# Difference Patterson map

### From Online Dictionary of Crystallography

Carte de différence de Patterson (*Fr*). Differenz-Patterson-Karte (*Ge*). Mappa di differenza di Patterson (*It*). Mapa de Patterson de diferencia (*Sp*).

## Definition

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 positions can be determined directly from the Patterson function calculated using measured structure-factor amplitudes. For proteins, there are too few heavy atoms for this approach to be successful. However, if an isomorphous derivative crystal is available (*i.e.* one whose symmetry and dimensions and contents, with the exception of heavy-atom addition, are minimally changed), a Patterson map of derivative ([math]F_{PH}[/math]) minus native ([math]F_P[/math]) 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 [math]|F^2_{PH} - F^2_P|[/math].

In practice, protein crystallographers normally calculate a **modulus difference-squared synthesis**, also known as an **isomorphous difference Patterson**, using coefficients [math](|F_{PH}| - |F_P|)^2[/math].

## See also

- Patterson and molecular-replacement techniques, and the use of noncrystallographic symmetry in phasing. L. Tong, M. G. Rossmann and E. Arnold.
*International Tables for Crystallography*(2008). Vol. B, ch. 2.3, pp. 244-281