Radius of gyration

What is radius of gyration?

The radius of gyration ($R_g$) quantifies the compactness of a protein structure. It measures how mass is distributed around a protein's center of mass—a compact, well-folded protein has a small $R_g$, while an extended or unfolded structure has a larger value.

$R_g$ is widely used in structural biology to assess folding states, compare conformational changes, and validate computationally predicted structures. Molecular dynamics simulations track $R_g$ over time to detect unfolding events or conformational transitions.

For sequence-based analysis of protein properties like composition and charge, see Protein Parameters. To visualize your structure alongside $R_g$ calculations, use the PDB Viewer.

How to calculate the radius of gyration?

The radius of gyration is the root-mean-square distance of all atoms from the protein's center of mass. The formula is:

$$R_g = \sqrt{\frac{\sum_{i=1}^{N} m_i \cdot (r_i - R_{cm})^2}{\sum_{i=1}^{N} m_i}}$$

Where:

• $m_i$ is the mass of atom $i$
• $r_i$ is the position of atom $i$
• $R_{cm}$ is the center of mass of all selected atoms
• $N$ is the total number of atoms

The tool uses atomic masses to weight each atom's contribution. Heavier atoms like sulfur have more influence than lighter atoms like hydrogen.

Atom selection

Different atom selections provide complementary information:

• All atoms: Uses every atom in the structure for a complete picture of molecular shape
• Backbone only (N, CA, C, O): Ignores side chains to focus on the protein fold itself
• Alpha carbons only (CA): Reduces noise from side chain conformations, commonly used in comparative analysis

Alpha carbon calculations are fastest and most reproducible across different structure sources (X-ray, NMR, computational models). Use all-atom calculations when side chain packing matters.

Empirical scaling

For globular proteins, $R_g$ follows a predictable relationship with chain length:

$$R_g \approx 2.2 \times N^{0.38} \text{ Å}$$

Where $N$ is the number of residues. A 100-residue globular protein typically has $R_g \approx 12\text{–}14$ Å. Values significantly above this suggest extended conformations or multi-domain arrangements.

Input requirements

• PDB Structure: Upload a PDB file or fetch directly from the RCSB PDB by entering a 4-character PDB ID (e.g., 1UBQ)

Settings

• Atom selection: Choose which atoms to include—all atoms, backbone only, or alpha carbons only
• Chains: Specify chain IDs to analyze (e.g., A or A,B). Leave empty to include all chains.

Understanding the results

The output table contains one row per chain or structure analyzed:

Interpreting values

The absolute $R_g$ value depends on protein size, so compare against expectations for your protein's length:

• Compact globular proteins: $R_g \approx 2.2 \times N^{0.38}$ Å
• Multi-domain proteins: Often 10–30% larger than single-domain proteins of similar size
• Intrinsically disordered proteins: Can be 50–100% larger than folded globular proteins

When comparing structures, small $R_g$ differences (< 1 Å) are often within experimental or computational uncertainty. Larger changes (> 2–3 Å) typically indicate meaningful conformational differences.

Common applications

Radius of gyration analysis helps answer several structural biology questions:

• Model validation: Compare predicted structure $R_g$ to experimental SAXS measurements
• Folding assessment: Verify that computational models produce compact, realistic structures
• Conformational analysis: Detect domain movements or unfolding by comparing $R_g$ across conditions
• Quality control: Identify outliers in batches of predicted or modeled structures