New expression of bimodal phase distributions in direct-method phasing of protein single-wavelength anomalous diffraction data

One of the essential points of the direct-method single-wavelength anomalous diffraction (SAD) phasing for proteins is to express the bimodal SAD phase distribution by the sum of two Gaussian functions peaked respectively at phi(h)'' + vertical bar Delta phi(h)vertical bar and phi(h)'' - vertical bar Delta phi(h)vertical bar. The probability for Delta phi(h) being positive (P(+)) can be derived based on the Cochran distribution in direct methods. Hence the SAD phase ambiguity can be resolved by multiplying the Gaussian function peaked at phi(h)'' - vertical bar Delta phi(h)vertical bar with P(+) and multiplying the Gaussian function peaked at phi(h)'' - vertical bar Delta phi(h)vertical bar with P(-) (= 1 - P(+)). The direct-method SAD phasing has been proved powerful in breaking SAD phase ambiguities, in particular when anomalous-scattering signals are weak. However, the approximation of bimodal phase distributions by the sum of two Gaussian functions introduces considerable errors. In this paper we show that a much better approximation can be achieved by replacing the two Gaussian functions with two von Mises distributions. Test results showed that this leads to significant improvement on the efficiency of direct-method SAD-phasing.