A sequence sub-sampling algorithm increases the power to detect distant homologues

Searching databases for distant homologues using alignments instead of individual sequences increases the power of detection. However, most methods assume that protein evolution proceeds in a regular fashion, with the inferred tree of sequences providing a good estimation of the evolutionary process. We investigated the combined HMMER search results from random alignment subsets (with three sequences each) drawn from the parent alignment (Rand-shuffle algorithm), using the SCOP structural classification to determine true similarities. At false-positive rates of 5%, the Rand-shuffle algorithm improved HMMER's sensitivity, with a 37.5% greater sensitivity compared with HMMER alone, when easily identified similarities (identifiable by BLAST) were excluded from consideration. An extension of the Rand-shuffle algorithm (Ali-shuffle) weighted towards more informative sequence subsets. This approach improved the performance over HMMER alone and PSI-BLAST, particularly at higher false-positive rates. The improvements in performance of these sequence sub-sampling methods may reflect lower sensitivity to alignment error and irregular evolutionary patterns. The Ali-shuffle and Rand-shuffle sequence homology search programs are available by request from the authors.     

Increased detection of structural templates using alignments of designed sequences

Protein structure prediction by comparative modeling benefits greatly from the use of multiple sequence alignment information to improve the accuracy of structural template identification and the alignment of target sequences to structural templates. Unfortunately, this benefit is limited to those protein sequences for which at least several natural sequence homologues exist. We show here that the use of large diverse alignments of computationally designed protein sequences confers many of the same benefits as natural sequences in identifying structural templates for comparative modeling targets. A large-scale massively parallelized application of an all-atom protein design algorithm, including a simple model of peptide backbone flexibility, has allowed us to generate 500 diverse, non-native, high-quality sequences for each of 264 protein structures in our test set. PSI-BLAST searches using the sequence profiles generated from the designed sequences ("reverse" BLAST searches) give near-perfect accuracy in identifying true structural homologues of the parent structure, with 54% coverage. In 41 of 49 genomes scanned using reverse BLAST searches, at least one novel structural template (not found by the standard method of PSI-BLAST against PDB) is identified. Further improvements in coverage, through optimizing the scoring function used to design sequences and continued application to new protein structures beyond the test set, will allow this method to mature into a useful strategy for identifying distantly related structural templates.     

Evaluation of PSI-BLAST alignment accuracy in comparison to structural alignments

The PSI-BLAST algorithm has been acknowledged as one of the most powerful tools for detecting remote evolutionary relationships by sequence considerations only. This has been demonstrated by its ability to recognize remote structural homologues and by the greatest coverage it enables in annotation of a complete genome. Although recognizing the correct fold of a sequence is of major importance, the accuracy of the alignment is crucial for the success of modeling one sequence by the structure of its remote homologue. Here we assess the accuracy of PSI-BLAST alignments on a stringent database of 123 structurally similar, sequence-dissimilar pairs of proteins, by comparing them to the alignments defined on a structural basis. Each protein sequence is compared to a nonredundant database of the protein sequences by PSI-BLAST. Whenever a pair member detects its pair-mate, the positions that are aligned both in the sequential and structural alignments are determined, and the alignment sensitivity is expressed as the percentage of these positions out of the structural alignment. Fifty-two sequences detected their pair-mates (for 16 pairs the success was bi-directional when either pair member was used as a query). The average percentage of correctly aligned residues per structural alignment was 43.5+/-2.2%. Other properties of the alignments were also examined, such as the sensitivity vs. specificity and the change in these parameters over consecutive iterations. Notably, there is an improvement in alignment sensitivity over consecutive iterations, reaching an average of 50.9+/-2.5% within the five iterations tested in the current study.     

