ISa

CORRECT is the scaling step of XDS.

An estimate for the overall quality of an experimental setup

A single number that depends on the overall quality of an experimental setup (beam, crystal, spindle, detector, cryo, software, ...) is the upper limit of I/sigma(I) for any reflection in your dataset - even if your crystal is great, all reflections are bound to be worse than that.

This number is called [math]\displaystyle{ {I/Sigma(I)}^{asymptotic} }[/math] ([Diederichs, Acta Cryst. (2010). D66, 733-740 http://dx.doi.org/10.1107/S0907444910014836])

What is that number? Scaling procedures (like the ones used in XDS, SCALA, SCALEPACK and DSCALEAVERAGE) scale (or rather, inflate) the variances of individual observations such that they match the experimental spread of symmetry-related observations. To this end, two contributions to the variance of a reflection are added: the first component is random error, and the other component is systematic error. The two values a and b appearing in the formula v(I)=a*(v0(I)+b*I^2) are printed out by CORRECT. a scales the random error component, a*b scales the systematic error component. For strong and well-measured reflections, the variance is dominated by the systematic error a*b*I^2 that is introduced by any beam /spindle / detector /cryo or other instability or malfunction. For weak reflections, a*v0(I), the variance from counting statistics, dominates.

Versions of XDS before May 10, 2010

A Unix command to obtain [math]\displaystyle{ {I/Sigma(I)}^{asymptotic} }[/math] from CORRECT.LP is

awk '/a *b *I/{getline;print ($1*($2+4e-4))^-0.5}' CORRECT.LP

The command just finds the line " a b INPUT DATA SET" in CORRECT.LP, grabs the values of "a" and "b" from the next line, and prints out 1/sqrt(a*(b+0.0004)).

The 0.0004 stems from the fact that the INTEGRATE step does its own adjustment of the variances, and the two adjustments (in INTEGRATE and CORRECT) have to be combined.

Versions of XDS since May 10, 2010

Newer versions print out [math]\displaystyle{ {I/Sigma(I)}^{asymptotic} }[/math] as "ISa".

As you can see from the formula, low values of a and b are good in the sense that a high upper limit of I/sigma(I) results. If e.g. the crystal is badly split or broken, or reflections are too close on the detector, or the data reduction is not good (wrong parameters), then the values of a and b are elevated.

If your crystal is good (and no matter how good your crystal is!), then a and b will reflect the quality of the other components of the experimental setup (e.g. beamline stability).

Practical considerations

In practice, both crystal quality and beamline quality limit the value of [math]\displaystyle{ {I/Sigma(I)}^{asymptotic} }[/math] . A good crystal (even with elevated mosaicity and medium resolution) should give a high value on a good beamline.

I have seen values around 15-20 for good crystals that still allowed my to solve a MAD structure, but that required high multiplicity of observations. Values around 30 allowed me to solve a sulfur-SAD structure at medium resolution (diffraction to 2.3 A, anomalous signal to 3 A). I have also seen a value around 40 for Z. Dauter's 0.98A Proteinase K (2ID8) sulfur-SAD data from J. Holton's APS/22-ID beamline, and recently even higher values were obtained at the SLS, beamline X06SA, with a Pilatus detector.

On the other hand, I have sometimes obtained values less than 10 with good test crystals. It is always good to discuss this with the people who are responsible for the beamline. They might know what is broken, or might be able to find out what went wrong.

A low [math]\displaystyle{ {I/Sigma(I)}^{asymptotic} }[/math] may be compensated by high multiplicity, at the expense of radiation damage. Conversely, high multiplicity is not needed to solve a structure, if the data have a high [math]\displaystyle{ {I/Sigma(I)}^{asymptotic} }[/math]. For molecular replacement and refinement, a high value of [math]\displaystyle{ {I/Sigma(I)}^{asymptotic} }[/math] is not strictly needed (but the maps are better with better data!).