Overview

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 [11], genetic algorithms [12], bond scaling algorithms with relaxation [13], and multicopy searches [14]. 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 [15], 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].


This method of loop generation has the advantage that is is fast, and has the guarantee of obtaining physically reasonable mainchain conformation. It was shown that for small loops, the search method can be very effective [2]. For longer loops however, no satisfactory conformations could be found in many cases [19,20]. While there was discrepancy in terms of the maximum loop length can be accurately modelled using a database approach (4 for Fidelis [19], 9 for van Vlijmen and Karplus [20]), it remains that this method does break down for long loops. There is hpe however that with the increase in size of the PDB database, the optimistic limit of 9 residues in 1997 can be pushed to loops of more than 10 residues.

Analytical approaches to the loop generation problem

The analytical loop closure problem was first studied by Go and Scheraga [21]. 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 [21]. 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 [22].

It should be noted that this loop-closure problem is not specific to computational geometry, and is in fact a classical problem is robotics.

References

1. Bruccoleri, RE and Karplus, M. Chain closure with bond angle variations. Macromolecules, 18, 2767-2773.

2. Moult, J and James, MNG. An algorithm for determining the conformation of polypeptide segments in proteins by systematic search. Proteins: Struct. Funct. Genet., 1, 146-163 (1986).

3. Bruccoleri, RE, Haber, E and Novotny, J. Structure of antibody hypervariable loops reproduced by a conformational search algorithm. Nature (London), 335, 564-568 (1988).

4. Dudek, M and Scheraga, HA. Protein structure prediction using a combination of sequence homology and global energy minimization. I. Global energy minimization of surface loops. J. Comp. Chem., 11, 121-151 (1990).

5. Fine, RM, Wang, H, Shenkin, PS, Yarmush, DL and Levinthal, C. Predicting antibody hypervariable loop conformations. II. Minimization and molecular dynamics studies of MCPC603 from many randomly generated loop conformations. Proteins: Struct. Funct. Genet., 1, 342-362 (1986).

6. Shenkin, S, Yarmush, DL, FIne, RM, Wang, H and Levinthal, C. Predicting antobody hypervariable loop conformation. I. Ensembles of random conformations for ringlike structures. Biopolymers, 26, 2053-2085 (1987).

7. Bruccoleri, RE and Karplus, M. Conformational sampling using high temperature molecular dynamics. Biopolymers, 29, 1847-1862 (1990).

8. Tanner, JJ, Nell, LJ and McCammon, JA. Anti-insulin antibody structure and conformation. II. Molecular Dynamics with explicit solvent. Biopolymers, 32, 23-31 (1992).

9. Collura, V, Higo, J and Garnier, J. Modelling of protein loops by simulated annealing. Protein Sci., 2, 1502-1510 (1993).

10. Carlacci, L and Englander, SW. The loop problem in proteins: a Monte Carlo simulated annealing approach. Biopolymers, 33, 1271-1286 (1993).

11. Finkelstein, AV and Reva, BA. Search for the stable state of a short chain in a molecular field. Prot. Eng., 5, 617-624 (1992).

12. McGarrah, DB and Judson, RS. Analysis of the genetic algorithm method of molecular conformation determination. J. Comp. Chem., 14, 1385-1395 (1993).

13. Zheng, Q, Rosenfeld, R, Vajda, S and DeLisi, C. Loop closure via bond scaling and relaxation. J. Comp. Chem., 14, 556-565 (1993).

14. Zheng, Q, Rosenfeld, R, DeLisi, C and Kyle, DJ. Multiple copy sampling in protein loop modelling: computational efficiency and sensitivity to dihedral perturbations. Protein Sci., 3, 493-506 (1994).

15. Jones, TA and Thirup, S. Using known substructures in protein model building and crystallography. EMBO J., 5, 819-822 (1986).

16. Claessens, M, VanCutsem, E, Lasters, I and Wodak, S. Modelling the polypeptide backbone with 'spare parts' from known protein structures. Protein Eng., 2, 335-345 (1989).

17. Summers, NL and Karplus, M. Modelling of globular proteins. A distance-based data search procedure for the construction of insertion/deletion regions and Pro - non-Pro mutations. J. Mol. Biol., 216, 991-1016 (1990).

18. Levitt, M. accurate modeling of protein conformation by automatic segment matching, J. Mol. Biol., 226, 507-533 (1992).

19. Fidelis, K, Stern, PS, Bacon, D and Moult, J. Comparison of systematic search and database methods for constructing segments of protein structure. Protein Eng., 7, 953-960 (1994).

20. vanVlijmen, HWT and Karplus, M. PDB based protein loop prediction: parameters for selection and methods for optimization. J. Mol. Biol., 267, 975-1001 (1997).

21. Go, N and Scheraga, HA. Ring closure and local conformational deformations of chain molecules. Macromolecules, 3, 178-186 (1990).

22. Wedemeyer, WJ and Scheraga, HA. Exact analytical loop closure in proteins using polynomial equations. J. Comp. Chem. , 8, 819-844 (1999).