Conformation reconstruction is an important challenge in computational biology. In this project we
develop a model for the 3D spatial organization of chromatin, a crucial component of numerous cellular
processes. The central object in this study is the so-called contact matrix. It represents the frequency
of contacts between each pair of genomic loci; it can thus be used to infer the 3D structure. The
following heuristic is usually applied to link the contact counts to the conformation: loci that are close
to each other in 3D space should have a higher contact value. Most of the existing methods that
operate on contact matrices are based on multidimensional scaling (MDS) and produce reconstructed
3D configurations in the form of a polygonal chain. However, none of them exploit the fact that the
target solution should be a smooth curve in 3D. The smoothness attribute is either ignored or indirectly
addressed via introducing highly non-convex penalties in the model. This typically leads to increased
computational complexity and instability of the reconstruction algorithm.
In this work we develop a novel approach for modeling chromatin
directly by a smooth curve. The performance of the methods is illustrated
on real Hi-C data computed for chromosome 20 and evaluated by means of orthogonal multiplex FISH
imaging.