Cascaded walks in protein sequence space: use of artificial sequences in remote homology detection between natural proteins

Over the past two decades, many ingenious efforts have been made in protein remote homology detection. Because homologous proteins often diversify extensively in sequence, it is challenging to demonstrate such relatedness through entirely sequence-driven searches. Here, we describe a computational method for the generation of 'protein-like' sequences that serves to bridge gaps in protein sequence space. Sequence profile information, as embodied in a position-specific scoring matrix of multiply aligned sequences of bona fide family members, serves as the starting point in this algorithm. The observed amino acid propensity and the selection of a random number dictate the selection of a residue for each position in the sequence. In a systematic manner, and by applying a 'roulette-wheel' selection approach at each position, we generate parent family-like sequences and thus facilitate an enlargement of sequence space around the family. When generated for a large number of families, we demonstrate that they expand the utility of natural intermediately related sequences in linking distant proteins. In 91% of the assessed examples, inclusion of designed sequences improved fold coverage by 5-10% over searches made in their absence. Furthermore, with several examples from proteins adopting folds such as TIM, globin, lipocalin and others, we demonstrate that the success of including designed sequences in a database positively sensitized methods such as PSI-BLAST and Cascade PSI-BLAST and is a promising opportunity for enormously improved remote homology recognition using sequence information alone.     

Context-specific amino acid substitution matrices and their use in the detection of protein homologs

The sequence homology detection relies on score matrices, which reflect the frequency of amino acid substitutions observed in a dataset of homologous sequences. The substitution matrices in popular use today are usually constructed without consideration of the structural context in which the substitution takes place. Here, we present amino acid substitution matrices specific for particular polar-nonpolar environment of the amino acid. As expected, these matrices [context-specific substitution matrices (CSSMs)] show striking differences from the popular BLOSUM62 matrix, which does not include structural information. When incorporated into BLAST and PSI-BLAST, CSSM outperformed BLOSUM matrices as assessed by ROC curve analyses of the number of true and false hits and by the accuracy of the sequence alignments to the hit sequences. These findings are also of relevance to profile-profile-based methods of homology detection, since CSSMs may help build a better profile. Profiles generated for protein sequences in PDB using CSSM-PSI-BLAST will be made available for searching via RPSBLAST through our web site http://lmbbi.nci.nih.gov/.     

Consensus sequences improve PSI-BLAST through mimicking profile-profile alignments

Sequence alignments may be the most fundamental computational resource for molecular biology. The best methods that identify sequence relatedness through profile-profile comparisons are much slower and more complex than sequence-sequence and sequence-profile comparisons such as, respectively, BLAST and PSI-BLAST. Families of related genes and gene products (proteins) can be represented by consensus sequences that list the nucleic/amino acid most frequent at each sequence position in that family. Here, we propose a novel approach for consensus-sequence-based comparisons. This approach improved searches and alignments as a standard add-on to PSI-BLAST without any changes of code. Improvements were particularly significant for more difficult tasks such as the identification of distant structural relations between proteins and their corresponding alignments. Despite the fact that the improvements were higher for more divergent relations, they were consistent even at high accuracy/low error rates for non-trivially related proteins. The improvements were very easy to achieve; no parameter used by PSI-BLAST was altered and no single line of code changed. Furthermore, the consensus sequence add-on required relatively little additional CPU time. We discuss how advanced users of PSI-BLAST can immediately benefit from using consensus sequences on their local computers. We have also made the method available through the Internet (http://www.rostlab.org/services/consensus/).     

Protein homology detection and fold inference through multiple alignment entropy profiles

Homology detection and protein structure prediction are central themes in bioinformatics. Establishment of relationship between protein sequences or prediction of their structure by sequence comparison methods finds limitations when there is low sequence similarity. Recent works demonstrate that the use of profiles improves homology detection and protein structure prediction. Profiles can be inferred from protein multiple alignments using different approaches. The "Conservatism-of-Conservatism" is an effective profile analysis method to identify structural features between proteins having the same fold but no detectable sequence similarity. The information obtained from protein multiple alignments varies according to the amino acid classification employed to calculate the profile. In this work, we calculated entropy profiles from PSI-BLAST-derived multiple alignments and used different amino acid classifications summarizing almost 500 different attributes. These entropy profiles were converted into pseudocodes which were compared using the FASTA program with an ad-hoc matrix. We tested the performance of our method to identify relationships between proteins with similar fold using a nonredundant subset of sequences having less than 40% of identity. We then compared our results using Coverage Versus Error per query curves, to those obtained by methods like PSI-BLAST, COMPASS and HHSEARCH. Our method, named HIP (Homology Identification with Profiles) presented higher accuracy detecting relationships between proteins with the same fold. The use of different amino acid classifications reflecting a large number of amino acid attributes, improved the recognition of distantly related folds. We propose the use of pseudocodes representing profile information as a fast and powerful tool for homology detection, fold assignment and analysis of evolutionary information enclosed in protein profiles.     

