01
Measure compactness
Rg summarizes how widely selected atoms are distributed around their center of mass.
Computational Analyses · Basic to Advanced
Radius of Gyration Explained Clearly
What Rg measures, how compactness is calculated around the center of mass, how to interpret increasing or decreasing values, when it is useful, and when it can mislead you.
02
Follow shape expansion
One Rg value per trajectory frame reveals compaction, expansion, or stable spatial size over time.
03
Interpret with context
Similar Rg values can belong to different shapes, so structural visualization and companion analyses remain essential.
Foundation
1. What is Radius of Gyration?
Radius of gyration, usually written as Rg, is a geometric measure of how far the mass of a molecular structure is distributed from its center of mass.
Simple definition
Rg answers this question: “How tightly or widely are the selected atoms distributed around their common center?” A compact structure generally has a smaller Rg than an expanded structure made from the same selected atoms.
Rg is normally reported in nanometres (nm) or ångströms (Å). Remember: 1 nm = 10 Å.
বাংলায় সহজ করে: Radius of Gyration দেখায় protein বা molecule-এর atom-গুলো তাদের center of mass-এর চারপাশে কতটা compact বা ছড়িয়ে আছে।
Important distinction: Rg is not the physical outer radius of a protein. It is a root-mean-square distribution of mass around the center of mass.
Unlike RMSD: Rg does not require a reference structure or least-squares alignment. It is calculated independently for each frame from the selected atoms in that frame.
Purpose
2. Why is Rg important?
Rg compresses the three-dimensional spread of many atoms into one interpretable measure of global compactness.
Global compactness
Shows whether the selected structure remains spatially compact, becomes more compact, or expands.
বাংলা: Structure compact আছে নাকি ছড়িয়ে যাচ্ছে তা বোঝায়।
Expansion or collapse
Helps detect global unfolding, domain separation, polymer collapse, or compaction events.
বাংলা: Protein প্রসারিত বা সংকুচিত হচ্ছে কি না দেখায়।
System comparison
Supports consistent comparison of apo and bound proteins, mutants, conditions, or replicate simulations.
বাংলা: একই selection ব্যবহার করলে বিভিন্ন system তুলনা করা যায়।
Significance in protein structure evaluation
- Tracks whether the overall fold stays compact during an MD trajectory.
- Detects expansion associated with partial unfolding or movement between domains.
- Detects compaction caused by folding, collapse, ligand-induced closure, or stronger intramolecular packing.
- Helps compare the spatial size of related systems when the same atom selection and workflow are used.
- Complements RMSD, RMSF, SASA, secondary structure, native contacts, PCA, and clustering.
বাংলায় সহজ করে: Rg protein-এর total compactness বোঝায়, কিন্তু কোন residue বা কোন অংশ বদলেছে তা একা বলে না।
Concept check
3. Is Rg molecular dynamics?
No. Molecular dynamics generates atomic coordinates over time. Radius of gyration is an analysis metric calculated from a structure or from every saved frame of that trajectory.
Relationship: MD produces frames → each frame has a center of mass → distances from that center are combined → one Rg value is plotted against time.
বাংলায় সহজ করে: MD হলো simulation; Rg হলো সেই simulation-এ molecule কতটা compact তা মাপার analysis।
Interactive learning
4. Animated Rg intuition
Move the compactness slider to see atoms approach or move away from the center of mass, while the enclosing Rg circle and calculated value update live.
Protein compactness visualizer
A teaching model showing how the same atom group can be compact or expanded.
Distances are measured from the center of mass
Selected atomsCenter of massAtom-to-center distances
0.00 ÅRadius of gyration
0.00 ÅMean atom distance
0.00 ÅFarthest atom
Moderately compact conformation
The selected atoms occupy a moderate spatial region around the center of mass. The Rg value reflects their root-mean-square spread, not the outermost molecular boundary.
বাংলা: Slider ডানে নিলে atom-গুলো center থেকে দূরে যায় এবং Rg বাড়ে। বামে নিলে atom-গুলো center-এর কাছে আসে এবং Rg কমে।
Live equation breakdown
See how atom mass and distance from the center contribute to the final Rg value.
