By the efficient generation of favorable interactions, and this prediction has been supported by recent docking-simulation studies. In contrast, less attention has been paid to the minor population of ring oligomers having simple n-fold rotational symmetry. In our statistical analysis of the PDB, we found that such ring complexes may contain even or odd numbers of subunits, and there is no bias toward even numbers. Ring-shaped oligomers have a wide variety of symmetry. Prime numbers of subunits give the “lowest” symmetry, and highly composite numbers having many divisors give the “highest” symmetry. A question then arises whether there is a biological or physical reason for rings to evolve with a prime number or highly composite number of subunits. To answer this question, we studied trp RNA binding attenuation protein as an illustrative case. TRAP is a ring-form homooligomer for which crystal structures are available of 11-mer and 12-mer forms. TRAP is found in various species of Bacillus, and plays a central role in the regulation of transcription and translation of the trp operon. The monomers of TRAP form a ring-form homo 11-mer with a minor component of 12-mer depending on the solution conditions. Each subunit of TRAP is composed of seven-stranded anti-parallel b-sheets and a bound tryptophan molecule. Recently, Tame et al. solved the crystal structure of 12-mer TRAP, which was produced artificially by joining the subunits of B. stearothermophilus TRAP in tandem with linkers of alanine residues. The crystal structure of TRAP. Allatom root mean square displacement between the monomer of the 11-mer and that of 12-mer was only 0.26 A˚. Despite their structural similarity, however, 12-mer TRAP is significantly less stable, as shown from the population of 12-mer in solution. In this study, we tried to address the influence of the differences in symmetry on the dynamics of the oligomers. The 12-mer structure was modeled with subunits carrying no peptide linkers to stabilize the 12-mer form. We performed 100 ns fully-atomistic MD simulations with an explicit water environment for both forms of TRAPs as well as normal mode analysis using an elastic network model. The normal mode analysis with group theory allows a clear description of symmetry in the thermal vibration. Based on the results of the normal mode analysis, we looked into the details of the fluctuations observed in the trajectories of the MD simulations. The vibrational dynamics of the two TRAPs, the wild-type the engineered 12-mer, were investigated by focusing on their differences in rotational symmetry. First, the normal mode analysis of the perfectly symmetric TRAP system with the group theoretical approach showed that the normal modes on the ring can be viewed as a stationary wave characterized by wave nodes, and that the low frequency normal modes tended to select relatively soft regions, the subunit interfaces, as the wave nodes. Because commensurable with 12 but not with 11, the wave nodes were located at the subunit interfaces in the 12-mer, but were frequently situated at the rigid core region of the subunits in the 11-mer. This observation was BYL719 PI3K inhibitor utilized to study the thermally-fluctuating pseudo-symmetric systems through fullyatomistic MD simulations. In the MD snapshots, we observed similar vibrational motions as in the normal modes. In particular, large subunit interfacial deformations in the 12-mer caused larger displacements of entire subunits, while in the 11-mer, wave modes located at the subunit cores caused larger. Generalization of these observations leads to a hypothesis that ring-form proteins of higher symmetry, with a highly composite number of subunits, undergo relatively large global deformations of the ring.