Fast assignment of protein structures to sequences using the intermediate sequence library PDB-ISL

MOTIVATION: For large-scale structural assignment to sequences, as in computational structural genomics, a fast yet sensitive sequence search procedure is essential. A new approach using intermediate sequences was tested as a shortcut to iterative multiple sequence search methods such as PSI-BLAST. RESULTS: A library containing potential intermediate sequences for proteins of known structure (PDB-ISL) was constructed. The sequences in the library were collected from a large sequence database using the sequences of the domains of proteins of known structure as the query sequences and the program PSI-BLAST. Sequences of proteins of unknown structure can be matched to distantly related proteins of known structure by using pairwise sequence comparison methods to find homologues in PDB-ISL. Searches of PDB-ISL were calibrated, and the number of correct matches found at a given error rate was the same as that found by PSI-BLAST. The advantage of this library is that it uses pairwise sequence comparison methods, such as FASTA or BLAST2, and can, therefore, be searched easily and, in many cases, much more quickly than an iterative multiple sequence comparison method. The procedure is roughly 20 times faster than PSI-BLAST for small genomes and several hundred times for large genomes. AVAILABILITY: Sequences can be submitted to the PDB-ISL servers at http://stash.mrc-lmb.cam.ac.uk/PDB_ISL/ or http://cyrah.ebi.ac.uk:1111/Serv/PDB_ISL/ and can be downloaded from ftp://ftp.ebi.ac.uk/pub/contrib/jong/PDB_+ ++ISL/ CONTACT: sat@mrc-lmb.cam.ac.uk and jong@ebi.ac.uk     

Iterative sequence/secondary structure search for protein homologs: comparison with amino acid sequence alignments and application to fold recognition in genome databases

MOTIVATION: Sequence alignment techniques have been developed into extremely powerful tools for identifying the folding families and function of proteins in newly sequenced genomes. For a sufficiently low sequence identity it is necessary to incorporate additional structural information to positively detect homologous proteins. We have carried out an extensive analysis of the effectiveness of incorporating secondary structure information directly into the alignments for fold recognition and identification of distant protein homologs. A secondary structure similarity matrix based on a database of three-dimensionally aligned proteins was first constructed. An iterative application of dynamic programming was used which incorporates linear combinations of amino acid and secondary structure sequence similarity scores. Initially, only primary sequence information is used. Subsequently contributions from secondary structure are phased in and new homologous proteins are positively identified if their scores are consistent with the predetermined error rate. RESULTS: We used the SCOP40 database, where only PDB sequences that have 40% homology or less are included, to calibrate homology detection by the combined amino acid and secondary structure sequence alignments. Combining predicted secondary structure with sequence information results in a 8-15% increase in homology detection within SCOP40 relative to the pairwise alignments using only amino acid sequence data at an error rate of 0.01 errors per query; a 35% increase is observed when the actual secondary structure sequences are used. Incorporating predicted secondary structure information in the analysis of six small genomes yields an improvement in the homology detection of approximately 20% over SSEARCH pairwise alignments, but no improvement in the total number of homologs detected over PSI-BLAST, at an error rate of 0.01 errors per query. However, because the pairwise alignments based on combinations of amino acid and secondary structure similarity are different from those produced by PSI-BLAST and the error rates can be calibrated, it is possible to combine the results of both searches. An additional 25% relative improvement in the number of genes identified at an error rate of 0.01 is observed when the data is pooled in this way. Similarly for the SCOP40 dataset, PSI-BLAST detected 15% of all possible homologs, whereas the pooled results increased the total number of homologs detected to 19%. These results are compared with recent reports of homology detection using sequence profiling methods. AVAILABILITY: Secondary structure alignment homepage at http://lutece.rutgers.edu/ssas CONTACT: anders@rutchem.rutgers.edu; ronlevy@lutece.rutgers.edu Supplementary Information: Genome sequence/structure alignment results at http://lutece.rutgers.edu/ss_fold_predictions.     

What is the minimum number of letters required to fold a protein?

