Protein loop modeling by using fragment assembly and analytical loop closure

Abstract

Protein loops are often involved in important biological functions such as molecular recognition, signal transduction, or enzymatic action. The three dimensional structures of loops can provide essential information for understanding molecular mechanisms behind protein functions. In this paper, we develop a novel method for protein loop modeling, where the loop conformations are generated by fragment assembly and analytical loop closure. The fragment assembly method reduces the conformational space drastically, and the analytical loop closure method finds the geometrically consistent loop conformations efficiently. We also derive an analytic formula for the gradient of any analytical function of dihedral angles in the space of closed loops. The gradient can be used to optimize various restraints derived from experiments or databases, for example restraints for preferential interactions between specific residues or for preferred backbone angles. We demonstrate that the current loop modeling method outperforms previous methods that employ residue-based torsion angle maps or different loop closure strategies when tested on two sets of loop targets of lengths ranging from 4 to 12.

Conformational Sampling of Flexible Ligand-binding Protein Loops

“…First, a set of 1,000 conformations at local energy minima were generated by using the FALC (Fragment Assembly and analytical Loop Closure) method. 4 This method collects fragment structures from proteins of similar sequence features in the structure database and randomly assembles the fragments to construct model loops. The triaxial loop closure (TLC) 24 is then applied to adjust backbone torsion angles so that the loop conformations fit into the rest of the protein body.…”

Exploring the energy landscapes of flexible molecular loops using higher‐dimensional continuation

“…Numerical methods able to isolate the whole conformational space and that are not affected by singularities also exist [46]. Finally, problems with more degrees of freedom can also be addressed with local perturbation techniques [58,35], with approaches where some of the variables are sampled and the rest is solved via inverse kinematics [15,14] or combining inverse kinematics, fragment assembly, and local optimization methods [26,36].…”

“…Like existing systematic approaches [2,42], though, the proposed technique can incorporate additional constraints so that the exploration is focused on the biologically feasible conformations given by the Ramachandra plots [48], or by the steric-clashes, both aspects difficult to incorporate in existing approaches such as the ones relying on closed-form inverse kinematics [26,38,15]. A search even more focused on the feasible conformations would require the use of database [21] or fragment assembly methods [55,36], something not considered in this work.…”

“…Like some of these methods, the procedure presented here is strongly based on the use of Jacobians to generate linear spaces tangent to the loop-closure variety, but in contrast with existing Jacobian-based techniques [22,18,59,36], the proposed procedure is aware of the presence of bifurcations, the only type of singularities that, to the best of our knowledge, has been shown to play a role in the context of Biochemistry [39]. Other types of singularities might affect the performance of the presented system, although their analysis is out of the scope of this paper.…”

“…This problem appears in many relevant situations such as when determining the valid conformations of cyclic molecules, when analyzing the movements of an atom chain with fixed ends, or when trying to complete the missing fragments in protein modeling [26,62,1,51,55,36]. In general, the loops are not rigid, but flexible, since they can undergo internal motions.…”