Reconstruction of polymer structures from contact maps with Deep Learning

For any polymer, the euclidean distance map (\textbf{D}) is defined as a matrix where $D_{ij}=d_{ij}^2$ where $d_{ij}$ is the distance between $i$ and $j$. This contains all the necessary information to re-create the structure. However certain biological experiments, especially Hi-C or NOESY NMR, are only able to provide us with a list of monomers that are within a certain cut-off distance ($r_c$). This is called a contact-map (\textbf{C}). We propose a deep auto-encoder that is able to reconstruct \textbf{D} when only provided with \textbf{C}. We test this network on ensembles of structures generated by MD simulations. We show that a deep auto-encoder is capable of reconstructing polymer structures simply from the contact map information. We propose that this network can be applied to single-cell Hi-C maps to reconstruct chromosome structures in individual cells.