🧬 Lecture Summary — SAXS & Cryo-EM Principles and Practice

Source:

🌟 PART 1 — Small-Angle X-ray Scattering (SAXS)

🔬 What is SAXS?

SAXS is a solution-state structural biology technique used to determine:

• Low-resolution structures
• Size range: ~10–500 Å
• Works on proteins, complexes, flexible systems

➡️ Unlike crystallography, SAXS studies molecules in native buffer conditions (page 1-2).

⚙️ SAXS Experimental Setup (image slide explained — page 2)

The diagram shows:

1. X-ray source
2. Monochromator → selects wavelength
3. Collimation (pinholes) → produces narrow beam
4. Dilute protein solution (~1% ≈ 10 mg/mL)
5. 2D detector measures scattered intensity

Important parameter:

|q| = rac{4pi sin heta}{lambda}

• q = scattering vector
• contains structural information (length scale)

👉 Small angles → large structural features.

🧊 SAXS vs Crystallography (image slide explained — page 2)

💡 SAXS is easier experimentally but harder computationally because of the inverse problem.

📊 Data Treatment and Inverse Scattering Problem (image slide — page 3)

SAXS measures:

I(q)

But we want:

➡️ Real-space structure

To obtain that we calculate:

🧮 Pair-distance distribution function — p(r)

• Probability of distances between points inside particle
• Gives:
  • Shape
  • Maximum size ( D_ )

This is an inverse problem because many shapes can give similar scattering.

📈 SAXS Plots You Must Know (page 4)

1️⃣ Scattering plot

• Raw data
• ( ln I(q) ) vs ( q )

2️⃣ Guinier plot

• ( ln I(q) ) vs ( q^2 )
• Gives:
  • Radius of gyration ( R_g )
  • Molecular weight estimate

3️⃣ p(r) plot

• Real-space information
• Gives particle shape.

🧩 Particle Shapes from p(r) (image slide — page 4)

Different curves correspond to:

• Sphere → symmetric bell shape
• Rod → skewed distribution
• Disk → different tail behavior
• Dumbbell → bimodal

💡 Therefore SAXS can distinguish overall topology even without atomic resolution.

🧮 Kratky Plot — Flexibility Indicator (page 5-6)

Plot:

s^2 I(s) ext{ vs } s

Interpretation:

👉 Normalized Kratky allows comparison across proteins.

📐 Porod Law (page 5)

At high q:

I(q) sim q^{-4}

• Used to estimate excluded volume
• Deviations → flexibility or disorder.

🧱 Ab-initio Dummy Atom Modeling (page 6-7)

Concept:

• Represent protein as many beads (dummy atoms)
• Optimize arrangement to fit SAXS curve
• Uses simulated annealing

Output: ➡️ Low-resolution molecular envelope.

Lysozyme example shown in slide.

🧬 Hybrid Modeling (page 7)

If atomic structure exists:

• Fit crystal structure into SAXS envelope
• Validate solution conformation.

👍 Why SAXS? (page 8)

Advantages:

• Native conditions
• No crystallization
• Small sample volumes
• Works at low concentration

Also:

• SANS (neutron) useful in high salt / D₂O contrast variation

❄️ PART 2 — Cryo-Electron Microscopy (Cryo-EM)

🚀 Resolution Revolution (page 10-11)

Slides show:

• Explosion in cryo-EM structures in PDB
• Nobel Prize 2017

Key reason:

• Direct electron detectors
• Algorithms (RELION etc.)

🧬 Single Particle Analysis (SPA)

Allows:

• High resolution (<3 Å possible)
• Example shown: GDH at 1.8 Å (page 12).

🧫 Structural Biology In situ — Tomography (page 13)

Tomography:

• Tilt series → 3D cellular reconstruction
• Allows studying molecules in cells

The slide shows neuromuscular synapse rendering.

🔬 MicroED (page 14)

Electron diffraction on nanocrystals

Advantages:

• Needs tiny crystals
• Bridges XRD and EM.

