EV Centrifugation Model

A web-based calculator for differential centrifugation parameters used in isolating extracellular vesicles (exosomes, microvesicles, etc.) by ultracentrifugation.

Live Demo: https://joadwe.github.io/ev-centrifugation-model/

Overview

This calculator implements the theoretical framework from:

Livshts, M. A. et al. "Isolation of exosomes by differential centrifugation: Theoretical analysis of a commonly used protocol." Sci. Rep. 5, 17319 (2015). doi:10.1038/srep17319

The tool calculates:

• Cut-off diameter (d*): Minimum vesicle size completely sedimented in a given time
• Pelleting fractions: Percentage of vesicles of a given size that sediment
• K-factor (clearing factor): Rotor efficiency metric for comparing rotors and converting run times
• Multi-step protocols: Track vesicle populations through complex differential centrifugation workflows

Features

1. Rotor Configuration

• SW (Swinging Bucket) and FA (Fixed Angle) rotor types
• Pre-loaded standard rotors from the manuscript (Table 1)
• Custom rotor parameters

2. Physics-Based Calculations

• Sedimentation coefficient: s = d²·Δρ/(18·η)
• Cut-off diameter for complete sedimentation
• Pelleting fractions accounting for:
  • SW rotors: Exponential sedimentation with uniform radial distribution
  • FA rotors: Elliptical tube cross-section geometry (from Supplement)

3. Visualization

• Interactive sedimentation profile plots (10–500 nm range)
• Cut-off diameter indication

4. K-Factor (Clearing Factor) Calculator

• Live K-factor display for the current rotor and RCF
• Compare all preset rotors at the same RCF with equivalent run times
• Convert run times between any two rotors: t_new = t_old × K_new / K_old
• Validated against Table 3 of the manuscript

5. Multi-Step Protocol Designer

• Design complex differential centrifugation workflows
• Track cumulative effects on vesicle populations (30–1000 nm)
• Support for both pellet and supernatant retention strategies

Usage

Quick Start

1. Select a rotor from the preset list or enter custom parameters
2. Set centrifugation conditions:
   • Rotation speed (RCF or RPM)
   • Centrifugation time
   • Cut-off size (optional)
3. View results: Pelleting fractions for standard vesicle sizes (50–150 nm)
4. Generate plot for visualization

Technical Details

Key Equations

Sedimentation Coefficient

s = d²(ρᵥ - ρₘ) / (18η)

where:

• d = particle diameter
• ρᵥ = vesicle density
• ρₘ = medium density
• η = medium viscosity

Cut-off Diameter (Complete Sedimentation)

d* = √[18η·ln(Rₘₐₓ/Rₘᵢₙ) / (Δρ·ω²·t)]

FA Rotor Pelleting (Elliptical Cross-Section)

P = (2/π)[arcsin(ξ) + ξ√(1-ξ²)]

where ξ = s·ω²·Rₐᵥ·t / Lₛₑ𝒹

This formula (from the Supplement) accounts for the elliptical horizontal cross-section of the tilted FA tube. The effective sedimentation path length is:

Lₛₑ𝒹 = D / cos(θ)

where D is the tube diameter and θ is the rotor angle from vertical.

K-Factor (Clearing Factor)

K = ln(Rₘₐₓ/Rₘᵢₙ) × 10¹³ / (3600 × ω²)

Uses the physical (actual) Rₘᵢₙ and Rₘₐₓ. A lower K means faster pelleting. Run times convert between rotors at the same RCF via:

t_new = t_old × K_new / K_old

RCF Convention

Important: RCF values are specified at Rₐᵥ (average radius), not Rₘₐₓ, following the manuscript's convention. This is critical for matching published data.

Validation

The calculator has been validated against Tables 2 and 3 of the manuscript for all 8 standard rotors (3 SW + 5 FA).

