Small-angle X-ray scattering measures how a beam of X-rays scatters off a molecule in solution — no crystal needed. Each bead here is a coarse-grained scattering centre (roughly one residue). The scattered intensity at momentum transfer q is the orientation-averaged Debye scattering equation, summed over every pair of beads:
I(q) = Σᵢ Σⱼ sin(q·rᵢⱼ) / (q·rᵢⱼ) rᵢⱼ = |rᵢ − rⱼ|
Because the molecule tumbles freely in solution, every orientation is already averaged into this single formula — that "sinc" term is exactly what a rotationally-averaged pair distance contributes to the scattering pattern.
At very low q, the curve is well approximated by the Guinier approximation:
I(q) ≈ I(0)·exp(−q²Rg²/3) valid for q·Rg < 1.3
so a straight-line fit of ln I(q) against q² over the low-q region recovers the radius of gyration Rg from its slope (−Rg²/3) — the same fit crystallographers run on real synchrotron/lab SAXS data. The panel compares that fitted Rg against the Rg computed directly from the bead coordinates:
Rg² = (1/N) Σᵢ |rᵢ − r_cm|²
- Fold shape — Globular gives a compact, roughly spherical native fold; Elongated gives a rod/dumbbell fold typical of fibrous or multi-domain proteins.
- Denaturation slider — morphs the beads from the folded conformation toward an extended random-walk chain, mimicking unfolding by heat or chaotropes. Rg grows, I(0) stays ~N² (same total scattering mass), and the Guinier region shrinks — exactly the signature real SAXS uses to detect unfolding.
- Chain length N — more residues means more scattering pairs and a larger, noisier molecule.
- Thermal motion — adds visual jitter approximating solution-phase Brownian fluctuation; it perturbs Rg/Dmax slightly frame to frame just as real ensemble averaging does.
Dmax, the maximum pairwise distance in the bead cloud, is the real-space counterpart SAXS analysis (via the pair-distance distribution function P(r)) extracts from the same scattering curve.