Once an initial target-template alignment is built, a variety of methods can be used to construct a 3D model for the target protein [1,2,3,4,5,6]. The original and still widely used method is modeling by rigid-body assembly [1,53,54]. This method constructs the model from a few core regions and from loops and sidechains, which are obtained from dissecting related structures. Another family of methods, modeling by segment matching, relies on the approximate positions of conserved atoms from the templates to calculate the coordinates of other atoms [55,56,57,58]. The third group of methods, modeling by satisfaction of spatial restraints, uses either distance geometry or optimization techniques to satisfy spatial restraints obtained from the alignment of the target sequence with the template structures [59,60,22,61,62]. Specifically, MODELLER, which belongs to this group of methods, extracts spatial restraints from two sources. First, homology-derived restraints on the distances and dihedral angles in the target sequence are extracted from its alignment with the template structures. Second, stereochemical restraints such as bond length and bond angle preferences are obtained from the molecular mechanics force field of CHARMM-22 [63] and statistical preferences of dihedral angles and non-bonded atomic distances are obtained from a representative set of all known protein structures. The model is then calculated by an optimization method relying on conjugate gradients and molecular dynamics, which minimizes violations of the spatial restraints (Figure 2). The procedure is conceptually similar to that used in determination of protein structures from NMR-derived restraints. The fourth group of comparative model building methods starts with an alignment and then searches the conformational space guided by a statistical potential function and somewhat relaxed homology restraints derived from the input alignment, in an attempt to overcome at least some alignment mistakes [64].
Accuracies of the various model building methods are relatively similar when used optimally. Other factors such as template selection and alignment accuracy usually have a larger impact on the model accuracy, especially for models based on less than 40% sequence identity to the templates. However, it is important that a modeling method allows a degree of flexibility and automation to obtain better models more easily and rapidly. For example, a method should allow for an easy recalculation of a model when a change is made in the alignment; it should be straightforward to calculate models based on several templates; and the method should provide tools for incorporation of prior knowledge about the target (e.g., cross-linking restraints, predicted secondary structure) and allow ab initio modeling of insertions (e.g., loops), which can be crucial for annotation of function. Loop modeling is an especially important aspect of comparative modeling in the range from 30 to 50% sequence identity. In this range of overall similarity, loops among the homologs vary while the core regions are still relatively conserved and aligned accurately. Next, we single out loop modeling and review it in more detail.
There are two approaches to loop modeling. First, the ab initio loop prediction is based on a conformational search or enumeration of conformations in a given environment, guided by a scoring or energy function. There are many such methods, exploiting different protein representations, energy function terms, and optimization or enumeration algorithms [24]. The second, database approach to loop prediction consists of finding a segment of mainchain that fits the two stem regions of a loop. The search for such a segment is performed through a database of many known protein structures, not only homologs of the modeled protein. Usually, many different alternative segments that fit the stem residues are obtained, and possibly sorted according to geometric criteria or sequence similarity between the template and target loop sequences. The selected segments are then superposed and annealed on the stem regions. These initial crude models are often refined by optimization of some energy function.
The loop modeling module in MODELLER implements the optimization-based approach [24]. The main reasons are the generality and conceptual simplicity of energy minimization, as well as the limitations on the database approach imposed by a relatively small number of known protein structures [65]. Loop prediction by optimization is applicable to simultaneous modeling of several loops and loops interacting with ligands, which is not straightforward for the database search approaches. Loop optimization in MODELLER relies on conjugate gradients and molecular dynamics with simulated annealing. The pseudo energy function is a sum of many terms, including some terms from the CHARMM-22 molecular mechanics force field [63] and spatial restraints based on distributions of distances [66] and dihedral angles [67] in known protein structures. The method was tested on a large number of loops of known structure, both in the native and near-native environments. Loops of 8 residues predicted in the native environment have a 90% chance to be modeled with useful accuracy (i.e., RMSD for superposition of the loop mainchain atoms is less than 2). Even 12-residue loops are modeled with useful accuracy in 30% of the cases. When the RMSD distortion of the environment atoms is 2.5, the average loop prediction error increases by 180, 25 and 3% for 4, 8 and 12-residue loops, respectively. It is not anymore too optimistic to expect useful models for loops as long as 12 residues, if the environment of the loop is at least approximately correct. It is possible to estimate whether or not a given loop prediction is correct, based on the structural variability of the independently derived lowest energy loop conformations.