Calculation of pair distribution functions from small-angle X-ray scattering protein data by direct transform

In a small-angle X-ray scattering analysis of protein molecules in solution the calculation of the pair distribution function, P ( r ), is invariably performed by an indirect Fourier transform. This approach models a P ( r ) to fit the available intensity data, I ( q ). The determination of P ( r ) via a direct transform from I ( q ) has been dismissed as unworkable since the range of q that is experimentally measured is necessarily incomplete. Here, it is shown that, provided suitable measures are taken to estimate unmeasured low-resolution data and avoid a sharp data truncation at the high-resolution data limit, the appearance of significant artifacts in the resulting P ( r ) may be circumvented. Using several examples taken from the Small Angle Scattering Biological Data Bank, it is demonstrated that the P ( r ) obtained by a direct transform are in close agreement with the P ( r ) obtained using the popular indirect transform program GNOM .