Disulfide Directory Reference

Detailed Description

[Introduction] [Geometry] [Process] [Statistics] [Results] [References]

Introduction

In chemistry, a disulfide bond is a single covalent bond derived from the coupling of thiol groups. The linkage is also called an SS-bond or disulfide bridge. The overall connectivity is therefore C-S-S-C. The terminology is almost exclusively used in biochemistry and bioorganic chemistry. Formally the connection is called a persulfide, in analogy to a peroxide (R-O-O-R), but this terminology is rare.

Disulfide bonds play an important role in the folding and stability of some proteins, usually proteins secreted to the extracellular medium. In that context, disulfide bonds are C-S-S-C bridges connecting two atom pairs in the protein backbone, a N-C pair, and a C-C pair, and a common problem is to determine the set of possible conformations of the whole chain, N-C-C-S-S-C-C-C, assuming the N-C and C-C terminii have a fixed, known position in 3-space. In the language of robot kinematics, and assuming the so-called rigid-geometry hypothesis, this problem is equivalent to the position analysis of a 6R loop.

Geometry

Next figure depicts the distance model a disulfide bond. The model fixes the same atom-atom distances as the one in [Wedemeyer and Scheraga 1999]. It is assumed that the 3D coordinates of $N_{A}$, $C_A^\alpha$, $C_B^\alpha$, $C_{B}$ are held fixed, while the positions of the four other atoms remain to be determined. All torsion angles are to be determined too, except $\Omega$ which is fixed to 90 degrees and determines the distance between the two $C^{\beta}$ atoms.

Process

This example is treated following this steps (from the main CuikSuite folder):

  • Generate the equations: Execute
  • Simplify the problem: To see the problem that is actually solved. Execute
    • bin/cuiksimplify examples/Disulfide/Disulfide
    • cat examples/Disulfide/Disulfide_simp.cuik
  • Solve the positional analysis problem: Execute
  • Visualize the solutions:

Statistics

Characteristics of the problem:

Nr. of indep. loops 1
Nr. of links 6
Nr. of joints 6
Nr. of equations (in the simplified system) 17
Nr. of variables (in the simplified system) 17

Here you have the statistics about the execution (on an Intel Core i7 at 2.9 Ghz).

Nr. of Empty boxes 82
Nr. of Solution boxes 8
Execution time (s) 5

Results

Here you have the 8 solutions you should obtain.

References

  • W. Wedemeyer and H. Scheraga, "Exact Analytical Loop Closure in Proteins Using Polynomial Equations", Journal of Computational Chemistry, Vol. 20, No. 8, pp. 819-844, 1999.

Files

file  Disulfide.world [code]
 A disulfide bond.