🧬 Lecture Summary — SAD Phasing, Anomalous Scattering & Density Maps

This lecture focuses on modern experimental phasing methods in X-ray crystallography, especially:

• Single-wavelength anomalous diffraction (SAD)
• Anomalous scattering physics
• Absorption edges & wavelength tuning
• Phase ambiguity & Harker construction
• Density modification & map improvement
• Difference maps used during model building

These concepts are core for solving the phase problem and ultimately obtaining a 3D electron density map of a protein.

⭐ 1. Modern Ways to Solve the Phase Problem

Historically, isomorphous replacement was used, but today the two dominant approaches are:

✅ Molecular Replacement (MR)

• Uses a known homologous structure as a model.
• Only requires a native dataset.
• Phases are calculated by:
  • Finding rotation
  • Finding translation
  • Using Patterson correlations.

✅ SAD (Single-wavelength anomalous diffraction)

• Experimental phasing method.
• Requires a heavy atom inside the protein (e.g., selenium).
• Only one diffraction dataset is needed.

These two methods dominate modern structure determination.

⚡ 2. X-ray Absorption — Why Heavy Atoms Matter

All materials absorb X-rays.

Important trends:

• Absorption decreases with increasing X-ray energy (shorter wavelength).
• Heavy atoms absorb much more strongly than light atoms.
• Proteins naturally contain sulfur → but sulfur absorption edges are usually outside usable X-ray range.
• Therefore we introduce heavier elements like selenium or mercury.

This is why:

👉 Methionine → selenometionine substitution is extremely common.

🔬 Absorption Edges

Heavy atoms show step-like features in absorption curves called:

🧠 X-ray absorption edges These occur when inner-shell electrons (K, L, M shells) are excited.

Around an edge we observe:

• Pre-edge features
• White line peak
• Extended fine structure

The exact edge position depends on chemical environment, so:

👉 A fluorescence scan of the crystal is done → to tune wavelength precisely for maximum anomalous signal.

📡 3. Atomic Scattering Factor — Now Becomes Complex

Normally:

f = f_0

Depends only on scattering angle (resolution) Independent of wavelength.

But near absorption edges:

f = f_0 + f' + i f''

Where:

• f′ (dispersive term) → real component
• f″ (anomalous term) → imaginary component

Key insight:

🧠 The imaginary component introduces a 90° phase shift in the scattering vector.

This breaks symmetry!

🚨 4. Friedel’s Law Breaks

Normally:

I(hkl) = I(-h -k -l)

But anomalous scattering causes:

❗ Intensity differences between Friedel pairs

These differences:

• Are extremely small
• But measurable
• Contain phase information

This is the fundamental signal used in SAD phasing.

🎯 5. Where Do We Collect Data for SAD vs MAD?

Around the absorption edge there are special wavelength positions:

SAD dataset

• Collected at peak wavelength
• Gives maximum anomalous signal (f″)

MAD datasets (multiple wavelengths)

• Peak → max anomalous signal
• Inflection point → minimum dispersive term
• Remote wavelength → near zero dispersive contribution

Differences between these datasets provide:

• Dispersive differences
• Anomalous differences

These help solve the heavy atom structure.

📐 6. SAD Phasing Geometry (Harker Construction)

SAD still has phase ambiguity:

• Two possible phase solutions exist.
• Figure of merit weighting chooses the most probable direction.

So SAD phasing is:

👉 Conceptually similar to isomorphous replacement But uses anomalous intensity differences instead of native vs derivative datasets.

Huge practical advantage:

⭐ Only one dataset is required.

🗺️ 7. Initial Experimental Maps Are Ugly 😅

Experimental phases are usually poor.

Result:

• Noisy electron density
• Hard to interpret

Therefore we apply:

🧠 Density Modification Techniques

1. Non-crystallographic symmetry averaging

• If multiple copies of protein exist in asymmetric unit
• Average density → improves signal.

2. Solvent flattening / solvent flipping

• Solvent regions should be featureless
• Enforcing this improves protein density.

3. Histogram matching

• Adjust density distribution to expected values at given resolution.

These improve:

⭐ Phase quality ⭐ Map interpretability

This process is called phase refinement.

🧩 8. From Experimental Map → Model Building

After density improvement:

• You trace Cα backbone
• Place side chains
• Build atomic model

Now you can compute:

• Calculated structure factors (Fc) vs
• Observed structure factors (Fo)

📊 9. Difference Maps — Finding Errors

Difference map:

Fo - Fc

Interpretation:

• Positive density → something missing in model
• Negative density → model built incorrectly

But commonly used map:

⭐ 2Fo–Fc map

• Shows full density
• Highlights model errors subtly
• Used during refinement.

Even stronger:

⭐ 3Fo–2Fc map

• Used to confirm uncertain features.

⚠️ Important Practical Reality — SAD Signal Is Tiny

Compared to isomorphous replacement:

• Anomalous differences are very very small
• Requires:
  • High redundancy
  • High multiplicity
  • Very precise measurements

This is critical for successful SAD phasing.

🧠 Big Picture — All Phasing Methods Compared

You now know three major phasing strategies:

1. Isomorphous Replacement

• Native vs heavy atom derivative
• Large intensity differences
• Historically important.

2. Molecular Replacement

• Uses homologous model
• No special experiment needed.

3. SAD / MAD

• Uses anomalous scattering
• Needs heavy atoms
• Requires very precise data.

All aim to recover:

⭐ Phase information → Electron density → Atomic model

🧬 Final Conceptual Flow

1. Collect diffraction intensities
2. Solve phase problem (MR / SAD / etc.)
3. Calculate experimental density map
4. Improve map with density modification
5. Build model
6. Use difference maps to refine
7. Obtain final protein structure