Rg Analysis: Best Practices

A guide to interpreting Radius of Gyration results, understanding what Rg measures, why it needs no alignment, and how to compare conditions rigorously.

Added in version 1.3.0: The Rg analysis plugin was added in PolyzyMD 1.3.0.

Note

Just need quick results? See the Quick Start Guide for copy-paste commands and minimal setup.

What is Radius of Gyration?

Radius of Gyration (Rg) measures the mass-weighted root mean square distance of atoms from the center of mass of a molecular selection:

\[ R_g = \sqrt{\frac{1}{M} \sum_{i=1}^{N} m_i \left\| \mathbf{r}_i - \mathbf{r}_{\text{cm}} \right\|^2} \]

Where:

\(m_i\) is the mass of atom \(i\)
\(\mathbf{r}_i\) is the position of atom \(i\)
\(\mathbf{r}_{\text{cm}} = \frac{1}{M}\sum_i m_i \mathbf{r}_i\) is the center of mass
\(M = \sum_i m_i\) is the total mass
\(N\) is the number of atoms in the selection

Rg is a measure of structural compactness: a lower Rg means the atoms are packed more tightly around the center of mass. Unlike RMSD, Rg does not require a reference structure or alignment — it is an intrinsic property of the current conformation.

What Rg Measures

Rg Behavior	Structural Interpretation
Low and stable	Compact, well-folded structure
Gradually increasing	Expansion — possible unfolding or swelling
Gradually decreasing	Compaction — tighter folding or collapse
Plateau after change	Equilibration to a new conformational state
Sudden jump up	Partial unfolding event or domain separation
Sudden jump down	Collapse or aggregation event
Oscillating	Sampling between compact and extended states

Interpreting Rg Values

Important

Rg is highly system-specific — it depends on protein size, shape, fold topology, and which atoms are included in the selection. There are no universal “good” or “bad” Rg values. Always compare Rg across conditions using the same selection and atom types rather than comparing against generic reference ranges.

Selection Matters

The choice of atoms for Rg calculation affects the result:

Selection	Best For
`protein`	Overall protein compactness (all atoms)
`protein and name CA`	Backbone compactness (less noise from sidechains)
`protein and name CA and resid 20:250`	Core region, excluding flexible termini
`chainID C`	Polymer compactness/extension
`protein or chainID C`	Combined enzyme-polymer system size

Rg Scales with Protein Size

Unlike RMSD (which is relatively size-independent for similar fold types), Rg scales roughly as:

\[ R_g \propto N^{\nu} \]

for proteins, where \(N\) is the number of residues and \(\nu\) is the Flory exponent. For compact globular proteins, the theoretical expectation is \(\nu = 1/3\) (solid sphere packing), though empirical fits to PDB structures give \(\nu \approx 0.38\)–\(0.40\) due to imperfect packing, voids, and surface roughness (Dima & Thirumalai, 2004). This means larger proteins have inherently larger Rg values. When comparing Rg across different proteins, normalize by the expected Rg for the protein size.

Rg vs Time: What to Look For

Stable Plateau (Ideal)

Rg (Å)
  20 |  ___________________________
     | /
  19 |/
     |
  18 |
     |
  17 +-----------------------------→ Time
     0    10   20   30   40   50 ns

A stable Rg plateau indicates the protein maintains consistent compactness throughout the simulation. The initial transient (if present) is equilibration.

Expansion (Possible Unfolding)

Rg (Å)
  25 |                          /
     |                         /
  23 |                        /
     |                       /
  21 |                ______/
     |_______________/
  19 +-----------------------------→ Time

A rising Rg trend suggests the protein is expanding — possibly unfolding, swelling, or sampling a more extended conformation. Possible responses:

Check for protein unfolding in a molecular viewer
Verify force field and simulation parameters
The system may genuinely be unstable under these conditions

Compaction

Rg (Å)
  20 |_______________
     |               \
  19 |                \
     |                 \_______
  18 |
     |
  17 +-----------------------------→ Time

A decreasing Rg trend indicates the protein is becoming more compact. This can indicate:

Polymer-induced stabilization and tighter packing
Hydrophobic collapse
Loss of secondary structure elements that maintain extended conformations

Sudden Jumps

A sharp Rg change mid-trajectory typically indicates a conformational transition. Check the structure at the jump to understand what happened:

Domain rearrangement or hinge motion
Partial unfolding or refolding
Ligand unbinding leading to structural change
Polymer wrapping or unwrapping

Tip

When you observe a jump, load the trajectory in a molecular viewer (e.g., VMD, PyMOL) and examine frames around the transition. Compare with the RMSD timeseries — a jump in Rg should correlate with RMSD changes if the same region is affected.

