A new algorithm to align three-dimensional maps of helical structures

By subtracting one three-dimensional (3-D) map from another, one can calcul ate a difference map that can reveal structural changes, such as conformati onal changes, not detectable by eye. Furthermore, statistical significances can be assigned to such differences. The validity of the features in the d ifference map, however, depends on the alignment of the two maps; that is, one needs to align the two 3-D maps so that densities corresponding to equi valent parts of the structures are at the same coordinates. An existing met hod using the Fourier-Bessel coefficients G(n,1)(R) is commonly used for th e alignment of maps of helical structures. This procedure works well if the two maps have most features in common. But if they do not, it is difficult to control which features are used in the alignment procedure since the co ntributions from different features in the map are not easy to separate. We devised a procedure using the radial transform of G(n,1()R) (i.e., g(n,1)( r)), which retains the powerful mathematical advantage of the Fourier-Besse l representation of the data and which provides the ability to select the r adial features used in the alignment procedure. We applied the new method t o 3-D maps of F-actin and F-actin decorated with various myosin motor const ructs. Whereas the procedure using G(n,1)(R) failed to align myosin-S1 deco rated actin to undecorated actin, the new procedure accurately aligned maps . (C) 1999 Elsevier Science B.V. All rights reserved.