Generating loop conformation for Homology Modeling
The core regions within homologous protein families, which mainly include secondary structure elements, are nearly superposable. These regions form the framework which serves as a starting point for comparative protein structure modeling. The non regular regions between these conserved regions however, and more particularly the peripheral loops, show significant structural variations. Modeling the structure of these variable regions in the context of the complete protein is one of the most difficult challengs for comparative modelling. While these variable regions are usually referred to as "loops", they include not only real loops between two secondary structure elements, but also fragments involving secondary structure.
The loop modelling problem involves (a) generating loop conformation that fits and, (b), selecting among all the possible conformation the most native-like structure. In this page, we focus on problem (a), and review three approaches to solve it: loop construction, loop selection from known protein fragments, and analytical methods.
Construction of loop conformations
The residues at the two termini of a gap in the "framework" of the target protein structure define endpoint criteria for loop building. Because of the fixed position of these two endpoints, and because the loop is usually short, building protein loops is usually a much more tractable than the general protein folding problem.
The construction method generate many loop conformations and filter out the ones that do not meet the endpoint criteria. They include exhaustive searches in dihedral angle space [1-4], minimum perturbation methods [5,6], molecular dynamics simulations [7,8], Monte Carlo searches, usually with simulated annealing [9,10], dynammic programming algorithms , genetic algorithms , bond scaling algorithms with relaxation , and multicopy searches . In all of these methods, the search for loop structures and their evaluation is done simultaneously.
Selecting loop conformation from libraries of protein fragments
The use of protein fragments for modelling was originally proposed by Jones and Thirup , in the context of electron density fitting. A similar approach was designed for comparative modelling by selecting fragments from the PDB that overlap the framework at both ends [16-18].
Analytical approaches to the loop generation problem
The analytical loop closure problem was first studied by Go and Scheraga . They showed that at least 6 degrees of freedom are required to close a loop of rigid bond lengths and bond angles, because six constraints must be satisfied in the translation and rotation of a coordinate frame from the first residue to the final residue of the loop. Go and Scheraga formulated these constraints as six equations in the loop dihedral angles, and applied these equations to building tripeptide loops . These equations must be solved numerically, and there is no guarantee that they have a solution. This problem has been revisited recently in Scheraga's lab, and a new analytical, efficient algorithm was developed, using spherical geometry and polynomial equations .
It should be noted that this loop-closure problem is not specific to computational geometry, and is in fact a classical problem is robotics.
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