Correlated dipolar and dihedral fluctuations in a protein

Correlation between dihedral fluctuations is a possible way to understand coordination between various amino acid residues of the protein. The nanosecond timescales of correlated fluctuations of dihedral angle do not allow direct probing by experimental methods. However, NMR experiments probe dipolar fluctuations given in terms of cross correlated relaxation (CCR) rates, expressed as zero frequency spectral density function (J) of the fluctuations of the mutual orientation of two spatially separated dipole vectors. Here we illustrate the correlation of protein dipolar and dihedral angle using molecular dynamics simulation of protein Ubiquitin (Ub) and GB3. We calculate CCR rates between protein bond vector from simulation and compare with CCR data obtained from NMR experiments. A good correlation between theoretical and experimental values is found. We further show that the zero frequency spectral functions of backbone dihedral{psi} auto-correlation function and dipole orientation fluctuations show strong correlations. These correlations are not sensitive to protein and forcefield parameters. Hence, CCR may act as a marker for protein backbone dihedral fluctuations.