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Conversion from Dihedral angle representation to Cartesian representation

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Conversion from Dihedral angle representation to Cartesian representation


I'm very new here. In fact, it is my first post. I'm a computer scientist which is studying protein structure prediction in ab initio modeling.

My doubt is concern about conversion of protein from dihedral angles representation to Cartesian representation. Where distances, angles and dihedrals of protein are stored? What algorithm is used for it?

I've read about Rosetta ab initio algorithm uses dihedral angles representation and computes energies of protein conformation. Therefore, I understood that it is necessary to convert from dihedral angles representation to Cartesian representation. For this is necessary to give for algorithm information about each atom of protein: distances between atoms connected, value of angle with third atom and dihedral angle with four atom.

In this way, I've implemented SN-Nerf algorithm based on article below:
Jerod Parsons, J. Bradley Holmes, J. Maurice Rojas, Jerry Tsai, Charlie E. M. Strauss (2005). "Practical conversion from torsion space to Cartesian space for in silico protein synthesis". Journal of Computational Chemistry 26 (10): 1063–1068. doi:10.1002/jcc.20237

My representation of atoms of each amino acid was based on CHARMM 27 force-field.

Therefore, my main question is concerned about the parameters and the algorithm are used by Rosetta to convert from dihedral angles representation to Cartesian representation.

I thanks any help.

Best regards,

Post Situation: 
Sat, 2012-02-25 11:57

I forgot to tell that I want to see the Rosetta parameters for this conversion because I would like to understand these parameters and try to use in my conversion algorithm, if it is possible.

Sorry my failure.

Best regards.

Sat, 2012-02-25 12:17

Rosetta is capable of storing atom bonds, angles, and dihedrals (two, three, and four body terms) to rebuild 3D coordinates from internal coordinates. In the specific case of ab initio, only dihedrals are handled; bond lengths and angles are built from scratch at predetermined ideal values. The ideal values are encoded in the residue parameters (params) files; these are at rosetta_database/chemical/residue_type_sets/fa_standard/residue_types. Lengths are in angstroms and the others are in degrees.

The code that handles the conversion back and forth is the atom_tree. Here's one bit of documentation: This publication covers the fold_tree, which is a coarse representation of the atom_tree: I'm pretty sure this one has stuff on the atom_tree in it, too: Methods Enzymol. 2011;487:545-74.
ROSETTA3: an object-oriented software suite for the simulation and design of macromolecules.
Leaver-Fay A, Tyka M, Lewis SM, Lange OF, Thompson J, Jacak R, Kaufman K, Renfrew PD, Smith CA, Sheffler W, Davis IW, Cooper S, Treuille A, Mandell DJ, Richter F, Ban YE, Fleishman SJ, Corn JE, Kim DE, Lyskov S, Berrondo M, Mentzer S, Popović Z, Havranek JJ, Karanicolas J, Das R, Meiler J, Kortemme T, Gray JJ, Kuhlman B, Baker D, Bradley P.
Department of Biochemistry, University of North Carolina, Chapel Hill, North Carolina, USA.

If those don't answer it, tell me and I'll get someone to dig up the right reference.

Sun, 2012-02-26 10:24


 A discussion of the method used in Rosetta and comparison to multiple alternative methods is provided in this paper:


J Comput Chem. 2005 Jul 30;26(10):1063-8.

Practical conversion from torsion space to Cartesian space for in silico protein synthesis.


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.

Fri, 2016-09-02 10:08