# Presentation: 014220

## Considerations in Collection of Anomalous Data

- Bill Furey

## What on earth does “anomalous” mean?

***English***: *“**Not conformed to rule or system; deviating from normal**”*
***Diffraction***: Anomalous Scattering is not simply dependent on a free-electron model for the atom.  Instead photons that have an energy that is near that of a transition of an atom will experience a phase and amplitude shift during scattering.

## Isomorphous Replacement with heavy atoms
MAD/SAD, a variant of IR
Molecular replacement if we have a decent model.

- MAD/SAD, a variant of IR
- Molecular replacement if we have a decent model.

**How do we solve structures?****  We must somehow estimate phases so we can perform the inverse Fourier transform, the Fourier synthesis.**

## Perutz’s Fundamental Idea: Isomorphous Replacement

- We find that, for some things, we can approximate  |FH| with |FPH| - |FP|.  This often suffices for us to solve for the positions of the heavy atom as if it were a small-molecule structure.

## So for some particular reflection and a particular heavy atom, we can begin to find the phase:

**So for some particular reflection and a particular heavy atom, we can begin to find the phase:**

- Knowing the position of the heavy atom allows us to calculate FH.  Then we use FP = FPH + (-)FH to show that the phase triangles close with a **two-fold ambiguity**, at G and at H.  There are several ways to resolve the ambiguity.

## One way to resolve the ambiguity is to use a second isomorphous heavy-atom derivative.

## A second technique involves use of anomalous (resonant) scattering from a heavy atom.

**A second technique involves use of anomalous (resonant) scattering from a heavy atom.**

- In this case, when the photon energy is at a transition energy of a heavy atom, the resonance between the electrons on the heavy atom and the x-rays cause a phase and amplitude shift.  The symmetry of diffraction (from the front *vs *back of the Bragg planes) is broken.  **Friedel’s Law is broken!  **This can be measured and used.

## Excitation Scans

**One way to represent this resonance** is plots of the shifts in the real part (f ’) and imaginary part (f ”) of the scattering of x-rays as a function of the photon energy.

*From Ramakrishnan’s study of GH5 *

- real

- imaginary

- f ’

- f o

- Scattering Power

**Excitation Scans**
- We can observe the Δf” by measuring the **absorption** of the x-rays by the atom. Often we us the fluorescence of the absorbing atom as a **measure of absorptivity**. That is, we measure an **“excitation” **spectrum.

- f ”

## How to get Δf ’?

**One way to represent this resonance** is plots of the shifts in the real part (f’) and imaginary part (f”) of the scattering of x-rays as a function of the photon energy.

*From Ramakrishnan’s study of GH5 *

- real

- imaginary

- f’

- fo

- f”

- Scattering Power

**How to get ****Δ****f ****’****?**
- The real, “dispersive” component is calculated from Δf” by the Kramers-Kronig relationship.  Very roughly, Δf’ is the negative first derivative of Δf”.

- f’

## One way to represent this resonance is plots of the shifts in the real part (f’) and imaginary part (f”) of the scattering of x-rays as a function of the photon energy.

**One way to represent this resonance** is plots of the shifts in the real part (f’) and imaginary part (f”) of the scattering of x-rays as a function of the photon energy.

*From Ramakrishnan’s study of GH5 *

- real

- imaginary

- f’

- fo

- f”

- Scattering Power

## How to get f ’?

- The “real,” dispersive component is calculated from f” by the Kramers-Kronig relationship.  Very roughly, it’s the negative first derivative of f”.

**Excitation Scans**
- We can observe the Δf” by measuring the **absorption** of the x-rays by the atom. Often we us the fluorescence of the absorbing atom as a **measure of absorptivity**. That is, we measure an **“excitation” **spectrum.

## The tunability of the synchrotron source allows us to choose precisely the energy (wavelength) we need.

**The tunability of the synchrotron source allows us to choose precisely the energy (wavelength) we need.**

## Or the use of very low energy (Cr anode at 2.3Å) enhances the natural anomalous signal for measurement of anomalous data without a synchrotron.

## One can see how to choose wavelengths to get large phase contrast for MAD phasing

*Spectrum from Phizackerly, Hendrickson, et al. Study of Lamprey Haemoglobin.*

**One can see how to choose wavelengths to get large phase contrast for MAD phasing**

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**Maximum Imaginary Signal**

**Maximum Real Signal**

## This Multiwavelength Anomalous Diffraction method often gives very strong phase information and is the source of many new structures.

**This ****M****ultiwavelength ****A****nomalous ****D****iffraction method often gives very strong phase information and is the source of many new structures.**

## What about Single-wavelength Anomalous Diffraction phasing – SAD? 

- There’s aleady a lot of phasing information in a strong Anomalous signal.
- It’s essentially like Single Isomorphous Replacement – one must resolve the phase ambiguity somehow.

- One can resolve it with other phasing information, like solvent flattening or non-crystallographic symmetry.
- This works only with VERY accurate data.
**How do we measure accurate data for either MAD or SAD?**

## Measuring accurate Anomalous Diffraction Data

- Think about how you’ll measure the F**h** and F**-h** data:
***Use the Friedel Flip***: take one sweep, say 0-60, then flip by 180 deg and do it again, 180-240. (Some call this the “inverse beam.”)

- The 0-1 image is identical to the 180-181 image, except they’re reversed by a mirror perpendicular to the rotation axis.

## Align the crystal so a mirror plane in the diffraction pattern is perpendicular to the rotation axis.  The reflections across the mirror will be equivalent to Fh and F-h although they’re not precisely that (maybe h k l and h –k l).

- Pay special attention to avoiding systematic errors:
- Damage – **don’t take data from dead crystals; change the crystal.**
- Absorption – (**especially for long wavelengths!!**) keep the crystal mount small; use the physical symmetry of the crystal to make absorption similar for F**h**** **and F**-h**
- Different crystal volumes exposed – make sure that the part of the crystal in the beam is the same for F**h**** **and F**-h**

## “Correcting” systematic errors

- The best way is to measure the same data *again* in some symmetrically equivalent way – measure “redundant” data.
- The first thing is to take a full 360° rotation of data.
- The next thing to do is to realign the x-tal to rotate about a different axis.
- Bend the loop
- Use a mini-kappa orienter

***Much more useful ***than taking more than 360 degrees!

## The reason SAD phasing works

- The sources, detectors, and diffractometers are extremely good – giving accurate as well as precise data.
- The software is very mature.
- Data reduction programs are excellent, making the most of weak data.
- Methods to find and refine heavy atoms make the best of weak signals.
- The phase-correction methods embedded in solvent flattening and non-crystallographic symmetry averaging are amazingly effective.