0.2 Protein inverse kinematics and the loop closure problem  (Page 5/5)

Unlike classic inverse-kinematics solutions that use Jacobian matrices , , or general numerical approaches, CCD is free of singularities and does not depend on initial guesses forsolutions. Compared to inverse kinematics techniques with optimization that suffer from high computational times, CCD iscomputationally fast. Unlike other methods such as random tweak, CCD gives predictable behavior and suffers from no anomalies whenadditional constraints are added to the dihedrals (e.g. constraints imposed by the physical-chemical forces on the protein). Suchproperties make CCD very appealing.

Because CCD solves for the degrees of freedom of a chain one at a time, the method finds the optimal values for allthe degrees of freedom of the chain iteratively, according to some order. CCD iterates over the degrees of freedom according to apredetermined order (e.g. a straightforward implementation of the method may use the identity order, where degrees of freedom arenumbered consecutively in increasing order from the base to the end effector of the chain), solving for each one of them at a time. Thisprocess of iterating over all the degrees of freedom can be repeated a maximum number of times or until the end effector lies within anepsilon distance of its position and orientation in space.

While not able to enumerate all the solutions to the degrees of freedom, CCD guarantees it will find asolution if one exists. Given a configuration of the chain and a target position and orientation for the chain's end effector, CCDiteratively modifies the degrees of freedom of the chain until either it runs out of iterations or it manages to satisfy the spatialconstraint on the end effector. Due to its computational efficiency (linear time complexity on the number of degrees of freedom of thechain), CCD has been applied to determine atomic positions of missing mobile loops of arbitrary length . A similar application complete missing loops in partially resolvedcrystallographic structures can be found in , , .

A recent application of CCD to not just loops but any fragment of a protein polypeptide chain can be foundin . The work in applies CCD to configurations of a fragment that are sampled uniformly at random to obtain an ensembleof fragment configurations that connects with the rest of the protein polypeptide chain. Careful attention is paid to the energeticrefinement of the obtained fragment configurations in order to ensure the biological relevance of the configurations at roomtemperature. The usage of CCD in to obtain an ensemble of biologically meaningful configurations of a fragment of the polypeptide chain isan interesting application to capture the flexibility of a fragment in the context of a given protein structure. By generating ensemblesof biologically relevant configurations for fragments that are defined consecutively and with significant overlap over the proteinpolypeptide chain, the work in offers a novel approach to capture the flexibility of the entire polypeptide chain.

Recommended reading

• Canutescu, A.A. and R.L. Dunbrack. [PDF] . Cyclic Coordinate Descent: A Robotics Algorithm for Protein Loop Closure. Protein Science, 12:963-72, 2003.
• Craig, J.J. Introduction to Robotics, chapter 4. Reading, MA: Addison-Wesley, 1989.
• van den Bedem, H. and Lotan, I. and Deacon, A. M. and Latombe, J.-C.. [PDF] . Computing protein structures from electron density maps: the missing loop problem. Algorithmic Foundations of Robotics VI, 345-360,2005.
• Shehu, A. and Clementi, C. and Kavraki, L.E. [PDF] . Modeling Protein Conformational Ensembles: From Missing Loops to Equilibrium Fluctuations. Proteins: Structure, Function, Bioinformatics, 65(1):164-179, 2006.
• Coutsias, E. A. and Seok, C. and Wester, M. J. and Dill, K. A. [LINK] . Resultants and loop closure. International Journal of Quantum Chemistry, 106(1):176-189,2005.