GENERAL EXPRESSION FOR PROBABILISTIC ESTIMATION OF MULTIPHASE STRUCTURE-INVARIANTS IN THE CASE OF A NATIVE PROTEIN AND MULTIPLE DERIVATIVES- APPLICATION TO ESTIMATES OF THE 3-PHASE STRUCTURE-INVARIANTS
Nh. Hu et Ys. Liu, GENERAL EXPRESSION FOR PROBABILISTIC ESTIMATION OF MULTIPHASE STRUCTURE-INVARIANTS IN THE CASE OF A NATIVE PROTEIN AND MULTIPLE DERIVATIVES- APPLICATION TO ESTIMATES OF THE 3-PHASE STRUCTURE-INVARIANTS, Acta crystallographica. Section A, Foundations of crystallography, 53, 1997, pp. 161-167
Concise probabilistic formulae with definite crystallographic implicat
ions are obtained from the distribution for eight three-phase structur
e invariants (3PSIs) in the case of a native protein and a heavy-atom
derivative [Hauptman (1982). Acta Cryst. A38, 289-294] and from the di
stribution for 27 3PSIs in the case of a native and two derivatives [F
ortier, Weeks & Hauptman (1984). Acta Cryst. A40, 646-651]. The main r
esults of the probabilistic formulae for the four-phase structure inva
riants are presented and compared with those for the 3PSIs. The analys
is directly leads to a general formula of probabilistic estimation for
the n-phase structure invariants in the case of a native and m deriva
tives. The factors affecting the estimated accuracy of the 3PSIs are e
xamined using the diffraction data from a moderate-sized protein. A me
thod to estimate a set of the large-modulus invariants, each correspon
ding to one of the eight 3PSIs, that has the largest \Delta\ values an
d relatively large structure-factor moduli between the native and deri
vative is suggested, which remarkably improves the accuracy, and thus
a phasing procedure making full use of all eight 3PSIs is proposed.