Extending the Debye scattering equation for diffraction from a cylindrically averaged group of atoms: detecting molecular orientation at an interface.

The Debye scattering equation is now over 100 years old and has been widely used to interpret diffraction patterns from randomly oriented groups of atoms. The present work develops and applies a related equation that calculates diffraction intensity from groups of atoms randomly oriented about a fixed axis, a scenario that occurs when molecules are oriented at an interface by the presentation of a binding motif as in antibody binding. Using an example biomolecule, the high level of sensitivity of the diffraction pattern to the orientation of the molecule and to the direction of the incident beam is shown. The use of the method is proposed not only for determining the orientation of molecules in biosensors and at membrane interfaces, but also for determining molecular conformation without the need for crystallization.