Structural fluctuations of a protein are essential for a protein to function and fold. By using molecular dynamics (MD) simulations of the model α/β protein VA3 in its native state, the coupling between the main-chain (MC) motions [represented by coarse-grained dihedral angles (CGDAs) γ(n) based on four successive C(α) atoms (n - 1, n, n + 1, n + 2) along the amino acid sequence] and its side-chain (SC) motions [represented by CGDAs δ(n) formed by the virtual bond joining two consecutive C(α) atoms (n, n + 1) and the bonds joining these C(α) atoms to their respective C(β) atoms] was analyzed. The motions of SCs (δ(n)) and MC (γ(n)) over time occur on similar free-energy profiles and were found to be subdiffusive. The fluctuations of the SCs (δ(n)) and those of the MC (γ(n)) are generally poorly correlated on a ps time-scale with a correlation increasing with time to reach a maximum value at about 10 ns. This maximum value is close to the correlation between the δ(n)(t) and γ(n)(t) time-series extracted from the entire duration of the MD runs (400 ns) and varies significantly along the amino acid sequence. High correlations between the SC and MC motions [δ(t) and γ(t) time-series] were found only in flexible regions of the protein for a few residues which contribute the most to the slowest collective modes of the molecule. These results are a possible indication of the role of the flexible regions of proteins for the biological function and folding.