⚙️ Transmission Electron Microscope (TEM)

🧲 Lens System (image slide — page 16)

Three main lens systems:

1. Condenser lens → focuses beam on sample
2. Objective lens → forms first image
3. Projector lenses → magnify image

🔦 TEM vs Light Microscopy (page 16-17)

Similarities:

• Imaging optics
• Magnification stages
• Specimen holder

Differences:

• Glass lenses vs electromagnetic lenses
• Resolution limited by wavelength in LM
• Electron beam causes radiation damage

📜 History Slide (page 17)

Timeline shows:

• 1920s → wave nature discovery
• 1930s → first TEM
• Later → resolution improvements.

⚡ Why Use Electrons? (page 19)

Electrons:

• Very small wavelength → high resolution
• Strong interaction with matter

BUT:

• Cause damage
• Low penetration.

🧠 New Technologies (page 19)

• Phase plates
• Direct detectors
• Cs correctors
• Automation
• Movie mode

These enabled modern cryo-EM success.

❄️ Cryo-EM SPA Workflow (page 20)

Image slide shows full pipeline:

1. Purify protein
2. Apply to grid
3. Plunge freeze in liquid ethane
4. Collect movies
5. Particle picking
6. 2D classification
7. 3D reconstruction
8. Atomic modeling

🧊 Vitrification (page 21)

• Grid diameter ≈ 3 mm
• Holes ≈ 1-2 µm
• Flash freezing → amorphous ice

Preserves native structure.

🎥 Movie Collection + Drift Correction (page 22)

Instead of single image:

• Collect dose-fractionated frames
• Align → reduce motion blur.

🧱 2D Classification (page 22)

• Average similar particle views
• Remove junk particles.

🧬 3D Reconstruction (page 23)

• Combine many orientations
• Produce density map.

🧪 Negative Stain vs Cryo-EM (page 24)

🧬 Applications (page 25)

Cryo-EM enables:

• Ligand binding mapping
• Huge complexes
• Dynamics
• Quality control
• Epitope mapping

Examples shown include virus and ribosome.

👍 Advantages of Cryo-EM (page 26)

• No crystallization
• Handles heterogeneity
• Small sample amounts

👎 Disadvantages

• Low SNR
• Expensive equipment
• Time-consuming data collection
• Size limit (~200 kDa typical).

⚛️ PART 3 — Image Formation in EM

🌊 Electrons: Wave-Particle Duality (page 31)

Electrons:

• Scatter like particles
• Interfere like waves

Therefore images arise from:

• Amplitude contrast
• Phase contrast.

⚫ Amplitude Contrast (page 32)

Mechanism:

• Electrons absorbed or scattered
• Fewer reach detector
• Dense regions appear dark

Dominant in:

➡️ Negative stain EM.

🌈 Phase Contrast (page 33-35)

Mechanism:

• Elastic scattering changes phase of electron wave
• Interference creates image

Dominant in:

➡️ Cryo-EM.

⚡ Elastic vs Inelastic Scattering (page 35)

🔊 Signal-to-Noise Problem (page 37)

Macromolecules resemble water in EM:

➡️ Hard to distinguish → low contrast.

Therefore:

• Need averaging
• Filtering
• Classification.

🔢 Fourier Space in EM (page 38-40)

Key idea:

• Images easier processed in Fourier space

Applications:

• Filtering
• CTF correction
• Alignment
• 3D reconstruction

Low frequencies → overall shape High frequencies → fine details.

📏 Nyquist Sampling (page 41)

Rule:

pixel size le rac{1}{2} ext{ smallest feature}

Otherwise:

➡️ Aliasing (information loss).

📷 Modulation Transfer Function (MTF) (page 42)

Measures detector performance:

• How well spatial frequencies preserved
• Ideal value = 1.

📡 Direct Electron Detectors (page 43-46)

Advantages:

• Electron counting
• Super-resolution
• Motion correction

Result:

➡️ Huge resolution improvement.

🧠 FSC — Resolution Determination (page 48)

Gold-standard method:

1. Split data in half
2. Process independently
3. Compare maps

Correlation threshold → resolution.

🧹 Particle Selection (page 50)

Keep:

• Well-aligned particles

Reject:

• Junk / misclassified

Iterative refinement improves map.

⭐ FINAL BIG PICTURE

SAXS

• Low-resolution solution shape
• Fast & flexible
• Complementary to high-resolution methods

Cryo-EM

• High-resolution structures
• No crystallization
• Best for large complexes

EM Image Formation

• Phase interference physics
• Requires Fourier processing
• Modern detectors → resolution revolution.