Protein backbone structure determination using RDC: An inverse kinematics approach with fast and exact solutions

• Published in: International journal of quantum chemistry Vol. 113; no. 8; pp. 1095 - 1106
• Main Authors: Pantos, Sotirios I., Tiligada, Ekaterini
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 15.04.2013; Wiley Subscription Services, Inc
• Subjects: Algorithms; backbone fold; Chemistry; Heuristic; inverse kinematics; Kinematics; MAPLE implementation; Physical chemistry; polynomial equation; Quantum physics; RDC measurement; Studies
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.24166

Residual dipolar couplings (RDC) of proteins dissolved in anisotropic media promise to speed up the determination of protein structures. We consider the backbone as a robotic mechanism and formulate inverse kinematics problems using RDC restraints from two media. The φ, ψ of each secondary structure element (SSE) are computed from oriented vectors in consecutive peptide planes. We search for the optimum conformation joining the solutions of two independent backbone halves. The matrix transforming the vector Z of a global frame from one SSE into the other determines their orientation. Three distance constraints between two oriented SSE determine their relative position by solving nine polynomial equations. The benefit of this method is that complete and accurate solutions are obtained overcoming the local minima problems of heuristic procedures. The algorithm is implemented on MAPLE using the least number of experimental data; the runtimes take an order of seconds on a common PC. © 2013 Wiley Periodicals, Inc. Most of the existing computational methods for protein structure determination with nuclear magnetic resonace (NMR) rely on stochastic and heuristic protocols overlooking the fast analytic‐type algebraic methods as unrealistic alternates. An algebraic methodology is here introduced to reinforce this alternate point of view as realistic and effective. A unified and efficient methodology that reduces the computations of protein backbone conformation to a problem of robust, easily soluble, linear and nonlinear equation solving is introduced.