UNIQUENESS AND THE ABINITIO PHASE PROBLEM IN MACROMOLECULAR CRYSTALLOGRAPHY

The crystallographic phase problem is indeterminate in the absence of additional chemical information. A successful ab initio approach to th e macromolecular phase problem must employ sufficient chemical constra ints to limit the solutions to a manageably small number. Here we show that commonly employed chemical constraints - positivity, atomicity a nd a solvent boundary - leave the phase problem greatly underdetermine d for Fourier data sets of moderate (2.5-3.0 angstrom) resolution. Ent ropy maximization is also beset by multiple false solutions: electron- density maps are readily generated which satisfy the same Fourier ampl itude constraints but have higher entropies than the true solution. We conclude that a successful ab initio approach must make use of high-r esolution Fourier data and/or stronger chemical constraints. One such constraint is the connectivity of the macromolecule. We describe a rap id algorithm for measuring the connectivity of a map, and show its uti lity in reducing the multiplicity of solutions to the phase problem.