Oscillations

Regular Rg oscillations suggest the system samples between compact and extended conformational states. This is often seen with:

Breathing motions in multi-domain enzymes
Allosteric transitions
Polymer wrapping/unwrapping cycles

For oscillating systems, report the range and period of oscillation rather than just the mean Rg.

How PolyzyMD Handles Autocorrelation

Rg timeseries are correlated — adjacent frames are similar because MD evolves continuously. PolyzyMD automatically accounts for this:

Computes Rg timeseries using MDAnalysis AtomGroup.radius_of_gyration()
Estimates correlation time (τ) via autocorrelation function integration
Computes effective sample size — n_independent = n_frames / (2τ)
Reports autocorrelation-corrected SEM — SEM = σ / √n_independent

Example Autocorrelation Output

Run: Whole Protein
  Correlation time: 3821 ps (3.8 ns)
  Statistical inefficiency: 473.7
  Independent samples: 19 (from 9000 frames)
  SEM (corrected): 0.098 Å

This means:

Rg values decorrelate over ~3.8 ns timescales
You effectively have 19 independent measurements from 9000 frames
The reported SEM properly accounts for this correlation

Multi-Run Analysis: Why and When

Why Multiple Runs?

Different Rg selections answer different questions:

Run Label	Selection	Question
“Whole Protein”	`protein`	Overall protein compactness?
“Protein Backbone”	`protein and name CA`	Backbone compactness (less side-chain noise)?
“Core Region”	Core residues only	Is the structured core stable?
“Polymer”	`chainID C`	Is the polymer extended or collapsed?
“Enzyme+Polymer”	`protein or chainID C`	Overall conjugate compactness?

When to Use Multi-Run

Always include at least one whole-protein or backbone Rg run as a baseline
Add core-region runs when flexible termini or loops dominate the signal
Add polymer runs when studying enzyme-polymer conjugate behavior
Add combined runs when the relative sizes of enzyme and polymer matter

Independent Ranking

Each run is ranked independently across conditions. This prevents averaging Rg from structurally different selections (which would be meaningless):

Rankings:
  Whole Protein:     With Polymer < No Polymer (compaction)
  Protein Backbone:  With Polymer < No Polymer (compaction)
  Polymer:           100% SBMA < 100% EGMA (more compact polymer)

Why No Alignment or Reference?

Rg is intrinsically translation and rotation invariant. The quantity being measured — the mass-weighted spread of atoms around their center of mass — does not depend on the absolute position or orientation of the molecule in the simulation box.

Mathematically, this is because:

The center of mass \(\mathbf{r}_{\text{cm}}\) moves with the molecule
The distances \(\|\mathbf{r}_i - \mathbf{r}_{\text{cm}}\|\) are internal coordinates

This gives Rg several practical advantages over RMSD:

No alignment artifacts — RMSD can be affected by imperfect alignment
No reference structure needed — no need to choose centroid, average, or external
Simpler configuration — only label and selection are required
Complementary information — Rg and RMSD together give a more complete picture

Note

This does not mean Rg is “better” than RMSD — they measure different things. RMSD tells you how much the structure has changed from a specific reference. Rg tells you how compact the structure is, regardless of what it looked like before. Use both for comprehensive structural analysis.

Replicates vs Longer Simulations

The LiveCoMS Recommendation

“Multiple independent simulations are preferable to a single long simulation” — Grossfield et al. (2018)

Why Replicates Matter for Rg

Multiple Replicates	Single Long Simulation
Truly independent starting points	Frames remain correlated
Tests reproducibility of compactness	May be trapped in metastable state
Robust SEM from replicate means	SEM requires autocorrelation correction
Parallelizable	Sequential

How Many Replicates?

Replicates	Statistical Power	Practical Guidance
1	Descriptive only	Exploratory — no inferential statistics
3	Large effects (d > 2)	Minimum for publication
5	Medium effects (d > 1.3)	Recommended standard

Note

With only 1 replicate, PolyzyMD still computes Rg and reports within-trajectory statistics (mean, SEM from autocorrelation correction). Comparison across conditions requires at least 2 replicates per condition for pairwise t-tests.

