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To design anticancer drug Taxol working more efficiently, looking at details of microtubules' dynamic behavior has become more important for researchers worldwide. According to this issue, dynamic stability analysis of microtubule-associated proteins (MAPs) using the state-space technique based on three-dimension elasticity theory is presented. Besides, the MAPs structure is under various body pressure. The state-space technique is applied along the radial direction, and the differential quadrature method (DQM) along the axial direction in the case of another end supports. The novelty of the current study considers the various boundary conditions for MAPs structure and body pressure, which is implemented on the proposed model using the theory of Three-dimension (3D) elasticity. The validity of applied solutions is examined by comparing results with those of available literature, experimental data, and molecular dynamic (MD) simulation outcomes. A thorough parametric investigation is conducted on the effect of initial stress, boundary conditions, and geometry of the shell (such as mid-radius to thickness and length to mid-radius ratios) on the dynamic stability of the MAPs structures under initial stress. [ABSTRACT FROM AUTHOR]