DETERMINATION OF 3D VIRAL STRUCTURE FROM SOLUTION X-RAY SCATTERING. Yibin Zheng, Peter C. Doerschuk, School of Electrical and Computer Eng., Purdue Univ., West Lafayette, IN 47907 USA, John E. Johnson, Dept. of Molecular Biology, The Scripps Research Inst., La Jolla, CA 92037 USA, yibin@ecn.purdue.edu, doerschu@ecn.purdue.edu, j ackj @scripps.edu
A new method for determining the low-resolution 3D structure of icosahedrally-symmetric viruses from solution x-ray scattering is proposed and demonstrated on cowpea mosaic virus (CpMV) data. In spherical coordinates, the electron density [[rho]](x) is represented as a sum of icosahedral harmonics Tl,n([[theta]],[[phi]]) with radially-dependent weights Al,n(r). The Tl,n([[theta]],[[phi]]) are used because, for any choice of Al,n(r)., the resulting [[rho]](x) is icosahedrally-symmetric. The Al,n(r) are represented as a sum of spherical Bessel functions zl([[alpha]]l,pr) with weights cl,n,p. The zl([[alpha]]l,pr) are used because the Fourier transform of zl([[alpha]]l,pr) can be computed analytically. Linear combinations of zl([[alpha]]l,pr)[[opthyphen]]are used such that [[rho]](x) is non-zero only between fixed inner (R-) and outer (R+) radii where the inner radius can be non-zero (e.g., empty particles). The two radii (R- and R+) and the weights cl,n,p are the only parameters in the model and the model can represent any icosahedrally-symmetric [[rho]](x). The major short-coming of this representation is that it does not restrict [[rho]](x) to be positive. To determine the parameters from the experimental data, we use the Levenberg-Marquardt method to minimize # k8|I(k)--I(k)|2dkI(k) is the experimental data and I(k) is the predicted scattering pattern as a function of cl,n,p. We have applied this method to experimental data (0.004279-0.020853Å-1) for CpMV resulting in 3D reconstructions at 30Å resolution which accurately follow the known atomic resolution structures. In comparison to our previous work (ACA-95 Abstract W155; Biophysical J. 69(2):619-639, August 1995), the optimization required here is easier to compute and the model can represent a general [[rho]](x). This work was supported by NSF grant BIR9513594.