Table 2 — Pelleting at 30 min, 10,000×g

Rotor	Type	d* (nm)	150nm	120nm	100nm	70nm
SW 40Ti	SW	321	30%	20%	14%	7%
SW28	SW	308	31%	21%	15%	7%
MLS-50	SW	230	51%	34%	25%	12%
Type 45 Ti	FA	210	62%	41%	29%	14%
Type 60 Ti	FA	170	88%	61%	43%	22%
Type 70 Ti	FA	169	88%	62%	43%	22%
F-45-24-15	FA	128	100%	95%	73%	38%
TLA 110	FA	125	100%	98%	76%	40%

40/40 tests pass with ≤1% difference from expected values.

Table 3 — K-Factor and Equivalent Times at 10,000×g

Rotor	Type	K-Factor	Equiv. Time	d* (nm)	150nm	120nm	100nm	70nm
SW 40Ti	SW	2774.6	58 min	231	53%	36%	26%	13%
SW28	SW	2547.2	54 min	229	52%	35%	25%	13%
MLS-50	SW	1426	30 min	230	51%	34%	25%	12%
Type 45 Ti	FA	2103.9	44 min	173	86%	59%	42%	21%
Type 60 Ti	FA	1601	34 min	159	96%	68%	49%	24%
Type 70 Ti	FA	1573.8	33 min	161	94%	67%	48%	24%
F-45-24-15	FA	765.9	16 min	175	84%	57%	41%	20%
TLA 110	FA	658.9	14 min	182	79%	53%	38%	19%

56/56 tests pass (K-factor, equivalent time, d*, and pelleting fractions).

Running Validation

cd tests
python3 validate.py

Project Structure

centrifugation/
├── index.html          # Main web interface
├── calc.js             # Calculator logic
├── style.css           # Styling
├── data/
│   ├── table1.csv      # Rotor specifications
│   ├── table2.csv      # Expected pelleting results
│   └── table3.csv      # Expected K-factor results
├── docs/
│   └── 41598_2015_BFsrep17319_MOESM1_ESM.pdf  # Manuscript supplement
├── tests/
│   └── validate.py     # Validation against Tables 2 & 3 (96 tests)
├── README.md           # This file
└── .gitignore

References

1. Livshts, M. A. et al. (2015). Isolation of exosomes by differential centrifugation: Theoretical analysis of a commonly used protocol. Scientific Reports, 5, 17319. doi:10.1038/srep17319

2. Original web calculator (archived): vesicles.niifhm.ru

Default Parameters

The calculator uses the following default medium properties (matching the manuscript):

• Vesicle density: 1.15 g/cm³
• Medium density: 1.0 g/cm³ (PBS/water)
• Medium viscosity: 1.55 cP (PBS at 20°C)

These can be adjusted for different experimental conditions (e.g., sucrose gradients).

Technical Notes

Implementation Details

• JavaScript: Vanilla JS, no framework dependencies
• Plotting: Plotly.js for interactive visualizations
• Validation: Python 3 with standard library only

Browser Compatibility

• Modern browsers with ES6+ support
• Tested on Chrome, Firefox, Safari, Edge

License

This project is open source and available under the MIT License.

Acknowledgments

• Based on the theoretical framework by Livshts et al. (2015)
• Inspired by the original web calculator at vesicles.niifhm.ru
• Formula derivations from the manuscript's supplementary information

Contributing

Contributions are welcome! Please feel free to submit issues or pull requests.

Development

1. Clone the repository
2. Open index.html in a browser (or serve with a local HTTP server)
3. Make changes to calc.js, index.html, or style.css
4. Run validation: python3 tests/validate.py

Citation

If you use this calculator in your research, please cite the original manuscript:

@article{livshts2015isolation,
  title={Isolation of exosomes by differential centrifugation: Theoretical analysis of a commonly used protocol},
  author={Livshts, Mikhail A and Khomyakova, Elena and Evtushenko, Evgeniy G and Lazarev, Vassili N and Kulemin, Nikolay A and Semina, Svetlana E and Generozov, Edward V and Govorun, Vadim M},
  journal={Scientific Reports},
  volume={5},
  number={1},
  pages={17319},
  year={2015},
  publisher={Nature Publishing Group UK London}
}

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Disclaimer: This tool is for research and educational purposes only. Always verify results independently and consult the primary literature for your specific application.