This lecture discusses two closely related analytical approaches used in Small-Angle X-ray Scattering (SAXS):
Both are tools to interpret how proteins scatter at higher Q values, and both help us understand shape, compactness, and flexibility
Porod showed that objects with:
have scattering that follows a simple power law at sufficiently high Q:
I(Q) propto Q^{-4}
This is known as Porod’s Law
At large Q (wide angles), the intensity decays with a slope of −4 on a log-log plot.
Key condition:
The Q value must be large relative to the size of the object.
So the law applies in the wide-angle region where fine structural details dominate.
More generally:
I(Q) propto Q^{-D}
Where D = Porod exponent
The exponent tells you about the shape of the object:
| Structure Type | Porod Exponent | Interpretation |
|---|---|---|
| Globular particle (sphere) | −4 | Compact object |
| Rod | −3 | 1D-like structure |
| Disk | −2 | 2D-like structure |
| Random coil polymer | ≈ −2 | Unfolded / IDP |
| Fully extended chain | −1 | Highly stretched polymer |
This connects scattering decay directly to geometry.
Although very useful in material science, it is less common in protein SAXS because:
Instead of directly fitting the Porod exponent, we use that decay behavior graphically in a different way…
➡️ This leads to Kratky analysis
A classic Kratky plot is:
Q^2 I(Q) quad ext{vs} quad Q
Why multiply by ( Q^2 )?
Because it amplifies differences between compact and unfolded states.
Recall:
Now multiply by ( Q^2 ):
Q^2 cdot Q^{-4} = Q^{-2}
→ Decays quickly → Peak and then falls down
Q^2 cdot Q^{-2} = constant
→ Plateau
Q^2 cdot Q^{-1} = Q
→ Keeps increasing
| Behavior | Interpretation |
|---|---|
| Bell-shaped peak, then decay | Compact, folded |
| Plateau | Unfolded |
| Rising curve | Extended chain |
| Intermediate shape | Partially flexible |
This gives a quick qualitative readout of protein flexibility
The classic plot depends on:
So two proteins with the same shape but different sizes can look very different.
That’s misleading.
To fix this, we normalize using:
We plot:
(qR_g)^2 cdot rac{I(Q)}{I(0)} quad ext{vs} quad qR_g
This:
On a dimensionless Kratky plot:
These are exact for a sphere.
If your protein matches this → it is globular and compact.
If the peak:
→ Indicates increasing disorder or flexibility
Behavior:
Ideal random chain → plateau near 2
Disordered proteins → plateau between 1 and 2
You cannot extract exact disorder percentages, but you can confidently say:
In protein science:
The dimensionless Kratky plot is one of the fastest and most powerful visual diagnostics in SAXS.