Comparing Conditions

What PolyzyMD Computes

For each Rg run, the comparison produces:

Statistic	Description
Ranking	Conditions sorted by mean Rg (lowest = most compact)
Percent change	Relative to control condition
Direction	`compaction` (< −1%), `expansion` (> +1%), or `unchanged`
t-statistic	Two-sample t-test on replicate means
p-value	Two-tailed significance
Cohen’s d	Effect size magnitude
ANOVA	Omnibus F-test when 3+ conditions (per-run)

Direction Labels

PolyzyMD classifies the direction of change based on percent change in mean Rg relative to control:

Percent Change	Direction	Meaning
< −1%	`compaction`	Treatment makes the protein more compact
> +1%	`expansion`	Treatment makes the protein less compact
−1% to +1%	`unchanged`	No meaningful difference in compactness

Interpreting the Comparison

Rg Comparison — Whole Protein
================================
Ranking (lower = more compact):
  1. 100% SBMA:   17.812 ± 0.038 Å
  2. No Polymer:  18.256 ± 0.044 Å
  3. 100% EGMA:   18.891 ± 0.061 Å

100% SBMA vs No Polymer:
  Change: -2.4% (compaction), p=0.0123*, d=1.87 (large)

100% EGMA vs No Polymer:
  Change: +3.5% (expansion), p=0.0078*, d=2.14 (large)

ANOVA: F=22.31, p=0.0018* (significant across all conditions)

Reading this output:

SBMA polymer significantly compacts the enzyme (lower Rg)
EGMA polymer significantly expands it (higher Rg)
The ANOVA confirms at least one condition differs from the others
Large Cohen’s d values mean these are substantial effects

Common Pitfalls

1. Insufficient Equilibration

Symptom: Rg mean and comparison results change with different --eq-time values.

Cause: Including the initial equilibration phase biases the mean.

Solution: Plot the Rg timeseries (or RMSD timeseries) and visually identify when the plateau begins. Set --eq-time to skip the transient:

polyzymd compare run rg -f comparison.yaml --eq-time 20ns

2. Comparing Different Selections

Symptom: Rg values are not comparable across runs or publications.

Cause: Different atom selections yield different Rg magnitudes.

Solution: Always report the exact selection string. Compare only runs with identical selections.

3. Over-Interpreting Small Differences

Symptom: Claiming significance for 0.05 Å Rg differences.

Cause: Not accounting for uncertainty.

Solution: Always report uncertainty and check statistical significance:

# WRONG: "Condition A (18.256 Å) is less compact than B (18.291 Å)"
# RIGHT: "Condition A (18.256 ± 0.044 Å) and B (18.291 ± 0.038 Å)
#         are not significantly different (p = 0.62, unchanged)"

4. Ignoring Timeseries Shape

Symptom: Reporting only mean Rg without inspecting the timeseries.

Cause: Two conditions can have the same mean Rg but very different dynamics (one stable, one drifting upward then returning).

Solution: Always examine the Rg timeseries plots. Use polyzymd compare plot-all to generate them automatically.

5. Confusing Rg with RMSD

Symptom: Expecting RMSD-like values (1–3 Å) from Rg analysis.

Cause: Rg and RMSD measure fundamentally different quantities. Rg values are typically much larger (12–25 Å for whole proteins).

Solution: Understand that Rg is an absolute size measure, while RMSD is a relative deviation measure. A 1 Å change in Rg is typically a smaller relative change than a 1 Å change in RMSD.

6. Ignoring Replicate Variation

Symptom: Reporting within-trajectory SEM as the total uncertainty.

Cause: Treating autocorrelation-corrected SEM as sufficient.

Solution: Use replicate-based statistics when available. The replicate SEM captures system-level variability that within-trajectory analysis cannot:

Replicate 1: mean Rg = 18.234 Å
Replicate 2: mean Rg = 18.291 Å
Replicate 3: mean Rg = 18.244 Å

Replicate mean: 18.256 Å
Replicate SEM:  0.044 Å  ← This is the gold standard uncertainty

7. Using Inappropriate Selections

Symptom: Rg timeseries is noisy or dominated by flexible regions.

