🧬 Lecture Summary: SAXS and Cryo-Electron Microscopy

This lecture covers two major structural biology techniques:

1️⃣ Small-Angle X-ray Scattering (SAXS) – low-resolution structural analysis in solution 2️⃣ Cryo-Electron Microscopy (Cryo-EM) – high-resolution imaging of macromolecules

Both techniques help scientists determine the structure of proteins and complexes without crystallizing them.

1️⃣ Small-Angle X-ray Scattering (SAXS)

📌 What SAXS Measures

SAXS measures how X-rays scatter when they hit molecules in solution.

It provides information about overall size and shape of particles.

Typical structural scale:

• 10–500 Å (1–50 nm)
• Good for large proteins and complexes

So SAXS gives low-resolution structural information.

Think of it as:

👉 seeing the silhouette of a protein

not the individual atoms.

2️⃣ SAXS Experimental Setup

The SAXS experiment consists of several components.

Main components

1️⃣ X-ray source

Produces X-ray beam.

2️⃣ Monochromator

Ensures only one wavelength is used.

3️⃣ Sample

Usually dilute protein solution (~1% or ~10 mg/mL).

4️⃣ Detector

Measures scattered X-rays.

The scattering vector is defined as:

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

Where:

• θ = scattering angle
• λ = X-ray wavelength

The detector records the scattering intensity I(q).

3️⃣ Crystallography vs SAXS

Key takeaway:

SAXS studies proteins in their natural environment.

But you lose detailed atomic information.

4️⃣ Data Treatment in SAXS

The raw SAXS data must be processed before interpretation.

Typical workflow:

1️⃣ Collect scattering intensity 2️⃣ Convert 2D detector image → 1D scattering curve 3️⃣ Perform background subtraction 4️⃣ Normalize data 5️⃣ Analyze curves

This produces the function:

I(q)

which describes how the sample scatters X-rays at different angles.

5️⃣ The Pair Distance Distribution Function p(r)

One of the most important SAXS analyses.

What is p(r)?

It describes the distribution of distances between atoms inside the particle.

Think of it as:

👉 a histogram of all distances inside the protein

From the scattering curve we can calculate:

p(r)

This solves the inverse scattering problem.

Why inverse?

Because:

• We measure scattering
• We want structure

So we mathematically convert I(q) → p(r).

6️⃣ SAXS Plots You Must Know

Three key plots appear in almost every SAXS analysis.

📊 1. Scattering Plot

Plot:

ln I(q) ext{ vs } q

This is the raw scattering data.

It shows how intensity decreases as scattering angle increases.

📊 2. Guinier Plot

Plot:

ln I(q) ext{ vs } q^2

Used to determine:

• Radius of gyration (Rg)
• Molecular weight estimate

Important concept:

The Guinier region corresponds to very small angles.

From the slope:

R_g^2 = -3 imes slope

This tells you how large the particle is.

📊 3. p(r) Plot

Plot:

p(r) ext{ vs } r

Shows internal distance distribution.

From this we obtain:

• Dmax = maximum dimension
• overall shape

Examples of shapes from p(r):

7️⃣ Kratky Plot (Protein Folding Indicator)

The Kratky plot evaluates protein flexibility.

Plot:

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

Interpretation:

This is a quick test of protein disorder.

8️⃣ Porod Law

At high scattering angles:

I(q) propto q^{-4}

This law indicates sharp particle boundaries.

Porod analysis helps determine:

• particle volume
• surface properties

9️⃣ Ab Initio Modeling in SAXS

Even though SAXS gives low-resolution data, we can reconstruct approximate shapes.

This uses:

Dummy atom modeling

The protein is represented by many small spheres.

Optimization algorithms (e.g., simulated annealing) adjust these spheres until the calculated scattering fits the data.

Example used in slides:

🧬 Lysozyme shape reconstruction.

🔬 SAXS + Atomic Structures

If we already know the atomic structure (from crystallography), we can:

1️⃣ Compute theoretical SAXS scattering 2️⃣ Compare it with experimental SAXS data

This checks if the solution structure matches the crystal structure.

10️⃣ Why Use SAXS?

Advantages:

✔ native conditions ✔ no crystallization required ✔ small sample volume ✔ works at low concentration

SAXS is often used for:

• flexible proteins
• large complexes
• conformational changes

🧊 Cryo-Electron Microscopy (Cryo-EM)

The second part of the lecture introduces Cryo-EM.

This technique is currently revolutionizing structural biology.

11️⃣ The Cryo-EM Resolution Revolution

Cryo-EM used to give low resolution.

But new technologies improved it dramatically:

• direct electron detectors
• better image processing
• automation

Result:

Structures reaching ~1.8 Å resolution.

Because of this breakthrough:

🏆 2017 Nobel Prize in Chemistry

awarded to:

• Jacques Dubochet
• Joachim Frank
• Richard Henderson

12️⃣ Single Particle Analysis (SPA)

Cryo-EM commonly uses Single Particle Analysis.

