Computing 3D chromatin configurations from contact probability maps by Inverse Brownian Dynamics

The three-dimensional organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state -- accessibility and the amount of gene expression -- of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In the present work, an Inverse Brownian Dynamics (IBD) method has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the -globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. We also address the normalization problem of the contact count matrix and argue that extra measurements of polymer properties such as radius of gyration may be required to resolve the problem.\n\nSIGNIFICANCEChromosome conformation capture experiments such as 5C and Hi-C provide information on the contact counts between different segments of chromatin, but not the interaction strengths that lead to these counts. Here a methodology is proposed by which this inverse problem can be solved, namely, given the contact probabilities between all segment pairs, what is the pair-wise interaction strength that leads to this value? With the knowledge of pair-wise interactions determined in this manner, it is then possible to evaluate the 3D organization of chromatin and to determine the true relationship between contact probabilities and spatial distances.