Alpha-helical coiled-coils are common protein structural motifs with varied mechanical roles, such as, tropomyosin in muscle contraction or neck-stalks of kinesins and myosins, in motor proteins. Using computer simulations, we characterized elastic properties of coiled-coils both, globally and locally. Normal mode analysis for global elastic properties revealed a buckling instability due to inherently present weak non-bonded forces. We characterized this using a critical buckling length (lc). For coiled-coils, lc was significantly less than their persistence length thereby governing the filament conformation. We also found that mutations to the hydrophobic residues at the knob-into-hole interface affect elasticity of coiled-coils significantly. We built a flexibility map of tropomyosin using a local fluctuation analysis and found regional variations in flexibilities due to such breaks in the knob-into-hole packing. Overall, flexibility varies by more than twofold and increases towards the C-terminal region of the molecule. Actin binding sites in zones and broken core regions due to acidic residues at the hydrophobic face such as, the Asp137 and the Glu218, are found to be the most labile with moduli for splay and broad face bending as 70 nm and 116 nm, respectively. Such variations in flexibility could be relevant to the tropomyosin function, especially for moving across the non-uniform surface of F-actin to regulate myosin binding. Non-claret disjunction (Ncd), is a Kinesin-14 family protein that walks to the microtubule's minus end. Although available structures show its alpha-helical coiled-coil neck in either pre- or post-stroke orientations, little is known about the transition between these two states. Using a combination of molecular dynamics simulations and structural analyses, we find that the neck travel is a guided diffusion involving sequential intermediate contacts with the motor head. The post-stroke is at a higher free-energy minimum than the pre-stroke. The importance of intermediate contacts correlates with the existing motility data including those of mutant Ncds and other members of the kinesin-14 family. While the forward motion has a ~4.5 kBT (kB: Boltzmann constant, T = 300 K) free energy barrier, recovery stroke goes nearly downhill in free energy. The hysteresis in forward and reverse neck motion energetics arises from the mechanical compliance of the protein, and together with guided diffusion, it may be key for the directed motility of Ncd. Although it is known that neighboring Ncds on a microtubule (MT) have an attractive interaction and a group of Ncds act cooperatively, the physical basis of neither this attraction nor the cooperativity is known. From structural analysis of Ncd neighbors on an MT lattice we find that steric hindrances between the coiled-coil neck-stalks of longitudinal neighbors drive synchrony among a group of Ncds on a single protofilament. Across lateral dimers, surface loop L2 of the motor-head (MH) that is not bound to the MT (unbound-MH) in a pre-stroke dimer, is seen to have strong attraction to the nucleotide pocket in the MH that is bound to MT (bound-MH) of its off-axis neighbor. Such an attraction will however impede the motility in both the dimers. We hence propose rules that drive motor binding to an MT site in the presence of immediate neighbors such that motility of the group is not compromised. The unbound-MH, whose role in the walking step of an Ncd was unclear, is thus seen to regulate MT decoration.