Instead of crystallizing proteins, we image thousands of individual molecules.

Then computationally combine them.

Cryo-EM SPA Workflow

The workflow is:

1️⃣ Protein purification 2️⃣ Apply sample to EM grid 3️⃣ Plunge freeze in liquid ethane (vitrification) 4️⃣ Image with electron microscope 5️⃣ Collect movies 6️⃣ Particle picking 7️⃣ 2D classification 8️⃣ 3D reconstruction 9️⃣ Build atomic model

13️⃣ Vitrification

Samples are frozen extremely fast.

This produces vitreous ice, which:

✔ preserves native structure ✔ avoids crystal formation

Procedure:

Protein grid → plunge into liquid ethane.

Temperature ≈ −180°C.

14️⃣ Negative Stain vs Cryo-EM

Two EM sample preparation methods.

Negative Stain

Uses heavy metal salts (e.g., uranyl acetate).

Advantages:

• easy
• high contrast
• cheap

Disadvantages:

• low resolution (~2–4 nm)
• sample dried

Cryo-EM

Flash-frozen samples.

Advantages:

✔ native environment ✔ atomic resolution possible

Disadvantages:

• lower contrast
• requires expensive equipment

15️⃣ Transmission Electron Microscope (TEM)

TEM works similarly to a light microscope but uses electrons instead of light.

Main components:

• electron source
• condenser lens
• objective lens
• projector lens
• detector

Electrons have extremely small wavelengths.

This gives very high resolution.

16️⃣ Why Use Electrons?

Compared with light:

Shorter wavelength → higher resolution.

17️⃣ Contrast in Electron Microscopy

Images rely on contrast.

Two types:

Amplitude Contrast

Occurs when electrons are absorbed or scattered away.

Heavier atoms scatter more electrons.

This reduces intensity reaching the detector.

Result:

dark regions in image.

Phase Contrast

Electrons behave like waves.

When passing through atoms:

• phase shifts occur
• scattered waves interfere

The interference creates the image.

Cryo-EM mostly relies on phase contrast.

18️⃣ Electron–Sample Interactions

Three main events occur:

1️⃣ No scattering

Electron passes straight through.

2️⃣ Elastic scattering

Electron deflects but loses no energy.

Important for image formation.

3️⃣ Inelastic scattering

Electron loses energy.

Causes:

• radiation damage
• noise.

19️⃣ Signal-to-Noise Problem

Biological samples are mostly:

💧 water + light atoms

Therefore:

• electrons scatter weakly
• signal is weak

This causes low signal-to-noise ratio.

To solve this:

➡ average many particles.

20️⃣ Fourier Transforms in Cryo-EM

Images are analyzed in Fourier space.

Why?

Because it simplifies image processing.

Fourier transforms help with:

• filtering
• resolution estimation
• alignment
• reconstruction

Spatial Frequency Concept

Noise often occurs in high frequencies.

21️⃣ Filtering

Common filters:

These improve image quality.

22️⃣ Nyquist Sampling

Important imaging principle.

To resolve a structure of size d, pixel size must be:

pixel ≤ d/2

Otherwise:

⚠ aliasing occurs (loss of information).

23️⃣ Direct Electron Detectors

Modern Cryo-EM uses DDD cameras.

Advantages:

✔ electron counting ✔ better sensitivity ✔ reduced blurring ✔ motion correction

This technology enabled the resolution revolution.

24️⃣ Electron Counting

Detector records individual electron hits.

Instead of measuring intensity, it counts electrons.

Benefits:

• improved accuracy
• higher resolution.

25️⃣ Super-Resolution

Direct detectors can locate electrons with sub-pixel precision.

This increases effective resolution beyond pixel size.

26️⃣ 3D Reconstruction

After particle alignment:

• projections from many angles are combined.

Using back-projection algorithms we reconstruct a 3D density map.

27️⃣ Resolution Determination

Resolution is measured with:

Fourier Shell Correlation (FSC)

Procedure:

1️⃣ Split dataset into two halves 2️⃣ Build two independent models 3️⃣ Compare similarity

This avoids overfitting.

Called the Gold-standard FSC.

28️⃣ Particle Classification

Not all particles are good.

During 2D classification:

Particles are grouped into classes.

Then:

✔ good classes kept ❌ bad particles rejected

Only the best particles are used for final reconstruction.

29️⃣ Applications of Cryo-EM

Cryo-EM can be used for:

• large protein complexes
• ribosomes
• viruses
• membrane proteins
• protein dynamics
• ligand binding studies
• epitope mapping

Examples:

• haemoglobin structure
• viral capsids
• ribosome complexes

🧠 Key Concepts to Remember

SAXS

✔ solution scattering ✔ low-resolution shape ✔ Guinier → Rg ✔ p(r) → particle size ✔ Kratky → folding state

Cryo-EM

✔ single particle analysis ✔ vitrified samples ✔ phase contrast imaging ✔ Fourier reconstruction ✔ atomic resolution possible

📚 Simple Intuition