Radius of gyration

Calculate the radius of gyration (Rg) for protein structures from PDB files.

Docs

Input

PDB Structure

Atom selection

Chains

Output

Configure input settings on the left, then click "Generate"

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

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:

Column	Description
ID	Structure/chain identifier
Num Atoms	Number of atoms included in the calculation
Rg (Å)	Radius of gyration in angstroms

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

Related tools

Aggrescan3D

Faithful static-mode Aggrescan3D tool for per-residue aggregation propensity analysis from a single protein structure.

Protein charge plot

Plot net charge vs pH for protein sequences. Visualize how protein charge changes across pH 0-14 and identify the isoelectric point (pI) where the net charge crosses zero.

FindPept

Match experimental peptide masses against theoretical digest fragments of a protein sequence. Identify peptides from mass spectrometry data by peptide mass fingerprinting.

Hydropathy plot

Generate Kyte-Doolittle hydropathy plots to visualize hydrophobic and hydrophilic regions along protein sequences. Identify transmembrane domains and surface-exposed regions.

Hydrophobicity plot

Generate hydrophobicity plots using 24 different amino acid scales. Visualize hydrophobic and hydrophilic regions for protein analysis, epitope prediction, and membrane protein studies.

IPC 2.0 (isoelectric point calculator)

Isoelectric Point Calculator 2.0 - Predict protein/peptide isoelectric point (pI) using 18+ validated pKa scales, SVR models, and deep learning. Supports proteins, peptides, and comprehensive analysis.

Peptide cutter

Predict protease and chemical cleavage sites across a protein sequence for up to 39 enzymes simultaneously. Identify where each enzyme cuts, the cleavage residue, and context window around each site.

Peptide mass calculator

Cleave a protein sequence with a chosen protease and compute the masses of the resulting peptides. Supports multiple enzymes, missed cleavages, chemical modifications, and different ion types for mass spectrometry experiment planning.

PROPKA 3

Predict pKa values of ionizable groups in proteins and protein-ligand complexes from 3D structure. PROPKA calculates environment-driven pKa shifts for standard ionizable residues, terminal groups, and supported ligand atom types.

Protein parameters

Calculate protein parameters, including molecular weight, theoretical pI, extinction coefficients, aromaticity, secondary structure fractions, atomic composition, estimated half-life, and several indices, including instability, aliphatic index, and GRAVY.

What is radius of gyration?

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

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}

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:

Column	Description
ID	Structure/chain identifier
Num Atoms	Number of atoms included in the calculation
Rg (Å)	Radius of gyration in angstroms

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

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