Cause: Including highly flexible termini, disordered loops, or solvent atoms in the selection.

Solution: Match your selection to your scientific question:

Whole-protein Rg → "protein" or "protein and name CA"
Core stability → exclude flexible termini with specific residue ranges
Polymer behavior → "chainID C"

Fragment Mode Best Practices

Added in version 1.3.0.

When your selection contains multiple disconnected molecules (e.g., many polymer chains in solution), use calculation_mode: "fragments" to compute per-fragment Rg and reduce to a meaningful per-frame average. Without fragment mode, the whole-group Rg is dominated by the spatial separation between molecules rather than individual chain conformations.

Selection Strategy

Use resname-based selections for polymer fragment mode. These are more robust than chainID or segid because residue names are consistently assigned during system building, whereas chain and segment IDs can be reassigned during topology manipulations:

Recommended — resname-based selection

- label: polymer_blob_rg
  selection: "resname SBM or resname EGM or resname EGP"
  calculation_mode: fragments

Less robust — chainID may be reassigned

- label: polymer_blob_rg
  selection: "chainID C"
  calculation_mode: fragments

Verify Fragment Count

Before running large production analyses, verify that MDAnalysis detects the expected number of fragments with a quick test:

import MDAnalysis as mda

u = mda.Universe("topology.pdb", "trajectory.dcd")
ag = u.select_atoms("resname SBM or resname EGM or resname EGP")
print(f"Atoms: {len(ag)}, Fragments: {len(ag.fragments)}")

If the fragment count does not match the expected number of independent polymer chains, check your topology for unexpected bonds bridging chains.

When to Use Each Mode

Scenario	Recommended mode
Single protein chain	`selection` (default)
Single polymer chain	`selection`
Many polymer chains in solution	`fragments`
Oligomer populations	`fragments`
Protein + single polymer combined	`selection`

Fragment Weighting

equal (default): Arithmetic mean — all fragments contribute equally regardless of size. Best when fragments are similar in length and you want to treat each chain as an independent observation.
mass: Mass-weighted mean — heavier fragments contribute more. Best when fragment sizes vary significantly and you want the average to reflect the total material, not just the chain count.

Statistical Comparison with Fragment Mode

The reduced Rg timeseries (per-frame mean across fragments) is the primary metric used for cross-condition statistical comparison (t-tests, ANOVA, ranking). This is stored in rg_values in the NPZ sidecar and drives the mean, SEM, and correlation time reported in JSON results.

The fragment Rg distribution is supplementary — it provides conformational insight but is not used for hypothesis testing. Use it to understand why conditions differ, not whether they differ.

Interpreting Distribution Plots

Distribution plots provide a deeper view of Rg behavior beyond mean and SEM.

Reduced Rg Distribution

The reduced distribution shows the spread of per-frame Rg values (one value per frame). Because each frame’s value is already an average over multiple fragments (in fragment mode), this distribution is relatively narrow — a consequence of the central limit theorem.

Use reduced distributions to:

Compare overall conformational states across conditions
Identify bimodal behavior (two distinct conformational states)
Assess whether conditions produce overlapping or distinct Rg ranges

Fragment Rg Distribution

The fragment distribution pools ALL individual fragment Rg values across all frames and all replicates. It captures the full range of sizes that individual chains adopt, including rare extended or collapsed conformations that average out in the reduced series.

Use fragment distributions to:

Detect conformational heterogeneity within a population
Identify subpopulations of chains with distinct sizes
Understand the physical origin of differences seen in reduced distributions

Comparing Reduced and Fragment Distributions

Observation	Interpretation
Reduced distributions differ, fragment distributions also differ	All chains shift conformational state uniformly
Reduced distributions differ, fragment distributions overlap	Differences arise from a few outlier chains
Reduced distributions overlap, fragment distributions differ	Individual chains sample different states that average out
Both distributions overlap	No meaningful conformational difference

Tip

If reduced distributions overlap but fragment distributions differ, this suggests individual chains are sampling different conformational states that cancel out in the average. This is a sign of conformational heterogeneity that merits visual inspection of trajectories.

