Flexibility and rigidity index for chromosome packing, flexibility and dynamics analysis

The packing of genomic DNA from double helix into highly-order hierarchical assemblies has a great impact on chromosome flexibility, dynamics and functions. The open and accessible regions of chromosomes are primary binding positions for regulatory elements and are crucial to nuclear processes and biological functions. Motivated by the success of flexibility-rigidity index (FRI) in biomolecular flexibility analysis and drug design, we propose an FRI-based model for quantitatively characterizing chromosome flexibility. Based on Hi-C data, a flexibility index for each locus can be evaluated. Physically, flexibility is tightly related to packing density. Highly compacted regions are usually more rigid, while loosely packed regions are more flexible. Indeed, a strong correlation is found between our flexibility index and DNase and ATAC values, which are measurements for chromosome accessibility. In addition, the genome regions with higher chromosome flexibility have a higher chance to be bound by transcription factors. Recently, the Gaussian network model (GNM) is applied to analyze the chromosome accessibility and a mobility profile has been proposed to characterize chromosome flexibility. Compared with GNM, our FRI is slightly more accurate (1% to 2% increase) and significantly more efficient in both computational time and costs. For a 5Kb resolution Hi-C data, the flexibility evaluation process only takes FRI a few minutes on a single-core processor. In contrast, GNM requires 1.5 hours on 10 CPUs. Moreover, interchromosome interactions can be easily combined into the flexibility evaluation, thus further enhancing the accuracy of our FRI. In contrast, the consideration of interchromosome information into GNM will significantly increase the size of its Laplacian (or Kirchhoff) matrix, thus becoming computationally extremely challenging for the current GNM. The software and supplementary document are available at https://github.com/jiajiepeng/FRI_chrFle.