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Practical conversion from torsion space to Cartesian space for in silico protein synthesis
Author(s) -
Parsons Jerod,
Holmes J. Bradley,
Rojas J. Maurice,
Tsai Jerry,
Strauss Charlie E. M.
Publication year - 2005
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.20237
Subject(s) - cartesian coordinate system , computer science , algorithm , dot product , ansi c , pentium , cartesian product , solver , torsion (gastropod) , computational science , parallel computing , mathematics , discrete mathematics , geometry , software , medicine , surgery , programming language
Many applications require a method for translating a large list of bond angles and bond lengths to precise atomic Cartesian coordinates. This simple but computationally consuming task occurs ubiquitously in modeling proteins, DNA, and other polymers as well as in many other fields such as robotics. To find an optimal method, algorithms can be compared by a number of operations, speed, intrinsic numerical stability, and parallelization. We discuss five established methods for growing a protein backbone by serial chain extension from bond angles and bond lengths. We introduce the Natural Extension Reference Frame (NeRF) method developed for Rosetta's chain extension subroutine, as well as an improved implementation. In comparison to traditional two‐step rotations, vector algebra, or Quaternion product algorithms, the NeRF algorithm is superior for this application: it requires 47% fewer floating point operations, demonstrates the best intrinsic numerical stability, and offers prospects for parallel processor acceleration. The NeRF formalism factors the mathematical operations of chain extension into two independent terms with orthogonal subsets of the dependent variables; the apparent irreducibility of these factors hint that the minimal operation set may have been identified. Benchmarks are made on Intel Pentium and Motorola PowerPC CPUs. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 1063–1068, 2005