Anharmonicity and Debye-Waller Factors in Biomolecules

Abstract

It is common practice to use Debye Waller factors [exp(—W)] in the interpretation of x-ray patterns or to infer atomic motions in biomolecules for comparison with molecular dynamics simulations. Usually W is taken to be proportional to (u ²), which in turn is taken to be proportional to temperature T. For any real system both of these assumptions are wrong in principle, since they depend entirely on purely harmonic potentials. As a practical matter in many cases anharmonicity is weak, but these are cases where significant structural accommodations do not take place. However, when dealing with repuckering of the ribose in DNA or ground state multiplicity in biomolecular conformational motions the role of anharmonicity must be addressed properly; quasi-harmonic methods may be both quantitatively and qualitatively misleading. This is a short review of the theory of the Debye Waller factor, particularly in the classical limit.