Figure 2 The flowchart for comparative protein structure modeling.

II. STEPS IN COMPARATIVE MODELING

A.Identifying Known Protein Structures Related to the Target Sequence

The first task in comparative modeling is to identify all protein structures related to the target sequence, some of which will be used as templates. This is greatly facilitated by databases of protein sequences and structures and by software for scanning those databases [16–19]. The target sequence can be searched against sequence databases such as PIR [20], GenBank [21], or TrEMBL/SWISS-PROT [12] and/or structure databases such as the Protein Data Bank [13,22], SCOP [23], DALI [24], and CATH [25] (Table 1). Searching against sequence databases can be useful even if it identifies only proteins of unknown structure, because such sequences can be used to increase the sensitivity of the search for the template structures (see below). At present, the probability of finding related proteins of known structure for a sequence picked randomly from a genome ranges from 20% to 70% [8–11].

There are three main classes of protein comparison methods that are useful in fold identification. The first class compares the target sequence with each of the database sequences independently, using pairwise sequence–sequence comparison [26]. The performance of these methods in sequence searching [27] and fold assignments has been evaluated exhaustively [28]. The most popular programs in the class include Fasta [29] and BLAST [30]. Program MODELLER, which implements all the stages in comparative modeling [31], can also automatically search for proteins with known 3D structure that are related to a given sequence. It is based on the local dynamic programming method for pairwise sequence comparison [32].

The second class of methods rely on multiple sequence comparison to improve greatly the sensitivity of the search [10,33–36]. The best-known program in this class is PSI-BLAST [36]. Another similar approach that appears to perform even slightly better than PSI-BLAST has been described [10]. It begins by finding all sequences in a sequence database that are clearly related to the target and easily aligned with it. The multiple alignment of these sequences is the target sequence profile. Similar profiles are also constructed for all potential template structures. The templates are then found by comparing the target sequence profile with each of the template sequence profiles, using a local dynamic programming method that relies on the common BLOSUM62 residue substitution matrix [33]. These more sensitive fold identification techniques are especially useful for finding structural relationships when sequence identity between the target and the template drops below 25%. In fact, methods of this class, which rely on multiple sequence information, appear to be currently the most sensitive fully automated approach to detecting remote sequence–structure relationships [8,36–38].

The third class of methods rely on pairwise comparison of a protein sequence and a protein structure; that is, structural information is used for one of the two proteins that are being compared, and the target sequence is matched against a library of 3D profiles or threaded through a library of 3D folds. These methods are also called fold assignment, threading, or 3D template matching [39–43,238]. They are reviewed in Refs. 44–46 and evaluated in Ref. 47. These methods are especially useful when it is not possible to construct sequence profiles because there are not enough known sequences that are clearly related to the target or potential templates.

What similarity between the target and template sequences is needed to have a chance of obtaining a useful comparative model? This depends on the question that is asked of a model (Section VI). When only the lowest resolution model is required, it is tempting to use one of the statistical significance scores for a given match that is reported by virtually any sequence comparison program to select the best template. However, it is better to proceed with modeling even when there is only a remote chance that the best template is suitable for deriving a model with at least a correct fold. The usefulness of the template should be assessed by the evaluation of the calculated 3D model. This is the best approach, because the evaluation of a 3D model is generally more sensitive and robust than the evaluation of an alignment (Section V) [9].

B.Aligning the Target Sequence with the Template Structures

Once all the structures related to the target sequence are identified, the second task is to prepare a multiple alignment of the target sequence with all the potential template structures [16,48–50]. When the sequence identity between the target and the template is higher than approximately 40%, this is straightforward. The gaps and errors in the alignments

are rare, whether they are prepared automatically or manually. However, at 30% sequence identity, the fraction of residues that are correctly aligned by pairwise sequence–sequence comparison methods is only 80% on average, and this number drops sharply with further decrease in sequence similarity [51]. Thus, an additional effort in obtaining a more accurate alignment is needed because comparative modeling cannot, at present, recover from an incorrect alignment; the quality of the alignment is the single most important factor determining the accuracy of the 3D model.

