# Difference Patterson map

An application of Patterson methods for solution of crystal structures, typically proteins with heavy-atom derivatives, where the Patterson function is calculated using structure-factor coefficients based on the difference between the heavy-atom derivative and the native molecule.

### Discussion

Patterson methods for determining diffraction phases depend on the symmetries of interatomic vectors that show up as peaks in a three-dimensional map of the Patterson function. For small molecules containing a heavy atom, the heavy-atom *i.e.* one whose symmetry and dimensions and contents, with the exception of heavy-atom addition, are minimally changed), a Patterson map of derivative (\(F_{PH}\)) minus native (\(F_{P}\)) structure factors will be dominated by the vectors between the heavy atoms, and thus allow a solution of the coordinates of the heavy atoms.

A true difference Patterson function, representing the difference between the Patterson of the derivative minus the Patterson of the native protein, should be calculated using as coefficients:

\[\left | F^2 _{PH}-F^2_P \right |\]

In **modulus difference-squared synthesis**, also known as an **isomorphous difference Patterson**, using coefficients \[(|F_{PH}-F_P|)^2\].

### See also

- Patterson and molecular-replacement techniques. M. G. Rossmann and E. Arnold.
*International Tables for Crystallography*(2006). Vol. B, ch. 2.3, pp. 235-263