Experimental studies have shown that the full sequence complexity of naturally occurring proteins is not required to generate rapidly folding and functional proteins, i.e. proteins can be designed with fewer than 20 letters. This raises the question of what is the minimum number of amino acid types required to encode complex protein folds? Here, we investigate this issue from three aspects. First, we study the minimum sequence complexity that can reserve the necessary structural information for detection of distantly related homologues. Second, we compare the ability of designing foldable model sequences over a wide range of reduced amino acid alphabets, which find the minimum number of letters that have the similar design ability as 20. Finally, we survey the lower bound of alphabet size of globular proteins in a non-redundant protein database. These different approaches give a remarkably consistent view, that the minimum number of letters required to fold a protein is around ten.     

NdPASA: a novel pairwise protein sequence alignment algorithm that incorporates neighbor-dependent amino acid propensities

Sequence alignment has become one of the essential bioinformatics tools in biomedical research. Existing sequence alignment methods can produce reliable alignments for homologous proteins sharing a high percentage of sequence identity. The performance of these methods deteriorates sharply for the sequence pairs sharing less than 25% sequence identity. We report here a new method, NdPASA, for pairwise sequence alignment. This method employs neighbor-dependent propensities of amino acids as a unique parameter for alignment. The values of neighbor-dependent propensity measure the preference of an amino acid pair adopting a particular secondary structure conformation. NdPASA optimizes alignment by evaluating the likelihood of a residue pair in the query sequence matching against a corresponding residue pair adopting a particular secondary structure in the template sequence. Using superpositions of homologous proteins derived from the PSI-BLAST analysis and the Structural Classification of Proteins (SCOP) classification of a nonredundant Protein Data Bank (PDB) database as a gold standard, we show that NdPASA has improved pairwise alignment. Statistical analyses of the performance of NdPASA indicate that the introduction of sequence patterns of secondary structure derived from neighbor-dependent sequence analysis clearly improves alignment performance for sequence pairs sharing less than 20% sequence identity. For sequence pairs sharing 13-21% sequence identity, NdPASA improves the accuracy of alignment over the conventional global alignment (GA) algorithm using the BLOSUM62 by an average of 8.6%. NdPASA is most effective for aligning query sequences with template sequences whose structure is known. NdPASA can be accessed online at http://astro.temple.edu/feng/Servers/BioinformaticServers.htm.     

Assessment of a rigorous transitive profile based search method to detect remotely similar proteins

Profile-based sequence search procedures are commonly employed to detect remote relationships between proteins. We provide an assessment of a Cascade PSI-BLAST protocol that rigorously employs intermediate sequences in detecting remote relationships between proteins. In this approach we detect using PSI-BLAST, which involves multiple rounds of iteration, an initial set of homologues for a protein in a 'first generation' search by querying a database. We propagate a 'second generation' search in the database, involving multiple runs of PSI-BLAST using each of the homologues identified in the previous generation as queries to recognize homologues not detected earlier. This non-directed search process can be viewed as an iteration of iterations that is continued to detect further homologues until no new hits are detectable. We present an assessment of the coverage of this 'cascaded' intermediate sequence search on diverse folds and find that searches for up to three generations detect most known homologues of a query. Our assessments show that this approach appears to perform better than the traditional use of PSI-BLAST by detecting 15% more relationships within a family and 35% more relationships within a superfamily. We show that such searches can be performed on generalized sequence databases and non-trivial relationships between proteins can be detected effectively. Such a propagation of searches maximizes the chances of detecting distant homologies by effectively scanning protein "fold space".     

Identification of membrane-bound and secreted proteins from Echinococcus granulosus by signal sequence trap

The signal sequence trap technique was applied to identify genes coding for secreted and membrane bound proteins from Echinococcus granulosus, the etiologic agent of cystic hydatid disease. An E. granulosus protoscolex cDNA library was constructed in the AP-PST vector such that randomly primed cDNAs were fused with a placental alkaline phosphatase reporter gene lacking its endogenous signal peptide. E. granulosus cDNAs encoding a functional signal peptide were selected by their ability to rescue secretion of alkaline phosphatase by COS-7 cells that had been transfected with the cDNA library. Eighteen positive clones were identified and sequenced. Their deduced amino acid sequences showed significant similarity with amino acid transporters, Krebs cycle intermediates transporters, presenilins and vacuolar protein sorter proteins. Other cDNAs encoded secreted proteins without homologues. Three sequences were transcribed antisense to E. granulosus expressed sequence tags. All the mRNAs were expressed in protoscoleces and adult worms, but some of them were not found in oncospheres. The putative E. granulosus secreted and membrane bound proteins identified are likely to play important roles in the metabolism, development and survival in the host and represent potential targets for diagnosis, drugs and vaccines against E. granulosus.     

