Computational Straightening of Images of Curved Macromolecular Helices by Cubic Spline Interpolation Facilitates Structural Analysis By Fourier Methods

Powerful methods based on Fourier analysis have been devised for deducing the helical symmetries of macromolecular filaments and reconstructing their 3-dimensional density maps from electron images of negatively stained specimens. However, their applicability is restricted by the requirement that the particles be precisely straight. Only a limited number of specimens are sufficiently rigid to meet this constraint. Filamentous particles that exhibit varying degrees of flexibility constitute a much wider class of specimens, but their curvature impairs the coherence of their diffraction patterns. A solution to this problem is afforded by computational a posteriori straightening, effected by interpolating the digitized images on to a curvilinear coordinate system defined by the curve described by the particle axis. Here, we describe an algorithm for this purpose based on natural cubic spline interpolation, and illustrate its operation with model data and as applied to a flexuous biological specimen.