Mass-weighted Rg
rCOM = Σmᵢrᵢ / Σmᵢ
Rg = √[Σmᵢdᵢ² / Σmᵢ]
Rg = √[Σmᵢdᵢ² / Σmᵢ]
Here, dᵢ is the distance from atom i to the center of mass. Atoms with larger masses contribute more when mass weighting is used.
0.00Σm·d²
0.00Σm
0.00 Å√(Σm·d²/Σm)
| Atom | Mass | d (Å) | m·d² |
|---|
Step 1: Calculate the center of mass from all selected atomic positions and masses.
Step 2: Measure each atom’s distance from that center.
Step 3: Square each distance and multiply it by the atom’s mass.
Step 4: Divide the weighted sum by total mass and take the square root.
বাংলা: প্রথমে center of mass বের করা হয়। তারপর প্রতিটি atom center থেকে কত দূরে তা মেপে mass দিয়ে weight করা হয় এবং সবশেষে square root নিয়ে Rg পাওয়া যায়।
Method
5. How is Rg calculated?
Correct molecule reconstruction and atom selection are as important as the equation.
Select the molecular group
Choose the protein, backbone, Cα atoms, domain, complex, polymer, ligand, or another biologically meaningful atom group.
বাংলা: প্রশ্ন অনুযায়ী সঠিক atom group নির্বাচন করতে হবে।
Make the molecule whole
Correct periodic-boundary wrapping so one molecule is not artificially split across opposite sides of the simulation box.
বাংলা: PBC-এর কারণে molecule ভেঙে থাকলে আগে whole করতে হবে।
Calculate the center of mass
For the selected atoms, calculate the mass-weighted average position. Some software can use other weights, but the method must be reported.
বাংলা: নির্বাচিত atom-এর mass ও position দিয়ে center of mass বের করা হয়।
Measure atom-to-center distances
For each atom, calculate its three-dimensional distance from the center of mass in the same frame.
বাংলা: প্রতিটি atom center of mass থেকে কত দূরে তা মাপা হয়।
Weight, average, and square-root
Square each distance, apply the chosen weight, divide by the total weight, and take the square root.
বাংলা: distance square করে mass দিয়ে weight এবং average করে square root নেওয়া হয়।
Repeat for every trajectory frame
Calculate one Rg value per frame and plot Rg against simulation time.
বাংলা: প্রতিটি frame-এর Rg নিয়ে সময়ের বিপরীতে graph তৈরি করা হয়।
No structural fitting is normally required: translation does not change internal distances from the center of mass, and rotation does not change the total scalar Rg. However, PBC reconstruction remains essential.
Physical meaning
6. What does the value physically represent?
Smaller Rg
The selected mass is concentrated closer to its center of mass. For the same system and selection, this usually indicates a more compact spatial distribution.
বাংলা: ছোট Rg মানে atom-গুলো center-এর কাছে এবং structure তুলনামূলক compact।
Larger Rg
The selected mass is distributed farther from its center of mass. This may indicate expansion, extended loops, domain separation, unfolding, or a naturally elongated shape.
বাংলা: বড় Rg মানে atom-গুলো বেশি ছড়ানো; তবে এটি সবসময় unfolding নয়।
Do not use a universal cutoff: A normal Rg depends strongly on molecular size, sequence, topology, domain arrangement, oligomeric state, atom selection, and environment.
Atom selection
7. Which atoms should be selected?
Whole-protein heavy atoms
Measures compactness using all non-hydrogen protein atoms. It captures both backbone and side-chain packing but may be more sensitive to side-chain rearrangements.
বাংলা: Backbone ও side chain-সহ পুরো protein compactness দেখায়।
Backbone atoms
Useful for monitoring the global fold while reducing sensitivity to side-chain motion. Define exactly which backbone atoms were used.
বাংলা: Side chain noise কমিয়ে protein fold-এর compactness দেখায়।
Cα atoms
Provides a simplified representation with one atom per residue. It is useful for consistent comparisons but is not identical to an all-atom mass distribution.
