Radius of gyration

How to calculate radius of gyration from a PDB file?

Upload a .pdb or .ent structure, or fetch a PDB entry such as 1CRN from RCSB. Choose all atoms, backbone atoms, or alpha carbons, then calculate. The results contain one geometric radius of gyration in angstroms per selected chain, using the first model with non-water coordinates in each file.

Worked example: crambin (1CRN)

For the RCSB 1CRN coordinates, leave Chains empty. Running each Atom selection gives these results:

Atom selection	id	num_atoms	rgyr_angstrom
All atoms (default)	1CRN_A	327	9.666
Backbone only (N, CA, C, O)	1CRN_A	184	9.587
Alpha carbons only (CA)	1CRN_A	46	9.676

These values were verified against the stored 1CRN coordinate file and an independent pair-distance calculation. Different coordinate versions or atom selections can give different results.

Input

Input	Accepted content
PDB Structure	Fixed-column PDB coordinates in .pdb or .ent files
RCSB fetch	A PDB ID whose coordinates are available in PDB format
File size	Up to 50 MiB per file
Upload count	Up to 10 files per upload, subject to the account's file limit

Coordinates must be finite numbers in the PDB x, y and z fields (columns 31-54). Windows line endings and a leading UTF-8 byte order mark are supported. FASTA sequences, spreadsheet coordinates, PDF documents and mmCIF files are not PDB coordinate inputs.

Files that cannot be analyzed are named in a warning when other files succeed. If no file produces results, the tool returns an error describing the problem. No partial chain calculation is returned from a file with invalid coordinate records.

Settings

Setting	Options and behavior	Default
Atom selection	All atoms includes non-water ATOM and HETATM records, including hydrogens if present. Backbone only (N, CA, C, O) selects those atom names. Alpha carbons only (CA) selects CA atom names. Calcium ions are excluded from the backbone and alpha-carbon selections.	All atoms
Chains	Comma-separated chain IDs, such as A or A,B. Each selected chain is analyzed separately. IDs match case exactly first; a case-insensitive match is used only when unambiguous. Missing chains are reported.	Empty, all chains

All selections exclude recognized water residues. The backbone and alpha-carbon selections use atom names rather than a full chemical classification of each residue. Inspect unusual ligands or modified residues before comparing structures.

Results

Column	Meaning
id	PDB header ID plus chain ID, for example 1CRN_A. If the header has no ID, the uploaded filename without .pdb or .ent is used.
num_atoms	Number of selected coordinate records in the chain
rgyr_angstrom	Geometric radius of gyration in Å, rounded to three decimal places

The results table supports copying and exporting as CSV or Excel. Files and chains remain in input order. Repeated header/chain IDs across files produce a warning; their rows are retained.

Blank chain IDs are reported as A. A file containing both blank chain IDs and chain A is rejected to avoid merging distinct chains. Assign a distinct ID to the blank chain before analyzing that file.

What does radius of gyration measure?

Radius of gyration measures how widely the selected coordinates are distributed around their center. ProteinIQ calculates the root-mean-square distance from the geometric center, giving every selected coordinate record equal weight:

$$\mathbf{r}_{center} = \frac{1}{N}\sum_{i=1}^{N}\mathbf{r}_i$$ $$R_g = \sqrt{\frac{1}{N}\sum_{i=1}^{N}\left\|\mathbf{r}_i-\mathbf{r}_{center}\right\|^2}$$

Here, $N$ is the selected atom count and $\mathbf{r}_i$ is an atom's position in angstroms. This is the unit-weight form of VMD's radius-of-gyration calculation. Atomic masses and occupancies do not weight the result. In contrast, MDAnalysis's radius of gyration uses masses. Match the weighting, selected atoms and coordinate units before comparing values between programs.

A single selected atom has $R_g=0$. Translating or rotating a chain does not change its radius of gyration.

Models, alternate locations and assemblies

Only the first model containing non-water atoms is analyzed. Additional coordinate models produce a warning. This includes NMR ensembles and multi-model PDB files; the result is not an ensemble average or a trajectory analysis.

Alternate locations in PDB records describe alternative atomic positions. This calculator retains all selected alternate-location records with equal weight and reports their presence. It does not choose a conformer or use occupancies. Prepare a single conformer for comparisons that require one position per atom.

Selecting several chains returns separate chain radii. It does not calculate the radius of the complete complex or reconstruct a biological assembly. Non-water ligands and ions sharing a chain ID contribute to All atoms.

How should I interpret the result?

A smaller value means the selected coordinates are more compact. Compare structures with similar composition, chain boundaries, atom selections and preparation. Size, missing residues, ligand inclusion, hydrogen inclusion and alternate locations can all change the value.

There is no universal Rg cutoff for correct folding or a meaningful conformational change. Rg alone cannot validate a predicted model. It also does not reproduce a SAXS-derived radius directly, because solution scattering uses a different weighting and can include solvent and ensemble effects.

Use the PDB Viewer to inspect chain content and missing regions. For complementary measurements, solvent-accessible surface area describes exposure, while structural RMSD compares matching coordinates between structures. Protein Parameters calculates sequence-based properties rather than coordinate compactness.

FAQ

Does this calculator use atomic masses?

No. It uses equal weights and a geometric center. This preserves the calculator's geometric Rg method; it is not a mass-weighted result.

Why are there several rows for one PDB file?

Each selected chain receives its own row. Selecting A,B does not combine chains A and B into one object.

Why did a chain disappear after selecting alpha carbons?

The first coordinate model may contain no CA records for that chain. Chains with no matching atoms are omitted and reported. Calcium ions named CA are not treated as alpha carbons.

Can I calculate radius of gyration from a protein sequence?

This tool requires three-dimensional coordinates. A sequence does not uniquely determine a geometric radius of gyration.