In the more difficult alignment problems, it is frequently beneficial to rely on the multiple structure and sequence information as follows [52]. First, the alignment of the potential templates is prepared by superposing their structures. Typically, all residues

˚

whose Cα atoms are within 3.5 A of each other upon least-squares superposition are aligned. Next, the sequences that are clearly related to the templates and easy to align with them are added to the alignment. The same is done for the target sequence. And finally, the two profiles are aligned with each other, taking structural information into account as much as possible [53–55]. In principle, most sequence alignment and structure comparison methods can be used for these tasks [16,18,53,56]. In practice, it is frequently necessary to edit manually the positions of insertions and deletions to ensure that they occur in a reasonable structural context. For example, gaps are favored outside secondary structure segments, in exposed regions, and between residues that are far apart in space. Secondary structure prediction for the target sequence or its profile is also frequently useful in obtaining a more accurate alignment to the template structures [57]. Although 3D profile matching and threading techniques are relatively successful in identifying related folds, they appear to be somewhat less successful in generating correct alignments [47]. When there is an uncertainty about a region in the alignment, the best way to proceed is to generate 3D models for all alternative alignments, evaluate the corresponding models, and pick the best model according to the 3D model evaluation rather than the alignment score (Section V) [58,59].

Once a multiple alignment is constructed, matrices of pairwise sequence similarities are usually calculated and employed to construct a phylogenetic tree that expresses the relationships among the proteins in the family [60]. All significantly different structures in the cluster that contains the target sequence are usually used as templates in the subsequent model building [61], although other considerations should also enter into the template selection. For example, if the model is prepared to study the liganded state of a protein, then a template in the liganded state is preferred over a template without a ligand. Some methods allow short segments of known structure, such as loops [62], to be added to the alignment at this stage [31].

C. Model Building

1. Modeling by Assembly of Rigid Bodies

The first approach and one still widely used in comparative modeling is to assemble a model from a small number of rigid bodies obtained from the aligned protein structures [1,2,63]. This approach is based on the natural dissection of the protein structure into conserved core regions, variable loops that connect them, and side chains that decorate the backbone. For example, the following semiautomated procedure is implemented in the computer program COMPOSER [64] (Table 1). First, the template structures are selected and superposed. Second, the ‘‘framework’’ is calculated by averaging the coordinates of the Cα atoms of structurally conserved regions in the template structures. Third,

the core main chain atoms of each core region in the target model are obtained by superposing on the framework the core segment from the template whose sequence is closest to that of the target. Fourth, the loops are generated by scanning a database of all known protein structures to identify the structurally variable regions that fit the anchor core regions and have a compatible sequence [65]. Fifth, the side chains are modeled based on their intrinsic conformational preferences and on the conformation of the equivalent side chains in the template structures [66]. And finally, the stereochemistry of the model is improved either by a restrained energy minimization or a molecular dynamics refinement. The accuracy of a model can be somewhat increased when more than one template structure is used to construct the framework and when the templates are averaged into the framework using weights corresponding to their sequence similarities to the target sequence [67]. For example, differences between the model and X-ray structures may be slightly smaller than the differences between the X-ray structures of the modeled protein and the homologs used to build the model. Possible future improvements of modeling by rigid-body assembly include incorporation of rigid-body shifts such as the relative shifts in the packing of α-helices [68].

2. Modeling by Segment Matching or Coordinate Reconstruction

The basis of modeling by coordinate reconstruction is the finding that most hexapeptide segments of protein structure can be clustered into only 100 structurally different classes [69]. Thus, comparative models can be constructed by using a subset of atomic positions from template structures as ‘‘guiding’’ positions, then identifying and assembling short allatom segments that fit these guiding positions. The guiding positions usually correspond to the Cα atoms of the segments that are conserved in the alignment between the template structure and the target sequence. The all-atom segments that fit the guiding positions can be obtained either by scanning all the known protein structures, including those that are not related to the sequence being modeled [70,71], or by conducting a conformational search restrained by an energy function [72,73]. For example, a general method for modeling by segment matching is guided by the positions of some atoms (usually Cα atoms) to find the matching segments in the representative database of all known protein structures [74]. This method can construct both main chain and side chain atoms and can also model gaps. It is implemented in the program SEGMOD which is part of the Genemine package (Table 1). Even some side chain modeling methods [75] and the class of loop construction methods based on finding suitable fragments in the database of known structures [62] can be seen as segment-matching or coordinate reconstruction methods.

3. Modeling by Satisfaction of Spatial Restraints

The methods in this class begin by generating many constraints or restraints on the structure of the target sequence, using its alignment to related protein structures as a guide. The restraints are generally obtained by assuming that the corresponding distances between aligned residues in the template and the target structures are similar. These homol- ogy-derived restraints are usually supplemented by stereochemical restraints on bond lengths, bond angles, non-bonded atom–atom contacts, etc., which are obtained from a molecular mechanics force field. The model is then derived by minimizing the violations of all the restraints. This can be achieved by either distance geometry or real-space optimization. For example, an elegant distance geometry approach constructs all-atom models from lower and upper bounds on distances and dihedral angles [76,77]. Lower and upper bounds on Cα–Cα and main chain–side chain distances, hydrogen bonds, and conserved