context of protein–protein interaction networks

Recent advances in experimental technologies allow for the detection of a complete cell proteome. Proteins that are expressed at a particular cell state or in a particular compartment as well as proteins with differential expression between various cells states are commonly delivered by many proteomics studies. Once a list of proteins is derived, a major challenge is to interpret the identified set of proteins in the biological context. Protein–protein interaction (PPI) data represents abundant information that can be employed for this purpose. However, these data have not yet been fully exploited due to the absence of a methodological framework that can integrate this type of information. Here, we propose to infer a network model from an experimentally identified protein list based on the available information about the topology of the global PPI network. We propose to use a Monte Carlo simulation procedure to compute the statistical significance of the inferred models. The method has been implemented as a freely available web‐based tool, PPI spider ( http://mips.helmholtz‐muenchen.de/proj/ppispider ). To support the practical significance of PPI spider, we collected several hundreds of recently published experimental proteomics studies that reported lists of proteins in various biological contexts. We reanalyzed them using PPI spider and demonstrated that in most cases PPI spider could provide statistically significant hypotheses that are helpful for understanding of the protein list.     

Edge-based scoring and searching method for identifying condition-responsive protein-protein interaction sub-network

MOTIVATION: Current high-throughput protein-protein interaction (PPI) data do not provide information about the condition(s) under which the interactions occur. Thus, the identification of condition-responsive PPI sub-networks is of great importance for investigating how a living cell adapts to changing environments. RESULTS: In this article, we propose a novel edge-based scoring and searching approach to extract a PPI sub-network responsive to conditions related to some investigated gene expression profiles. Using this approach, what we constructed is a sub-network connected by the selected edges (interactions), instead of only a set of vertices (proteins) as in previous works. Furthermore, we suggest a systematic approach to evaluate the biological relevance of the identified responsive sub-network by its ability of capturing condition-relevant functional modules. We apply the proposed method to analyze a human prostate cancer dataset and a yeast cell cycle dataset. The results demonstrate that the edge-based method is able to efficiently capture relevant protein interaction behaviors under the investigated conditions. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Substituting random forest for multiple linear regression improves binding affinity prediction of scoring functions: Cyscore as a case study

Background

State-of-the-art protein-ligand docking methods are generally limited by the traditionally low accuracy of their scoring functions, which are used to predict binding affinity and thus vital for discriminating between active and inactive compounds. Despite intensive research over the years, classical scoring functions have reached a plateau in their predictive performance. These assume a predetermined additive functional form for some sophisticated numerical features, and use standard multivariate linear regression (MLR) on experimental data to derive the coefficients.

Results

In this study we show that such a simple functional form is detrimental for the prediction performance of a scoring function, and replacing linear regression by machine learning techniques like random forest (RF) can improve prediction performance. We investigate the conditions of applying RF under various contexts and find that given sufficient training samples RF manages to comprehensively capture the non-linearity between structural features and measured binding affinities. Incorporating more structural features and training with more samples can both boost RF performance. In addition, we analyze the importance of structural features to binding affinity prediction using the RF variable importance tool. Lastly, we use Cyscore, a top performing empirical scoring function, as a baseline for comparison study.

Conclusions

Machine-learning scoring functions are fundamentally different from classical scoring functions because the former circumvents the fixed functional form relating structural features with binding affinities. RF, but not MLR, can effectively exploit more structural features and more training samples, leading to higher prediction performance. The future availability of more X-ray crystal structures will further widen the performance gap between RF-based and MLR-based scoring functions. This further stresses the importance of substituting RF for MLR in scoring function development.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-291) contains supplementary material, which is available to authorized users.     

Structural studies of human purine nucleoside phosphorylase: towards a new specific empirical scoring function

Human purine nucleoside phosphorylase (HsPNP) is a target for inhibitor development aiming at T-cell immune response modulation. In this work, we report the development of a new set of empirical scoring functions and its application to evaluate binding affinities and docking results. To test these new functions, we solved the structure of HsPNP and 2-mercapto-4(3H)-quinazolinone (HsPNP:MQU) binary complex at 2.7 Å resolution using synchrotron radiation, and used these functions to predict ligand position obtained in docking simulations. We also employed molecular dynamics simulations to analyze HsPNP in two conditions, as apoenzyme and in the binary complex form, in order to assess the structural features responsible for stability. Analysis of the structural differences between systems provides explanation for inhibitor binding. The use of these scoring functions to evaluate binding affinities and molecular docking results may be used to guide future efforts on virtual screening focused on HsPNP.     

Four-body scoring function for mutagenesis

MOTIVATION: There is a need for an efficient and accurate computational method to identify the effects of single- and multiple-residue mutations on the stability and reactivity of proteins. Such a method should ideally be consistent and yet applicable in a widespread manner, i.e. it should be applied to various proteins under the same parameter settings, and have good predictive power for all of them. RESULTS: We develop a Delaunay tessellation-based four-body scoring function to predict the effects of single- and multiple-residue mutations on the stability and reactivity of proteins. We test our scoring function on sets of single-point mutations used by several previous studies. We also assemble a new, diverse set of 237 single- and multiple-residue mutations, from over 24 different publications. The four-body scoring function correctly predicted the changes to the stability of 169 out of 210 mutants (80.5%), and the changes to the reactivity of 17 out of 27 mutants (63%). For the mutants that had the changes in stability/reactivity quantified (using reaction rates, temperatures, etc.), an average Spearman rank correlation coefficient of 0.67 was achieved with the four-body scores. We also develop an efficient method for screening huge numbers of mutants of a protein, called combinatorial mutagenesis. In one study, 64 million mutants of a cold-shock nucleus binding domain protein 1CSQ, with six of its residues being changed to all possible (20) amino acids, were screened within a few hours on a PC, and all five stabilizing mutants reported were correctly identified as stabilizing by combinatorial mutagenesis.     

Effective scoring function for protein sequence design

We have developed an effective scoring function for protein design. The atomic solvation parameters, together with the weights of energy terms, were optimized so that residues corresponding to the native sequence were predicted with low energy in the training set of 28 protein structures. The solvation energy of non-hydrogen-bonded hydrophilic atoms was considered separately and expressed in a nonlinear way. As a result, our scoring function predicted native residues as the most favorable in 59% of the total positions in 28 proteins. We then tested the scoring function by comparing the predicted stability changes for 103 T4 lysozyme mutants with the experimental values. The correlation coefficients were 0.77 for surface mutations and 0.71 for all mutations. Finally, the scoring function combined with Monte Carlo simulation was used to predict favorable sequences on a fixed backbone. The designed sequences were similar to the natural sequences of the family to which the template structure belonged. The profile of the designed sequences was helpful for identification of remote homologues of the native sequence.