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Background: Single-molecule microscopic experiments can measure the mechanical response of proteins to pulling forces applied externally along different directions (inducing different residue pairs in the proteins by uniaxial tension). This response to external forces away from equilibrium should in principle, correlate with the flexibility or stiffness of proteins in their folded states. Here, a simple topology-based atomistic anisotropic network model (ANM) is shown which captures the protein flexibility as a fundamental property that determines the collective dynamics and hence, the protein conformations in native state. Methods: An all-atom ANM is used to define two measures of protein flexibility in the native state. One measure quantifies overall stiffness of the protein and the other one quantifies protein stiffness along a particular direction which is effectively the mechanical resistance of the protein towards external pulling force exerted along that direction. These measures are sensitive to the protein sequence and yields reliable values through computations of normal modes of the protein. Results: ANM at an atomistic level (heavy atoms) explains the experimental (atomic force microscopy) observations viz., different mechanical stability of structurally similar but sequentially distinct proteins which, otherwise were implied to possess similar mechanical properties from analytical/theoretical coarse-grained (backbone only) models. The results are exclusively demonstrated for human fibronectin (FN) protein domains. Conclusions: The topology of interatomic contacts in the folded states of proteins essentially determines the native flexibility. The mechanical differences of topologically similar proteins are captured from a high-resolution (atomic level) ANM at a low computational cost. The relative trend in flexibility of such proteins is reflected in their stability differences that they exhibit while unfolding in atomic force microscopic (AFM) experiments. [ABSTRACT FROM AUTHOR]