Characterization of the spatiotemporal properties of the chromatin is essential to gaining insights into the physical bases of gene co-expression, transcriptional regulation, and epigenetic modifications. The Gaussian Network Model (GNM) has proven in recent work to serve as a useful tool for modeling chromatin structural dynamics, using Hi-C data. We will present the methodology for exploring collective dynamics of chromosomal structures at hierarchical levels of resolution, from single gene loci to topologically associating domains or entire chromosomes, using the GNM. The GNM permits us to identify long-range interactions between gene loci, shedding light on the role of cross-correlations between distal regions of the chromosomes in regulating gene expression. Notably, GNM analysis performed across diverse cell lines highlights the conservation of the global/cooperative movements of the chromatin across different types of cells. Variations driven by localized couplings between genomic loci, on the other hand, underlie cell differentiation, underscoring the significance of the 4D properties of the genome in defining cellular identity. Finally, we demonstrate the close relation between the cell-type dependent mobility profiles of gene loci and their gene expression patterns, underscoring the role of chromosomal 4D features in defining cell-specific differential expression of genes.