Modeling the Molecular Distance Geometry Problem Using Dihedral Angles

An alternative formulation based on dihedral angles to the molecular distance geometry problem with imprecise distance data is presented. This formulation considers the additional hypothesis of a particular ordering such that all distances \(||x_i-x_j||=d_{ij}\), \(|i-j|<3\), are known. Considering that bond length and angles are given a priori in a protein backbone, there is always at least one of such ordering in instances involving real protein data. This hypothesis reduces by 2/3 the number of variables of the problem and allows us to calculate the derivatives of the standard Cartesian coordinates representation with respect to the dihedral angles. Numerical experiments illustrate the correctness and viability of the proposed formulation.