Authors: Keith Watenpaugh, Debra Holland, Stephan Freer & Jim Stewart

Contact: Keith Watenpaugh, Physical and Analytical Chemistry,

The Upjohn Company, Kalamazoo, MI 49001, USA;

FINDKB provides two algorithms for determining the linear scale factor k and exponential thermal scale factor ΔB, which will place the observed structure factor data for two different derivatives on the same scale. The first derivative dataset is usually that of the 'parent' or 'native' protein while the second data set is that of a heavy atom isomorphous derivative. The first algorithm is a least-squares process using all the data in one group. The second algorithm uses the method of Singh and Ramaseshan (1966) in which a Wilson-like plot of a function of FP, F of the parent, FD, average FD(+) and FD(-) of the derivative against is used to obtain the scales k and ΔB between dataset 1 and dataset 2.

Calculation Algorithms

The First Algorithm

If a sandr line is not entered, the simple least-squares fit (ignoring the anomalous scattering signal) is used. The linear scale k, and the exponential scale ΔB are calculated by least-squares. These place the structure factor data of dataset 2 data on the same relative scale as dataset 1 data using the following expression:

F(1) = k exp(Δ) F(2)

The data may be specified either by dataset ID's or by lrrefl: item numbers (see the BDF section at the back of the manual). Data for both sets must be specified in the same way, i.e., ID's only or item numbers only. If data are specified by dataset IDs, F = 0.5 *[F(+) + F(-)] will be used if both F(+) and F(-) have been measured for a particular reflection, otherwise F is set to the member of the (+)/(-) pair that was measured. If data are specified by item number, this specifies the single quantity used for F (no averaging is possible). A reflection is skipped if data for either data set were not measured.

The Second Algorithm

Matthews (1966) and Singh and Ramaseshan (1966) have suggested a more elegant method for determining k and ΔB for the scaling between the native, or parent, dataset and the derivative dataset. In the following summary, these definitions will be used:

average F of the Friedel related pair, FP(+) and FP(-), for an (h,k,l) reflection.

average F of the Friedel related pair for the derivative crystal.

k linear F(rel) scale factor to place the derivative F's on the proper scale of the parent F's.

ΔB exponential scale factor to force the derivative F's to decay as a function of s in the same way as the parent F's.

In this method, the scale factors and anomalous scattering contribution are estimated from the equation

where

scale for the parent F

scale for the isomorph

ratio of the real to anomalous scattering signal 2|

parent structure factor amplitude

] / 2

ΔI []

The reflections are divided into small intervals of sinθ and the mean values used to generate Wilson-like plots. Least-squares fit of the intercept and its slope, as well as the scale factor k = / and ΔB are calculated.

Several passes through the scaling process my be necessary. A first pass using the simple least-squares method may be used first to get an approximate fit followed by the sandr method. Sometimes the very low order reflections should by ignored by setting a minimum sinθ/λ cutoff.

File Assignments

Reads reflection data from the input archive bdf

Optionally writes corrected data to the output archive bdf

Examples

FINDKB c2 c2pt bdf

In this typical case, the mean of F(+) and F(-) for data set C2PT will be scaled to the mean of F(+) and F(-) for data set C2. An output bdf will be produced.

FINDKB 2304 2314

F(-) will be scaled to F(+) for the second data set on the bdf. No output bdf will be written.

FINDKB 4304 4314 squared

F(-)² will be scaled to F(+)² for the fourth data set on the bdf. No output bdf will be written.

References

Matthews, B.W. 1966. The Determination of the Protein and Anomalously Scattering Heavy Atom Groups in Protein Crystals. Acta Cryst. 20, 230-239.

Singh, A.K., and Ramaseshan, S. 1966. The Determination of Heavy Atom Positions in Protein Derivatives. Acta Cryst. 21, 279-280.