Predicting the 3D structure of protein chains from the linear sequence of amino acids is a fundamental open problem in computational molecular biology [1]. Any approach to the problem must deal with the basic fact that protein structures are translation and rotation invariant. To address this invariance, we have proposed a machine learning approach to protein structure prediction [4] based on the predic- tion of topological representations of proteins, in the form of contact or distance maps. The contact or distance map is a 2D representation of neighborhood rela- tionships consisting of an adjacency matrix at some distance cuto(cid:11) (typically in the range of 6 to 12 (cid:23)A), or a matrix of pairwise Euclidean distances. Fine-grained maps are derived at the amino acid or even atomic level. Coarse maps are obtained by looking at secondary structure elements, such as helices, and the distance between their centers of gravity or, as in the simulations below, the minimal distances be- tween their C(cid:11) atoms.