Dynein is a cytoskeletal molecular motor protein that moves along the microtubule (MT) and transports various cellular cargos during its movement. Using standard Molecular Dynamics (MD) simulation, Principle Component Analysis (PCA), and Normal Mode Analysis (NMA) methods, this investigation studied large-scale movements and local interactions of dynein's Microtubule Binding Domain (MTBD) when bound to tubulin heterodimer subunits. Examination of the interactions between the MTBD segments, and their adjustments in terms of intra- and intermolecular distances at the interfacial area with tubulin heterodimer, particularly at α-H16, β-H18, and β-tubulin C-terminal tail (CTT), was the main focus of this study. The specific intramolecular interactions, electrostatic forces, and the salt bridge residue pairs were shown to be the dominating factors in orchestrating movements of the MTBD and MT interfacial segments in the dynein's low-high-affinity binding modes. Important interactions included β-Glu447 and β-Glu449 (CTT) with Arg3469 (MTBD-H6), Lys3472 (MTBD-H6-H7 loop) and Lys3479 (MTBD-H7); β-Glu449 with Lys3384 (MTBD-H8), Lys3386 and His3387 (MTBD-H1). The structural and precise position, orientation, and functional effects of the CTTs on the MT-MTBD, within reasonable cut-off distance for non-bonding interactions and under physiological conditions, are unavailable from previous studies. The absence of the residues in the highly flexible MT-CTTs in the experimentally solved structures is perhaps in some cases due to insufficient data from density maps, but these segments are crucial in protein binding. The presented work contributes to the information useful for the MT-MTBD structure refinement.