COMPASS: a tool for comparison of multiple protein alignments with assessment of statistical significance

We present a novel method for the comparison of multiple protein alignments with assessment of statistical significance (COMPASS). The method derives numerical profiles from alignments, constructs optimal local profile-profile alignments and analytically estimates E-values for the detected similarities. The scoring system and E-value calculation are based on a generalization of the PSI-BLAST approach to profile-sequence comparison, which is adapted for the profile-profile case. Tested along with existing methods for profile-sequence (PSI-BLAST) and profile-profile (prof_sim) comparison, COMPASS shows increased abilities for sensitive and selective detection of remote sequence similarities, as well as improved quality of local alignments. The method allows prediction of relationships between protein families in the PFAM database beyond the range of conventional methods. Two predicted relations with high significance are similarities between various Rossmann-type folds and between various helix-turn-helix-containing families. The potential value of COMPASS for structure/function predictions is illustrated by the detection of an intricate homology between the DNA-binding domain of the CTF/NFI family and the MH1 domain of the Smad family.     

Assessment of a Rigorous Transitive Profile Based Search Method to Detect Remotely Similar Proteins

Abstract

Profile-based sequence search procedures are commonly employed to detect remote relationships between proteins. We provide an assessment of a Cascade PSI-BLAST protocol that rigorously employs intermediate sequences in detecting remote relationships between proteins. In this approach we detect using PSI-BLAST, which involves multiple rounds of iteration, an initial set of homologues for a protein in a ‘first generation’ search by querying a database. We propagate a ‘second generation’ search in the database, involving multiple runs of PSI-BLAST using each of the homologues identified in the previous generation as queries to recognize homologues not detected earlier. This non-directed search process can be viewed as an iteration of iterations that is continued to detect further homologues until no new hits are detectable. We present an assessment of the coverage of this ‘cascaded’ intermediate sequence search on diverse folds and find that searches for up to three generations detect most known homologues of a query. Our assessments show that this approach appears to perform better than the traditional use of PSI-BLAST by detecting 15% more relationships within a family and 35% more relationships within a superfamily. We show that such searches can be performed on generalized sequence databases and non-trivial relationships between proteins can be detected effectively. Such a propagation of searches maximizes the chances of detecting distant homologies by effectively scanning protein “fold space”.     

Distant homology detection using a LEngth and STructure-based sequence Alignment Tool (LESTAT)

A new machine learning algorithm, LESTAT (LEngth and STructure-based sequence Alignment Tool) has been developed for detecting protein homologs having low-sequence identity. LESTAT is an iterative profile-based method that runs without reliance on a predefined library and incorporates several novel features that enhance its ability to identify remote sequences. To overcome the inherent bias associated with a single starting model, LESTAT utilizes three structural homologs to create a profile consisting of structurally conserved positions and block separation distances. Subsequent profiles are refined iteratively using sequence information obtained from previous cycles. Additionally, the refinement process incorporates a "lock-in" feature to retain the high-scoring sequences involved in previous alignments for subsequent model building and an enhancement factor to complement the weighting scheme used to build the position specific scoring matrix. A comparison of the performance of LESTAT against PSI-BLAST for seven systems reveals that LESTAT exhibits increased sensitivity and specificity over PSI-BLAST in six of these systems, based on the number of true homologs detected and the number of families these homologs covered. Notably, many of the hits identified are unique to each method, presumably resulting from the distinct differences in the two approaches. Taken together, these findings suggest that LESTAT is a useful complementary method to PSI-BLAST in the detection of distant homologs.     

