  We consider a generic representation problem of internal coordinates (bond
lengths, valence angles, and dihedral angles) and their transformation to
3-dimensional Cartesian coordinates of a biomolecule. We show that the
internal-to-Cartesian process relies on correctly predicting chemically subtle
correlations among the internal coordinates themselves, and learning these
correlations increases the fidelity of the Cartesian representation. This
general problem has been solved with machine learning for proteins, but with
appropriately formulated data is extensible to any type of chain biomolecule
including RNA, DNA, and lipids. We show that the internal-to-Cartesian process
relies on correctly predicting chemically subtle correlations among the
internal coordinates themselves, and learning these correlations increases the
fidelity of the Cartesian representation. We developed a machine learning
algorithm, Int2Cart, to predict bond lengths and bond angles from backbone
torsion angles and residue types of a protein, and allows reconstruction of
protein structures better than using fixed bond lengths and bond angles, or a
static library method that relies on backbone torsion angles and residue types
on a single residue. The Int2Cart algorithm has been implemented as an
individual python package at https://github.com/THGLab/int2cart.
