Protein Loop Modeling

Chemically, a protein is built up by a serial linkage of amino acids (so-called residues) from a set of 20 different types. The three-dimensional structure of proteins (conformation) is primarily determined by few local structure motifs called secondary structures (α-helix and β-sheet) and by their relative spatial arrangements. The fragments that connect the Secondary Structure Elements (SSE) are called loops. Protein loops do not only serve as connectors for secondary structures, but also play important roles for the protein's function, folding and stability. Loops are frequently involved in mediating processes like signaling, ligand binding and protein-protein interactions.

Loops are often located at the molecular surface of proteins and hence exposed to the solvent. Among others, this is one reason for the structural variability of protein loops, which makes the experimental characterization of loops inaccurate and thus the computational prediction of its structure a challenging task.

The search for physically reasonable loop conformations or conformational ensembles for given protein structures is known as the loop modeling problem. Depending on the research community loop modeling is also refered to as fragment/gap completion, loop closure or fragment fitting. Loop modeling can be interpreted as a slightly simpler instance of the general ab initio protein structure prediction problem. So, first, loop fragments are relatively short with respect to the length of the entire protein chain, and, second, the ends of the loop are constrained by the position and orientation of the fixed ends (anchor residues) of the protein backbone (loop closure constraints).

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For the computational prediction of loop structure, extensive search in the constrained conformation space (closure space) is necessary to find energetically favorable loop conformations close to the native state. Like in structure prediction of entire proteins, a physics-based energy function is used to estimate the quality of the sampled loop conformations.

One reasonable way of modeling the loops is to treat it as an Inverse Kinematics (IK) problem formulated for robotic manipulators by controlling the motion of the loop backbone with respect to its degrees of freedom (DOF). One end of the loop is fixed to a protein segment, corresponding to the base of a kinematic chain in robotic terminology. The other end is then interpreted as an end effector whose motion is controlled to reach a target pose consistent with the loop closure constraint.

However, most of the suggested methods published over the last decades are limited in the maximum length of a loop that can be modeled, others are computationally inefficient. For treatable loop lengths, most methods succeed in finding a closed loop conformation, but without exploiting further information like structural knowledge extracted from databases, preferred torsional angles or the energy function for searching. Summarizing, there is no method available that is general and accurate enough to work in all modeling scenarios.

We propose a) Operational Space Control widely established and applied in modern robotics to tackle the loop length limitation and b) an approach based on Rapidly-exploring Random Tree (RRT) introduced in robot motion planning to effectively perform search in constrained conformation space.

Further reading:
[1] A. Shehu, L. E. Kavraki. Modeling Structures and Motions of Loops in Protein Molecules. Entropy 2012, 14(2), 252-290.

Contact: Florian Kamm

References:
[2] Proteins, 2010. http://en.wikipedia.org/wiki/Protein

Funding

© AvH

Alexander von Humboldt professorship - awarded by the Alexander von Humboldt foundation and funded through the Ministry of Education and Research, BMBF,
July 2009 - June 2014