Use of residue pairs in protein sequence-sequence and sequence-structure alignments

Two new sets of scoring matrices are introduced: H2 for the protein sequence comparison and T2 for the protein sequence-structure correlation. Each element of H2 or T2 measures the frequency with which a pair of amino acid types in one protein, k-residues apart in the sequence, is aligned with another pair of residues, of given amino acid types (for H2) or in given structural states (for T2), in other structurally homologous proteins. There are four types, corresponding to the k-values of 1 to 4, for both H2 and T2. These matrices were set up using a large number of structurally homologous protein pairs, with little sequence homology between the pair, that were recently generated using the structure comparison program SHEBA. The two scoring matrices were incorporated into the main body of the sequence alignment program SSEARCH in the FASTA package and tested in a fold recognition setting in which a set of 107 test sequences were aligned to each of a panel of 3,539 domains that represent all known protein structures. Six procedures were tested; the straight Smith-Waterman (SW) and FASTA procedures, which used the Blosum62 single residue type substitution matrix; BLAST and PSI-BLAST procedures, which also used the Blosum62 matrix; PASH, which used Blosum62 and H2 matrices; and PASSC, which used Blosum62, H2, and T2 matrices. All procedures gave similar results when the probe and target sequences had greater than 30% sequence identity. However, when the sequence identity was below 30%, a similar structure could be found for more sequences using PASSC than using any other procedure. PASH and PSI-BLAST gave the next best results.     

Comparison of sequence profiles. Strategies for structural predictions using sequence information

Distant homologies between proteins are often discovered only after three-dimensional structures of both proteins are solved. The sequence divergence for such proteins can be so large that simple comparison of their sequences fails to identify any similarity. New generation of sensitive alignment tools use averaged sequences of entire homologous families (profiles) to detect such homologies. Several algorithms, including the newest generation of BLAST algorithms and BASIC, an algorithm used in our group to assign fold predictions for proteins from several genomes, are compared to each other on the large set of structurally similar proteins with little sequence similarity. Proteins in the benchmark are classified according to the level of their similarity, which allows us to demonstrate that most of the improvement of the new algorithms is achieved for proteins with strong functional similarities, with almost no progress in recognizing distant fold similarities. It is also shown that details of profile calculation strongly influence its sensitivity in recognizing distant homologies. The most important choice is how to include information from diverging members of the family, avoiding generating false predictions, while accounting for entire sequence divergence within a family. PSI-BLAST takes a conservative approach, deriving a profile from core members of the family, providing a solid improvement without almost any false predictions. BASIC strives for better sensitivity by increasing the weight of divergent family members and paying the price in lower reliability. A new FFAS algorithm introduced here uses a new procedure for profile generation that takes into account all the relations within the family and matches BASIC sensitivity with PSI-BLAST like reliability.     

Primary structures of ribosomal proteins from the archaebacterium Halobacterium marismortui and the eubacterium Bacillus stearothermophilus.

Approximately 40 ribosomal proteins from each Halobacterium marismortui and Bacillus stearothermophilus have been sequenced either by direct protein sequence analysis or by DNA sequence analysis of the appropriate genes. The comparison of the amino acid sequences from the archaebacterium H marismortui with the available ribosomal proteins from the eubacterial and eukaryotic kingdoms revealed four different groups of proteins: 24 proteins are related to both eubacterial as well as eukaryotic proteins. Eleven proteins are exclusively related to eukaryotic counterparts. For three proteins only eubacterial relatives-and for another three proteins no counterpart-could be found. The similarities of the halobacterial ribosomal proteins are in general somewhat higher to their eukaryotic than to their eubacterial counterparts. The comparison of B stearothermophilus proteins with their E coli homologues showed that the proteins evolved at different rates. Some proteins are highly conserved with 64-76% identity, others are poorly conserved with only 25-34% identical amino acid residues.     

Electric charge balance mechanism of extended soluble proteins

Extended proteins such as calmodulin and troponin C have two globular terminal domains linked by a central region that is exposed to water and often acts as a function-regulating element. The mechanisms that stabilize the tertiary structure of extended proteins appear to differ greatly from those of globular proteins. Identifying such differences in physical properties of amino acid sequences between extended proteins and globular proteins can provide clues useful for identification of extended proteins from complete genomes including orphan sequences. In the present study, we examined the structure and amino acid sequence of extended proteins. We found that extended proteins have a large net electric charge, high charge density, and an even balance of charge between the terminal domains, indicating that electrostatic interaction is a dominant factor in stabilization of extended proteins. Additionally, the central domain exposed to water contained many amphiphilic residues. Extended proteins can be identified from these physical properties of the tertiary structure, which can be deduced from the amino acid sequence. Analysis of physical properties of amino acid sequences can provide clues to the mechanism of protein folding. Also, structural changes in extended proteins may be caused by formation of molecular complexes. Long-range effects of electrostatic interactions also appear to play important roles in structural changes of extended proteins.