বাংলা: প্রতিটি residue-এর একটি Cα দিয়ে সহজ global compactness মাপা হয়।
Individual domain or structural core
Useful for multi-domain proteins where global Rg may be dominated by relative domain movement. Domain-wise Rg can reveal local compactness separately.
বাংলা: Multi-domain protein-এ প্রতিটি domain-এর compactness আলাদাভাবে দেখা যায়।
Protein–ligand complex
A combined complex Rg can be calculated, but ligand position and protein size may make interpretation difficult. Protein-only Rg is usually reported separately.
বাংলা: Complex Rg করা যায়, তবে protein-only result আলাদা রাখলে interpretation পরিষ্কার হয়।
Ligand or peptide alone
For a flexible ligand or peptide, Rg can describe internal extension or collapse. It does not reveal where the ligand sits in the binding pocket.
বাংলা: Ligand/peptide-এর shape compact নাকি extended তা দেখায়, binding position নয়।
Nucleic acid, membrane, or polymer systems
Rg is useful for DNA/RNA, polymers, micelles, and assemblies, but the selected group and axis interpretation must match the system geometry.
বাংলা: DNA, RNA, polymer ও membrane assembly-তেও Rg ব্যবহার করা যায়।
Best practice: Compare systems only when the atom selection, weighting, molecular composition, PBC processing, and units are consistent.
Reading the graph
8. How should an Rg plot be interpreted?
These patterns are clues, not automatic biological conclusions.
Stable plateau
Suggests the selected group maintains a broadly consistent spatial compactness. It does not prove complete equilibrium or unchanged conformation.
বাংলা: Plateau মানে compactness প্রায় একই আছে।
Gradual decrease
May indicate compaction, folding, collapse, domain closure, or tighter packing. Confirm with SASA, contacts, secondary structure, and visualization.
বাংলা: Rg কমলে structure compact হতে পারে।
Gradual increase
May indicate expansion, domain opening, loss of compact contacts, or partial unfolding. It can also be a legitimate functional transition.
বাংলা: Rg বাড়লে structure প্রসারিত হতে পারে, কিন্তু সবসময় damage নয়।
Large oscillations
May reflect breathing motions, flexible domains, repeated opening and closing, state exchange, inadequate sampling, or a PBC problem.
বাংলা: বড় fluctuation হলে breathing motion, state change বা technical error পরীক্ষা করুন।
Sudden jump
Could be a true rapid transition, complex dissociation, or an artefact from a molecule split by periodic boundaries. Inspect the trajectory immediately.
বাংলা: হঠাৎ jump হলে আগে PBC ও trajectory visualization দেখুন।
Two similar plateaus
Small differences may be meaningful or may fall within normal variability. Use replicates, block statistics, and uncertainty instead of judging curves visually.
বাংলা: ছোট difference-এর significance replicate ও statistics দিয়ে যাচাই করতে হবে।
Meaning of change
9. What does increasing or decreasing Rg mean?
| Observation | Possible interpretation | What must be checked | বাংলায় সংক্ষেপ |
|---|---|---|---|
| Rg decreases | Compaction, folding, collapse, domain closure, stronger packing, or loss of extended tails. | SASA, native contacts, secondary structure, domain distance, and visualization. | Structure compact হতে পারে। |
| Rg increases | Expansion, unfolding, domain opening, loop extension, dissociation, or elongated functional state. | RMSD, secondary structure, contacts, SASA, interdomain distances, and PBC. | Structure প্রসারিত হতে পারে। |
| Rg unchanged | Overall spatial size remains similar. | The conformation may still change internally; inspect RMSD, PCA, contacts, and shape. | Total size একই হলেও shape বদলাতে পারে। |
| Rg fluctuates | Normal breathing, flexible regions, opening/closing, state transitions, or insufficient sampling. | Amplitude, timescale, replicates, trajectory visualization, and axis components. | Breathing motion বা state change হতে পারে। |
Never write: “Lower Rg proves higher stability.” A lower value only indicates a more compact mass distribution for the chosen atoms. Stability requires broader structural and energetic evidence.
