Length-Dependent Collective Vibrational Dynamics in Alpha-Helices

Functions of protein molecules in nature are closely associated with their well-defined three-dimensional structures and dynamics in body fluid. So far, many efforts have been made to reveal the relation of protein structure, dynamics, and function, but the structural origin of protein dynamics, especially for secondary structures as building blocks of conformation transition, is still ambiguous. Here we theoretically uncover the collective vibrations of elastic poly-alanine alpha-helices and find vibration patterns that are distinctively different over residue numbers ranging from 20 to 80. Contrary to the decreasing vibration magnitude from ends to the middle region for short helices, the vibration magnitude for long helices takes the minimum at approximately 1/5 of helix length from ends but reaches a peak at the center. Further analysis indicates that major vibrational modes of helical structures strongly depend on their lengths, where the twist mode dominates in the vibrations of short helices while the bend mode dominates the long ones analogous to an elastic Euler beam. The helix-coil transition pathway is also affected by the alternation of the first-order mode in helices with different lengths. The dynamic properties of the helical polypeptides are promising to be harnessed for de novo design of protein-based materials and artificial biomolecules in clinical treatments.