🧬 Protein Crystallography — Full Educational Summary

🔬 1. Major methods in structural biology

Early slides introduce the four key structural biology techniques:

• X-ray diffraction (XRD)
• NMR spectroscopy
• Cryo-EM
• SAXS

📌 The image on page 2 shows these methods visually:

• XRD → diffraction spots
• NMR → spectra
• Cryo-EM → particle images
• SAXS → scattering curves

💡 Key idea: These methods differ in:

👉 Historically X-ray crystallography dominated large macromolecular structures (>30 kDa), but Cryo-EM is now rapidly growing.

🧪 2. Crystallography is interdisciplinary

Slide shows that crystallography involves:

• Physics → diffraction theory
• Chemistry → bonding / interactions
• Mathematics → Fourier transforms
• Biology → proteins
• Medicine → drug targets

📌 The image collage (page 2) represents:

• diffraction geometry
• molecular surfaces
• large synchrotron facilities

💡 Meaning: Protein structure determination is a systems science problem.

📈 3. Historical milestones

Important solved structures include:

• Hemoglobin (1937)
• Myoglobin (1960)
• Lysozyme (1965)
• Ribosome (~2000)
• Viral cores

💡 Shows the progression from small proteins → huge complexes.

⚙️ 4. The overall crystallography workflow

📌 The workflow image on page 4 shows the pipeline:

1️⃣ Protein purification 2️⃣ Crystallization 3️⃣ Data collection (diffraction pattern) 4️⃣ Phasing → electron density 5️⃣ Modelling → atomic model 6️⃣ Analysis → biological interpretation

💡 This is THE core exam flow.

🧫 5. Purification

Slide shows SDS-PAGE band (page 5).

Meaning:

• Protein must be pure and homogeneous
• Aggregates or mixtures destroy crystallization

💡 Crystallography is extremely sensitive to sample quality.

💎 6. Crystallization

Slide image shows colored crystal shapes (page 5).

Explanation:

• Proteins must form ordered repeating lattice
• Requires careful optimization of:
  • pH
  • salt
  • precipitant
  • temperature

🧊 7. Macromolecular crystals — very special!

Important points (page 9):

• Contain 40–75% water
• Not rigid solids → more like soft gels
• Enzymes may still be active
• Crystal contacts are weak intermolecular interactions

💡 Therefore:

👉 Crystal structure often reflects physiological conformation.

💧 8. Proteins in solution and crystallization driving forces

Slide explains protein surface properties:

• charged
• polar
• hydrophobic
• pH dependent

These determine aggregation vs crystallization.

Forces involved:

• Hydrophobic interactions
• van der Waals
• Polar interactions
• Metal coordination
• Disulfide formation

💡 Key concept:

Crystallization = balance between kinetics and thermodynamics

Too fast → precipitation Too slow → no nucleation

📊 9. Phase diagram of crystallization

📌 The diagram on page 11 is VERY important.

It shows regions:

• Undersaturated → protein dissolved
• Metastable → crystal growth only
• Supersaturated → nucleation possible
• Precipitation zone → amorphous aggregates

💡 Exam idea:

You must enter supersaturation zone carefully.

🧪 10. Crystallization methods

• Batch
• Dialysis
• Vapor diffusion (hanging/sitting drop)

💡 Vapor diffusion is most common.

Mechanism:

• Drop equilibrates with reservoir
• Water leaves drop → protein concentration increases → nucleation.

🧱 11. Unit cells and crystal lattice

Crystals = repeating unit cells.

📌 Slide image (page 12) shows:

• single molecule replicated billions of times

👉 Crystal = single molecule amplifier

This is why weak diffraction from one molecule becomes measurable.

Unit cell defined by:

• a, b, c lengths
• α, β, γ angles

📐 12. Crystal systems and symmetry

7 systems:

• cubic
• tetragonal
• hexagonal
• orthorhombic
• rhombohedral
• monoclinic
• triclinic

Symmetry operations:

• rotation
• screw axis
• translation
• inversion
• glide

📌 Slide with symmetry diagrams (page 16) shows:

Example:

• 2-fold rotation: (x,y,z) → (−x,y,−z)

💡 Important:

Space group = full symmetry description.

Total = 230 space groups Only ~65 common in proteins.

🧩 13. Asymmetric unit

Definition:

• Smallest unique part of crystal
• Whole crystal generated by symmetry

📌 Slide image (page 17) shows asymmetric unit copies filling unit cell.

⚡ 14. X-rays basics

Wavelength:

• ~0.1–100 Å

Good because:

• comparable to atomic spacing (~1–2 Å)

Historical:

• Röntgen discovery (1895)
• Laue diffraction (1910)

🔦 15. X-ray sources

Types:

• Sealed tube (simple)
• Rotating anode (stronger)
• Synchrotron (very intense, tunable)

📌 Slide image (page 21) shows synchrotron facility.

💡 Modern macromolecular crystallography mostly uses synchrotrons.

🎯 16. Diffraction experiment setup

📌 Image (page 22):

• X-ray beam
• crystal on goniometer
• detector
• rotation collects many frames

Key equation:

λmin = 12.4 / V

❄️ 17. Cryo-crystallography

Crystals flash frozen at 100 K.

Why?

• reduces radiation damage
• improves diffraction quality

Cryoprotectants:

• glycerol
• PEG
• sugars
• oils

📌 Image shows crystal in nylon loop.

🌊 18. Diffraction theory — wave interference

Huygens principle:

Each point scatters waves → interference pattern.

Constructive interference → reflection spot Destructive → no intensity.

📏 19. Bragg’s law (SUPER IMPORTANT)

2dsin heta = nlambda

Meaning:

• Reflection occurs when path difference = integer wavelength.

Consequences:

• Smaller d → larger angle → higher resolution

Typical protein resolution:

⭐ ~1.8–3 Å

🔢 20. Miller indices (hkl)

Define lattice planes.

Example slide shows plane that:

• spans a-axis
• cuts b-axis in half → k=2

So reflection = (1 2 0).

🧠 21. Diffraction from molecules vs crystals

Single molecule → weak scattering.

Crystal → signals add → measurable.

📌 Slide (page 32) illustrates waves from many atoms interfering.

🌌 22. Reciprocal space

Very key concept.

Reciprocal lattice spacing ∝ 1/d.

So:

• large unit cell → dense diffraction spots
• small cell → sparse pattern

Mathematical relationships between real and reciprocal axes shown (page 34).

⚪ 23. Ewald sphere

Virtual sphere of radius 1/λ.

Reflection occurs when reciprocal lattice point lies on sphere.

This explains:

• why crystal must rotate during data collection.

🌊 24. Fourier theory and wave addition

Structure factor:

F = sum F_j e^{iphi_j}

Meaning:

• Diffraction depends on amplitude AND phase.

📌 Phase problem = major challenge in crystallography.

Fourier theorem:

Any periodic function = sum of simple waves.

Electron density map obtained via Fourier transform of diffraction data.

⚛️ 25. Atomic scattering factors & B-factor

• heavier atoms scatter more
• scattering decreases at high angles

Debye-Waller factor:

T = e^{-B(sin heta/lambda)^2}

B-factor:

• measures atomic motion/disorder
• typical range 2–200 Ų

⭐ Final Key Takeaways

✔ Crystal = repeating unit cells ✔ Diffraction pattern encodes structure ✔ Bragg’s law links angle → resolution ✔ Fourier transform converts diffraction → electron density ✔ Symmetry + space group define crystal ✔ Cryo-cooling protects crystal ✔ High-quality purification & crystallization are critical