Sources of variation
10. What factors change Rg?
Molecular size
Larger proteins usually have larger absolute Rg values, so direct comparison across different sizes can be misleading.
Shape and domains
Elongated or multi-domain structures can have high Rg even when well folded and stable.
Flexible tails and loops
Termini and disordered regions can strongly increase both mean Rg and fluctuation.
Ligand or mutation
Binding or mutation may close, open, rigidify, or destabilize a protein architecture.
Temperature and solvent
Environmental conditions influence packing, expansion, hydration, and conformational sampling.
Oligomeric state
Association or dissociation changes the spatial mass distribution of a complex.
Atom selection
Cα, backbone, heavy atoms, domains, and full complexes produce different numerical values.
PBC processing
A molecule split across the box can generate an artificial and extremely large Rg.
Weighting method
Mass, unit, or other weights alter the contribution of individual atoms to the result.
বাংলায় সহজ করে: Protein size, shape, domain movement, flexible loop, ligand, mutation, temperature, solvent, PBC এবং atom selection—সবই Rg পরিবর্তন করতে পারে।
Advanced interpretation
11. Total Rg, axis components, and molecular shape
Total scalar Rg
The total Rg gives one overall spread value. It is rotationally invariant, meaning simple rotation of the same conformation does not change the total Rg.
বাংলা: পুরো molecule ঘুরলেও total Rg বদলায় না।
Rg around x-axis
Uses distances in the y–z plane. It describes mass spread perpendicular to the x-axis.
Rg around y-axis
Uses distances in the x–z plane. It describes mass spread perpendicular to the y-axis.
Rg around z-axis
Uses distances in the x–y plane. It describes mass spread perpendicular to the z-axis.
Axis caution: Cartesian x/y/z components depend on orientation unless the system has a meaningful fixed frame, such as a membrane normal or consistently aligned principal axes. Do not interpret axis components blindly.
Same total Rg does not mean same shape
A compact globular structure and a differently arranged structure can share a similar total Rg. Shape descriptors such as the gyration tensor eigenvalues, asphericity, acylindricity, relative shape anisotropy, domain distances, or principal-axis analysis provide additional information.
বাংলা: Total Rg একই হলেও molecular shape ভিন্ন হতে পারে; তাই advanced shape analysis দরকার হতে পারে।
Decision guide
12. When is Rg necessary, and when is it not enough?
Rg is especially useful when
- You need a global compactness indicator.
- You suspect folding, collapse, expansion, or domain opening.
- You compare related systems using identical atom selections.
- You study flexible peptides, polymers, nucleic acids, or assemblies.
- You need a companion metric for RMSD, SASA, contacts, or secondary structure.
বাংলা: Compactness, folding, expansion বা collapse দেখার জন্য Rg প্রয়োজনীয়।
Rg is not enough when
- You need residue-level flexibility—use RMSF.
- You need similarity to a reference—use RMSD or another structural similarity metric.
- You need ligand binding position—use ligand RMSD, contacts, distances, or interaction analysis.
- You need solvent exposure—use SASA.
- You need folding mechanism or state populations—use contacts, secondary structure, PCA, clustering, and free-energy analysis.
বাংলা: Rg একা residue flexibility, ligand binding বা exact conformation বলে না।
Companion analyses
13. Rg compared with other MD metrics
Rg vs RMSD
Rg measures compactness around the center of mass. RMSD measures coordinate deviation from a reference after fitting.
Rg vs RMSF
Rg is global. RMSF shows how strongly individual atoms or residues fluctuate around an average or reference position.
Rg vs SASA
Rg measures spatial spread of mass. SASA measures surface accessible to a solvent probe.
Rg vs end-to-end distance
Rg uses all selected atoms. End-to-end distance uses only two terminal points and can miss internal compaction.
Rg vs native contacts
Rg can change without specifying which contacts form or break. Native-contact analysis provides structural detail.
Rg vs PCA/clustering
Rg gives one compactness coordinate. PCA and clustering can identify different conformational states with similar Rg.
