Estimate protein diffusion from radius, temperature, viscosity, and molecular weight while exploring inverse calculations, diffusion times, correction factors, and downloadable reports for practical studies.
D is the translational diffusion coefficient.
kB is Boltzmann's constant.
T is absolute temperature in kelvin.
η is dynamic viscosity in pascal-seconds.
r is the hydrodynamic radius in meters.
Cf is the selected shape correction factor.
Protein diffusion describes random translational motion in liquids. Smaller proteins usually diffuse faster than larger proteins. Temperature also changes molecular motion and solvent resistance. Higher temperatures usually increase the diffusion coefficient. Greater solvent viscosity usually decreases the diffusion coefficient. These relationships make diffusion useful across biophysics and biochemistry. Researchers compare diffusion across proteins, buffers, and experimental temperatures. Diffusion can support estimates of transport and molecular mobility. However, concentration and intermolecular interactions may change measured values. Experimental context remains important.
The Stokes–Einstein equation treats a protein approximately as a sphere. It links thermal energy with hydrodynamic drag. The required radius is a hydrodynamic radius, not merely size. That radius represents resistance experienced during translational movement. The calculator can accept a measured radius directly. It can also estimate radius from molecular weight. That estimate assumes a spherical molecule with selected density. Real proteins may have hydration shells or elongated shapes. Their measured hydrodynamic radii can therefore differ substantially.
Viscosity strongly controls diffusion through fluid drag. Water viscosity changes noticeably with temperature. This calculator estimates water viscosity from entered temperature. PBS uses a simple approximate viscosity for convenience. Custom viscosity should be used for measured buffers. The optional correction factor represents extra drag from molecular shape. A factor above one lowers predicted diffusion. It should not replace experimental hydrodynamic information.
Random diffusion does not follow a fixed path. Mean-square displacement instead gives a characteristic distance. The calculator supports one, two, or three dimensions. It estimates diffusion time for a selected distance. It also estimates distance reached over selected time. These values describe statistical motion, not guaranteed travel. Crowding, binding, confinement, membranes, and aggregation may alter behavior. Use experimental measurements when high accuracy is required.
Model assumptions should always accompany reported diffusion estimates carefully.
| Example | Molecular weight | Approximate radius | Typical interpretation |
|---|---|---|---|
| Small globular protein | 10 kDa | 1.4–2.0 nm | Relatively rapid diffusion |
| Medium globular protein | 50 kDa | 2.5–3.5 nm | Moderate diffusion |
| Large globular protein | 150 kDa | 4.5–6.0 nm | Slower diffusion |
These ranges are illustrative rather than universal measurements.
| Liquid | Condition | Approximate viscosity |
|---|---|---|
| Water | 20 °C | 1.002 mPa·s |
| Water | 25 °C | 0.890 mPa·s |
| Water | 37 °C | 0.691 mPa·s |
| PBS | Room temperature | Approximately 1.0 mPa·s |
It measures how rapidly a protein spreads by diffusion.
Use the measured hydrodynamic radius whenever available.
Yes, but the estimate assumes spherical protein geometry.
Higher viscosity increases drag and slows protein motion.
It increases effective drag for non-ideal molecular shapes.
Yes, and this calculator adjusts water automatically.
No, they represent characteristic statistical diffusion scales only.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.