Rg as a Folding Diagnostic

Rg is a classical measure of protein folding state. The relationship between Rg and chain length follows distinct scaling laws (Flory, Principles of Polymer Chemistry, Cornell University Press, 1953; de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, 1979; Kohn et al., 2004):

State	Scaling	Description	Source
Folded globular	\(R_g \propto N^{1/3}\)	Compact, well-packed interior (empirical: \(\nu \approx 0.38\)–\(0.40\))	Dima & Thirumalai, 2004
Random coil	\(R_g \propto N^{0.588}\)	Unfolded, self-avoiding random walk (Flory: \(\approx 3/5\))	Kohn et al., 2004
Fully extended	\(R_g \propto N^{1.0}\)	Stretched, all-trans backbone (geometric limit)	—

Monitoring Rg during simulation can detect:

Unfolding: Rg increases from globular-like to coil-like values
Refolding: Rg decreases from extended to compact values
Molten globule: Rg slightly larger than native, high fluctuations

Tip

For enzyme-polymer conjugate studies, comparing Rg of the protein component across conditions (with/without polymer, different polymer compositions) can reveal whether the polymer stabilizes the native fold (maintains or reduces Rg) or destabilizes it (increases Rg).

Complementary Use with RMSD

Rg and RMSD provide complementary structural information. Using both together gives a more complete picture:

Rg Trend	RMSD Trend	Likely Explanation
Stable	Stable	Structurally stable, well-equilibrated
Increasing	Increasing	Unfolding or major conformational change
Stable	Increasing	Local rearrangement without overall size change
Increasing	Stable	Gradual expansion maintaining local structure
Decreasing	Increasing	Compaction with structural reorganization
Decreasing	Stable	Mild compaction maintaining fold

Important

When Rg and RMSD disagree, investigate further. For example, a stable Rg with increasing RMSD could mean a domain rotation that changes local structure without changing overall compactness. A molecular viewer is essential for interpreting such cases.

References

Primary References

Flory PJ. (1969) Statistical Mechanics of Chain Molecules. Wiley Interscience, New York.

Foundational work establishing the theoretical framework for polymer chain dimensions, including Rg scaling laws.

Lobanov MY, Bogatyreva NS, Galzitskaya OV. (2008) “Radius of Gyration as an Indicator of Protein Structure Compactness.” Molecular Biology 42(4):623-628. https://doi.org/10.1134/S0026893308040195

Systematic analysis of Rg as a compactness metric for protein structures, including empirical scaling relationships.

Additional References

Grossfield A, Patrone PN, Roe DR, Schultz AJ, Siderius DW, Zuckerman DM. (2018) “Best Practices for Quantification of Uncertainty and Sampling Quality in Molecular Simulations.” Living Journal of Computational Molecular Science 1(1):5067. https://doi.org/10.33011/livecoms.1.1.5067

Best practices for handling autocorrelation and uncertainty in MD observables including Rg timeseries.

Vitalis A, Pappu RV. (2009) “Methods for Monte Carlo Simulations of Biomacromolecules.” Annual Reports in Computational Chemistry 5:49-76.

Discussion of Rg as an order parameter for conformational sampling quality.

Rg Analysis: Best Practices

What is Radius of Gyration?

What Rg Measures

Interpreting Rg Values

Selection Matters

Rg Scales with Protein Size

Rg vs Time: What to Look For

Stable Plateau (Ideal)

Expansion (Possible Unfolding)

Compaction

Sudden Jumps

Oscillations

How PolyzyMD Handles Autocorrelation

Example Autocorrelation Output

Multi-Run Analysis: Why and When

Why Multiple Runs?

When to Use Multi-Run

Independent Ranking

Why No Alignment or Reference?

Replicates vs Longer Simulations

The LiveCoMS Recommendation

Why Replicates Matter for Rg

How Many Replicates?

Comparing Conditions

What PolyzyMD Computes

Direction Labels

Interpreting the Comparison

Common Pitfalls

1. Insufficient Equilibration

2. Comparing Different Selections

3. Over-Interpreting Small Differences

4. Ignoring Timeseries Shape

5. Confusing Rg with RMSD

6. Ignoring Replicate Variation

7. Using Inappropriate Selections

Fragment Mode Best Practices

Selection Strategy

Verify Fragment Count

When to Use Each Mode

Fragment Weighting

Statistical Comparison with Fragment Mode

Interpreting Distribution Plots

Reduced Rg Distribution

Fragment Rg Distribution

Comparing Reduced and Fragment Distributions

Rg as a Folding Diagnostic

Complementary Use with RMSD

References

Primary References

Additional References

See Also