বাংলায় সহজ করে: Rg compactness-এর জন্য ভালো, কিন্তু সঠিক conclusion-এর জন্য অন্য analysis-এর সঙ্গে ব্যবহার করতে হবে।
Quality control
14. Common Rg mistakes
Using a broken molecule across periodic boundaries
This can place parts of one molecule far apart and create a meaningless large Rg. Reconstruct the molecule and visually verify the trajectory.
বাংলা: PBC-তে molecule split থাকলে Rg ভুল হবে।
Comparing different atom selections
Cα, backbone, heavy-atom, and whole-complex Rg are not interchangeable. Use the same selection for comparisons.
বাংলা: আলাদা selection-এর Rg সরাসরি তুলনা করবেন না।
Claiming lower Rg means higher stability
A lower Rg only indicates greater compactness. A compact misfolded state can have low Rg, and a stable elongated protein can have high Rg.
বাংলা: কম Rg মানেই বেশি stable নয়।
Ignoring protein size or oligomeric state
Absolute Rg values depend strongly on system size and composition. Compare related systems or use suitable normalized/scaling approaches.
বাংলা: ভিন্ন size বা oligomer-এর absolute Rg তুলনায় সতর্ক থাকুন।
Interpreting axis components without a fixed orientation
Cartesian components can change when the molecule rotates. Use a meaningful frame, principal axes, or an aligned coordinate system.
বাংলা: Orientation ঠিক না থাকলে x/y/z Rg ভুলভাবে interpret হতে পারে।
Ignoring flexible termini
Long tails can dominate Rg changes even when the structural core is stable. Report both whole-protein and core/domain Rg when appropriate.
বাংলা: Flexible terminal অংশ total Rg বাড়াতে পারে।
Using only one trajectory
A single trajectory may not represent the underlying distribution. Independent replicates improve confidence in observed differences.
বাংলা: Replicate simulation ছাড়া ছোট difference নিশ্চিত বলা কঠিন।
Overinterpreting tiny visual differences
Report distributions, averages with uncertainty, block behaviour, and replicate variation instead of judging only line separation.
বাংলা: Graph দেখে ছোট difference-কে বড় conclusion বানাবেন না।
Recommended workflow
15. Practical Rg analysis sequence
Define the biological question
Decide whether you need whole-protein compactness, core compactness, domain behaviour, peptide collapse, or assembly size.
Choose a consistent atom group
Use the same composition and selection across compared systems.
Correct PBC and inspect the trajectory
Make the molecule whole and confirm that no frame is artificially split.
Calculate total and relevant components
Start with total Rg. Add domain-wise or axis-aware analysis only when scientifically meaningful.
Inspect distributions, not only the mean
Evaluate time evolution, histograms, transitions, block averages, and replicate variation.
Combine with structural evidence
Use visualization, RMSD, RMSF, SASA, contacts, secondary structure, PCA, clustering, and relevant distances.
GROMACS workflow
16. How to calculate Rg in GROMACS
The exact PBC workflow depends on whether the system is soluble, membrane-bound, oligomeric, or contains multiple molecular groups.
Step A — Remove discontinuous jumps
gmx trjconv -s md.tpr -f md.xtc -o md_nojump.xtc -pbc nojump
Select the molecular system or appropriate group. Visually verify that the molecule remains continuous.
Step B — Make molecules whole and center the system
gmx trjconv -s md.tpr -f md_nojump.xtc -o md_center.xtc -pbc mol -center -ur compact
Select the protein or complex for centering, then the system for output. Verify the result carefully, especially for membranes and multimers.
Step C — Calculate radius of gyration
gmx gyrate -s md.tpr -f md_center.xtc -o gyrate.xvg
Choose the desired analysis group, such as Protein, Backbone, C-alpha, or a custom domain group. GROMACS reports total Rg and components about the x, y, and z axes as a function of time.
বাংলা: প্রথমে PBC ঠিক করুন, molecule whole করুন, তারপর সঠিক group নির্বাচন করে gmx gyrate চালান।
Create a custom domain or core group
gmx make_ndx -f md.tpr -o index.ndx gmx gyrate -s md.tpr -f md_center.xtc -n index.ndx -o gyrate_domain.xvg
Create biologically meaningful groups and document residue ranges clearly.
