Computing 3D Chromatin Configurations from Contact Probability Maps by Inverse Brownian Dynamics

Abstract

The three-dimensional (3D) organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state-accessibility and 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, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In this work, a novel inverse Brownian dynamics method based on a coarse-grained bead-spring chain model 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 a-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. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.

Heterogeneous interactions and polymer entropy decide organization and dynamics of chromatin domains

“…Given that we have the optimal interaction strengths that satisfy the experimentally known contact probability constraints [29], we can answer the following important question: Are the measurable properties of a given bead-pair (e.g. r 5,30 ) solely determined by the interaction between those two particular beads ( ϵ 5,30 ) or are they influenced by the interactions among other bead-pairs as well?…”

“…We consider chromatin as a bead spring chain having optimal intra-chromatin interactions derived from 5C and Hi-C data using an Inverse Brownian Dynamics (IBD) algorithm [30]. The total energy of the chromatin bead spring chain, made of N beads, is U = U S + U SDK where is the spring potential between the adjacent beads i and ( i + 1), r i is the position vector of bead i, r 0 is the natural length and H is the stiffness of the spring [53].…”

“…Complementing recent experimental efforts, there have been several computational studies investigating chromatin organization. [18,19,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Many studies carried out "forward" simulations where the chromatin structure is predicted assuming a set of interaction strengths [42].…”

“…One requires an inverse method that can obtain the optimal interaction strengths such that experimentally known properties are recovered. Only a few studies has been carried out to optimize the interaction energy parameters to converge to the experimental contact [31, 48] We have recently developed an Inverse Brownian Dynamics (IBD) method to extract potential energy parameters that are consistent with HiC/5C experiments [30]. The method explicitly computes intra-chromatin interactions for every segment pair.…”

“…However, to simulate the formation and dynamics of domains, one requires optimal interaction strength parameters such that experimentally known properties are recovered. We have recently developed an Inverse Brownian Dynamics (IBD) method to extract potential energy parameters that are consistent with HiC-like experiments [29]. Using the intra-chromatin interactions computed from this method, in this work we go beyond the static picture and study chromatin fluctuations and dynamics perturbing epigenetic states.…”