Membrane and multimer warning: Generic centering can rearrange or visually separate membrane systems and oligomers. Use a topology-aware workflow and check multiple frames after processing.
Publication practice
17. What should be reported?
Software and version used for the Rg calculation.
Trajectory-processing and PBC reconstruction procedure.
Exact atom selection, residue range, molecule, or domain.
Mass-weighted, unit-weighted, or other weighting method.
Whether total Rg or axis components were analysed.
Time range, frame interval, units, and any smoothing.
Treatment of flexible tails, missing residues, or unresolved segments.
Replicate handling, average, distribution, and uncertainty.
Any normalized comparison used across different molecular sizes.
Companion analyses supporting the interpretation.
Example reporting sentence
“The mass-weighted radius of gyration of the selected protein heavy atoms was calculated for each production-trajectory frame after periodic-boundary reconstruction. Total Rg values were reported in nanometres as a function of simulation time and compared across independent replicas.”
বাংলা: Method section-এ selection, weighting, PBC processing, unit, time range এবং replicate পরিষ্কারভাবে লিখুন।
Frequently asked questions
18. Radius of Gyration FAQ
Does a stable Rg mean the protein is stable?
It supports the conclusion that global compactness is consistent, but it cannot prove correct folding, thermodynamic stability, convergence, or biological function.
বাংলা: Stable Rg compactness-এর ভালো ইঙ্গিত, কিন্তু stability-এর একমাত্র প্রমাণ নয়।
Is lower Rg always better?
No. A compact misfolded structure may have a low Rg, while a naturally elongated and stable protein may have a larger Rg.
বাংলা: কম Rg সবসময় ভালো নয়।
Why is my Rg suddenly extremely large?
First check whether the molecule is split across periodic boundaries or whether an oligomer dissociated. Then investigate a genuine conformational event.
বাংলা: আগে PBC এবং molecule continuity পরীক্ষা করুন।
Do I need to fit the trajectory before Rg?
Total scalar Rg does not require rotational or translational fitting. It does require a correctly reconstructed molecular group. Axis-specific interpretation may require a meaningful orientation.
বাংলা: Total Rg-এর জন্য fitting নয়, কিন্তু molecule whole করা জরুরি।
Why are Cα and heavy-atom Rg different?
They use different spatial and mass distributions. Side chains contribute to heavy-atom Rg but are absent from a Cα-only calculation.
বাংলা: Atom selection আলাদা বলে value আলাদা হয়।
Can two structures have the same Rg but different conformations?
Yes. Rg reduces the structure to one spread value. Different shapes and contact patterns can share the same Rg.
বাংলা: একই Rg হলেও conformation ভিন্ন হতে পারে।
Can Rg be used for a ligand?
Yes, especially for flexible ligands or peptides, but it describes internal compactness rather than binding-site location or binding strength.
বাংলা: Ligand shape compactness দেখা যায়, binding strength নয়।
Should solvent and ions be included?
Usually not when studying protein compactness, because mobile solvent and ions would dominate or distort the selected mass distribution.
বাংলা: Protein Rg-তে সাধারণত water ও ion বাদ দেওয়া হয়।
Quick glossary
19. Essential terms
Rg: mass distribution-এর RMS distanceCenter of mass: mass-weighted central positionCompactness: atom কতটা ঘনভাবে distributedPBC: periodic simulation box boundaryGyration tensor: directional mass-spread matrixAsphericity: sphere থেকে shape deviationAxis component: নির্দিষ্ট axis ঘিরে mass spreadHeavy atoms: hydrogen ছাড়া atom
Final interpretation rule
Radius of gyration tells you how widely the selected molecular mass is distributed around its center of mass. It does not independently prove structural stability, correct folding, ligand binding, convergence, or biological activity.
বাংলায় মূল কথা: Rg compactness বোঝার জন্য গুরুত্বপূর্ণ, কিন্তু সঠিক conclusion-এর জন্য trajectory visualization, RMSD, RMSF, SASA, contacts, secondary structure, PCA/clustering এবং replicate simulation-এর সঙ্গে মিলিয়ে দেখতে হবে।